Magnetism: Molecules to Materials V

Magnetism: Molecules to Materials V Edited by Joel S. Miller and Marc Drillon Magnetism: Molecules to Materials V Ed...

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Magnetism: Molecules to Materials V Edited by Joel S. Miller and Marc Drillon

Magnetism: Molecules to Materials V

Edited by J.S. Miller and M. Drillon

Further Titles of Interest:

J.S. Miller, M. Drillon (Eds.) Magnetism: Molecules to Materials IV 2003, ISBN 3-527-30429-0 J.S. Miller, M. Drillon (Eds.) Magnetism: Molecules to Materials III Nanosized Magnetic Materials 2002, ISBN 3-527-30302-2 J.S. Miller, M. Drillon (Eds.) Magnetism: Molecules to Materials II Molecule-Based Materials 2001, ISBN 3-527-30301-4 J.S. Miller, M. Drillon (Eds.) Magnetism: Molecules to Materials Models and Experiments 2001, ISBN 3-527-29772-3 F. Schüth, K.S.W. Sing, J. Weitkamp (Eds.) Handbook of Porous Solids 2002, ISBN 3-527-30246-8 F. Laeri, F. Schüth, U. Simon, M. Wark (Eds.) Host-Guest-Systems Based on Nanoporous Crystals 2003, ISBN 3-527-30501-7

Magnetism: Molecules to Materials V Edited by Joel S. Miller and Marc Drillon

Prof. Dr. Joel S. Miller Department of Chemistry University of Utah Salt Lake City UT 84112-0850 USA Prof. Dr. Marc Drillon CNRS Institut de Physique et Chimie des Matériaux de Strasbourg 23 Rue du Loess 67037 Strasbourg Cedex France All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate Library of Congress Card No.: Applied for British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at c 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Printed in the Federal Republic of Germany Printed on acid-free and chlorine-free paper Composition: EDV-Beratung Frank Herweg, Leutershausen Printing: betz-druck gmbh, Darmstadt Bookbinding: Litges & Dopf Buchbinderei, Heppenheim ISBN: 3-527-30665-X

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI 1

Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates Vasco Gama and Maria Teresa Duarte . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Basic Structural Motifs . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 ET Salts Based on Decamethylmetallocenium Donors . . . . . 1.2.2 ET Salts Based on Other Metallocenium Donors . . . . . . . . 1.3 Solid-state Structures and Magnetic Behavior . . . . . . . . . . . . . . 1.3.1 Type I Mixed Chain Salts . . . . . . . . . . . . . . . . . . . . . 1.3.2 Type II Mixed Chain [M(Cp*)2 ][M (L)2 ] Salts . . . . . . . . . 1.3.3 Type III Mixed Chain [M(Cp*)2 ][M (L)2 ] Salts . . . . . . . . 1.3.4 Type IV Mixed Chain [M(Cp*)2 ][M (L)2 ] Salts . . . . . . . . 1.3.5 Salts with Segregated Stacks not 1D Structures . . . . . . . . . 1.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1 2.2

2.3

2.4

Chiral Molecule-Based Magnets Katsuya Inoue, Shin-ichi Ohkoshi, and Hiroyuki Imai . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical and Optical Properties of Chiral or Noncentrosymmetric Magnetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Magnetic Structure and Anisotropy . . . . . . . . . . . . . . . 2.2.2 Nonlinear Magneto-optical Effects . . . . . . . . . . . . . . . . 2.2.3 Magneto-chiral Optical Effects . . . . . . . . . . . . . . . . . . Nitroxide-manganese Based Chiral Magnets . . . . . . . . . . . . . . 2.3.1 Crystal Structures . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Magnetic Properties . . . . . . . . . . . . . . . . . . . . . . . . Two- and Three-dimensional Cyanide Bridged Chiral Magnets . . . . 2.4.1 Crystal Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Two-dimensional Chiral Magnet [39] . . . . . . . . . . . . . . 2.4.3 Three-dimensional Chiral Magnet [40] . . . . . . . . . . . . .

1 1 4 4 6 7 7 21 23 30 36 37 39 41 41 41 42 43 48 49 49 51 53 54 54 57

VI

Contents

2.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . 2.5 SHG-active Prussian Blue Magnetic Films . . . . . . . . . 2.5.1 Magnetic Properties and the Magneto-optical Effect 2.5.2 Nonlinear Magneto-optical Effect . . . . . . . . . . 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes Jamie L. Manson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 “Binary” α-M(dca)2 Magnets . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Structural Aspects . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Canted Antiferromagnetism . . . . . . . . . . . . . . . . . . . . 3.2.4 Mechanism for Magnetic Ordering . . . . . . . . . . . . . . . . 3.2.5 Pressure-dependent Susceptibility . . . . . . . . . . . . . . . . 3.3 β-M(dca)2 Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Structural Evidence . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Magnetic Behavior of α-Co(dca)2 . . . . . . . . . . . . . . . . 3.3.3 Comparison of Lattice and Spin Dimensionality in αand β-Co(dca)2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Mixed-anion M(dca)(tcm) . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Crystal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Magnetic Properties . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Polymeric 2D (cat)M(dca)3 cat = Ph4 As, Fe(bipy)3 . . . . . . . . . . 3.5.1 (Ph4 As)[Ni(dca)3 ] . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 [Fe(bipy)3 ][M(dca)3 ]2 {M = Mn, Fe} . . . . . . . . . . . . . . 3.6 Heteroleptic M(dca)2 L Magnets . . . . . . . . . . . . . . . . . . . . . 3.6.1 Mn(dca)2 (pyz) . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Mn(dca)2 (2,5-Me2 pyz)2 (H2 O)2 . . . . . . . . . . . . . . . . . . 3.6.3 Mn(dca)2 (H2 O) . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.4 Fe(dca)2 (pym)·EtOH . . . . . . . . . . . . . . . . . . . . . . . 3.6.5 Fe(dca)2 (abpt)2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Dicyanophosphide: A Phosphorus-containing Analog of Dicyanamide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Conclusions and Future Prospects . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60 60 60 64 68 69

3

4

71 71 73 73 76 79 81 82 82 82 84 85 85 85 86 87 87 88 88 89 95 96 97 98 99 100 101

Molecular Materials Combining Magnetic and Conducting Properties Peter Day and Eugenio Coronado . . . . . . . . . . . . . . . . . . . . . 105 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.2 Interest of Conducting Molecular-based Magnets . . . . . . . . . . . . 106

Contents

4.2.1 Superconductivity and Magnetism . . . . . . . . . . 4.2.2 Exchange Interaction between Localised Moments and Conduction Electrons . . . . . . . . . . . . . . . 4.3 Magnetic Ions in Molecular Charge Transfer Salts . . . . . 4.3.1 Isolated Magnetic Anions . . . . . . . . . . . . . . . 4.3.2 Metal Cluster Anions . . . . . . . . . . . . . . . . . 4.3.3 Chain Anions: Maleonitriledithiolates . . . . . . . . 4.3.4 Layer Anions: Tris-oxalatometallates . . . . . . . . 4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

VII

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Lanthanide Ions in Molecular Exchange Coupled Systems Jean-Pascal Sutter and Myrtil L. Kahn . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Molecular Compounds Involving Gd(III) . . . . . . . . . . . . . . . . 5.2.1 Gd(III)–Cu(II) Systems . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Systems with Other Paramagnetic Metal Ions . . . . . . . . . . 5.2.3 Gd(III)-organic Radical Compounds . . . . . . . . . . . . . . . 5.3 Superexchange Mediated by Ln(III) Ions . . . . . . . . . . . . . . . . 5.4 Exchange Coupled Compounds Involving Ln(III) Ions with a First-order Orbital Momentum . . . . . . . . . . . . . . . . . . 5.4.1 Qualitative Insight into the Exchange Interaction . . . . . . . . 5.4.2 Quantitative Insight into the Exchange Interaction . . . . . . . 5.4.3 The Exchange Interaction . . . . . . . . . . . . . . . . . . . . . 5.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

108 111 111 131 143 146 153 155

5

6 6.1 6.2

6.3 6.4 6.5 6.6

Monte Carlo Simulation: A Tool to Analyse Magnetic Properties Joan Cano and Yves Journaux . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monte Carlo Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Metropolis Algorithm . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Thermalization Process . . . . . . . . . . . . . . . . . . . . . . 6.2.4 Size of Model and Periodic Boundary Conditions . . . . . . . 6.2.5 Random Number Generators . . . . . . . . . . . . . . . . . . . 6.2.6 Magnetic Models . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.7 Structure of a Monte Carlo Program . . . . . . . . . . . . . . . Regular Infinite Networks . . . . . . . . . . . . . . . . . . . . . . . . . Alternating Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finite Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exact Laws versus MC Simulations . . . . . . . . . . . . . . . . . . .

161 161 161 164 164 165 165 170 174 174 180 181 185 185 189 189 190 190 192 193 194 196 196 197 199 203 206 208

VIII

Contents

6.6.1 A Method to Obtain an ECS Law for a Regular 1D System: Fisher’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.2 Small Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.3 Extended Systems . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 Some Complex Examples . . . . . . . . . . . . . . . . . . . . . . . . . 6.8 Conclusions and Future Prospects . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Metallocene-based Magnets Gordon T. Yee and Joel S. Miller . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Electrochemical and Magnetic Properties of Neutral Decamethylmetallocenes and Decamethylmetallocenium Cations Paired with Diamagnetic Anions . . . . . . . . . . . . . . . . 7.3 Preparation of Magnetic Electron Transfer Salts . . . . . . . . . . . . 7.3.1 Electron Transfer Routes . . . . . . . . . . . . . . . . . . . . . 7.3.2 Metathetical Routes . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Crystal Structures of Magnetic ET Salts . . . . . . . . . . . . . . . . . 7.5 Tetracyanoethylene Salts (Scheme 7.2) . . . . . . . . . . . . . . . . . 7.5.1 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.2 Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.3 Chromium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.4 Other Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Dimethyl Dicyanofumarate and Diethyl Dicyanofumarate Salts . . . . . . . . . . . . . . . . . . . . 7.6.1 Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.2 Chromium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 2,3-Dichloro-5,6-dicyanoquinone Salts and Related Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8 2,3-Dicyano-1,4-naphthoquinone Salts . . . . . . . . . . . . . . . . . . 7.8.1 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8.2 Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8.3 Chromium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.9 7,7,8,8-Tetracyano-p-quinodimethane Salts . . . . . . . . . . . . . . . 7.9.1 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.9.2 Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.9.3 Chromium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.10 2,5-Dimethyl-N, N -dicyanoquinodiimine Salts . . . . . . . . . . . . 7.10.1 Iron and Manganese . . . . . . . . . . . . . . . . . . . . . . . . 7.11 1,4,9,10-Anthracenetetrone Salts . . . . . . . . . . . . . . . . . . . . . 7.12 Cyano and Perfluoromethyl Ethylenedithiolato Metalate Salts . . . . 7.12.1 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.12.2 Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

209 211 213 217 220 220

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224 226 226 226 227 230 230 232 232 232 233 233 234 235 236 236 237 238 238 238 239 239 239 239 240 240 241 241

Contents

7.13 7.14 7.15 7.16

Benzenedithiolates and Ethylenedithiolates . . . . . . . Additional Dithiolate Examples . . . . . . . . . . . . . . Bis(trifluoromethyl)ethylenediselenato Nickelate Salts Other Acceptors that Support Ferromagnetic Coupling, but not Long-range Order above ∼2 K . . . . . . . . . . 7.17 Other Metallocenes and Related Species as Donors . . 7.18 Muon Spin Relaxation Spectroscopy . . . . . . . . . . . 7.19 Mössbauer Spectroscopy . . . . . . . . . . . . . . . . . 7.20 Spin Density Distribution from Calculations and Neutron Diffraction Data . . . . . . . . . . . . . . . 7.21 Dimensionality of the Magnetic System and Additional Evidence for a Phase Transition . . . . . 7.22 The Controversy Around the Mechanism of Magnetic Coupling in ET Salts . . . . . . . . . . . . 7.23 Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.24 Research Opportunities . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Magnetic Nanoporous Molecular Materials Daniel Maspoch, Daniel Ruiz-Molina, and Jaume Veciana . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Inorganic and Molecular Hybrid Magnetic Nanoporous Materials . . 8.3 Magnetic Nanoporous Coordination Polymers . . . . . . . . . . . . . 8.3.1 Carboxylic Ligands . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Nitrogen-based Ligands . . . . . . . . . . . . . . . . . . . . . . 8.3.3 Paramagnetic Organic Polytopic Ligands . . . . . . . . . . . . 8.4 Summary and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

254 255 256 257

8

9 9.1 9.2

9.3

9.4

Magnetic Prussian Blue Analogs Michel Verdaguer and Gregory S. Girolami . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prussian Blue Analogs (PBA), Brief History, Synthesis and Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Formulation and Structure . . . . . . . . . . . . . . . . . . . . 9.2.2 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic Prussian Blues (MPB) . . . . . . . . . . . . . . . . . . . . . 9.3.1 Brief Historical Survey of Magnetic Prussian Blues . . . . . . 9.3.2 Interplay between Models and Experiments . . . . . . . . . . . 9.3.3 Quantum Calculations . . . . . . . . . . . . . . . . . . . . . . . High TC Prussian Blues (the Experimental Race to High Curie Temperatures) . . . . . . . . . . . . . . . . . . . . . . . 9.4.1 Chromium(II)–Chromium(III) Derivatives . . . . . . . . . . .

261 261 263 266 266 271 273 278 280 283 283 284 285 288 290 291 293 306 322 323

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Contents

9.4.2 Manganese(II) –Vanadium(III) Derivatives . . . . . . . . . 9.4.3 The Vanadium(II) –Chromium(III) Derivatives . . . . . . . 9.4.4 Prospects in High-TC Magnetic Prussian Blues . . . . . . . 9.5 Prospects and New Trends . . . . . . . . . . . . . . . . . . . . . . . 9.5.1 Photomagnetism: Light-induced Magnetisation . . . . . . 9.5.2 Fine Tuning of the Magnetisation . . . . . . . . . . . . . . 9.5.3 Dynamics in Magnetic and Photomagnetic Prussian Blues 9.5.4 Nanomagnetism . . . . . . . . . . . . . . . . . . . . . . . . 9.5.5 Blossoming of Cyanide Coordination Chemistry . . . . . . 9.6 Conclusion: a 300 Years Old “Inorganic Evergreen” . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Scaling Theory Applied to Low Dimensional Magnetic Systems Jean Souletie, Pierre Rabu, and Marc Drillon . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Non-critical-scaling: the Other Solutions of the Scaling Model . . . . 10.3 Universality Classes and Lower Critical Dimensionality . . . . . . . . 10.4 Phase Transition in Layered Compounds . . . . . . . . . . . . . . . . 10.5 Description of Ferromagnetic Heisenberg Chains . . . . . . . . . . . . 10.5.1 Application to Ferromagnetic S = 1 Chains . . . . . . . . . . 10.6 Application to the Spin-1 Haldane Chain . . . . . . . . . . . . . . . . 10.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

324 325 334 338 338 339 339 339 340 341 341

10

347 347 348 351 352 363 366 368 375 375

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

Preface

The development, characterization, and technological exploitation of new materials, particularly as components in ‘smart’ systems, are key challenges for chemistry and physics in the next millennium. New substances and composites including nanostructured materials are envisioned for innumerable areas including magnets for the communication and information sector of our economy. Magnets are already an important component of the economy with worldwide sales exceeding $30 billion per annum. Hence, research groups worldwide are targeting the preparation and study of new magnets especially in combination with other technologically important properties, e. g., electrical and optical properties. In the past few years our understanding of magnetism and magnetic materials, thought to be mature, has enjoyed a renaissance as it is being expanded by contributions from many diverse areas of science and engineering. These include (i) the discovery of bulk ferro- and ferrimagnets based on organic/molecular components with critical temperature exceeding room temperature, (ii) the discovery that clusters in high, but not necessarily the highest, spin states due to a large magnetic anisotropy or zero field splitting have a significant relaxation barrier that traps magnetic flux enabling a single molecule/ion (cluster) to act as a magnet at low temperature; (iii) the discovery of materials exhibiting large, negative magnetization; (iv) spin-crossover materials that can show large hysteretic effects above room temperature; (v) photomagnetic and (vi) electrochemical modulation of the magnetic behavior; (vii) the Haldane conjecture and its experimental realization; (viii) quantum tunneling of magnetization in high spin organic molecules; (viii) giant and (ix) colossal magnetoresistance effects observed for 3-D network solids; (x) the realization of nanosize materials, such as self organized metalbased clusters, dots and wires; (xi) the development of metallic multilayers and the spin electronics for the applications. This important contribution to magnetism and more importantly to science in general will lead us into the next millennium. Documentation of the status of research, ever since William Gilbert’s de Magnete in 1600, provides the foundation for future discoveries to thrive. As this millennium begins the time is appropriate to pool our growing knowledge and assess many aspects of magnetism. This series entitled Magnetism: Molecules to Mate-

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rials provides a forum for comprehensive yet critical reviews on many aspects of magnetism that are on the forefront of science today. Joel S. Miller Salt Lake City

Marc Drillon Strasbourg, France

List of Contributors

Joan Cano Laboratoire de Chimie Moléculaire Universtité de Paris-Sud 91405 Orsay France Eugenio Coronado Instituto de Ciencia Molecular Universitat de Valencia C/ Doctor Moliner 50 46100 Burjassot Spain Vasco Pires Silva da Gama Instituto Technológico e Nuclear Estrada Nacional 10 2686-953 Sacavém Portugal Peter Day Davy Faraday Research Laboratory The Royal Institution of Great Britain 21 Albemarle Street London W1S 4BS United Kingdom Marc Drillon Institut de Physique et Chimie des Matériaux de Strasbourg UMR 7504 du CNRS 23 Rue du Loess 67037 Strasbourg France

Maria Teresa Duarté Centro de Química Estrutural Instituto Superior Técnico Av. Rovisco Pais 1049-001 Lisboa Portugal Gregory S. Girolami Department of Chemistry University of Illinois Urbana-Champaign 61801 USA Hiroyuki Imai Institute for Molecular Science Okazaki National Institutes 38 Nishigounaka Myoudaiji Okazaki 444-8585 Japan Katsuya Inoue Institute for Molecular Science Okazaki National Institutes 38 Nishigounaka Myoudaiji Okazaki 444-8585 Japan Yves Journaux Laboratoire de Chimie Inorganique, URA 420 Université de Paris-Sud CNRS, BAT 420 91405 Orsay France

XIV

List of Contributors

Myrtil L. Kahn Institut de Chimie de la Matière Condensée de Boreaux – CNRS Avenue Dr. Schweitzer 33608 Pessac France

Pierre Rabu Institut de Physique et Chimie des Matériaux de Strasbourg UMR 75040 du CNRS 23 rue du Loess 67037 Strasbourg France

Jamie L. Manson Department of Chemistry and Biochemistry Estern Washington University 226 Science 526 5th St. Cheney, WA 99004 USA

Jean Souletie Centre de Recherche sur les très basses températures, CNRS 25 Avenue des Martyrs 38042 Grenoble France

Daniel Maspoch Institut de Ciència de Materials de Barcelona (CSIC) Campus Universitari de Bellaterra 08193 Cerdanyola Spain

Jean-Pascal Sutter Institut de Chimie de la Matière Condensée de Bordeaux – CNRS Avenue Dr. Schweitzer 33608 Pessac France

Joel S. Miller Department of Chemistry University of Utah Salt Lake City, UT 84112-0850 USA

Jaume Veciana Institut de Ciència de Materials de Barcelona (CSIC) Campus Universitari de Bellaterra 08193 Cerdanyola Spain

Shin-ichi Ohkoshi Research Center for Advanced Science and Technology The University of Tokyo 4-6-1 Komaba Meguro-ku Tokyo 153-8904 Japan

Michel Verdaguer Laboratoire de Chimie Inorganique et Matériaux Moléculaires Unité associée au C.N.R.S. 7071 Université Pierre et Marie Curie 4 place Jussieu 75252 Paris Cedex 05 France

Daniel Ruiz-Molina Institut de Ciència de Materials de Barcelona (CSIC) Campus Universitari de Bellaterra 08193 Cerdanyola Spain

Gordon T. Yee Department of Chemistry Virginia Polytechnic Institute and State University Blacksburg, VA 24061 USA

1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates Vasco Pires Silva da Gama and Maria Teresa Duarté

1.1 Introduction For the last 30 years metal-bis(1,2-dichalcogenate) anionic complexes have been extensively used as building blocks for the preparation of both conducting and magnetic molecular materials. Several of these materials show remarkable features and have made a significant contribution to the development of molecular materials science. It is worth mentioning some examples of the molecular materials based on metalbis(1,2-dichalcogenate) anionic complexes based that have made a significant contribution to the field of molecular material science, in the last decades. A large number of molecular conductors and even superconductors based on metal-bis(1,2dichalcogenate) anionic acceptors have been obtained [1] and Me4 N[Ni(dmit)2 ]2 (dmit = 1,3-dithiol-2-thione-4,5-dithiolate) was the first example of a π acceptor superconductor with a closed-shell donor [2]. The spin-Peierls transition was observed for the first time in the linear spin chain system TTF[Cu(tdt)2 ] [3] (TTF = tetrathiafulvalene; tdt = 1,2-ditrifluoromethyl-1,2-ethylenedithioate). The coexistence of linear spin chains and conducting electrons, was observed for the first time in the compounds Per2 [M(mnt)2 ] (M = Ni, Pd, Pt) [4] (mnt = 1,2-dicyano1,2-ethylene-dithiolato), presenting competing spin-Peierls and Peierls instabilities of the spin chains and 1D conducting electronic systems. A purely organic system with a spin-ladder configuration was observed for the first time in the compound DT-TTF2 [Au(mnt)2 ] [5] (DT-TTF = dithiophentetrathiafulvalene). A spin transition was observed in the compound [Fe(mnt)2 rad] [6], where rad = 2-(p-N-methylpyridinium)4,4,5,5-tetramethylimidazoline-1-oxyl. Ferromagnetic ordering was reported for NH4 [Ni(mnt)2 ]H2 O [7]. The discovery of the first molecule-based material exhibiting ferromagnetic ordering, the electron-transfer (ET) salt [Fe(Cp*)2 ]TCNE (TCNE = tetracyanoethylene), with TC = 4.8 K, in 1986 [8, 9], was a landmark in molecular magnetism and gave a significant impulse to this field. Since then among the strategies followed to obtain cooperative magnetic properties, considerable attention has been given to the linear-chain electron-transfer salts based on metallocenium donors and on planar acceptors. [10, 11]. Besides [Fe(Cp*)2 ]TCNE, bulk ferromagnetism was reported

2

1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

for other ET salts based on decamethylmetallocenes and on the conjugated polynitriles TCNE [12] and TCNQ [13] (TCNQ = 7,7,8,8-tetracyano-p-quinodimethane). An extensive study of these salts was made, covering a variety of aspects including the structure-magnetic property relationship [10], and the effects of spin variation and of spinless defects [10]. Furthermore they provided a valuable basis to test the various models that were proposed in order to explain the magnetic coupling and magnetic ordering in the molecule-based magnets [14, 15].

Fig. 1.1. Molecular structure of [Fe(Cp*)2 ][Ni(edt)2 ], showing the basic donor and acceptor molecules studied in this review.

Following the report of ferromagnetism for [Fe(Cp*)2 ]TCNE, metal bisdichalcogenate planar acceptors were also considered as suitable candidates for use in the preparation of ET salts with the radical metallocenium donors, and in the search for new molecular magnets the first metal bis-dichalcogenate based compounds were reported in 1989 [16, 17]. In particular the monoanionic forms of the metal bis-dichalcogenate (Ni, Pd, Pt) complexes seem particularly promising for ‘‘the synthesis of mixed-stack molecular charge-transfer salts that display cooperative magnetic phenomena due to (1) their planar structures, (2) delocalized electronic states, S = 1/2 spin state for the monomeric species, and (3) the possibility of extended magnetic interactions mediated by the chalcogen atoms’’ [17]. The work with ET salts based on metallocenium donors and on planar metal bisdichalcogenate radical anions is summarized in this chapter. Most of the materials studied to date are decamethylmetallocenium based ET salts, other compounds based on different metallocenium derivatives have also been reported and will be

1.1 Introduction S

S

[M(edt)2]

M

F3C

S

S

X

X

CF3

X

CF3

[M(tdt)2] (X = S) [M(tds)2] (X = Se)

M F3C

X

3

N

N S

S

[M(mnt)2]

M S

S

N

N X

X

[M(bdt)2] (X = S) [M(bds)2] (X = Se)

M X

S

X

S

S

S

M

X S

S

S

X S

S

S

S M S

[M(dmit)2] (X = S) [M(dmio)2] (X = O)

S

S

[M(D-tpdt)2]

Scheme 1.1 Schematic representation of the metal bis-dichalcogenate acceptors studied in this chapter.

referred to. The metal bis-dichalcogenate complexes mentioned in this chapter are represented in Scheme 1.1. As magnetic ordering is a bulk property, particular attention will be given to the supramolecular arrangements which determine the magnetic behavior. The crystal structure of the compounds will be correlated with the magnetic behavior of these ET salts. The magnetic coupling in the ET salts based on decamethylmetallocenium donors has been analyzed mainly through McConnell I [18] or McConnell II [19] mechanisms, and this issue is still a subject of controversy [15, 20]. Of these models, McConnell I has been most often used in the interpretation of the magnetic behavior of these salts, as, in spite of its simplicity, it has shown good agreement with the experimental observations. In this chapter the interpretation of the magnetic coupling will be analyzed in the perspective of this model. However, it should be mentioned that the validity of the McConnell I mechanism has been questioned both theoretically [21] and experimentally [22].

4


1.2 Basic Structural Motifs 1.2.1

ET Salts Based on Decamethylmetallocenium Donors

In most of the ET salts based on decamethylmetallocenium donors, due to the planar configurations of both the C5 Me5 ligands and of the metal bis-dichalcogenate acceptors the crystal structures are, with a few exceptions, based on linear chain arrangements of alternating donor and acceptor molecules. In these salts four distinct types of linear chain arrangements have been observed and are represented schematically in Figure 1.2. The type I chain arrangement corresponds to the most simple case of an alternated linear chain motif ··A− D+ A− D+ A− D+ ··, similar to that observed in several salts based on metallocenium donors and on acceptors such as TCNE and TCNQ [10]. In the case of the type II chain, the donors alternate with face-to-face pairs of acceptors, ··A− A− D+ A− A− D+ ··, as in this arrangement there is a net charge (−) per repeat unit, A− A− D+ , charge compensation is required. For the type III arrangement the linear chains consist of alternated face-to-face pairs of acceptors with side-by-side pairs of donors, ··A− A− D+ D+ A− A− D+ D+ ··. Finally in the type IV arrangement, the acceptors alternate with side-by-side pairs of donors, ··A− D+ D+ A− D+ D+ ··, in this case there is a net charge (+) per repeat unit, D+ D+ A− , which must be compensated. For most of the ET salts based on types I and III arrangements (neutral chains), only one type of chain arrangement was observed. However, in the case of compounds based on types II and IV arrangements (charged chains), more complex crystal structures could be observed, resulting from the required charge neutralization. Table 1.1 summarizes the unit cell parameters, space group symmetry, and the type of observed linear chain ar-

Fig. 1.2. Representation of the basic types of mixed chain sequences observed in the ET salts based on metallocene donors and on metal bis-dichalcogenate acceptors.

1.2 Basic Structural Motifs

5

Table 1.1. Unit cell parameters and chain type for the mixed chain salts. Compound

Chain Space Type Group

a, Å

b, Å

c, Å

α, ◦

β, ◦

C2/m C2/m C2/c C2/c P1 P1 P1 P1 P1 P1 C2/c C2/m P1 P1 P1 P1 P1 P1 C2/m P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P21 /c P21 /c P1 P1

13.319 13.44 14.417 14.302 8.490 8.581 8.582 8.580 8.606 8.618 11.352 16.802 12.106 9.713 11.347 11.415 9.907 9.996 16.374 14.133 14.133 9.650 9.731 9.760 9.782 9.738 9.772 7.763 9.787 11.720 20.360 10.053 9.619 9.591

13.699 13.66 12.659 12.697 10.278 10.464 10.472 10.547 10.521 10.560 21.848 21.095 14.152 11.407 14.958 14.940 12.104 11.554 10.84 14.620 14.620 11.439 19.044 19.101 17.885 19.119 17.896 19.126 19.241 16.282 10.237 10.281 9.622 9.681

8.719 8.96 18.454 18.415 10.936 11.132 11.158 11.138 11.138 11.239 14.969 12.942 14.394 11.958 10.020 10.020 14.464 15.108 19.530 16.055 16.055 16.643 35.677 35.606 19.163 35.698 19.198 35.564 35.587 9.606 15.443 15.577 11.253 11.252

90.00 90.0 90.00 90.00 106.79 107.96 108.41 109.49 108.81 109.49 90.00 90.00 108.94 100.90 97.68 97.40 82.44 109.72 90.00 88.43 88.43 71.14 105.22 105.02 74.84 105.27 75.12 104.50 103.98 100.66 90.00 90.00 79.72 78.17

125.06 124.2 95.17 94.63 103.95 103.65 103.57 103.20 102.89 102.78 103.73 94.52 96.37 113.20 94.36 94.58 85.80 97.62 88.02 80.25 80.25 73.24 94.91 94.72 81.58 94.36 81.45 95.26 94.69 106.03 107.54 104.89 78.66 78.47

[Fe(Cp*)2 ][Ni(edt)2 ] [Cr(Cp*)2 ][Ni(edt)2 ] [Fe(Cp*)2 ][Ni(tdt)2 ] [Mn(Cp*)2 ][Ni(tdt)2 ] [Fe(Cp*)2 ][Pt(tdt)2 ] [Fe(Cp*)2 ][Ni(tds)2 ] [Mn(Cp*)2 ][Ni(tds)2 ] [Cr(Cp*)2 ][Ni(tds)2 ] [Fe(Cp*)2 ][Pt(tds)2 ] [Mn(Cp*)2 ][Pt(tds)2 ] [Cr(Cp*)2 ][Pt(tds)2 ] α -[Fe(Cp*)2 ][Pt(mnt)2 ] β -[Fe(Cp*)2 ][Pt(mnt)2 ] [Fe(Cp*)2 ]2 [Cu(mnt)2 ] [Fe(Cp*)2 ][Ni(dmit)2 ] [Mn(Cp*)2 ][Ni(dmit)2 ] α -[Fe(Cp*)2 ][Pd(dmit)2 ] [Fe(Cp*)2 ][Pt(dmit)2 ] [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN [Fe(Cp*)2 ][Pd(dmio)2 ] [Fe(Cp*)2 ][Pt(dmio)2 ] [Fe(Cp*)2 ][Ni(dsit)2 ] [Fe(Cp*)2 ][Ni(bdt)2 ] [Mn(Cp*)2 ][Ni(bdt)2 ] [Cr(Cp*)2 ][Ni(bdt)2 ] [Mn(Cp*)2 ][Co(bdt)2 ] [Cr(Cp*)2 ][Co(bdt)2 ] [Fe(Cp*)2 ][Pt(bdt)2 ] [Cr(Cp*)2 ][Pt(bdt)2 ] [Fe(Cp*)2 ][Ni(bds)2 ]MeCN [Fe(Cp*)2 ][Ni(α -tpdt)2 ] [Cr(Cp*)2 ][Ni(α -tpdt)2 ] [Fe(C5 Me4 SCMe3 )2 ][Ni(mnt)2 ] [Fe(C5 Me4 SCMe3 )2 ][Pt(mnt)2 ]

I I I I I I I I I I I II I IV III III III III IV III III III IV IV IV IV IV IV IV IV I I I I

γ , ◦ Vol., Z Å3

90.00 90.0 90.00 90.00 101.98 101.82 101.79 101.76 101.30 101.30 90.00 90.00 90.51 92.66 109.52 109.63 82.73 93.78 90.00 86.38 86.38 89.72 97.99 98.15 82.91 98.34 82.09 97.87 98.31 81.75 90.00 90.00 76.62 77.38

1302 1320 3354 3333 846 881 882 881 891 899 3607 4473 2312 1185 1575 1582 1703 1616 3431 3260 3260 1657 6266 6293 3189 6298 3191 6314 6387 1723 3069 1556 984 984

2 2 4 4 1 1 1 1 1 1 4 6 3 1 2 2 2 2 4 4 4 2 8 8 4 8 4 8 8 2 4 2 1 1

T,

Ref.

20 20 -70 (a) -70 20 20 20 20 20 20 20 23 25 -120 (a) 20 20 (a) 20 20 20 20 20 20 20 20 20 20 -120 20 20 22 22

23 23 16 24 25 26 27 28 26 28 28 16 16 29 17 30 31 31 32 31 31 31 33 33 33 33 33 33 33 17 34 35 36 36

◦C

(a) Not given.

rangements for mixed chain ET salts based on metallocenium donors and metal bis-dichalcogenate acceptors. While in the case of the cyano radical based salts, most of the observed structures present a type I structural arrangement, in the case of the ET salts based on metal bis-dichalcogenate acceptors a much larger variety of arrangements was observed, as described above. The structural motifs in the [M(Cp*)2 ][M (L)2 ] ET salts are primarily determined by factors such as the dimensions of the anionic metal bisdichalcogenate complexes, the tendency of the acceptors to associate as dimers, the extent of the π system in the acceptor molecule, and the charge density distribution on the ligands. In the case of the [M(edt)2 ]− based salts, with the smaller acceptor, the size of the acceptor is similar to the size of the C5 Me5 ligand of the donor and only type I structural motifs (DADA chains) were observed. For the intermediate size

6


anionic complexes, [M(tdx)2 ]− , [M(mnt)2 ] and [Ni(α-tpdt)2 ]− , the most common structural motif obtained in ET salts based on those acceptors is also of type I. For the larger anionic complexes, [M(bdx)2 ]− and [M(dmix)2 ]− , types III and IV chain arrangements were observed, in both cases acceptor molecules (type IV) or faceto-face pairs of acceptors (type III) alternate with side-by-side pairs of donors. The complexes [M(mnt)2 ]− and [M(dmix)2 ]− , (M = Ni, Pd and Pt), frequently undergo dimerization in the solid state [37], and they are the only acceptors where the chain arrangements have face-to-face pairs of acceptors (structural motifs II and III). The variety of structural arrangements observed in the [M(mnt)2 ]− based compounds can be related to both the large extent of the π system and the high charge density on the terminal nitrile groups [38], as well as to the tendency of these complexes to form dimers.

1.2.2

ET Salts Based on Other Metallocenium Donors

Besides the decamethylmetallocenium based salts, in the compounds based on other metallocenium derivatives, mixed linear chain arrangements were only observed in the case of the salts [Fe(C5 Me4 SCMe3 )2 ][M(mnt)2 ], M = Ni and Pt, which present type I structural motifs. Some ET salts based on other metallocenium derivatives and on the acceptors [M(mnt)2 ]− and [M(dmit)2 ]− (M = Ni and Pt) have also been reported. In the case of these compounds, the crystal structure consists of segregated stacks of donors, ··D+ D+ D+ D+ ··, and acceptors, ··A− A− A− A− ··, which is a common situation in molecular materials, in particular in the case of molecular conductors. In spite of the fact that for most salts the dominant magnetic interactions between the metal bisdichalcogenate units are antiferromagnetic, there are cases where the interactions are known to be ferromagnetic, as in the case of the compounds n-Bu4 N[Ni(αtpdt)2 ] [34] and NH4 [Ni(mnt)2 ](H2 O, which was the first metal bis-dichalcogenate based material to present ferromagnetic ordering, with TC = 4.5 K [7]. The unit cell parameters of the ferrocenium derivative salts with crystal structures based on segregated acceptor stacks are shown in Table 1.2. Table 1.2. Unit cell parameters for the segregated stack salts. Space Group

a, Å

[Fe(Cp)2 ]2 [Ni(mnt)2 ]2 [Fe(Cp)2 ] P1 P1 [Fe(C5 Me4 SMe)2 ][Ni(mnt)2 ] P21 /n [Fe(C5 H4 R)2 ][Ni(mnt)2 ] (b) [Fe(Cp)(C5 H4 CH2 NMe3 )][Ni(mnt)2 ] P21 /n [Fe(Cp)(C5 H4 CH2 NMe3 )][Pt(mnt)2 ] P21 /n [Co(Cp)2 ][Ni(dmit)2 ] P1 P1 [Co(Cp)2 ][Ni(dmit)2 ]3 2MeCN

12.030 8.649 7.572 12.116 12.119 19.347 8.913

Compound

b, Å

c, Å

α, ◦

β, ◦

γ , ◦ Vol., Z T , Ref. ◦C Å3

13.652 15.462 87.91 77.62 72.56 14.080 15.358 65.27 77.77 80.78 28.647 16.374 90.00 93.10 90.00 30.094 7.139 90.00 103.97 90.00 30.112 7.244 90.00 103.97 90.00 25.289 9.698 100.60 96.02 76.01 21.370 7.413 99.19 91.06 101.40

2365 1654 3547 2531 2565 4517 1363

2 2 4 4 4 8 1

(a) 22 22 20 20 20 (a)

(a) Not given. (b) [Fe(C5 R)2 ]+ = 1,1 -bis[2-(4-(methylthio)-(E)-ethenyl]ferrocenium.

39 36 40 41 41 42 43

1.3 Solid-state Structures and Magnetic Behavior

7

1.3 Solid-state Structures and Magnetic Behavior After listing the general characteristics of the crystal structures of ET salts based on metallocenium donors and metal bis-dichalcogenate acceptors, we will discuss them based on the systematization proposed in Section 1.2 and correlate the supramolecular crystal motifs with the magnetic properties.

1.3.1

Type I Mixed Chain Salts

The magnetic behavior of the salts based on type I chains shows a considerable similarity, namely, in most cases, the dominant magnetic interactions are FM and several of these salts exhibit metamagnetic behavior. Table 1.3 summarizes the key magnetic properties of type I compounds. 1.3.1.1

[M(Cp*)2 ][Ni(edt)2 ]

The compounds [M(Cp*)2 ][Ni(edt)2 ], with M = Fe and Cr, are isostructural and the crystal structure [23] consists of a parallel arrangement of 1D alternated type I chains, ··A− D+ A− D+ A− D+ ··. In Figure 1.3(a) a view along the chain direction ([101]) is presented for [Fe(Cp*)2 ][Ni(edt)2 ]. The chains are regular and the Ni atoms sit above the Cp fragments from the donors, intrachain DA contacts, d (d = interatomic separation), shorter than the sum of the van der Waals radii (dW ), QW = d/dW < 1, were observed. These contacts involve a Ni atom from the acceptor and one of the C atoms from the C5 ring, with a Ni–C distance of 3.678 Å (QW = 0.99). For this compound the shortest interchain interionic separation was found in the in-registry pair II–IV, with AA C–C contacts of 3.507 Å (QW = 1.11), as shown in Figure 1.3(b). The out-of-registry pairs I–II, II–III and I–IV present a similar interchain arrangement, with DA C–S contacts (C from Me from the donor and an S from the acceptor) of 3.812 Å (QW = 1.11), the II–III pairwise arrangement is shown in Figure 1.3(c). At high temperatures, in the case of the [M(Cp*)2 ][Ni(edt)2 ] compounds, AFM interactions apparently dominate the magnetic behavior of the compounds, as seen by the negative θ value obtained from the Curie–Weiss fits, −5 and −6.7 for M = Fe and Cr respectively. A considerable field dependence of the obtained θ value for polycrystalline samples (free powder) was observed in the case of [Fe(Cp*)2 ][Ni(edt)2 ], suggesting the existence of a strong anisotropy in the magnetic coupling for this compound [23]. This was confirmed by the metamagnetic behavior observed at low temperatures, with TN = 4.2 K and HC = 14 kG at 2 K. A typical metamagnetic behavior was observed in single crystal magnetization measurements at 2 K [23], shown in Figure 1.4. With the applied magnetic field parallel to the chains a field induced transition from an AFM state to a high field FM

8


Table 1.3. Magnetic characterization of type I ET salts. Compound

SD ; SA

θ, K

Comments

Ref.

[Fe(Cp*)2 ][Ni(edt)2 ]

1/2; 1/2

−5

23

[Cr(Cp*)2 ][Ni(edt)2 ] [Fe(Cp*)2 ][Ni(tdt)2 ] [Mn(Cp*)2 ][Ni(tdt)2 ] [Mn(Cp*)2 ][Pd(tdt)2 ]

3/2; 1/2 1/2; 1/2 1; 1/2 1; 1/2

−6.7 15 2.6 3.7

[Fe(Cp*)2 ][Pt(tdt)2 ] [Mn(Cp*)2 ][Pt(tdt)2 ] [Fe(Cp*)2 ][Ni(tds)2 ] [Mn(Cp*)2 ][Ni(tds)2 ]

1/2; 1/2 1; 1/2 1/2; 1/2 1; 1/2

27 1.9 8.9 12.8

[Cr(Cp*)2 ][Ni(tds)2 ] [Fe(Cp*)2 ][Pt(tds)2 ]

3/2; 1/2 1/2; 1/2

4.0 9.3

[Mn(Cp*)2 ][Pt(tds)2 ]

1; 1/2

16.6

[Cr(Cp*)2 ][Pt(tds)2 ]

3/2; 1/2

9.8

[Fe(Cp*)2 ][Ni(α-tpdt)2 ]

1/2; 1/2

−5.1 (d)

[Mn(Cp*)2 ][Ni(α-tpdt)2 ] (f) [Cr(Cp*)2 ][Ni(α-tpdt)2 ] [Fe(C5 Me4 SCMe3 )2 ][Ni(mnt)2 ] [Fe(C5 Me4 SCMe3 )2 ][Pt(mnt)2 ] β-[Fe(Cp*)2 ][Pt(mnt)2 ]

1; 1/2 3/2; 1/2 1/2; 1/2 1/2; 1/2 1/2; 1/2

7.3 6.1 3 3 9.8

MM (a); TN = 4.2 K; HC = 14 kG (2 K) (b) (b) MM (a); TN = 2.4 K MM (a); TN = 2.8 K; HC = 0.8 kG (1.85 K) (b) MM (a) TN = 2.3 K; (b) MM (a); TN = 2.1 K; HC = 0.28 kG (1.6 K) (b) MM (a); TN = 3.3 K; HC = 3.95 kG (1.7 K) MM (a); TN = 5.7 K; HC = 4.05 kG (1.7 K) MM (c); TN = 5.2 K; HC1 = 5 kG, HC2 = 16 kG, (1.7 K) Tm ≈ 130 K (e); MM (a); TN = 2.6 K; HC = 0.6 kG (1.6 K) FM (g); TC = 2.2 K (b) (b) (b) (b)

23 16 24 24 10 24 26, 44 28, 44 28 26 28 28

34

35 35 36 36 16

(a) Metamagnetic transition. (b) No magnetic ordering observed down to 1.8 K. (c) Two field induced transitions were observed at low temperatures. (d) Non-Curie-Weiss behavior the given θ value relates to the high temperature region (T > Tm ). (e) Minimum inχT vs. T . (f) Crystal structure not yet determined. (g) Ferromagnetic transition.

state occurs at a critical field of 14 kG. While for measurements with the applied field perpendicular to the chains, no transition was observed and a linear field dependence was observed for the magnetization, as expected for an AFM. The magnetic behavior of [Fe(Cp*)2 ][Ni(edt)2 ] is consistent with the coexistence of FM intrachain interactions, due to DA intrachain short contacts, with AFM interchain interactions, resulting from the AD and AA interchain contacts. The nature of the intra and interchain magnetic interaction is in good agreement with the predictions of the McConnell I mechanism [26]. In this case the interchain interactions must be particularly large as they seem to be the dominant interactions

Fig. 1.3. (a) Perspective view of the crystal structure of [Fe(Cp*)2 ][Ni(edt)2 ] along the chain direction. (b) Interchain arrangement of the pair II–I V, d1 corresponds to the DA closest intrachain contact (3.678 Å, QW = 0.99) and d2 to the closest interchain contact (3.507 Å, QW = 1.11). (c) Interchain arrangement of the pair II–III, d3 is the closest interchain contact (3.812 Å, QW = 1.11). Hydrogen atoms were omitted for clarity.

1.3 Solid-state Structures and Magnetic Behavior 9

10


Magnetization (N PB)

2.0

1.5

1.0

0.5

0.0 0

10

20

30

40

Field (kG)

50

60

Fig. 1.4. Magnetization field dependence at 2 K, for a single crystal of [Fe(Cp*)2 ][Ni(edt)2 ], the closed symbols refer to measurements with applied field parallel to the DADA chains and the open symbols to the measurements with the applied field perpendicular to the chains.

at high temperatures, and they also lead to a quite high value for the critical field in the metamagnetic transition.

1.3.1.2

[M(Cp*)2 ][M (tdx)2 ]

The [Fe(Cp*)2 ][Ni(tdt)2 ] and [Mn(Cp*)2 ][M (tdt)2 ] with M = Ni, Pd and Pt are isostructural, and, as in the case of the [M(Cp*)2 ][Ni(edt)2 ] salts, a crystal structure based on an arrangement of parallel alternating DA linear chains [16] is observed, but with differences in the intra and interchain arrangements. A view normal to the chains of [Fe(Cp*)2 ][Ni(tdt)2 ] is shown in Figure 1.5(a). In these compounds the chains have a zigzag arrangement and the Cp sits above one of the NiS2 C2 fragments of the acceptor, as shown for [Fe(Cp*)2 ][Ni(tdt)2 ] in Figure 1.5(b). In this compound, no intrachain DA short contacts were found and the closest interatomic separation between the acceptor and the Cp ring corresponds to Ni–C contacts of 4.120 Å (QW = 1.11). In this salt the most relevant interchain contacts concern the out-of registry pairs I–II and I–IV, these arrangements are similar and the first one is shown in Figure 1.5(b). These pairs show interchain DA C–S contacts, involving C atoms of the Me groups of the donors and S atoms of the acceptors, with a separation of 3.728 Å (QW = 1.08). The magnetic behavior of the compounds [Fe(Cp*)2 ][Ni(tdt)2 ] and [Mn(Cp*)2 ][M (tdt)2 ], with M = Ni, Pd and Pt, is dominated by the intrachain DA FM interactions, as seen by the positive θ values obtained from the CurieWeiss fits (Table 1.3). At low temperatures the [Mn(Cp*)2 ][M (tdt)2 ] salts exhibit metamagnetic transitions, with TN = 2.4, 2.8 and 2.3 K for M = Ni, Pd and Pt respectively, HC = 600 G for M = Pd [24]. This behavior is attributed to the coexistence of FM intrachain interactions with interchain AFM interactions.


11

Fig. 1.5. (a) View of the crystal structure of [Fe(Cp*)2 ][Ni(tdt)2 ] along the chain direction (Me groups were omitted for clarity). (b) Interchain arrangement of the pair I–II, d1 corresponds to the DA closest intrachain contact (4.120 Å, QW = 1.11) and d2 to the closest interchain contact (3.728 Å, QW = 1.08). Hydrogen atoms were omitted for clarity.

The compounds [Fe(Cp*)2 ][Pt(tdt)2 ], [M(Cp*)2 ][Ni(tds)2 ], with M = Fe, Mn and Cr, [25–28] and [M(Cp*)2 ][Pt(tds)2 ], with M = Fe and Mn, [26, 28] are isostructural and the crystal structure consists of a parallel arrangement of alternated type I chains. The intrachain arrangement is similar to that of [Fe(Cp*)2 ][Ni(edt)2 ], with the Cp sitting above the Ni or Pt atoms from the acceptor, but distinct interchain arrangements were observed in these compounds. A view normal to the chains is shown in Figure 1.6(a) for [Fe(Cp*)2 ][Pt(tds)2 ]. Short intrachain DA contacts were observed in most of these salts, involving M (Ni or Pt) and carbons from the Cp rings from the donors, for the Pt–C contact in [Fe(Cp*)2 ][Pt(tds)2 ] the interatomic separation is 3.826 Å (QW = 0.98). For this series of compounds the shortest interchain interionic separation was found in the in-registry pair I–II, shown in Figure 1.6(b), and it corresponds to an AA Se–Se contact, with a distance of 4.348 Å (QW = 1.09). In the other interchain arrangements the interchain contacts are considerably larger and the closest separations occur for the I–IV pair (Figure 1.6(c)) involving two C atoms from the donor Me groups, with a separation of 4.263 Å (QW = 1.33) in the case of [Fe(Cp*)2 ][Pt(tds)2 ]. However [Cr(Cp*)2 ][Pt(tds)2 ] is not isostructural with these compounds, the intra and interchain arrangements are similar to those described above for [Fe(Cp*)2 ][Pt(tds)2 ] [28]. The magnetic behavior of the compounds [Fe(Cp*)2 ][Pt(tdt)2 ], [M(Cp*)2 ][Ni(tds)2 ] and [M(Cp*)2 ][Pt(tds)2 ] (M = Fe, Mn and Cr) is clearly dominated by the strong intrachain DA FM coupling, as can be seen by the high positive θ values (Table 1.3). The coexistence of an intrachain AFM interaction is responsible for the metamagnetic transitions, which are observed in several of those compounds, with TN = 2.1, 3.3, 5.7 K and HC = 0.28, 3.95, 4.05 kG

Fig. 1.6. (a) Perspective view of the crystal structure of [Fe(Cp*)2 ][Pt(tds)2 ] along the chain direction. (b) Interchain arrangement of the pair I–II, d1 corresponds to the DA closest intrachain contact (3.826 Å, QW = 0.98) and d2 to the closest interchain contact (4.348 Å, QW = 1.09). (c) Interchain arrangement of the pair I–IV, d3 is the closest interchain contact (4.263 Å, QW = 1.33). Hydrogen atoms were omitted for clarity.

12 1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates


13

2.6K 3.2K

2x105

2

Mag (emuG/mol)

Magnetization (NPB)

1.7K

8kG 4kG 2kG 1kG

0

Temp (K)

10

0 0

5

10

15

Field (kG) Fig. 1.7. Magnetization field dependence for [Fe(Cp*)2 ][Pt(tds)2 ], at 1.7, 2.6 and 3.2 K. The inset shows the magnetization temperature dependence at 1, 2, 4 and 8 kG.

for [Mn(Cp*)2 ][Ni(tds)2 ], [M(Cp*)2 ][Pt(tds)2 ] (M = Fe, Pt) respectively. The magnetization field dependence at 1.7, 2.6 and 3.2 K for [Fe(Cp*)2 ][Pt(tds)2 ] is shown in Figure 1.7, a sigmoidal behavior typical of metamagnetic behavior is observed for T < TN = 3.3 K [26]. For low applied magnetic fields (H < HC ), a maximum in the magnetization temperature dependence can be observed, corresponding to an AFM transition, which is suppressed with fields H > HC , as shown in the inset of Figure 1.7. The critical field temperature dependence obtained from the isothermal (closed symbols) and isofield (open symbols) measurements is shown in Figure 1.8. In the compounds [Fe(Cp*)2 ][Pt(tdt)2 ], [M(Cp*)2 ][Ni(tds)2 ] and [M(Cp*)2 ][Pt(tds)2 ] (M = Fe, Mn and Cr) the Se–Se (or S–S) contacts, are expected to give rise to strong AFM interchain interactions, as the contacts are relatively short and there is a significant spin density on those atoms. The intrachain DA contacts (along c) and the interchain AA (Se–Se or S–S) contacts (along a) are expected to give rise to quasi-2D magnetic systems (ac plane), as the other interchain contacts are expected to give rise to much weaker magnetic interactions. The situation is quite distinct from that observed in the compounds [M(Cp*)2 ][Ni(edt)2 ], [Fe(Cp*)2 ][Ni(tdt)2 ] and [Mn(Cp*)2 ][M (tdt)2 ], where the interchain magnetic interactions are expected to be considerably more isotropic, and for these compounds the magnetic systems can be described as quasi-1D. The distinct dimensionality of the magnetic systems is reflected in the fast saturation observed in the isothermals, just above HC , in the case of the salts with the quasi-2D magnetic systems, unlike the compounds presenting quasi-1D magnetic

14

1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates 6

HC (kG)

PM 4

2

AFM

0 1

2

3

Temperature (K)

4

Fig. 1.8. Critical field dependence for [Fe(Cp*)2 ][Pt(tds)2 ], where the closed and open symbols correspond to the data obtained with isothermal and isofield measurements respectively.

systems, where saturation occurs only at very high magnetic fields, when the temperature is not much lower than TN [26]. In the case of [Cr(Cp*)2 ][Pt(tds)2 ] metamagnetic behavior was also observed (TN = 5.2 K), but a rather complicated phase diagram was obtained. Below TN , two field induced transitions were observed to occur, and at 1.7 K the critical fields were 5 and 16 kG, respectively [28]. This is the first example of a metamagnetic transition on a [Cr(Cp*)2 ] based ET salt and the low temperature phase diagram is still under study [28]. The analysis of the crystal structures, the magnetic behavior and atomic spin density calculations of several ET salts based on decamethylferrocenium and on metal-bis(dichalcogenate) acceptors with structures consisting of arrangements of parallel alternating DA linear chains, allowed a systematic study of the intra and interchain magnetic interactions [26]. In the case of these compounds a spin polarization is observed in the metallocenium donors but not in the acceptors described so far. The analysis of the intrachain contacts in the perspective of the McConnell I mechanism suggests the existence of intrachain FM coupling, through the contacts involving the metal or chalcogen atoms (positive spin density) from the acceptors and the C atoms (negative spin density) from the Cp ring of the donors, which shows good agreement with the experimental observations. A variety of interionic interchain contacts were observed in these ET salts, AA (Se–Se, S–S and C–C), DD (Me–Me) and DA (Me–S), and all these contacts were observed to lead to AFM interchain coupling. A strict application of the McConnell I model was not possible in the case of the interchain contacts, as the shortest contacts would involve mediation through H or F atoms, which are expected to present a very small spin density [26]. However the results regarding the nature of the interchain magnetic coupling would be compatible with that model if the contacts involving H or F atoms were neglected, as all the atoms involved in these contacts present a posi-


15

tive spin density. This study revealed that metamagnetism, which was observed in several compounds presenting a crystal structure consisting of a parallel arrangement of alternated 1D chains, is expected to occur in other compounds presenting a similar solid state structure, in the case of the metal bis-dichalcogenate acceptors no spin polarization effect is found.

1.3.1.3

[Fe(C5 Me4 SCMe3 )2 ][M(mnt)2 ], M = Ni, Pt

The compounds [Fe(C5 Me4 SCMe3 )2 ][M(mnt)2 ] (M = Ni, Pt) are the only cases of salts based on metallocenium derivatives and [M(mnt)2 ]− complexes where the crystal structure is based on a 1D alternated type I structural motif [36]. As in the other salts described above, the crystal structure consists also of a parallel arrangement of the chains. For [Fe(C5 Me4 SCMe3 )2 ][Pt(mnt)2 ] a view along the chains is shown in Figure 1.9(a). In the chains the [Pt(mnt)2 ]− units are considerably tilted in relation to the chain direction, as shown in Figure 1.9(b), and short interatomic DA intrachain distances were observed, involving one C from the Cp and a S atom from the acceptor, with a C–S distance of 3.501 Å (QW = 1.01). Relatively short interchain interionic distances were observed in the out-of-registry pair I–IV (and the similar II–III) and in the in-registry pair II–IV. For the I–IV pair arrangement, shown in Figure 1.9(b), the shortest contact involves one S from the acceptor and a C atom from a Me group of the donor, with a S–C distance of 3.787 Å (QW = 1.10). While for the II–IV out-of-registry pair, shown in Figure 1.9(c), the shortest contact concerns one N atom from the acceptor and a C from one of the donors Me groups, with a N–C separation of 3.372 Å (QW = 1.09). The magnetic behavior of [Fe(C5 Me4 SCMe3 )2 ][M(mnt)2 ] (M = Ni, Pt) is dominated by FM interactions (θ = 3 K, M = Ni and Pt), which can be attributed to the DA intrachain interactions. The intrachain interactions are expected to be AFM. As in the previous compounds exhibiting this type of structure metamagnetic behavior is also expected to occur at low temperatures.

1.3.1.4

β-[Fe(Cp*)2 ][Pt(mnt)2 ]

The crystal structure of β-[Fe(Cp*)2 ][Pt(mnt)2 ] consists of parallel alternated D+ A− D+ A− (type I) chains, which are isolated by chains of D+ [A2 ]2− D+ units. A projection of the crystal structure along the stacking direction, [100], is shown in Figure 1.10(a). In the DADA chains the [Pt(mnt)2 ]− are considerably tilted in relation to the chain direction, sitting on top of the ethylenic C=C of the mnt2− ligands from the acceptors. A pair of the closest DADA chains (I–II) is shown in Figure 1.10(b) and they are considerably separated (16.576 Å). Short interatomic DA intrachain distances were observed, involving one C from the Cp and a S atom from the acceptor, with a C–S distance of 3.632 Å (QW = 1.05). A pair of the closest DADA chains is shown in Figure 1.10(b). One of the D+ [A2 ]2− D+ chains

Fig. 1.9. (a) View of the structure along the chains for [Fe(C5 Me4 SCMe3 )2 ][Pt(mnt)2 ]. (b) Interchain arrangement of the pair I–IV, d1 corresponds to the DA closest intrachain contact (3.501 Å, QW = 1.01) and d2 to the closest interchain contact (3.787 Å, QW = 1.10). (c) Interchain arrangement of the pair II–IV, d3 is the closest interchain contact (3.372 Å, QW = 1.09). Hydrogen atoms were omitted for clarity.


Fig. 1.10. (a) Perspective view of the structure along the DADA chain direction. (b) Interchain arrangement of the pair I–II, d1 corresponds to the DA closest intrachain contact (3.632 Å, QW = 1.01). (c) View of a D[A2 ]D chain. Hydrogen atoms were omitted for clarity.


18


is shown in Figure 1.10(c), in the DAAD units the acceptors are strongly dimerized with a Pt-Pt distance of 3.574 Å (QW = 0.78). The magnetic susceptibility of β-[Fe(Cp*)2 ][Pt(mnt)2 ] follows Curie–Weiss behavior with θ = 9.8 K. The dominant ferromagnetic interactions are assigned to the magnetic intrachain DA interactions from the type I chains, as the contribution from the D+ [A2 ]2− D+ unit chains is expected to be only from the donors due to the strong dimerization of the acceptors, S = 0 for [A2 ]2− , and no intrachain close contacts were observed to exist.

1.3.1.5

[M(Cp*)2 ][Ni(α-tpdt)2 ]

The crystal structure of [Fe(Cp*)2 ][Ni(α-tpdt)2 ], in spite of presenting the type I structural chain motif, is considerably different from the structures presented so far [34]. The crystal structure consists of alternate layers of donors, [Fe(Cp*)2 ]+ , and acceptors, [Ni(α-tpdt)2 ]− , parallel to the ab plane (ab layers). A projection of the crystal structure along a is shown in Figure 1.11(a) for [Fe(Cp*)2 ][Ni(α-tpdt)2 ]. In the acceptor layers, relatively short interionic AA distances were found, involving S atoms from the central NiS4 fragment and a C atom from the thiophenic fragment of the ligand, as shown Figure 1.11(b). The S· · ·C separations are 3.723 and 3.751 Å, exceeding the sum of the van der Waals radii (3.450 Å) by 8 and 9% respectively. Short interlayer interionic DA distances were found, involving C atoms from the Cp rings and the S atom from the thiophenic fragment from the acceptors, with S· · ·C distances of 3.530 and 3.610 Å, exceeding the sum of the van der Waals radii by 2 and 5% respectively. These contacts give rise to a set of layers (bc layers) composed of parallel alternated DADA chains, as shown in Figure 1.11(c). The chains in adjacent layers are almost perpendicular to each other, running along directions alternating from 2b + c to 2b − c. Two chains from adjacent layers are shown in Figure 1.11(d) along with two anionic ab layers. The chains in the bc layers present an out-of registry arrangement. Short interionic DA interchain distances were observed, involving a S from the MS2 C2 fragment from the acceptor and a C from the Me groups in the donor, with S-C separations exceeding the sum of the van der Waals radii by less than 8%, as shown in Figure 1.11(c). The contacts between the chain in adjacent layers correspond to the (S–C) AA contacts previously mentioned in the case of the acceptor ab layers. The compounds [M(Cp*)2 ][Ni(α-tpdt)2 ], M = Fe and Cr, although not isostructural, present a similar solid state structure. In the case of [Cr(Cp*)2 ][Ni(α-tpdt)2 ] the crystal structure is more symetric than the analogue with M = Fe. The contacts are of the same order and the most significant difference between the two structures is the arrangement of the molecules in the acceptor ab layers, unlike the case of [Fe(Cp*)2 ][Ni(α-tpdt)2 ], where there was only one type of relevant AA contact, because of a short S–C distance, for [Cr(Cp*)2 ][Ni(α-tpdt)2 ], the S atom (from the central NiS4 fragment) is close to two distinct C atoms from the thiophenic


19

Fig. 1.11. Projection of the structure along a for [Fe(Cp*)2 ][Ni(α-tpdt)2 ] (Me groups were omitted for clarity). (b) View of an acceptor layer, showing the closest AA separations (S–C) d1 and d2 (3.775 and 3.721 Å, QW = 1.09 and 1.08). (c) Partial view of the crystal structure illustrating two consecutive anionic layers and two orthogonal DADA chains. (d) View of the structure showing parallel DADA chains, the shortest interionic separations are shown, d3 and d4 correspond to the intrachain contacts (3.519 and 3.622 Å, QW = 1.02 and 1.05) and d5-d7 are interchain DA (S–C) separations (3.671, 3.694, 3.722 Å, QW = 1.06, 1.06 and 1.08). Hydrogen atoms were omitted for clarity.

fragment, with separations of the same order, 3.768 and 3.756 Å (QW = 1.09 and 1.08). However the closest contact involves the same C in both compounds. In the case of the compound [Fe(Cp*)2 ][Ni(α-tpdt)2 ] [34] a minimum is observed in the temperature dependence of the χT product. at 130 K, which is consistent either with ferrimagnetic behavior or with a change in the type of the dominant magnetic interactions. A Curie–Weiss fit to the experimental data in the high

20


temperature regime gave a θ value of −5.1 K. At low temperatures metamagnetic behavior was observed in the case of [Fe(Cp*)2 ][Ni(α-tpdt)2 ], with TN = 2.6 K and HC = 600 G, at 1.7 K. The temperature dependence of HC is shown in Figure 1.12. In the case of [M(Cp*)2 ][Ni(α-tpdt)2 ], with M = Mn and Cr [35], at high temperatures, the magnetic susceptibility follows a Curie–Weiss behavior, with θ values of 7.3 and 6.1 K, showing dominant ferromagnetic interactions for these compounds. A FM transition that was observed to occur in case of [Mn(Cp*)2 ][Ni(α-tpdt)2 ], at 2.2 K, as denoted by a maximum observed in the real and imaginary contributions of the ac susceptibility. No hysteresis was observed in the isothermals below TC = 2.2 K, for low applied magnetic fields, the magnetization isothermals showed a drastic increase and a very slow and nearly linear increase is observed above 5 kG (M = 2.5 N µB ), reaching a value of 3.0 N µB at 120 kG, which is consistent with the spin only (gA = gD = 2.0) value for the saturation magnetization, Msat = gA SA + gD SD = 3.0 N µB . The poor quality of the crystals of this compound has so far prevented crystal structure determination, however a crystal structure similar to that observed for the Fe and Cr analogues, is expected for this compound. Unlike the previously mentioned acceptors, calculations predict a spin polarization effect in the case of [Ni(α-tpdt)2 ]− , and small negative spin densities are expected in the S atom and in one of the carbons from the thiophenic ring [35]. As a consequence a competition between FM and AFM (DA or AA) interactions is expected. From the room temperature crystal structure analysis the stronger interionic contact is expected to be AFM as it corresponds to the intrachain DA contact involving two atoms with negative spin densities, a S from the thiophenic ring of the acceptor and a C from the C5 ring of the donor. The shorter AA contacts from the anionic layers are expected to give rise to FM interactions, as the spin densities of the atoms do not have the same sign. The high temperature magnetic behavior of the [M(Cp*)2 ][Ni(α-tpdt)2 ] salts indicates AFM dominant interactions, which is consistent with the McConnell I model predictions for the DA interactions. However the change in the nature of the magnetic interactions in the case of [Fe(Cp*)2 ][Ni(α-tpdt)2 ], remains an open question. This change can be attributed to small variations in the interionic contacts on cooling. In both intrachain DA and interlayer AA arrangements, besides the shorter contacts referred to before, there are also slightly longer interionic separations, which could lead to different types of interactions for both the DA and AA contacts. As observed in the [Fe(Cp*)2 ] based compound, in the case of [Cr(Cp*)2 ][Ni(α-tpdt)2 ], the shorter contacts involve atoms with the same spin density parity (AFM coupling) and a competition between AFM and FM interactions is expected. The experimental results indicate that in this case the FM interactions dominate the magnetic behavior of this compound. The distinct magnetic behavior found in [M(Cp*)2 ][Ni(α-tpdt)2 ], with M = Fe, Mn and Cr, can be related to the competition between the FM and AFM interactions and the small differences in the DA overlap observed in the DADA chains. The poor quality of the crystals of [Mn(Cp*)2 ][Ni(α-tpdt)2 ] has so far


21

1.0

H C (kG)

0.8

PM

0.6

0.4

AFM

0.2

0.0 1.0

1.5

2.0

2.5

3.0

Temperature (K)

3.5

Fig. 1.12. Critical field dependence for [Fe(Cp*)2 ][Ni(α-tpdt)2 ], where the closed and open symbols correspond to the data obtained with isothermal and isofield measurements respectively.

prevented crystal structure determination, however a crystal structure similar to that observed for the Cr analogue is expected for this compound, considering the magnetic behavior observed in these compounds.

1.3.2

Type II Mixed Chain [M(Cp*)2 ][M (L)2 ] Salts

This type of chain arrangement was observed only in the case of α[Fe(Cp*)2 ][Pt(mnt)2 ]. In the crystal structure, layers of parallel DAADAA (type II) chains, with a net charge (−) per repeat unit, [A2 ]2− D+ , alternate with layers presenting a D+ D+ A− repeating unit, with a net (+) per repeat unit [16]. A view of the crystal structure along the type II chain direction, [100], is shown in Figure 1.13(a). In the type II chain layers the acceptors are strongly dimerized with a Pt–Pt distance of 3.575 Å (QW = 0.78) and the [A2 ]2− D+ [A2 ]2− D+ chains present an out-of-registry arrangement, as shown in Figure 1.13(b). Apart from the AA contacts no other short contacts were observed in these layers. The DDA layer presents a unique arrangement, where the donors sit on top of the extremity of the acceptors, these DDA units form edge to edge chains, as shown in Figure 1.13(c). In these layers the closest interionic separations involve one C from the Cp and a S atom from the acceptor, with a C–S distance of 3.952 Å (QW = 1.15). The magnetic susceptibility of α-[Fe(Cp*)2 ][Pt(mnt)2 ] follows Curie–Weiss behavior with θ = 6.6 K [16]. The dominant ferromagnetic interactions are assigned to the magnetic DA interactions from the DDA layers, as the contribution from the [A2 ]2− D+ chains is expected to be only from the isolated donors due to the strong dimerization of the acceptors, S = 0 for [A2 ]2− .

Fig. 1.13. (a) View of the structure of α-[Fe(Cp*)2 ][Pt(mnt)2 ] along the DAADAA (type II) chains. (b) View of a type II chain layer. (c) View of the DDA layer, d1 corresponds to the closest contact (3.952 Å, QW = 1.15). Hydrogen atoms were omitted for clarity.



1.3.3

23

Type III Mixed Chain [M(Cp*)2 ][M (L)2 ] Salts

The acceptor-acceptor magnetic interactions play a key role in the magnetic behavior of the [M(Cp*)2 ][M (L)2 ] salts based on type III chains, and in most cases the AA interactions are AFM. Table 1.4 summarizes the key magnetic properties of type III [M(Cp*)2 ][M (L)2 ] compounds. Table 1.4. Magnetic characterization of type III [M(Cp*)2 ][M (L)2 ] salts. Compound

SD ; SA

θ, K

Comments

Ref.

[Fe(Cp*)2 ][Ni(dmit)2 ] [Mn(Cp*)2 ][Ni(dmit)2 ] α-[Fe(Cp*)2 ][Pd(dmit)2 ] β-[Fe(Cp*)2 ][Pd(dmit)2 ] (f) [Fe(Cp*)2 ][Pt(dmit)2 ] [Fe(Cp*)2 ][Ni(dmio)2 ] (f) [Fe(Cp*)2 ][Pd(dmio)2 ] [Fe(Cp*)2 ][Pt(dmio)2 ] [Fe(Cp*)2 ][Ni(dsit)2 ]

1/2; 1/2 1; 1/2 1/2; 1/2 1/2; 1/2 1/2; 1/2 1/2; 1/2 1/2; 1/2 1/2; 1/2 1/2; 1/2

−7.6 (a) 2 (d) −22.3 2.6 −14.4 −19.0 −24.7 −33.3 −18.9

(b); Tm = 30 K (c) FM (e); TC = 2.5 K (b) (b) (b) (b) (b) (b) (b)

45 46 31 45 45 45 45 45 31

(a) Non-Curie–Weiss behavior the given θ value relates to the high temperature region (T > Tm ). (b) No magnetic ordering down to 1.8 K. (c) Minimum in χT vs. T . (d) Estimated value from χ T vs. T plot in Ref. [46]. (e) Ferromagnetic transition. (f) Crystal structure not yet determined.

1.3.3.1

[M(Cp*)2 ][M (dmit)2 ] (M = Fe; M = Ni, Pt and M = Mn; M = Ni)

The salts [Fe(Cp*)2 ][M(dmit)2 ], with M = Ni [17] and Pt [31], and [Mn(Cp*)2 ][Ni(dmit)2 ] [30] are isostructural and the crystal structure consists of 2D layers composed of parallel type III chains, ··A− A− D+ D+ A− A− D+ D+ ··, where face-to-face pairs of acceptors alternate with side-by-side pairs of donors. A view of the structure along the chain direction is shown in Figure 1.14(a) for [Fe(Cp*)2 ][Ni(dmit)2 ]. The chains are regular and the Cp fragments of the donor sit above dmit ligands of the acceptor, as shown for [Fe(Cp*)2 ][Ni(dmit)2 ] in Figure 1.14(b). Intrachain AA short contacts are observed in the [Ni(dmit)2 ]− dimers, involving a Ni atom and one of the sulfur atoms from the five-membered C2 S2 C ring from the ligand, with a Ni–S distance of 3.792 Å (QW = 0.96). The intrachain DA separation is considerably larger and the shorter contacts between the acceptor and the Cp rings correspond to a S–C contact (S from the C2 S2 C fragment) with distances of 3.611 and 3.659 Å (QW = 1.05 and 1.06). Several short AA (S–S) interchain contacts were observed in this compound and the crystal structure can be better described as being based on layers of out-of-registry parallel chains, one of these layers is shown in Figure 1.14(b). The intralayer interchain contacts are

Fig. 1.14. (a) Perspective view of the crystal structure of [Fe(Cp*)2 ][Ni(dmit)2 ] along the stacking direction (hydrogen atoms were omitted for clarity). (b) View of one layer of the type II chains, d1 corresponds to the intradimer (AA) closest contact (3.792 Å, QW = 0.96), and d2 and d3 to short interchain contacts (3.422 and 3.547 Å, QW = 0.93 and 0.96) (Me groups were omitted for clarity). (c) View of two neighboring chains from different layers, d4 is the closest interlayer contact (3.375 Å, QW = 0.91) (Me groups were omitted).



25

shorter than the intrachain and two types of contacts are observed. The longer contact involves one of the S from the central MS4 fragment and one of the S from the ligand C2 S2 C fragment, with a S–S distance of 3.547 Å (QW = 0.96), and the shorter contact involves two S atoms from the central MS4 fragment, with a S–S distance of 3.422 Å (QW = 0.93). There are also interchain interlayer AA short contacts, involving S atoms from the C2 S2 C ligand fragments, with a S–S distance of 3.375 Å (QW = 0.91), as shown in Figure 1.14(c). In spite of the similarities in the crystal structures of the compounds [Fe(Cp*)2 ][M(dmit)2 ], with M = Ni and Pt, and [Mn(Cp*)2 ][Ni(dmit)2 ], they present distinct magnetic behaviors. In the case of [Fe(Cp*)2 ][M(dmit)2 ], a minimum in the temperature dependence of χ T , is observed at 30 K [45], as shown in Figure 1.15. This can be attributed to a change in the dominant magnetic interactions, due to structural changes on cooling. At high temperatures the magnetic susceptibility follows Curie-Weiss behavior, with a θ value of −7.6 K, which clearly indicates that AFM interactions are dominant. However, below Tm = 30 K, χT increases rapidly, indicating that FM become dominant in that region, this is further confirmed by the magnetization field dependence at low temperatures, which for low applied magnetic fields increases faster than predicted by the Brillouin function (solid line) and at high fields slowly approaches the saturation magnetization, as shown in Figure 1.16. In the case of [Mn(Cp*)2 ][Ni(dmit)2 ] a FM transition was reported to occur at 2.5 K [46], the field cooled (FCM), zero field cooled (ZFCM) and remnant (REM) magnetization temperature dependences are shown in Figure 1.17. This is the first and only case, to date, in this class of compounds to present FM ordering and this behavior was analyzed in the light of the McConnell I mechanism, namely for the intradimer magnetic interactions due to a spin polarization effect in the acceptor molecules. According to the McConnell I model these interactions are predicted to be FM as the atoms involved in the intradimer contacts

FT (emu K mol-1)

2.0

1.5

1.0

0.5 0

100

200

Temperature (K)

300

Fig. 1.15. χT temperature dependence for [Fe(Cp*)2 ][Ni(dmit)2 ] (squares) and [Fe(Cp*)2 ][Pt(dmit)2 ] (circles).

Magnetization (NPB)

26


2.0

1.0

0.0 0

20

40

Field (kG)

60

Fig. 1.16. Magnetization field dependence for [Fe(Cp*)2 ][Ni(dmit)2 ] (squares) and [Fe(Cp*)2 ][Pt(dmit)2 ] (circles) at 1.8 K. The solid line corresponds to the Brillouin function considering the donor and acceptor spins, while the dashed line corresponds only to the contribution from the donor molecules.

Fig. 1.17. Field-cooled (FCM), zero-field-cooled (ZFCM) and remnant (REM) magnetization temperature dependences of [Mn(Cp*)2 ][Ni(dsit)2 ] (reproduceded with permission from Ref. [46]).

present different signs in the atomic spin density, the Ni atom presents a positive spin density while in the S atoms from the C2 S2 C ligands fragments, the spin density is negative [47]. In the case of [Fe(Cp*)2 ][Pt(dmit)2 ] the magnetic behavior is dominated by AFM interactions as the magnetic susceptibility follows Curie– Weiss behavior, with a θ value of −14.4 K [45], and the χT product decreases on cooling, as shown in Figure 1.15. For this compound the magnetization isothermals (circles in Figure 1.16) at low temperature are consistent with total cancella-


27

tion of the magnetic contribution from the acceptors, and the magnetization field dependence follows the Brillouin function for the isolated donors, [Fe(Cp*)2 ]+ , (dashed line) as shown in Figure 1.16. In the case of [Fe(Cp*)2 ][M(dmit)2 ] (M = Ni and Pt), the S–S intra and interlayer short contacts are expected to lead to AFM interactions, as the spin density of the atoms involved in the shorter contacts have the same sign. Considering that these contacts are even shorter than the intradimer ones (FM coupling), dominant AFM interactions are expected, which is consistent with the observed negative θ values for [Fe(Cp*)2 ][Pt(dmit)2 ], and for [Fe(Cp*)2 ][Ni(dmit)2 ], at high temperatures. The change in behavior observed in the case of [Fe(Cp*)2 ][Ni(dmit)2 ], can originate from a weakening of the intra and interlayer AFM interactions. It is worth mentioning that, in the case of the interchain intralayer interactions, the shorter contacts (involving two S atoms from the central MS4 fragment) are expected to be AFM, while the weaker contacts (involving a S from the central MS4 fragment and one of the S from the C2 S2 C fragment) are predicted to give rise to FM interactions. In this case a slight change in the interionic arrangement could change the nature of the intralayer magnetic interactions. A similar situation was reported in the case of NH4 [Ni(mnt)2 ] · H2 O, which shows dominant AFM interactions at high temperatures (T > 100 K), for low temperatures FM interactions become dominant and ferromagnetic ordering is exhibited at 4.5 K [7]. The magnetic behavior of [Fe(Cp*)2 ][Ni(dmit)2 ] is still puzzling and requires further study.

1.3.3.2

[Fe(Cp*)2 ][M(dmio)2 ] (M = Pd and Pt), α-[Fe(Cp*)2 ][Pd(dmit)2 ] and [Fe(Cp*)2 ][Ni(dsit)2 ]

The compounds [Fe(Cp*)2 ][M(dmio)2 ], with M = Pd and Pt, are isostructural and the crystal structure consists of a parallel arrangement of 1D type III chains. The solid state structure is similar to that observed in [Fe(Cp*)2 ][Ni(dmit)2 ] and presents a similar layered motif. However, for [Fe(Cp*)2 ][M(dmio)2 ] (M = Ni and Pt) the dimers show a different configuration, in this case no slippage is observed in the dimer and a short Pd–Pd contact was observed in the case of [Fe(Cp*)2 ][Pd(dmio)2 ], with a Pd–Pd distance of 3.481 Å (QW = 0.76). In this compound short intralayer AA contacts were also detected, involving a S from the central MS4 fragment and one of the S from the C2 S2 C fragment, with a S–S distance of 3.669 Å (QW = 0.99). No interlayer short contacts were observed for [Fe(Cp*)2 ][Pd(dmio)2 ]. The compound α-[Fe(Cp*)2 ][Pd(dmit)2 ] is not isostructural with [Fe(Cp*)2 ][M(dmio)2 ], with M = Pd and Pt, but presents a similar molecular arrangement in the crystal structure. Again, in the case of α[Fe(Cp*)2 ][Pd(dmit)2 ], a strong dimerization was observed for the acceptors, presenting also short Pd–Pd contacts, with a distance of 3.485 Å (QW = 0.76). Short intralayer contacts, similar to those observed in the previous compound, were ob-

28


served, with a S–S distance of 3.558 Å (QW = 0.96). No interlayer short contacts were observed for α-[Fe(Cp*)2 ][Pd(dmit)2 ]. The magnetic susceptibility of [Fe(Cp*)2 ][M(dmio)2 ] (M = Pd and Pt) and α-[Fe(Cp*)2 ][Pd(dmit)2 ] follows Curie–Weiss behavior, with θ values of −24.7, −33.3 and −22.3 K, respectively. The magnetic behavior is clearly dominated by the AFM intradimer interactions. At low temperatures, the magnetic field dependence follows the predicted values for the isolated donors, as in the case of [Fe(Cp*)2 ][Pt(dmit)2 ]. Unlike the [Ni(dmit)2 ] and [Pt(dmit)2 ] based compounds, for [Fe(Cp*)2 ][M(dmio)2 ] (M = Pd and Pt) and [Fe(Cp*)2 ][Pd(dmit)2 ] the short intradimer contacts are expected to lead to strong AFM interactions, which is inagreement with the experimental observations. The crystal structure of [Fe(Cp*)2 ][Ni(dsit)2 ] is similar to those described previously in this section. In this salt the acceptors are strongly dimerized through Ni–Se bonds, the Ni(dsit)2 units are slipped (see Figure 1.18) and the metal adopts a square pyramidal conformation, with an apical Ni–Se distance of 2.555 Å, which is slightly larger than the average equatorial Ni–Se bond distance, 2.330 Å. The magnetic susceptibility of [Fe(Cp*)2 ][Ni(dsit)2 ] follows Curie–Weiss behavior, with a θ value of −19.8 K. The magnetic behavior is clearly dominated by the AFM intradimer interactions. At low temperatures, the magnetic field dependence follows the predicted values for the isolated donors, as in the case of the analogous compounds presenting dominant AFM interactions, described previously. In the case of β-[Fe(Cp*)2 ][Pd(dmit)2 ] dominant FM interactions (θ = 2.6 K) were observed and the crystal structure in this compound is expected to be similar either to that described for [Fe(Cp*)2 ][Ni(dmit)2 ] or to that reported for [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN, which will be described in the next section (Section 1.3.4.1.). For [Fe(Cp*)2 ][Ni(dmio)2 ] the observed large negative θ value (−19 K) suggests that this compound must present a crystal structure similar to those reported for the Pd and Pt analogues or for α-[Fe(Cp*)2 ][Pd(dmit)2 ]. The supramolecular arrangement in the type III chain based salts, at high temperatures, is consistent with the existence of dominant AFM interactions through AA interactions. For the compounds with dominant FM interactions at low temperatures, the magnetic behavior can be related to the distinct dimer arrangements. The dimer arrangements along with the dimer overlap are illustrated in Figure 1.18, for [Fe(Cp*)2 ][Ni(dmit)2 ] α-[Fe(Cp*)2 ][Pd(dmit)2 ] and [Fe(Cp*)2 ][Ni(dsit)2 ]. As stated before the contacts in the case of [Fe(Cp*)2 ][Ni(dmit)2 ] are expected to give rise to FM intradimer interactions, while in the case of the other two compounds AFM intradimer interactions are anticipated.

Fig. 1.18. The dimer arrangements and dimer overlapping are illustrated for [Fe(Cp*)2 ][Ni(dmit)2 ] (top) and α-[Fe(Cp*)2 ][Pd(dmit)2 ] (center) and [Fe(Cp*)2 ][Ni(dsit)2 ] (bottom).


30


1.3.4

Type IV Mixed Chain [M(Cp*)2 ][M (L)2 ] Salts

The magnetic behavior of the [M(Cp*)2 ][M (L)2 ] salts based on type IV chains shows a strong dependence on the intra and interchain arrangments. Table 1.5 summarizes the key magnetic properties of type IV [M(Cp*)2 ][M (L)2 ] compounds. Table 1.5. Magnetic characterization of type IV [M(Cp*)2 ][M (L)2 ] salts. Compound

SD ; SA

θ, K

Comments

Ref.

[Fe(Cp*)2 ][Ni(dmio)2 ]MeCN [Fe(Cp*)2 ][Ni(bds)2 ]MeCN [Fe(Cp*)2 ][Ni(bdt)2 ] [Mn(Cp*)2 ][Ni(bdt)2 ]

1/2; 1/2 1/2; 1/2 1; 1/2 1; 1/2

2.0 0 (b) −5.6 (c) −22.6

32 17 33, 48 33, 48

[Cr(Cp*)2 ][Ni(bdt)2 ] [Fe(Cp*)2 ][Co(bdt)2 ] (f) [Mn(Cp*)2 ][Co(bdt)2 ] (f) [Cr(Cp*)2 ][Co(bdt)2 ] [Fe(Cp*)2 ][Pt(bdt)2 ] [Mn(Cp*)2 ][Pt(bdt)2 ] (f)

3/2; 1/2 3/2; 1 3/2; 1 3/2; 1 1/2; 1/2 1; 1/2

+6.2 −23.0 −4.9 −2.5 −12.6 −20.5

[Cr(Cp*)2 ][Pt(bdt)2 ] [Fe(Cp*)2 ]2 [Cu(mnt)2 ]

3/2; 1/2 1/2; 1/2

+6.0 −8.0

(a) (a) (a); Tm = 40 K (d) Tm = 20 K (d); MM (e): TN = 2.3 K; HC = 200 G (2 K) (a) (a) (a) (a) (a); Tm = 125 K (d) Tm = 100 K (d); FIM (g): TC = 2.7 K (a) (a)

33, 48 33 33 33 33 33 33 29

(a) No magnetic ordering observed down to 1.8 K. (b) θ value in the high temperature region, at low temperatures θ > 0. (c) Non-Curie–Weiss behavior the given θ value relates to the high temperature region (T > Tm ). (d) Minimum in χT vs. T . (e) Metamagnetic transition. (f) Crystal structure not yet determined. (g) Ferrimagnetic transition.

1.3.4.1

[Fe(Cp*)2 ][Ni(dmio)2 ]MeCN

The crystal structure of [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN consists of 2D layers composed of parallel ··D+ D+ A− D+ D+ A− ·· chains (type IV), where side-by-side pairs of donors alternate with an acceptor, with a net charge (+) per repeat unit (D+ D+ A− ) [32]. These charged layers are separated by acceptor layers, as represented in the view along [010] in Figure 1.19, for [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN. The chains are regular and the Cp fragments of the donor sit above the dmio ligands of the acceptor, as shown in Figure 1.19(a). In this compound, unlike the previous compounds, the C5 Me5 ligands from [Fe(Cp*)2 ]+ present an eclipsed conformation. No interionic short contacts are observed in [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN. The closest interionic intrachain (DA) separation involves a S atom from the central

Fig. 1.19. (a) View of the crystal structure of [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN along the stacking direction (hydrogen atoms were omitted for clarity). (b) View of the DDA layer, d1 corresponds to the intrachain (DA) closest contacts (3.945 Å, QW = 1.14) (Me groups were omitted for clarity). (c) View of the anionic layer, d2 is the closest interlayer contact (3.777 Å, QW = 1.02).


32


MS4 fragment of the acceptor and one of the C atoms from the C5 ring of the donor, with a S–C distance of 3.945 Å (QW = 1.14). The chains in the layers are quite isolated and the solvent molecules are located in cavities between the DDA chains layers and the anionic layers, as shown in the view of the structure in Figure 1.19(b). Short contacts were observed in the anionic layers involving S atoms from the five-membered C2 S2 C ring of the dmio ligands, with a S–S distance of 3.777 Å (QW = 1.02), as shown in Figure 1.19(c). Relatively close AA contacts between the DDA chains and the anionic layers were also observed in [Fe(Cp*)2 ][Ni(dmio)2 ], involving O atoms from the acceptor layers and S atoms from the C2 S2 C ring of the dmio ligands, with a O–S distance of 3.398 Å (QW = 1.05). In the case of [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN, FM interactions dominate the magnetic behavior of the compounds [32], as seen from the positive θ value (2 K) obtained from the Curie–Weiss fit. The observed magnetic behavior is attributed to the intrachain interactions, as the contacts in the anionic layers are expected to give rise to AFM interactions since the spin density of the atoms involved in these contacts have the same sign.

1.3.4.2

[Fe(Cp*)2 ][Ni(bds)2 ]MeCN

The crystal structure of [Fe(Cp*)2 ][Ni(bds)2 ], as that of [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN, consists of 2D layers composed of parallel ··D+ D+ A− D+ D+ A− ·· chains (type IV), which are separated by acceptor layers [17], as represented in the view along [100] in Figure 1.20(a). In the case of [Fe(Cp*)2 ][Ni(bds)2 ]MeCN, the chains are not regular and while one of the Cp fragments of the donor sits above the C6 ring of the ligand, the second is displaced towards the center of the acceptor. For the first Cp the closest DA interatomic separation (C–C) has a distance of 3.451 Å (QW = 1.08), while for the second Cp the closest DA contact (C–Se) corresponds to a distance of 3.752 Å (QW = 1.04), as shown in Figure 1.20(b). The DDA chains are relatively isolated and the solvent is located in cavities between the chains. In the case of [Fe(Cp*)2 ][Ni(bds)2 ]MeCN no short interionic interlayer distances were observed involving molecules in the DDA layers, not in acceptor layers or even in the anionic layers. The magnetic behavior of this compound is dominated by FM interactions [17], which are attributed to the observed DA intrachain contacts.

1.3.4.3

[M(Cp*)2 ][M (bdt)2 ] (M = Fe, Mn and Cr; M = Co, Ni and Pt)

[Cr(Cp*)2 ][M (bdt)2 ] (M = Ni and Co) are isostructural, and, as in the case of the [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN and [Fe(Cp*)2 ][Ni(bds)2 ]MeCN salts, a crystal structure, based on a DDA type IV chain supramolecular arrangement, is observed [33]. However in [Cr(Cp*)2 ][M (bdt)2 ] the pairs of donors are perpendicular to each other, unlike the previous compounds, where the donor molecules are


33

Fig. 1.20. (a) Perspective view of the crystal structure of [Fe(Cp*)2 ][Ni(bds)2 ]MeCN normal to the chain direction (hydrogen atoms were omitted for clarity). (b) View of the DDA layer, d1 and d2 correspond to the intrachain (DA) closest contacts (3.451 and 3.752 Å, QW = 1.08 and 1.04) (Me groups were omitted for clarity).

parallel. A view along the chain direction, [101], is shown in Figure 1.21(a) for [Cr(Cp*)2 ][Ni(bdt)2 ]. The shorter DA intrachain separations involve S atoms from the acceptors and C atoms from the Cp rings of the donors (aligned with the chain direction) presenting S–C distances of 3.702 and 3.857 Å (QW = 1.07 and 1.12), as shown in the view of a DDA chain layer represented in Figure 1.21(b). The chains in the same layer are relatively isolated, but short distances between the chains and anions on the anionic layers were observed. As shown in Figure 1.21(c), besides the intrachain contacts, relatively short interaionic separations were also observed between molecules in the chains and in the anionic layers. AA contacts were observed involving C atoms from the terminal C6 ring of the ligands and Ni atoms from the acceptors in the anionic layer, with a C–Ni distance of 4.206 Å (QW = 1.14). DA contacts were also observed involving one of the C atoms from the Cp ring of the donor perpendicular to the chain axis and one of the C atoms from the C6 ring of the acceptor, with a C–C distance of 3.453 Å (QW = 1.08). Short contacts were also observed in the anionic layers, as shown in Figure 1.21(d), with distances of 3.633 and 3.340 Å (QW = 1.05 and 1.04), for S–C and C–C contacts respectively. In the case of [Fe(Cp*)2 ][M (bdt)2 ] (M = Ni and Pt), [Mn(Cp*)2 ][M(bdt)2 ] (M = Ni and Co), and [Cr(Cp*)2 ][Pt(bdt)2 ], the crystal structures show a duplication of the unit cell along b, but present similar supramolecular packing [33]. In the case of the compounds [M(Cp*)2 ][Co(bdt)2 ] (M = Fe, Mn and Cr) and [Cr(Cp*)2 ][M (bdt)2 ] (M = Ni and Pt), the magnetic susceptibility follows Curie– Weiss behavior. The [M(Cp*)2 ][Co(bdt)2 ] salts present dominant AFM interactions (θ = −23, −4.9 and −2.5 K for M = Fe, Mn and Cr respectively) [33], while the [Cr(Cp*)2 ][M (bdt)2 ] present dominant FM interactions (θ = 6.2 and 6.0 K for M = Ni and Pt respectively) [33]. In the case of the compounds [Fe(Cp*)2 ][M (bdt)2 ] and [Mn(Cp*)2 ][M (bdt)2 ], with M = Ni and Pt, a minimum in the temperature

34


Fig. 1.21. (a) View of the crystal structure of [Fe(Cp*)2 ][Pt(bdt)2 ] along the chain direction (hydrogen atoms were omitted for clarity). (b) View of the DDA layer, d1 and d2 correspond to the intrachain (DA) closest contacts (3.702 and 3.857 Å, QW = 1.07 and 1.12) (Me groups were omitted for clarity). (c) View of one of the DDA stacks and acceptors from neighboring acceptor layers, d3 and d4 correspond to interlayer contacts (3.453 and 4.206 Å, QW = 1.08 and 1.14). (d) View of the anionic layer, d5 (S–C) and d6 (C–C) are the closest interlayer contacts (3.633 and 3.340 Å, QW = 1.05 and 1.04).

dependence of χ T is observed at 40, 125, 20 and 130 K for M/M = Fe/Ni, Fe/Pt, Mn/Ni and Mn/Pt respectively [33]. For these compounds the minima are attributed to ferrimagnetic behavior, as in the case of [Mn(Cp*)2 ][Pt(bdt)2 ] FIM ordering was observed at 2.7 K [33]. The magnetization field dependence, at 1.8 K, is shown in Figure 1.22 (squares), after a fast increase at low fields the magnetization attains an almost constant value that is in good agreement with that predicted for FIM ordering, Msat = SD gD − SA gA ≈ 1.57 N µB , calculated for SA = 1/2, gA = 2.06 [49], SD = 1 and gD = 2.6 (due to the high g anisotropy of the donor the gD value was obtained from susceptibility temperature dependence at high temperatures). The magnetization field dependence, at 2 K, of [Mn(Cp*)2 ][Ni(bdt)2 ] is also shown in Figure 1.22 (circles). A metamagnetic transition was observed to occur in this compound, with TN = 2.3 K and HC = 200 G at 2 K [33, 48], as


35

Msat (FIM)

1

M (NPB)

Magnetization (NPB)

2

0.4

0.0 0

500

H (G)

0 0

20

40

Field (kG)

60

Fig. 1.22. Magnetization field dependence for [Mn(Cp*)2 ][Pt(bdt)2 ] (squares) and [Fe(Cp*)2 ][Ni(bdt)2 ] (circles) at 1.8 K. The inset shows the low field sigmoidal behavior observed in the case of [Fe(Cp*)2 ][Ni(bdt)2 ].

shown in the inset of Figure 1.22. The magnetization values above the critical field, in the high field state, are of the same order as those observed in the case of [Mn(Cp*)2 ][Pt(bdt)2 ] and are considerably inferior than the FM saturation magnetization value, Msat = SD gD + SA gA ≈ 3.53 N µB , calculated for SA = 1/2, gA = 2.06 [49], SD = 1 and gD = 2.5 (the gD value was obtained from the susceptibility temperature dependence at high temperature). Then the high field state of [Mn(Cp*)2 ][Ni(bdt)2 ] is consistent with a FIM state. The complexity of the crystal structure of the [M(Cp*)2 ][M (bdt)2 ] salts prevents clear interpretation of the magnetic behavior and the discussion of the correlation between the crystal structures and the magnetic properties. 1.3.4.4

[Fe(Cp*)2 ]2 [Cu(mnt)2 ]

[Fe(Cp*)2 ]2 [Cu(mnt)2 ] presents a crystal structure based on an arrangement of DDA type IV chains. Unlike the other compounds based on these types of chains in [Fe(Cp*)2 ]2 [Cu(mnt)2 ] the chains are neutral, as the acceptor is a dianion, [Cu(mnt)2 ]2− , and there are no anionic layers in this compound [29]. A view along the chain direction, [101], is shown in Figure 1.23(a) for [Fe(Cp*)2 ]2 [Cu(mnt)2 ]. In this compound both donors, from the DD pair in the repeat unit, are perpendicular to the chain direction, as shown in Figure 1.23(b). Short intrachain contacts were observed and involve the Cu from the acceptor and a C from one of the Me groups in the donor, with a Cu–C distance of 3.562 Å (QW = 0.96). The side-by side donors are relatively close and C–C distances of 3.826 Å (QW = 1.20) were observed, involving C atoms from the Cp fragments. No short interionic intrachain contacts were observed and the chains are essentially isolated. For [Fe(Cp*)2 ]2 [Cu(mnt)2 ] the magnetic susceptibility follows Curie–Weiss behavior, with θ = −7.95 K [29]. The dominant antiferromagnetic interactions observed for this compound are consistent with the type of contacts, C–S (DA) or

36


Fig. 1.23. (a) Perspective view of the crystal structure of [Fe(Cp*)2 ]2 [Cu(mnt)2 ] along the chain direction. (b) View of one of the DDA chains, where d1 is the closest interionic contact (3.562 Å, QW = 1.05), relatively short DD separations (d2 = 3.826 Å, QW = 1.20) were detected. Hydrogen atoms were omitted for clarity.

C–C (DD), observed in the crystal structure, as the spin density is expected to be of the same sign in the atoms involved in the contacts.

1.3.5

Salts with Segregated Stacks not 1D Structures

Most of the ET salts based on decamethylmetallocenium radical donors and on planar metal dichalcogenide radical anions reported so far present crystal structures with mixed linear chain basic motifs. The only known exception is [Fe(Cp*)2 ][Ni(mnt)2 ], which exhibits a non-1D crystal structure based on a D+ [A2 ]2− D+ repeat unit [16]. In the case of this compound the magnetic behavior is dominated by intradimer antiferromagnetic interactions. As most of the work with this type of ET salts was essentially motivated by the results obtained with the salts based on decamethylmetalocenium donors and polynitrile planar acceptors, the use of different metallocenium derivatives was limited to a small number of compounds. Among these only the [Fe(C5 Me4 SCMe3 )2 ][M(mnt)2 ], M = Ni and Pt, which was described previously, presented crystal structures based on mixed linear chain motifs. The work developed with salts of other metallocenium derivative donors, including also diamagnetic donors, was also motivated by the observation of ferromagnetic ordering in NH4 [Ni(mnt)2 ]H2 O [7], as the magnetic ordering in this compound is only due to the acceptors. At room temperature, the crystal structure of this salt consists of regular stacks of eclipsed acceptors and the magnetic behavior of NH4 [Ni(mnt)2 ]H2 O is dominated by AFM interactions down to ca. 100 K, where a structural transition

1.4 Summary and Conclusions

37

occurs, below this temperature FM interactions become dominant, and magnetic ordering occurs at 4.5 K. In the case of the salts with [M(mnt)2 )]− (M = Ni and Pt) acceptors, the anionic stacks are isolated from each other by the cations and within the stacks the [M(mnt)2 )]− units form dimers. The magnetic behavior of these compounds is dominated by AFM interactions between the acceptor units in the dimers.

1.4 Summary and Conclusions In this chapter we have reviewed the study of ET salts based on metallocenium radical donors and on planar metal bis-dichalcogenate radical anions. The crystal structures ( all molecular and crystal structure representations were performed using SCHAKAL-97 [50]) of these salts were correlated with the magnetic properties, and the magnetic coupling was analyzed in the perspective of the McConnell I mechanism. The use of the planar metal bis-dichalcogenate acceptors in the preparation of new molecule-based materials followed the report of bulk ferromagnetism in decamethylmetallocenium-based ET salts with small polynitrile acceptors such as TCNE and TCNQ. One of the goals related to the use of the metal bisdichalcogenate acceptors is to obtain an increase in the dimensionality in relation to polynitrile-based ET salts and, as a consequence, to obtain new materials with interesting cooperative magnetic properties. A large number of new ET salts have been obtained, presenting a variety of molecular arrangements, which depend essentially on the size of the anionic complexes, on the tendency of the acceptors to associate as dimers and also on the extent of the π system in the ligands. These salts exhibit a large variety of magnetic behavior. Different types of magnetic ordering were observed at low temperatures. ET salts with small acceptors such as [M(edt)2 ]− , [M(tdt)2 ]− and [M(tds)2 ]− (M = Ni, Pd, Pt), where the delocalized electrons are confined to the central M(S2 C2 )2 fragment, present crystal structures based on parallel arrangements of alternated DADA chains, and in several of these compounds metamagnetic behavior was observed, in good agreement with the predictions of the McConnell I mechanism. In ET salts based on anionic complexes with a large extent of the π system of the ligands two types of structures were observed, depending on the tendency of the complexes to form dimers. In the cases of [M(dmit)2 ]− and [M(dmio)2 ]− , which show a strong tendency to dimerize, in most cases the crystal structure consists of an arrangement of 2D layers composed of parallel chains, where face-to-face pairs of acceptors alternate with side-by-side pairs of donors, DDAA. The magnetic behavior of these ET salts is strongly dependent on the AA interactions, where a competition between FM and AFM interactions is expected. AFM dominant inter-

38


actions were observed at high temperatures, in good agreement with the McConnell I mechanism predictions. In the case of [M(Cp*)2 ][Ni(dmit)2 ] (M = Fe and Mn) at low temperatures FM becomes dominant and in the case of [Mn(Cp*)2 ][Ni(dmit)2 ] a FM transition occurs at 2.5 K, this is attributed to a change in the type of the dominant magnetic interactions. In the case of the ET salts based on anionic complexes presenting a large extent of the π system but no tendency to exist as dimers, such as [Ni(bds)2 ]− , [M(bdt)2 ]− (M = Co, Ni and Pt), and [Cu(mnt)2 ]2− , in general the crystal structures are based on 2D layers consisting of parallel chains where acceptors alternate with pairs of donors, ADDADD, and these layers are separated by layers of acceptors. In these compounds the relative orientation of the donor pairs depends on the acceptors. In the case of [Fe(Cp*)2 ][Ni(bds)2 ] the donors are parallel and with their axes roughly aligned along the stacking direction, for [Fe(Cp*)2 ]2 [Cu(mnt)2 ] the donors are also parallel but their axes are perpendicular to the stacking direction, while for the [M(Cp*)2 ][M (bdt)2 ] salts the donors from the pairs are perpendicular, one is aligned with the stacking direction and the other is perpendicular to it. While for [Fe(Cp*)2 ][Ni(bds)2 ] and [Fe(Cp*)2 ]2 [Cu(mnt)2 ] the magnetic behavior is dominated by the intrachain DA magnetic interactions, which were observed to be FM and AFM respectively. In the case of the [M(Cp*)2 ][M (bdt)2 ] compounds, a large number of contacts were observed in the relatively complex structure, and a variety of magnetic behaviors was observed. In spite of the simplicity of McConnell I model, it has shown to be quite effective in the interpretation of the magnetic behavior in the ET salts based on metallocenium radical donors and on planar metal bis-dichalcogenate radical anions. However in the compounds presenting complex structures with possible competition between FM and AFM intermolecular contacts, e. g. the compounds [M(Cp*)2 ][Ni(α-tpdt)2 ], [M(Cp*)2 ][M (dmit)2 ] and [M(Cp*)2 ][M (bdt)2 ], it was not possible to achieve a clear understanding of the magnetic behavior with that model. The study of these type of ET salts, which began in the late 80s, has gained renewed interest in recent years and a large number of compounds are still under study. Besides the significant number of compounds presenting metamagnetism, the use of acceptors showing spin polarization, leads to salts presenting other types of ordering, such as ferro and ferrimagnetism. The use of these types of acceptors seems quite promising for the preparation of new molecule-based materials.

Acknowledgments The authors wish to thank their co-workers, in particular D. Belo, S. Rabaça, R. Meira, I.C. Santos, J. Novoa and R.T. Henriques. The financial support from Fundação para a Ciência e Tecnologia is gratefully acknowledged.

References

39

References 1. A. Kobayashi, H. Kobayashi, in Handbook of Organic Conductive Molecules and Polymers, ed. H.S. Nalwa, John Wiley, Chichester, 1997, Vol. 1, p. 249. 2. A. Kobayashi, H. Kim, Y. Sasaki et al., Chem. Lett. 1987, 1819. 3. J.W. Bray, H.R. Hart, Jr., L.V. Interrante et al., Phys. Rev. Lett. 1975, 35, 744. 4. M. Almeida, R.T. Henriques, in Handbook of Organic Conductive Molecules and Polymers, ed. H.S. Nalwa, John Wiley, Chichester, 1997, Vol. 1, p. 87. 5. C. Rovira, J. Veciana, E. Ribera et al., Angew. Chem. Int. Ed. Engl., 1997, 36, 2323. 6. J.P. Sutter, M. Fettouhi, C. Michaut et al., Angew. Chem. Int. Ed. Engl., 1996, 35, 2113. 7. M.L. Allan, A.T. Coomber, I.R. Marsden et al., Synth. Met., 1993, 55-57, 3317. 8. J.S. Miller, J.C. Callabrese, H. Rommelmann et al. J. Am. Chem. Soc., 1987, 109, 769. 9. S. Chittipedi, K.R. Cromack, J.S. Miller et al., Phys. Rev. Lett., 1987, 58, 2695. 10. J.S. Miller, A.J. Epstein, in Research Frontiers in Magnetochemistry, ed. C. J. O’Connor, World Scientific, Singapore, 1993, p. 283. 11. J.S. Miller, A.J. Epstein, in E. Coronado, P. Delhaès, D. Gatteschi, J.S. Miller (ed.) Molecular Magnetism: From Molecular Assemblies to Devices, ed. E. Coranado, P. Delhaès, D Gatteschi et al., Kluwer, Dordrecht, 1996, p. 379. 12. (a) G.T. Yee, J.M. Manriquez, D.A. Dixon et al., Adv. Mater. 1991, 3, 309; (b) D.M. Eichhorn, D.C. Skee, W.E. Broderick et al., Inorg. Chem. 1993, 32, 491; (c) J.S. Miller, R.S. McLean, C. Vasquez et al., J. Mater. Chem. 1993, 3, 215. 13. (a) W.E. Broderick, D.M. Eichhorn, X. Liu et al., J. Am. Chem. Soc. 1995, 117, 3641; (b) W.E. Broderick, J.A. Thompson, E.P. Day et al., Science 1990, 249, 401; (c) W.E. Broderick, B.M. Hoffman, J. Am. Chem. Soc. 1991, 113, 6334. 14. O. Kahn, Molecular Magnetism, VCH, New York, 1993, Chapter 11. 15. J.S. Miller, A.J. Epstein, Angew. Chem. Int. Ed. Engl. 1994, 33, 385. 16. J.S. Miller, J.C. Calabrese, A.J. Epstein, Inorg. Chem. 1989, 28, 4230. 17. W.E. Broderick, J.A. Thompson, M.R. Godfrey et al., J. Am. Chem. Soc. 1989, 111, 7656. 18. H.M. McConnell, J. Chem. Phys. 1963, 39, 1910. 19. H.M. McConnell, Proc. Robert A. Welch Found. Conf. Chem. Res. 1967, 11, 144. 20. O. Kahn, Molecular Magnetism, VCH, New York, 1993, Chapter 12. 21. M. Deumal, J. J. Novoa, M. J. Bearpark et al., J. Phys, Chem. A 1998, 102, 8404. 22. M. Deumal, J. Cirujeda, J. Veciana et al., Chem. Eur. J. 1999, 5, 1631. 23. V. Gama, D. Belo, S. Rabaça et al., Eur. J. Inorg. Chem. 2000, 9, 2101. 24. W.E. Broderick, J.A. Thompson, B.H. Hoffman, Inorg. Chem. 1991, 30, 2960. 25. J.S. Miller, personal communication. 26. S. Rabaça, R. Meira, L.C.J. Pereira et al., Inorg. Chim. Acta. 2001, 326, 89. 27. S. Rabaça, R. Meira, V. Gama et al., Acta Crystallogr., Sect. C., submitted. 28. S. Rabaça, R. Meira, L.C.J. Pereira et al., manuscript in preparation. 29. M. Fettouhi, L. Ouahab, M. Hagiwara et al., Inorg. Chem. 1995, 34, 4152. 30. (a) C. Faulmann, personal communication; (b) Communication in the 4th International Symposium on Crystalline Organic Metals, Superconductors and Ferromagnets (ISCOM2001), Hokkaido, Japan, September 10–14, 2001 (p. 127 in the Book of Abstracts). 31. S. Rabaça, M.T. Duarte, V. Gama, manuscript in preparation. 32. M. Fettouhi, L. Ouahab, E. Codjovi et al., Mol. Cryst. Liq. Cryst. 1995, 273, 29. 33. S. Rabaça, D. Belo, H. Alves et al., manuscript in preparation.

40 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47.

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D. Belo, H. Alves, S. Rabaça et al., Eur. .J. Inorg. Chem. 2001, 12, 3127. D. Belo, J. Mendonça, R. Meira et al., manuscript in preparation. S. Zürcher, V. Gramlich, D. Arx, A. Togni, Inorg. Chem. 1998, 37, 4015. S. Alvarez, R. Vicente, R. Hoffmann, J. Am. Chem. Soc. 1985, 107, 6253. M. Sano, H. Adachi, H. Yamatera, Bull. Chem. Soc. Jpn. 1981, 54, 2636. M.W. Day, J. Qin, C. Yang, Acta Crystallogr., Sect. C 1998, 54, 1413. M. Hobi, S. Zürcher, V. Gramlich et al., Organometallics 1996, 15, 5342. A. Pullen, C. Faulmann, K.I. Pokhodnya et al., Inorg. Chem. 1998, 37, 6714. F. Qi, Y. Xiao-Zeng, C. Jin-Hua et al., Acta Crystallogr., Sect. C 1993, 49, 1347. C. Faulmann, F. Delpech, I. Malfant et al., J. Chem. Soc., Dalton Trans. 1996, 2261. V. Gama, S. Rabaça, C. Ramos et al., Mol. Cryst. Liq. Cryst. 1999, 335, 81. S. Rabaça, V. Gama, D. Belo et al., Synthetic Met. 1999, 103, 2303. C. Faulmann, A.E. Pullen, E. Rivière et al., Synthetic Met. 1999, 103, 2296. Y. Journaux, Communication in the 6th FIGIPS Meeting on Inorganic Chemistry, Barcelona, Spain, July 15–20, 2001 (p. 49 in the Book of Abstracts). 48. V. Gama, D. Belo, I.C. Santos et al., Mol. Cryst. Liq. Cryst. 1997, 306, 17. 49. J.A. McCleverty, Progress in Inorganic Chemistry, Vol. 10, ed. by F.A. Cotton, Interscience, New York, 1968, p. 49. 50. E. Keller, SCHAKAL-97, A Computer Program for the Graphical Representation of Molecular and Crystallographic Models, Krystallographisches Institut der Universitat Freiburg, Germany, 1997.

2 Chiral Molecule-Based Magnets Katsuya Inoue, Shin-ichi Ohkoshi, and Hiroyuki Imai

2.1 Introduction Construction of molecule-based magnetic materials, which possess additional properties such as conductivity [1–4], photoreactivity [5, 6] or optical properties is currently a challenging target. Specific goals for these molecule-based magnets include the rational design of a magnet having (i) a desired geometrical structure and/or dimensionality and (ii) an optical transparency [7, 8]. The physical characteristics of current interest involve optical properties, particularly with respect to natural optical activity. In the case of a magnet with non-centrosymmetric structure, the space-inversion and time-reversal symmetry are simultaneously broken. Moreover, when a magnet is characterized by chiral structure, the magnetic structure of the crystal is expected to be a chiral spin structure. These magnets display not only asymmetric magnetic anisotropy but also various types of magneto-optical phenomena such as the non-linear magneto-optical effect and magneto-chiral dichroism [9–11]. Materials in this category are not only of scientific interest, but also afford the possibility for use in new devices. To obtain non-centrosymmetric and chiral molecule-based magnets, the geometric symmetry such as chirality must be controlled in the molecular structure as well as in the entire crystal structure. In this chapter we describe recent results regarding the construction, structure and magnetic and optical properties of molecule-based magnets with non-centrosymmetric and chiral structures.

2.2 Physical and Optical Properties of Chiral or Noncentrosymmetric Magnetic Materials Magnetic dipole moment and electric dipole moment are extremely important static forces in solid state physics. The investigation of the properties and the search for magnetic materials that contain ferroelectric order are subjects of increasing interest [11, 12]. These multiferroic materials possess specific properties due to the com-

42

2 Chiral Molecule-Based Magnets

bined effect of ferromagnetic nature and ferroelectric nature in the same phase. The generation of an electric dipole asymmetric field in the crystal is readily achieved by introduction of chirality or non-centrosymmetric structure. These classes of materials are not identical to ferroelectric materials; however, they exhibit an electric dipole asymmetric field in the crystal or material. They are expected to possess unique magnetic anisotropy, field induced second harmonic generation and the magneto-chiral optical effect due to the electric dipole asymmetric field.

2.2.1

Magnetic Structure and Anisotropy

In terms of the magnetic structure of chiral or non-centrosymmetric magnetic materials, the following aspects must be considered: (i) all spins are sited in asymmetric physical and magnetic positions, and (ii) the materials exhibit an electronic dipole moment. On the basis of (i), the spins experience an asymmetric magnetic dipole field. The asymmetric magnetic dipole moments operate the spins aligned asymmetrically through spin–orbital interaction. In order to facilitate matters, we assume that the spins are sited on a helix and the ferro- or ferrimagnetic interaction occurs between nearest neighbor spins. In this case, the spins are aligned in helical or conical spin alignment by an asymmetric magnetic dipole field and ferromagnetic interaction. (Figure 2.1(a) and (b)) Moreover, chiral crystals display an internal asymmetric electronic dipole field, thus, all magnetic spins are tilted by Dzyaloshinsky–Moriya interaction. (Figure 2.1(c))

(a)

(b)

(c)

Fig. 2.1. Expected magnetic structure for chiral magnets.

2.2 Properties of Chiral or Noncentrosymmetric Magnetic Materials

2.2.2

43

Nonlinear Magneto-optical Effects

Chiral magnets can exhibit nonlinear magneto-optical effects due to their noncentrosymmetric structure and spontaneous magnetization. Over the last 15 years, the nonlinear magneto-optical phenomena have been intensively studied [14–22] and magnetization-induced second harmonic generation (MSHG) has received special attention due to its large magnetic effects, e. g., the second-order nonlinear Kerr rotation on the Fe/Cr magnetic film surface is close to 90◦ [16]. In the electric dipole approximation, second harmonic generation (SHG) is allowed in media with broken inversion symmetry [23]. Most magnetic materials are, however, centrosymmetric and, hence, the MSHG are mainly reported from the surface of magnetic materials [15, 16]. MSHG observations from the bulk crystals are limited. For antiferromagnetic materials, only chromium oxide Cr2 O3 [17] and yttrium-manganese oxide YMnO3 [18] are reported to exhibit MSHG. The reports of bulk MSHG for ferromagnetic materials are limited to Bi-substituted yttrium iron garnet (Bi:YIG) magnetic film [19–21] and a ternary-metal Prussian blue analog ((FeIIx CrII1−x )1.5 [CrIII (CN)6 ]·7.5H2 O)-based magnetic film [22]. The MSHG effect is useful for the topography of magnetic domains [24]. Furthermore, applying a magnetic field can control the MSHG signal [20–22]. Hence, an attractive method for studying nonlinear optics is to prepare ferromagnetic materials, which display SH activity. Chiral magnets are advantageous when compared to conventional metal or metal oxide magnetic materials because the space-inversion and time-reversal symmetry are simultaneously broken. In the following sections, the theoretical background of bulk MSHG is described and, as an example, the MSHG effect on a Bi:YIG ferromagnetic film is explained.

2.2.2.1

Theoretical Background of MSHG

In the electric dipole approximation, the polarization, P, can be written as a function of E [23]: . P = χ (1) · E + χ (2) : EE + χ (3) .. EEE,

(2.1)

where E is the electric field of the incident wave and χ (n) is the nth nonlinear optical susceptibility tensor. When E is sufficiently weak, Eq. (2.1) is dominated by the first term and P takes a simple linearized form. In contrast, as E increases, the second optical response of the second term dominates Eq. (2.1) [23] and the second optical response, Pi (2ω), can be rewritten as: Pi (2ω) = χij(2)k (−2ω; ω, ω)Ej (ω)Ek (ω),

(2.2)

where Ej (ω) and Ek (ω) are the fundamental optical fields. The second-harmonic optical susceptibility tensor (χij(2)k ) is expressed as:

44






  (2) (2) (2) (2) (2) χxxx χxyy χxzz χxyz χxzx Px(2) (2) (2) (2) (2) (2)  Py(2)  = ε0  χyxx χyyy χyzz χyyz χyzx (2) (2) (2) (2) (2) (2) Pz χzxx χzyy χzzz χzyz χzzx

 Ex2   Ey2  (2)   χxxy 2   (2)   Ez  χyxy   2E E y z  (2)  χzxy  2Ez Ex  2Ex Ey

(2.3)

where the x, y and z denote the optical field directions in the laboratory frame. Next the susceptibilities of magnetic substances will be examined. The linear susceptibility χ (1) in Eq. (2.1) can be written as a function of its local magnetization M: magn(1)

χij(1) (M) = χijcr(0) + χij K

magn(2)

MK + χij KL MK ML + . . . ,

(2.4)

where K and L denote the indices of the axial vector M. In Eq. (2.4), χijcr(0) is magn(1) magn(2) the nonmagnetic (crystallographic) portion and χij K and χij KL are the linear and bilinear magnetic parts that describe the Faraday (or Kerr) effect and magnetic birefringence, respectively [25–27]. The non-vanishing elements in each tensor are determined by space-time symmetry operations. The χij(1) is transferred to the dielectric constant εij , i.e., εij = δij + 4π χij(1) (δij : Kronecker’s delta). Usually, δij describes the magneto-optical effects such as the Faraday effect. In ferromagnetic substances, which have noncentrosynmetric structures, the simultaneous breaking of space and time-reversal symmetry leads to the coexistence of crystallographic and magnetization-induced electric-dipole contributions to the nonlinear optical susceptibility. Under these circumstances, the second-order nonlinear susceptibility tensor, χij(2)k , can be written as: magn(1)

χij(2)k (M) = χijcr(0) k + χij kL

magn(2)

ML + χij kLM ML MM + . . . , magn(1)

(2.5) magn(2)

+ χij kLM + . . . where χijcr(0) k is the crystallographic portion and the terms χij kL describe the effect of the local magnetic order [28]. These magnetic terms lead to magneto-optical effects in SHG. The total SH polarization of a magnetic medium in the electric dipole approximation can be written as: magn(1)

Pi (2ω) = Picr(0) (2ω) + Pi =

(2ω)

χijcr(0) k (−2ω; ω, ω)Ej (ω)Ek (ω) magn(1) +χij kL (−2ω, ω, ω, 0)Ej (ω)Ek (ω)ML (ω) magn(1)

+ ...,

(2.6)

(2ω) are the crystallographic and magnetic contribuwhere Picr(0) (2ω) and Pi magn(1) tions, respectively. The properties of Picr(0) (2ω) and Pi (2ω) are remarkably cr(0) cr(0) different. Pi (2ω) is represented by a polar tensor χij k of rank 3 as described in magn(1) magn(1) Eq. (2.3), but Pi (2ω) is described by an axial tensor χij kL of rank 4 [14]. magn(1) In nonabsorbing materials, the χijcr(0) is real, but χij kL is an imaginary tensor k


45

[14]. The corresponding nonlinear waves have a 90◦ phase shift and thus cannot interfere. However, if one or both of them are complex, then interference is allowed and leads to effects, which are linear to the magnetization. In addition, the magn(1) (2ω) are different; Picr(0) (2ω) temperature dependence of Picr(0) (2ω) and Pi magn(1) probes the degree of a crystal lattice noncentrosymmetry, but Pi (2ω) reflects a temperature variation in the magnetization. 2.2.2.2

Experimental Set-up

Figure 2.2 shows schematically the experimental set-up used for MSHG measurements in the authors’ laboratory. Incident radiation is provided from an optical parametric amplifier (Clark-MXR Vis-OPA; pulse width: 190 fs; repetition: 1 kHz) pumped by a frequency-doubled Ti:Sapphire laser (Clark-MXR CPA-2001; photon energy: 1.60 eV) or a Q-switched Nd:YAG laser (HOYA Continuum Minilite II; pulse width: 6 ns; repetition: 15 Hz). Transmitted SH light is detected by a photomultiplier through color filters and a monochromator. Polarization combinations between the incident and SH radiation are adjusted using a babinet-soleil compensator and a pair of polarizers. A cryostat controls the temperature of the samples. The magnetic field is applied along the direction of light propagation using the electromagnet coil of a magneto-optical meter. Sample S-polarized light

Filter

Filter

Monochromator PMT

Laser Polarizer / Wave plate Ti:Sapphire laser

Electromagnet

Analyzer

External magnetic field

Fig. 2.2. Schematic illustration of the SHG measurement system. The magnetic field was applied along the light propagation direction using an electromagnetic coil.

2.2.2.3

Bulk MSHG of a Ferromagnetic Material

The magnetic terms of the second-order nonlinear susceptibility in Eq. (2.5) lead to the magneto-optical effects in SHG. For example, Cr2 O3 has a centrosymmetric structure (point group 3m) and above the Néel temperature all elements of χijcr(0) k

46


are zero. However, a noncentrosymmetric spin ordering (magnetic point group magn(1) 3m) below the Néel temperature creates non-zero elements of χij kL , inducing SH radiation [17]. In contrast, strain-induced Bi:YIG has a noncentrosymmetric structure. Thus, below the magnetic ordering temperature (TC ) the tensor elements magn(1) in both χijcr(0) are non-zero [19–21]. As an example the MSHG effect on k and χij kL the (111) film of Bi:YIG is described. In a Bi:YIG film, the distortion of the crystal structure breaks the space-inversion symmetry, which is evident in the SHG [29] and linear magnetoelectric effects. The crystal structure is in a non-centrosymmetric point group, 3m (C3v ), and has a threefold axis along the normal of the film. In this situation, the non-linear polarization is expressed by: (2) (2) (Ex2 − Ey2 ) + 2xxzx Ex Ex Px(2) = xxxx (2) (2) Py(2) = −2xxxx Ex Ey + 2xxzx Ex Ey (2) (2) 2 Pz(2) = xzxx (Ex2 − Ey2 ) + xzzz Ez

(2.7)

where the x and y axes are perpendicular to the mirror plane m (y//[110]). This equation shows that SHG is allowed at normal and oblique incidences. Pisarev et al. measured the SHG intensity (I ) angular dependence at the normal incidence of the pump radiation as function of the rotation angle (ϕ) of the film around its normal. I is described by: I = E 4 cos2 (3ϕ + α)

(2.8)

where α is the angle between the axes of the polarizer and the analyser. This equation can predict the angle dependence of I and is shown in Figure 2.3(a) and (b). In a nonmagnetized (111) film, the SHG signal is observed with a 60◦ periodicity in the rotational anisotropy. In fact, Pisarev et al. observed such a SHG pole-figure pattern. In 1997, Pavlov et al. observed the magnetization-induced SHG effects of this (111) film by applying a transversal magnetic field. In this film, the SHG rotational anisotropy Iij (2ω, ϕ) is expressed as: IXX (2ω, ϕ) = E 4 (A cos2 3ϕ + BM 2 + 2CM cos 3ϕ) IY Y (2ω, ϕ) = E 4 A sin2 3ϕ ,

(2.9)

where XX and Y Y denote input-output polarizations of the light in the laboratory environment. In addition, A, B, and C are combinations of real and imaginary magn(1) . For the XX polarization combination, a linear magnetic parts of χijcr(0) k and χij kL response is expected to be observed as the calculated plots in Figure 2.3(a) and (b), magn(1) but for Y Y the Pi (2ω) is zero. The horizontal line passing through 0◦ and 180◦ on each plot corresponds to the mirror plane, m. Figure 2.3(c) shows the observed rotational anisotropy of the IXX at 295 K. The experimental data is consistent with the tensor analysis prediction. The magnetized (111) film showed a 120◦ periodicity for XX polarizations, with a 60◦ rotation +M and −M states. Thus, applying an


(a)

47

12 10 8 6 4 2 0 0

(b)

50

100

120

150

200

90 15

250

300

350

60

30

150

180

0 15

0

210

330

240

300 270

(c)

180º

0º

Fig. 2.3. MSHG of (111) film Bi:YIG. Predicted angle dependence of SH intensity (a) and rotational anisotropy (b) of the SHG intensity on (111) film, based on Eq. (2.8) and (2.9). Thin solid, thick solid, and dotted lines are zero, positive, and negative external magnetic fields, respectively. (c) Data of Pavlov et al. [20]: solid circles denote +M state and open circles the −M state. XX denotes the input-output polarization combinations. Magnetic contrast (difference between the +M and −M theoretical fits) is indicated by dark (positive) and light (negative) shadowed areas.

external magnetic field can change the SHG response. A, B, and C are obtained by fitting the data to Eq. (2.9). Figure 2.4 shows the temperature variations of the crystallographic (A), interference (2CM), and pure magnetic (BM2 ) contributions to the SHG intensity for the (111) film. The crystallographic contribution decreases linearly with temperature, but the magnetization-related contributions vanish at Tc . The interference term of 2CM shows a (1 − T /Tc ) dependence, but the pure magnetic portion of BM2 vanishes at Tc .

48


Fig. 2.4. The observed temperature variations of crystallographic, magnetization-induced, and interference terms in the SHG intensity for the (111) film. Reproduced with permission from Ref. [20].

Section 2.5 will show another example of the bulk MSHG effect on ferromagnetic material composed of an electrochemically synthesized (FeIIx CrII1−x )1.5 [CrIII (CN)6 ] · 7.5H2 O magnetic film.

2.2.3

Magneto-chiral Optical Effects

In 1982, Wagniere and Meier theoretically predicted the influence of a static magnetic field on the absorption coefficient of a chiral molecule [9]. In 1984, Barron and Vbrancich referred to this effect as magneto-chiral dichroism (MChD). This effect is a combined effect of the natural optical activity of chiral material and the Faraday effect of the magnet (Figure 2.5) [10]. This MChD effect involves the absorption coefficient of materials, which is dependent upon the direction of magnetization and light. In 1997, Rikken and Raupach observed the MChD effect of tris(3-trifluoroacetyl-±-camphorato)europium (III) in the paramagnetic state [11].

(a) (c)

01#0CVWTCN1RVKECN#EVKXKV[

M

hν

ਇᢧಽሶ

Chiral Molecule

(b)

I0

Chiral magnet crystal

If

J νR

M

/1#/CIPGVKE1RVKECN#EVKXKV[ (CTCFC['HHGEV

/CIPGV

Ib

J νR

Magneto-Chiral Dichroism

hν

Chiral magnet crystal

I0 I

f

I

b

NOA + MOA

Fig. 2.5. Schematic illustration of (a) natural optical activity, (b) Faraday effect, and (c) magneto-chiral dichroism.

2.3 Nitroxide-manganese Based Chiral Magnets

49

The MChD effect depends on the magnitude of the magnetic moment. It is important to generate fully chiral molecule-based magnets which are expected to exhibit a strong MChD effect.

2.3 Nitroxide-manganese Based Chiral Magnets From the conformation study of the Mn(hfac)2 complexes with oligo-nitroxide radicals, (see Vol. II, Chapter 2), one-dimensional complexes exclusively form isotactic polymeric chains. In these complexes, two tert-butylaminoxyl groups are rotated out of the phenylene ring plane in a conrotatory manner; each molecule in the crystal has no symmetry element and is, therefore, chiral, i. e., R or S. Consequently, the 1-D polymeric chains are isotactic as all units are of the same chirality. The crystal lattice as a whole is achiral due to the presence of enantiomeric chains. When chiral organic radicals are employed in lieu of achiral biradicals, the chiral substituent group will induce chirality in the main one-dimensional chain.

2.3.1

Crystal Structures

On the basis of requirements of molecular design, bismonodentate bisaminoxyl radical 1 [30] or nitronylnitroxide radical 2 [31] with a chiral organic substituent must be employed as bridging ligands of manganese(II) bishexafluoroacetylacetonate, MnII (hfac)2 . X-ray crystal structure analysis revealed that both complexes [1·Mn(hfac)2 ]n and [2·Mn(hfac)2 ]n crystallize in the chiral space groups P 1 and P 21 21 21 , respectively. The molecular structures of these complexes are depicted in Figure 2.6. The MnII ion exists in an octahedral coordination environment with four oxygen atoms of two hfac anions and two oxygen atoms of different radical molecules in both crystals. As a result, the MnII ion and the chiral radical 1 or 2 form a one-dimensional structure. The shortest interchain contacts between the Mn ion and the oxygen atom O of the radical’s NO group exceeds 9 Å, whereas the shortest MnII –MnII interchain distance is greater than 10 Å in both crystals. In the S O

O S O

N

N

1

O O

N

N

2

O

Scheme 2.1

50


Fig. 2.6. Crystal structures of (a) [1·Mn(hfac)2 ]n and (b) [2·Mn(hfac)2 ]n .

crystal of [1·Mn(hfac)2 ]n , the bisaminoxyl radicals are bound to the MnII ion in trans-coordination to one another. In this complex, two tert-butylaminoxyl groups are rotated out of the phenylene ring plane in a conrotatory manner; all molecules in the crystal display S axis chirality. Since no inversion centers are present in this space group, the chains are isotactic as all units and the crystal lattice as a whole, are chiral. In the case of [2·Mn(hfac)2 ]n , The radicals are bound to the MnII ion in ciscoordination to one another. A detailed description of the coordination sphere of the MnII ion must take into account the possible configurations resulting from the cis-coordination arrangement, which can lead to the or configuration. In this complex, the metal center exhibits the all configuration. Due to the use of the chiral ligand, the complex crystallized in a chiral space group, therefore, no chirality of the Mn(II) exists in this crystal. The absolute configuration of the metal center is often affected by the chirality of organic ligands; additionally, our result shows a similar effect of the chiral carbon atom of 1. No inversion centers are present in this space group; consequently, the chains are isotactic as all units, and the crystal lattice as a whole, are chiral.

2.3 Nitroxide-manganese Based Chiral Magnets

2.3.2

51

Magnetic Properties

[1·Mn(hfac)2 ]n : The µeff value of 4.91 µB (χmol T = 3.01 emu K mol−1 ) at 300 K is less than the theoretical value of 6.43 µB for paramagnetic spins of two 1/2 spins of an organic radical and one 5/2 spin of d5 MnII , whereas it is larger than that of 3.87 µB for two 1/2 spins of organic radicals and 5/2 spins of d5 MnII in antiferromagnetic coupling. In concert with a lack of a minimum at lower temperature, the room temperature µeff value suggests the occurrence of strong (more negative than −300 K) antiferromagnetic coupling between the MnII ion and the aminoxyl radical as a ligand (Figure 2.7). When the measurement was conducted in 5 Oe, the magnetic susceptibility displayed a cusp at 5.4 K (Figure 2.7, inset). Magnetization at 1.8 K revealed metamagnetic behavior (Figure 2.8). A saturation magnetization value of ca. 2.7 µB was reached at 1.8 K at 3 T. When the interaction between the MnII ion and 1 is antiferromagnetic, the value for [1·Mn(hfac)2 ]n is expected to be 3 µB (5/2 − 2/2 = 3/2), which is in close agreement with the observed value. This magnetic behavior is similar to that found in a Mn(hfac)2 complex with non-chiral biradicals. (See Vol. II, Chapter 2). [2·Mn(hfac)2 ]n : The µeff value of 6.48 µB (χmol T = 5.25 emu K mol−1 ) at 300 K is equal to the theoretical value of 6.16 µB for isolated spins of one 1/2 spin of an organic radical and one 5/2 spin of d5 MnII ion. The µeff value increased with decreasing temperature. In concert with the lack of a minimum at lower temperature, the room temperature µeff value suggests the occurrence of strong (more negative

Fig. 2.7. Temperature dependence of effective magnetic moment for the polycrystalline sample of [1·Mn(hfac)2 ]n . Inset: Temperature dependence of the magnetization in 5 Oe.

52


Fig. 2.8. Field dependence of the magnetization of [1·Mn(hfac)2 ]n .

Fig. 2.9. Temperature dependence of effective magnetic moment for the polycrystalline sample of [2·Mn(hfac)2 ]n . Inset: Temperature dependence of the magnetization in 5 Oe.

than −300 K) antiferromagnetic coupling between the nitronyl nitroxide radical and the MnII ion (Figure 2.9). Magnetization measurements have been performed at 2 K (Figure 2.10). Magnetization increases very rapidly, reaching a plateau of ca. 3.6 µB at 1.5 T. When the interaction between the MnII ion and 2 is antiferromagnetic, the value for [2·Mn(hfac)2 ]n is expected to be 4 µB (5/2−1/2 = 4/2), which

2.4 Two- and Three-dimensional Cyanide Bridged Chiral Magnets

53

Fig. 2.10. Field dependence of the magnetization of [2·Mn(hfac)2 ]n .

is in close agreement with the observed value. When the field cooled magnetization (FC) and zero field cooled magnetization measurements (ZFC) were carried out in a much lower field of 5 Oe over the temperature range 1.8 K to 20 K, the magnetic moment value increased sharply at ca. 5 K. Both the measurements exhibited a plateau below 4.2 K (Figure 2.9, inset). AC susceptibility measurements revealed that [2·Mn(hfac)2 ]n behaves as a ferrimagnet at 4.6 K.

2.4 Two- and Three-dimensional Cyanide Bridged Chiral Magnets The major strategy relating to crystal design for magnetic materials exhibiting higher ordering temperature and spontaneous magnetization involves generation of an extended multidimensional array of paramagnetic metal ions with bridging ligands. The cyanide-bridged Prussian-blue systems are well known as the most suitable for this purpose. These systems are generally obtained as bimetallic assemblies with a three-dimensional cubic cyanide network by the reaction of hexacyanometalate [MIII (CN)6 ]3− with a simple metallic ion MII [32–35]. Extensive research has led to the production of a material displaying magnetic ordering at Tc as high as 372 K [36]. On the one hand, the attention of some chemists has been ¯ and Ohba focused on specific coordination sites around MII in this system. Okawa have found that some organic molecules can be incorporated into this system as a chelating or bidentate ligand L to MII [37, 38]. The incorporation of such a ligand leads to the blockade of some coordinated linkages to MII of cyanide groups in [MIII (CN)6 ]3− . It follows that various novel structures have been obtained in this system, depending on the organic molecule. This method affords the possibility

54


of crystal design in cyanide-bridged systems. In this section, we will describe the crystal design of a chiral magnet utilizing a cyanide-bridged system; additionally, several examples are presented.

2.4.1

Crystal Design

When chiral molecule-based magnets exhibiting higher ordering temperature and spontaneous magnetization are constructed, the chirality in the entire crystal structure as well as the high dimensionality of the extended arrays must be maintained. It is more convenient for the cyanide-bridged systems to circumvent these difficulties in order to construct higher-T c chiral magnets. Some chiral diamine ligands serve as candidates for the chiral source in the entire crystal structure of this system. In other words, a target magnetic compound can be generated by the reaction between a hexacyanometalate [MIII (CN)6 ]3− and a mononuclear complex [MII (L)n ] based on chiral diamines, as shown in Scheme 2.2. Note, however, that, in order to obtain a ferromagnet, the combination of MII and MIII in the crystallization stage which generates ferromagnetic interaction through MIII -CN-MII must be known. This method holds many possibilities with respect to obtaining various chiral magnets via alteration of the component substances.

O

H 2N

NH2

(R) or (S)-1,2diaminopropane

2.4.2 2.4.2.1

H 2N

NH2

(R) or (S)alanamide

H 2N

NH2

(R, R) or (S, S)cycrohexanediamine

Scheme 2.2

Two-dimensional Chiral Magnet [39] Crystal Structure

This compound crystallizes in the non-centrosymmetric P 21 21 21 space group. Xray crystal structure analysis reveals that it consists of two-dimensional bimetallic sheets. Each [Cr(CN)6 ]3− ion involves four cyanide groups in order to bridge with four adjacent MnII ions within the ab plane (Figure 2.11). The adjacent Cr–Mn distances through cyanide bridges within the ab plane are approximately 5.35 Å, which is slightly longer than those in the 3D chiral magnet K0.4 [CrIII (CN)6 ][MnII (S)pn](S)-pnH0.6 (see next section). In addition to one MnII and one [Cr(CN)6 ]3− ion, an asymmetric unit in this crystal also associates with one mono-protonated (S or R)-diaminopropane ((S or R)-pnH) and two water molecules. An octahedron around a MnII ion is completed with one (S or R)-pnH and one water molecule


55

Fig. 2.11. Crystal structure of [Cr(CN)6 ][Mn(S or R)-pnH(H2 O)](H2 O)].

which separate adjacent bimetallic sheets along the c-axis. The shortest and the second shortest inter-sheet metal separation are observed between the Cr and Mn atoms (the distances are 7.31 and 7.77 Å, respectively). In contrast, the shortest inter-sheet homo-metal contacts are more than 8 Å. This observation suggests that the ferromagnetic interaction operates preferentially between bimetallic sheets.

2.4.2.2

Magnetic Properties

The temperature dependence of magnetic susceptibility is shown in Figure 2.12, using χmol T versus T plots. The χmol T value is 5.01 emu K mol−1 (6.33 µB ) at 300 K, and decreases with decreasing temperature down to a minimum value of 3.65 emu K mol−1 (5.41 µB ) at 85 K. The extrapolated effective magnetic moment value is 7.07 µB , which is in close agreement with the non-coupled paramagnetic high spin in the high temperature limit of 5/2+3/2 → 7.07 µB (Figure 2.12, inset). Upon further cooling, the χmol T value increases and diverges. The 1/χmol versus T plot in the range 300 to 140 K obeys the Curie–Weiss law with a Weiss temperature θ = −77.0 K. This indicates that the antiferromagnetic interaction operates between the adjacent CrIII and MnII ions through cyanide bridges at temperatures above 140 K. The abrupt increase in the χmol T value around 40 K suggests the onset of three-dimensional magnetic ordering. Both the field cooled (FC) and the zero field cooled magnetization measurements (ZFC) with a low applied field (5 G) in the temperature range 5 K to 100 K display a longrange magnetic ordering below 38 K (Figure 2.13). As shown in Figure 2.14, the magnetization (M) increases sharply with an applied field and is saturated rapidly. The saturation magnetization value of MS = 2 µB is in close agreement with the theoretical value of antiferromagnetic coupling between CrIII and MnII ions. The hysteresis loop (the remnant magnetization of 1800 emu G mol−1 and the coercive field of 10 Oe) was observed at 5 K, suggesting a soft magnetic behavior.

56


Fig. 2.12. Temperature dependence of the χmol T value of [Cr(CN)6 ][Mn(S or R)pnH(H2 O)](H2 O)]. Inset: χeff − 1/T plot.

Fig. 2.13. Temperature dependence of the magnetization of [Cr(CN)6 ][Mn(S or R)pnH(H2 O)](H2 O)] in a low field (5 Oe).


57

Fig. 2.14. Field dependence of the magnetization of [Cr(CN)6 ][Mn(S or R)-pnH(H2 O)](H2 O)] at 5 K.

2.4.3 2.4.3.1

Three-dimensional Chiral Magnet [40] Crystal Structure

This compound crystallizes in the non-centrosymmetric P 61 space group. X-ray crystallography reveals that it consists of a three-dimensional chiral polymer (Figure 2.15). Each [Cr(CN)6 ]3− ion utilizes two cyanide groups to bridge two MnII ions forming helical loops along the c-axis, whereas two of the remaining

Fig. 2.15. Crystal structure of K0.4 [CrIII (CN)6 ][MnII (S)-pn](S)pnH0.6 .

58


four cyanide groups connect the adjacent loops. The shortest intra- and interloop Mn–Cr distances are 5.21 and 5.31 Å, respectively. The MnII ion exists in an octahedral environment with four cyanide groups of four distinct [Cr(CN)6 ]3− and two nitrogen atoms of (S)-pn. In this crystal, two kinds of counter ion are included so as to maintain overall neutrality. One is a potassium ion and the other is monoprotonated diaminopropane (S)-pnH; the site occupancy of which is 0.4 : 0.6, respectively. These counter ions are located within the cavity of helical loops. 2.4.3.2

Magnetic Properties

The magnetic behavior of the crystal under 5000 G is shown in Figure 2.16 as a plot of χmol T versus T . The χmol T value is 4.88 emu K mol−1 (6.25 µB ) at room temperature and decreases with decreasing temperature down to a minimum value of 3.66 emu K mol−1 (5.41 µB ) at 110 K. Upon further cooling, the χmol T value increases. The 1/χmol versus T plot in the range 300 to 110 K obeys the Curie– Weiss law with a Weiss temperature θ = −30.9 K. This observation indicates that the antiferromagnetic interaction operates between the adjacent CrIII and MnII ions through cyanide bridges at temperatures above 110 K. The abrupt increase in the χmol T value around 60 K suggests the onset of three-dimensional magnetic ordering. The extrapolated effective magnetic moment value of 7.2 µB is in close agreement with the theoretical value in the high temperature limit (Figure 2.16, inset). Low-field magnetization measurements under an applied field of 5 G in the temperature range 5 to 100 K were performed in order to confirm a longrange

Fig. 2.16. Temperature dependence of the χmol T value of K0.4 [CrIII (CN)6 ][MnII (S)-pn](S)pnH0.6 . Inset: χeff − 1/T plot.


59

Fig. 2.17. Temperature dependence of the magnetization of K0.4 [CrIII (CN)6 ][MnII (S)-pn](S)pnH0.6 in a low field (5 Oe).

Fig. 2.18. Field dependence of the magnetization of K0.4 [CrIII (CN)6 ][MnII (S)-pn](S)-pnH0.6 at 5 K.

magnetic ordering around 60 K. Both field cooled magnetization (FCM) and the zero field cooled magnetization (ZFCM) curves show an abrupt increase in M below 53 K (Figure 2.17). The field dependence of magnetization at 5 K also reveals that the magnetization (M) is saturated rapidly in the presence of an applied field. (Figure 2.18) The saturation magnetization MS = 2 µB is close to the theoretical value of antifer-

60


romagnetic coupling between CrIII and MnII ions. A hysteresis loop (the remnant magnetization of 30 emu G mol−1 and the coercive field of 12 G) was observed at 2 K, suggesting soft magnetic behavior.

2.4.4

Conclusion

The present compounds provide proof that the cyanide-bridged system affords much potential for the design of molecule-based materials. The use of chiral ligands in the synthesis of compounds based on the cyanide-bridged system leads to two- and three-dimensional chiral magnetic networks. These systems are candidates for asymmetric magnetic anisotropy, as well as for magneto-optical properties including magneto-chiral dichroism (MChD). This phenomenon is attributable to the ease with which these systems modulate optical activity, magnetization, ordering temperature and crystal color by changing paramagnetic metal ions and organic chiral ligands.

2.5 SHG-active Prussian Blue Magnetic Films Electrochemically synthesized ternary metal Prussian blue analog-based magnetic films can display MSHG. (FeIIx CrII1−x )1.5 [CrIII (CN)6 ]·7.5H2 O magnetic films show a Faraday effect in the visible region and bulk SHG. Applying an external magnetic field rotates the polarization plane of the SH light and the rotation angle is greater than that from the Faraday effect. This SH rotation is caused by the magnetic linear term in the second-order nonlinear optical susceptibility. In this section, the magnetic properties, Faraday effect, SHG, and MSHG effects of these magnetic films are described.

2.5.1

Magnetic Properties and the Magneto-optical Effect

Figure 2.19 illustrates schematically the crystal structure of Prussian blue analogs. The thin films composed of (FeIIx CrII1−x )1.5 [CrIII (CN)6 ]·7.5H2 O are prepared by reducing aqueous solutions, which contain K3 [Cr(CN)6 ], CrCl3 , and FeCl3 onto SnO2 -coated glass electrodes under aerobic conditions [41]. Insoluble polynuclear metal cyanide thin films, which are ca. 2 µm thick, are deposited onto an electrode surface when the reduction potential vs. SCE is −0.84 V and the loaded electrical capacity is 600 mC. The color changes of the obtained (FeIIx CrII1−x )1.5 [CrIII (CN)6 ]·7.5H2 O transparent films, which are dependent on x, are due to the intervalence transfer (IT) band of FeII and CrIII in the visible region.

2.5 SHG-active Prussian Blue Magnetic Films

O

H H O

H H

BIII

O HH O H

H

H

C N

H O

O

O

O

61

H H H O

H H H

H

O

AII

H

H H

H H

O

H H

O

Fig. 2.19. Schematic illustration of Prussian blue analogs: III AII 1.5 [B (CN)6 ]·7.5H2 O.

H O H

For example, the films for x = 0, x = 0.20, x = 0.42, and x = 1 are colorless, violet, red, and orange, respectively. As indicated in Figure 2.20, their IT bands shift from a shorter wavelength to a longer wavelength in the visible region as x decreases; e. g., λmax = 434 nm (x = 1); 496 nm (x = 0.42); 506 nm (x = 0.20); 510 and 610 nm (x = 0) [41]. The magnetic susceptibility and magnetization of these thin films are dependent on x. The saturation magnetizations (Ms ) for x = 0 and x = 1 at fields up to 5 T were 1.0 µB and 6.7 µB , respectively, and intermediate compositions vary systematically as a function of x. The minimum value of Ms is observed in a film with an x value close to 0.11 because the parallel spins (CrIII and FeII ) and the anti-parallel spins (CrII ) are partially or even completely canceled, depending on x. In addition, the magnetization vs. temperature curves below Tc exhibit various 1.5

1.0

Abs.

1 0.42 0.20 0

0.5

0.0 400

600

800

Wavelength (nm)

1000

1200

Fig. 2.20. Vis-near-IR absorption spectra for x = 0, 0.20, 0.42, and 1.

62


Magnetization (G cm3 mol-1)

2000

1 0 0.08 0.11 0.42 0.13

1500 1000 500 0 -500 -1000 0

50

100

150

Temperature (K)

200

250

Fig. 2.21. Magnetization vs. temperature plots of electrochemically synthesized II III (FeII x Cr1−x )1.5 [Cr (CN)6 ] ·7.5H2 O films in a field of 10 Oe.

behaviors, which are dependent on x (field = 10 G) (Figure 2.21). Particularly, for compounds in which x is between 0.11 and 0.15, negative values of magnetization are exhibited below particular temperatures (compensation temperatures, Tcomp ) [42–44]. Molecular field theory qualitatively reproduces these temperature dependent observations when two types of exchange couplings between nearest neighbor sites, FeII –CrIII (JFeCr = 0.9 cm−1 ) and CrII –CrIII (JCrCr = −9.0 cm−1 ), are considered. Therefore, these phenomena are observed because the positive magnetization due to the CrII sublattice and the negative magnetizations due to the FeII and CrIII sublattices have different temperature dependences. Due to their transparency, the Faraday effect of Prussian blue analog-based magnetic films is in the visible region [45]. The Faraday ellipticity (FE) spectrum of the film for x = 1 shows a strong positive peak due to an IT band around 450 nm (Figure 2.22(a)). For this film, the Faraday effect increases below the Tc and the magnitude increases as the temperature decreases. In the Faraday rotation (FR) spectra, the dispersive line is observed at the same wavelength (Figure 2.22(b)). As x decreases, the FE peak shifts to a longer wavelength and their intensities gradually decrease. Figure 2.22(c) and (d) show the FE and FR spectra of a film where x = 0.33 at 50 K in an applied magnetic field of 10 kOe. The observed Faraday rotation angle is less than 0.22◦ for a given thickness at wavelengths between 350 and 900 nm and the rotation angles at wavelengths of 775 and 388 nm were 0.065◦ and 0.079◦ , respectively.

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.00

0.02

0.04

0.06

0.08

0.10

0.12

400

400

450

450

500

500

600

650

550 600 650 Wavelength (nm)

Wavelength (nm)

550

700

700

750

750

800

800

d

b 0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

400

400

450

450

500

500

550

600

650

550 600 650 Wavelength (nm)

Wavelength (nm)

700

700

750

750

800

800

II III Fig. 2.22. Faraday spectra of (FeII x Cr1−x )1.5 [Cr (CN)6 ]·7.5H2 O films in an applied magnetic field of 10 kOe: Faraday ellipticity (a) and Faraday rotation (b) for x = 0 at 7 K. Faraday ellipticity (c) and Faraday rotation (d) for x = 0.33 at 50 K.

c

Faraday ellipticity (degree)

Faraday ellipticity (Angle/ degree)

Faraday rotation (Angle/degree) Faraday rotation (Angle/degree)

a

2.5 SHG-active Prussian Blue Magnetic Films 63

64


2.5.2

Nonlinear Magneto-optical Effect

The crystal structure of Prussian blue analogs is centrosymmetric face-centered cubic (fcc) and hence the bulk SHG should be forbidden in the electric dipole approximation. In fact, powder samples of (FeIIx CrII1−x )1.5 [CrIII (CN)6 ]·7.5H2 O do not exhibit SHG over the entire range of x. However, the electrochemically synthesized films, which incorporate three metal ions, show SHG. Figure 2.23(a) shows the SH intensity dependence on x at room temperature in films that are approximately 2 µm thick. The SH signal for the electrochemically synthesized films is observed when 0 < x ≤ 0.42 [46] and its intensity increases drastically with x. Figure 2.23(b) shows the SH intensity in the films when x = 0.33 as a function of the film thickness. The observed oscillation of the SH intensity indicates a coherent correlation, clearly demonstrating that the observed SHG is from the bulk crystal and not from the surface. Figure 2.23(c) shows the Maker’s fringe patterns of the film when x = 0.25 for the polarization combinations of PIN –POUT and SIN –POUT . The SH intensity is zero at 0◦ and increases monotonically as the angle changes up to 55◦ . This fringe pattern is well known in poled ceramics, poled glasses, and poled polymers and indicates that the electric polarization is perpendicular to the film plane (C∞v ). The estimated magnitude of the nonlinear optical susceptibility χzyy of the film with x = 0.25 is approximately 1/7 of the susceptibility χxxx of quartz. The following mechanism is consistent with the origin of the observed SHG. The estimated bond length of the FeII –NC–CrIII lattice is 5.31 Å from the lattice parameter of FeII1.5 [CrIII (CN)6 ] [47], which is greater than that of the CrII –NC–CrIII lattice (5.19 Å [48, 49]). Therefore, the incorporation of FeII ions into the CrII –NC–CrIII lattice may strain the lattice. [CrIII (CN)6 ] defects maintain the charge balance in the present compound and these defects are preferentially generated next to the FeII sites rather than the CrII sites in order to avoid generating lattice strain. The film is grown perpendicular to the electrode and the distorted structure is accumulated in this direction, as shown schematically in Figure 2.24. In addition, the AFM observation (not shown) indicates that the microcrystals are also perpendicular to the film plane and thus the electric dipole moment could be perpendicular to the film plane. In fact, careful analysis of the XRD pattern indicates that the structure of (FeIIx CrII1−x )1.5 [CrIII (CN)6 ]·7.5H2 O (0 < x < 1) is not symmetrical face-centered cubic, but a noncentrosymmetric monoclinic structure of the space group C2 . This noncentrosymmetric orientation of the crystal structure induces the SHG in this system. The magnetic effect on the polarization of SH radiation is measured using the film with x = 0.33. Although the SH polarization does not exhibit rotation in the presence of an external magnetic field at 300 K, the rotation of the SH output is observed at 50 K, which is below TC (Figure 2.25). Moreover, reversing the applied magnetic field inverts the rotational direction. The rotation angle of the SH output is approximately 1.3◦ , which is much greater than the Faraday rotation angle of 0.079◦ , at 50 K in an applied magnetic field of 10 kOe. Furthermore, the SH optical rotation due to remnant magnetization is also observed and the angle


65

SH intensity (a. u.)

Film Powder

0

0.2

0.4

0.6

0.8

1

4

5

SH intensity (a.u.)

Compositional factor x

0

1

2

3

Film thickness (Pm)

SH intensity (a. u.)

100 90 80

Pin-Pout

70 60 50 40 30 20 10

Sin-Pout

0 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70

Angle (degree)

Fig. 2.23. (a) The SH intensity of PIN –POUT polarization combination versus x in the film and II III ◦ powder forms of (FeII x Cr1−x )1.5 [Cr (CN)6 ]·7.5H2 O (incident angle: 45 ). The thickness of all the films was about 2 µm. (b) The SH intensity of PIN –POUT polarization combination versus the film thickness () for x = 0.33. (c) Maker’s fringe pattern of the film for x = 0.25 in the polarization combination of PIN –POUT and SIN –POUT at room temperature.

66


SnO2 coated glass

Fe(II) Cr(II) Cr(III)CN6

water

II

Cr

CN

III

Cr

Fig. 2.24. Schematic illustration of the crystal structure and electric polarization in electroII III chemically synthesized (FeII x Cr1−x )1.5 [Cr (CN)6 ]·7.5H2 O films.

is 0.25◦ at 50 K The magnetic linear term of χij kL explains this SH rotation because reversing the magnetic field inverts the rotational direction. The optical symmetry of the present films in the paramagnetic region is confirmed to be C∞v (the nonzero components are xzx = yzy, xxz = yyz, zxx = zyy, zzz in the polar tensor of rank 3) due to the out-of-plane orientation of polycrystals with magn(1) a C2 space group. Below TC , the χij kL term and the χijcrk term are added to the nonlinear susceptibility. This axial tensor of rank 4 has nonzero components of xyzZ = −yxzZ, xxxY = −yyyX, xyyY = −yxxX, yxyY = −xyxX, xzzY = −yzzX, and zxzY = −zyzX [50]. Here, the magnetic field was applied along the direction of light propagation, i. e., the x and z axes at the film frame, and the incident light was polarized to the s-direction (i. e., y axis). Applying a magnetic field should radiate the p- and s-polarized SH outputs by the zyy tensor component magn(1) in the χijcrk part and the yyyX tensor component in the χij kL part, respectively. Moreover, if the applied magnetic field is inverted, then the phase of the s-polarized SH output should be inverted because the sign of the yyy component is changed by the yyyX component. This tensor behavior reproduces the experimental data very well. Thus, the observed SH rotation is due to the magnetic linear term. The relative value of the magnetic yyyX tensor component can be evaluated from the observed SH rotation angle. To estimate this tensor component, the laboratory frame x y z is used. The source terms of the p- and s-polarized SH outputs can be rewritten as magn(1) magn(1) cr χxcr y y = χzyy sin θ and χy y y Z = −χyyyX sin θ, respectively. Then, the tangent magn(1) magn(1) cr(0) of the rotation angle is described as |χy y y Z |/|χxcr y y | = |χyyyX |/|χzyy |. The magn(1) cr(0) |χyyyX |/|χzyy | and from the rotation angle in Figure 2.25 the estimated ratio is 0.023 at 50 K under 10 kOe. Moreover, the above relationship suggests that the rotation angle is independent of the incident angle. In fact, the observed rotation magn(1)


SH intensity (a.u.)

M(+)

67

M(-)

±1.3°

-30

0

30

Analyzer rotation angle (degree)

Fig. 2.25. The SH intensity vs. the analyzer angle in the film for x = 0.33 in an applied magnetic field of 10 kOe at 50 K. The analyzer angle of 0◦ corresponds to the direction of s-polarized SH radiation.

angles of the SH polarization are similar to the incident angles, in the range 5 < θ < 35◦ . The microscopic origin of MSHG is mainly considered to be due to the interaction of the spin-orbit coupling through the electric-dipole nonlinearity, which is allowed by the broken inversion symmetry. Figure 2.26 shows the temperature dependence of the SH intensity without an applied magnetic field for films where x = 0.25 and 0.13. The observed SH intensity dependence on temperature in films when x = 0.25 resembles the magnetization vs. temperature plots. When x = 0.13, the shape of the SH dependence on temperature nearly corresponds to the absolute value of magnetization vs. temperature plots in Figure 2.21. Hence, the magnetic domains are randomly oriented under magn(1) the zero field cooling conditions and the contribution of χij kL is compensated by integrating the magnetic domains. Therefore, the possibility of a contribution magn from theχij k term can be excluded. It is known that the magnetic strain relates to the magnetization value, but reversing the magnetization does not change its sign. Thus the main origin of the SH intensity dependence on temperature is the magnetic crystal strain. The numerous different structures of molecule-based magnets are an advantage for bulk SHG and MSHG since some molecule-based magnets are noncentrosymmetric, and simultaneously have a second-order optical nonlinearity and spontaneous magnetization. In fact, Gatteschi et al. and Nakatani et al., respectively, reported SHG in a methoxyphenyl nitronyl-nitroxide radical crystal [51] and in hybrid layered materials such as [(dmaph)PPh3 ][MnII CrIII (ox)3 ] [52]. In these systems, some interference effects are observed and from this point of view, chiral magnets are useful in studying non-linear magneto-optics of magnetic materials.

68

2 Chiral Molecule-Based Magnets 2.0

0.13

SH intensity (a.u.)

1.8

0.25

1.6

6 EQO R

6%

1.4 1.2 1.0

㨪㨪

0.8

0 0.6 0

50

100

150

200

250

300

Temperature (K)

Fig. 2.26. Temperature dependence of the SH intensities generated from the films for x = 0.13 and 0.25 in a zero applied magnetic field (PIN –POUT polarization).

2.6 Conclusion Notable features of molecule-based magnets include designability and transparency. A novel category of materials suitable for chiral or noncentrosymmetric magnets has been successfully fabricated for application in the field of moleculebased magnetic materials. These materials display new optical phenomena such as the magnetization-induced nonlinear optical effect and the magneto-chiral optical effect due to their noncentrosymmetric or chiral magnetic structure. This category of materials is of keen scientific interest, and, moreover, these materials afford the possibility of use in new types of devices. In this chapter, we have described the design, structure, and some of the physical properties for several new chiral and noncentrosymmetric molecule-based magnets. These systems afford the possibility of opening new fields in magnetism.

Acknowledgments ¯ K.I. and H.I. acknowledge their co-workers Professor H. Okawa and Dr. M. Ohba (University of Kyushu) and Professor K. Kikuchi (Tokyo Metropolitan University). S.O. acknowledges his co-workers Professor K. Hashimoto and Dr. K. Ikeda (The University of Tokyo).

References

69

References 1. 2. 3. 4. 5. 6. 7. 8.

9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42.

M. Kurmoo, P. Day et al., J. Am. Chem. Soc. 1995, 117, 12209. L. Balicas, J.S. Brooks, K. Storr et al., Phys. Rev. Lett. 2001, 87, 067002. S. Uji, H. Shinagawa, T. Terashima et al., Nature 2001, 410, 908. E. Coronado, J.R. Galan-Mascaros, C.J. Gomez-Garcia et al., Nature 2000, 408, 447. O. Sato, T. Iyoda, A. Fujishima et al., Science 1996, 272, 704. S. Karasawa, H. Kumada, N. Koga et al., J. Am. Chem. Soc. 2001, 123, 9685. C. Bellitto, P. Day, J. Chem. Soc. Chem. Commun. 1978, 511. P. Day, in Supramolecular Engineering of Synthetic Metallic Materials, Conductors and Magnets, NATO ASI Series vol. C518, Eds. J. Veciana, C. Rovira, D.B. Amabilino, Kluwer, New York, 1999, p. 253. G. Wagniere, A. Mejer, Chem. Phys. Lett. 1982, 93, 78. L.D. Barron, J. Vrbancich, Mol. Phys. 1984,110, 546. G.L.J.A. Rikken, E. Raupach, Nature 1997, 390, 493. M. Fiebig, Th. Lottermoser, D. Fröhlich et al., Nature 2002, 419, 818. N.A. Hill, J. Phys. Chem. B 2000, 104, 6694. R.-P. Pan, H.D. Wei, Y.R. Shen, Phys. Rev. B 1989, 39, 1229. U. Pustogowa. W. Hübner, K.-H. Bennemann, Phys. Rev. B1994, 49, 10031. Th. Rasing. M.G. Koerkamp, B. Koopmans, J. Appl. Phys. 1996, 79, 6181. M. Fiebig, D. Fröhlich, B.B. Krichevtsov et al., Phys. Rev. Lett. 1994, 73, 2127. D. Fröhlich, St. Leute, V.V. Pavlov et al. Phys. Rev. Lett. 1998, 81, 3239. O.A. Aktsipetrov, O.V. Braginskii, D.A. Esikov, Sov. J. Quantum Electron. 1990, 20, 259. V.V. Pavlov, R.V. Pisarev, A. Kirilyuk et al., Phys. Rev. Lett.1997, 78, 2004. V.N. Gridnev, V.V. Pavlov, R.V. Pisarev et al., Phys. Rev. B 2001, 63, 184407. K. Ikeda, S. Ohkoshi, K. Hashimoto, Chem. Phys. Lett. 2001, 349, 371. Y.R. Shen, The Principles of Nonlinear Optics, Wiley, New York, 1984. M. Fiebig, D. Fröhlich, St. Leute et al., Appl. Phys. B 1998, 66, 265. M. Faraday, Philos. Trans. R. Soc. 1846, 136, 1. J. Kerr, Rep. Brit. Assoc. Adv. Sci. 1876, 40. R.V. Pisarev, in Physics of Magnetic Dielectrics, Nauka, Leningrad, 1974. A.V. Petukhov, I.L. Lyubchanskii, Th. Rasing, Phys. Rev. B 1997, 56, 2680. R.V. Pisarev, B.B. Krichevtsov, V.N. Grindev et al., J. Phys. C. 1993, 5, 8621. H. Kumagai, K. Inoue, Angew. Chem. Int. Ed. Engl. 1999, 38, 1601. H. Kumagai, A.S. Markosyan, K. Inoue, Mol. Cryst. Liq. Cryst. 2000, 343, 97. For example: T. Mallah, S. Thièbaut, M. Veldaguer et al., Science 1993, 262, 1554. S. Ferlay, T. Mallah, R. Ouahès et al., Nature 1995, 378, 701. W.R. Entley, G.S. Girolami, Science 1995, 268, 397. S. Ferlay, T. Mallah, R. Ouahès et al., Inorg. Chem. 1999, 38, 229. S.M. Holmes, G.S. Girolami, J. Am. Chem. Soc. 1999, 121, 5593. M. Ohba, N. Usuki, N. Fukita et al., Angew. Chem. Int. Ed. Engl. 1999, 38, 1795. ¯ M. Ohba, H. Okawa, Coord. Chem. Rev. 2000, 198, 313. ¯ K. Inoue, K. Kikuchi, M. Ohba, H. Okawa, Angew. Chem. Int. Ed., 2003, 42, 4810. K. Inoue, H. Imai, P.S. Ghalsasi et al., Angew. Chem. Int. Ed. Engl. 2001, 48, 4242. S. Ohkoshi, A. Fujishima, K. Hashimoto, J. Am. Chem. Soc. 1998, 120, 5349. S. Ohkoshi, Y. Abe, A. Fujishima et al., Phys. Rev. Lett. 1999, 82, 1285.

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2 Chiral Molecule-Based Magnets S. Ohkoshi, T. Iyoda, A. Fujishima et al., Phys. Rev. B 1997, 56, 11642. S. Ohkoshi, K. Hashimoto, Phys. Rev. B 1999, 60, 12820. S. Ohkoshi, M. Mizuno, G.J. Hung et al., J. Phys. Chem. B 2000, 104, 9365. K. Ikeda, S. Ohkoshi, K. Hashimoto, J. Appl. Phys. 2003, 93, 1371. S. Ohkoshi, K. Hashimoto, J. Am. Chem. Soc. 1999, 121, 10591. T. Mallah, S. Thiebaut, M. Verdaguer et al., Science 1993, 262, 1554. O. Sato, T. Iyoda, A. Fujishima et al., Science 1996, 271, 49. R. Birss, Symmetry and Magnetism, North Holland, Amsterdam, 1966. A. Caneschi, D. Gatteschi, P. Rey et al., Inorg. Chem. 1991, 30, 3936. P.G. Lacroix, R. Clèment, K. Nakatani et al., Science 1994, 263, 658.

3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes Jamie L. Manson

Abstract Several magnetic solids comprised of dicyanamide (dca), [N(CN)2 ]− , bridging ligands have been shown to possess interesting magnetic behavior. Among these are the binary solids M(dca)2 {M = V, Cr, Mn, Fe, Co, Ni and Cu} which have rutile-like structures and order either canted anti- or ferromagnetically with critical temperatures ranging between 1.7 and 47 K. It has also been possible to construct architectures that incorporate organic co-ligands (e. g. pyrazine, pyrimidine) into the framework which contribute to the bulk cooperative magnetic behavior. In this chapter, these structures and their subsequent magnetic behavior are described and some comparisons drawn between the related M(tcm)2 (tcm = tricyanomethanide) compounds. Future prospects for new materials are also discussed.

3.1 Introduction The dicyanamide (dca) anion, [N(CN)2 ]− , is an extremely versatile ligand for assembling transition metal cations into various lattice and spin arrays. First utilized by Köhler [1] nearly three decades ago, this anion has been resurrected by many research groups worldwide, exploiting its coordinative properties in an attempt to “engineer” polymeric structures that exhibit bulk magnetic behavior [2]. Although many interesting structure types have been synthesized and characterized, only a handful display cooperative magnetic properties which is the scope of this review. As shown in Scheme 3.1, the dicyanamide anion can coordinate to a metal ion in several ways: (i) monodentate through one of the nitrile nitrogen atoms, (ii) bidentate through both nitrile N atoms, (iii) bidentate through one nitrile and the amide N-atom, (iv) tridentate through both nitriles and the central amide N-atom and, (v) tetradentate where the central amide and one of the nitrile nitrogen atoms are µ-coordinated while the remaining nitrile moiety is bis-bidentate to two different metal ions. These bonding modes arise from the various canonical forms of the [N(CN)2 ]− ion. All of these coordination schemes have been observed experi-

72

3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes

mentally except for (iii). For instance, scheme (i) is observed in several molecular species such as the spin crossover complex Fe(abpt)2 (dca)2 {abpt = 4-amino-3,5bis(pyridin-2-yl)-1,2,4-triazole} that contains no covalent bonding interactions between metal centers [3]. The second mode, scheme (ii), occurs most frequently and has been observed exclusively in various polymeric 1-, 2- and 3D network structures. So far, the “binary” M(dca)2 {M = V, Cr, Mn, Fe, Co, Ni, Cu and Cd} compounds are the only known examples that portray bonding scheme (iv) [4–14]. Scheme (v) occurs only in diamagnetic Na(dca) [15] and Tl(CH3 )2 (dca) [16].

N

C

N

C

N

N M

M

(i)

C

C

N

C

N M

(ii) M

M

N

N

C

N

N M

M

(iii)

C

N (iv)

C

N M

M

M

N

C

N

C

N M

M

(v)

Scheme 3.1. Possible dicyanamide coordination modes.

A related polycyano species is the tricyanomethanide (tcm) anion, [C(CN)3 ]− which affords bonding characteristics similar to dca [1a, 17]. The most significant difference between them is the symmetry of these planar anions; dca has nominal C2v symmetry while tcm is D3h . When all three nitrile nitrogen atoms of either species coordinate to a metal ion, spin frustration is a plausible exchange scenario [18]. Owing to symmetry considerations, tcm is more susceptible because an equilateral geometry is produced that leads to a greater number of degenerate ground state spin configurations. This is not to say that frustration does not occur in the case of µ3 -bonded dca but the lack of the third nitrile substituent imposes shorter 3-atom exchange paths relative to tcm which offers only 5-atom bridges that greatly alter the magnetic exchange. Three-coordinate tcm, as found in divalent M(tcm)2 {M = V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Cd, and Hg}, leads to 3D rutile-like network structures that possess large “zeolitic-like” channels that are filled by a second identical interpenetrating lattice, Figure 3.1 [18, 19]. The relationship to the rutile phase of TiO2 is readily apparent with the M2+ cations and the large tcm− anions replacing Ti4+ and O2− , respectively. The obvious difference between these systems is the lack of interpenetration observed in the more compact TiO2 lattice. Moreover, the 3-fold symmetry of tcm− could afford geometrical spin frustration since it can be regarded as a 3D analog of the Kagomé lattice [20]. From a magnetism point-of-view, the V-, Cr-,

3.2 “Binary” α-M(dca)2 Magnets

73

and Mn(tcm)2 compounds are the most interesting. The V- and Cr-analogs afford Weiss constants of −69 and −45 K, respectively, indicating sizeable antiferromagnetic interactions between M2+ ions via M–N≡C–C–C≡N–M linkages [18a]. A significantly reduced θ -value of −5.1 K was found for S = 5/2 Mn(tcm)2 [18b]. The MnN6 coordination sphere is a nearly perfect octahedron with Mn–N distances ranging between 2.22 and 2.27 Å. In contrast, the Cr2+ ion in Cr(tcm)2 has an S = 2 ground state that is susceptible to Jahn–Teller distortion (Cr–N distances of 2.08 and 2.45 Å) and, as a result, the effect of spin frustration is diminished, which stabilizes long-range antiferromagnetic ordering below 6.12 K, as shown by specific heat and neutron diffraction data [18a]. Above 6.12 K, the magnetic susceptibility data show a broad maximum centered near 10 K which has been attributed to 2D Ising behavior. The V2+ ion in V(tcm)2 is S = 3/2 and does not have an orbital contribution to the magnetic moment similar to the half-integer spin Mn compound. In the light of the amorphous nature of V(tcm)2 samples, it is likely to have an analogous undistorted crystal structure akin to Mn(tcm)2 and exhibit marked spin frustration, as observed, although no maximum in χ(T ) was detected above 2 K [18a]. The remaining paramagnetic transition metal ions in the first row display magnetic properties associated with single ion anisotropy and no long range magnetic ordering [18c, 19]. It has also been possible to build a variety of other crystalline lattices by introducing potentially bridging organic ligands into the design strategy [21]. Such efforts have not yet yielded magnetically ordered systems.

3.2 “Binary” α-M(dca)2 Magnets Independently and simultaneously, several research groups worldwide have studied the M(dca)2 compounds [4–14]. Combining paramagnetic M2+ and dca− ions in a 1:2 stoichiometry in concentrated aqueous media leads to rapid precipitation of polycrystalline powders of various colors, depending on M. Slow diffusion or solvent evaporation of dilute aqueous solutions over a long period of time affords well-formed crystals for M = Mn, Co and Cu. Unlike other well-known polycyano species, it is very difficult to produce and stabilize a radical anion form of dca. Hence the dca anion (as well as tcm) is diamagnetic, in contrast to electron acceptors such as TCNE, TCNQ, and DCNQI [22]. Like many other polycyano species, dca− is a weak-field ligand.

3.2.1

Structural Aspects

The crystal structures of the M(dca)2 salts are similar to M(tcm)2 (see Figure 3.1) except for the lack of double-interpenetrating lattices in the former. For M = Mn, Cr, Mn, Fe, Co, Ni and Cu, the compounds crystallize in the orthorhombic space

74


Fig. 3.1. Rutile-like crystal structure of double-interpenetrating M(tcm)2 depicting the two individual lattices.

group Pnnm with four molecules per unit cell and M = V, Cr are believed to be isostructural, based on powder X-ray diffraction data [4–14]. A summary of useful crystallographic parameters is provided in Table 3.1. The divalent metal ions in this class of solids possess octahedral coordination environments (also referred to as α-phase) consisting of four nitrile nitrogen atoms in the equatorial plane and two axially-bonded amide-N atoms from six different dca− ligands, Figure 3.2. One-dimensional “chains” propagate along the c-axis which are further connected

Fig. 3.2. Octahedral coordination sphere of the M2+ ion as found in α-M(dca)2 .

amorphous 5.922(2) 6.1126(3) 6.14998(6) 6.1486(4) NR 5.970(1) 6.0109(3) 5.9853(2) 5.9735(2) 6.120(1)

a (Å)

– 7.478(3) 7.2723(3) 7.31503(6) 7.3155(3) NR 7.060(1) 7.0724(4) 7.1030(2) 7.0320(2) 7.339(1)

b (Å) – 7.564(3) 7.5563(4) 7.53668(6) 7.5371(2) NR 7.406(1) 7.3936(4) 7.39384(7) 7.29425(7) 7.173(1)

c (Å) – 334.9(3) 335.90(3) 339.054(6) 339.02(3) NR 312.15(8) 314.32(3) 314.34(1) 306.40(3) 322.17(8)

V (Å3 ) Tc (K) 12.4 47 16 16 16.55(3) 18.5 9 8.7 9.22(4) 21.3(2) 1.7

θ (K) −69 −154 −25 −16 NR 3 9.7 9 9 21 0.7 6800 1000 4919 7000 5400 8000 11000 NR 14000 11,900 NR

M (emu Oe mol−1 )a 20 250 406 750 800 17800 710 NR 800 7000 NR

Hc (Oe)b 0.017 0.74 0.13 0.05 60 K. The zero-field and field-cooled M(T ) data are somewhat field-dependent, where the bifurcation temperature decreases with increasing field from 9.2 (50 Oe) to 8.5 (100 Oe) and then to 8.0 K (500 Oe). Measurements obtained using ac susceptibility (Hdc = 0 Oe, Hac = 1 Oe) show a frequency dependence that typically arises from a spin-disordered ground state such as that found in spin glasses and superparamagnets [34]. This finding attests to the synthetic route utilized to prepare bulk β-Co(dca)2 which is largely amorphous. Similar to the α-phase, hysteresis was observed with Hcr = 680 Oe (2 K). Furthermore, cooling well below TN reveals a second phase transition at 2.7 K that has been ascribed to a spin reorientation.

3.4 Mixed-anion M(dca)(tcm)

3.3.3

85

Comparison of Lattice and Spin Dimensionality in α- and β-Co(dca)2

Recall that the Tc reported for α-Co(dca)2 is nearly identical to that of β-Co(dca)2 . This is very surprising in that the two polymorphs possess completely different topologies (2D versus 3 D) and bond connectivities that directly effect the superexchange properties. It was shown previously that the dominant exchange path in the α-form consists of Co–N≡C–N–Co (3-atom pathway) while it must be Co– N≡C–N–C≡N–Co (5-atom pathway) in the β-phase. In low-dimensional magnetic systems, long range magnetic ordering can only occur if intermolecular interactions are of sufficient magnitude. This is undoubtedly the case for β-Co(dca)2 which exists as 2D closely packed layers. The shortest metal-metal separations for α- and β-Co(dca)2 , respectively, are 5.933 and 4.480 Å [based on the Zn(dca)2 compound]. The smaller distance found in the β-phase arises because of interdigitation of neighboring layers. Clearly, the number of magnetic nearest-neighbors (and most likely next-nearest neighbors) plays an important role in any magnetic system and is no different here. There are eight magnetic nearest-neighbors in α-Co(dca)2 while there are only four (within a layer) in β-Co(dca)2 . This indicates that a dipolar exchange mechanism must be operative, which promotes a relatively large interaction energy that offsets the weaker interaction afforded by the longer Co–N≡C–N–C≡N–Co pathway. It is worth noting that, based on a mean-field argument, the exchange coupling constant, J /kB , is a factor of ∼1.6 larger for β-Co (−0.7 K) compared to that computed for the rutile-like phase (0.45 K).

3.4 Mixed-anion M(dca)(tcm) 3.4.1

Crystal Structure

Combining stoichiometric amounts of M, dca and tcm in aqueous solution leads to a new series of compounds of M(dca)(tcm) {M = Co, Ni, Cu} composition [35]. It was noted that trace amounts of M(tcm)2 impurities were present in all samples, as shown by powder X-ray diffraction. The structure of this mixed anion polymer is regarded as a hybrid between the interpenetrating M(tcm)2 and non-interpenetrating α-M(dca)2 solids, Figure 3.14. As a result, a new selfpenetrating network is formed that has an analogous rutile-like motif. The structure consists of three long tcm bridges and one short/two long links of dca. Multiple lattice interpenetration is thwarted owing to the significantly smaller M3 (dca)3 six-membered rings present in the structure. Simplistically, 1D ML2 “chains” are tethered together by the shorter M–Namide dca links to afford the

86


Fig. 3.14. Structural diagram of the mixedanion compound M(dca)(tcm) {M = Co, Ni, Cu}. Shaded, filled and open spheres represent M, C and N, respectively.

3D network. Four chains in TiO2 form a square channel while the interconnected chains in the M(dca)(tcm) network do not, which promotes the novel self-penetrating feature. Further details of the structure can be found in Ref. [35].

3.4.2

Magnetic Properties

Dc magnetization and ac susceptibility measurements suggest that the M = Co and Ni systems are ferromagnetic or weakly ferromagnetic while M = Cu is a simple paramagnet between 2 and 300 K. Long range magnetic ordering occurs below 3.5 (Co) and 8.0 K (Ni), values ∼1/3 those of the corresponding M(dca)2 compounds [35]. χ T (T ) for both materials gradually increases upon cooling, reaching maximal values close to TN . Small dc fields show a fairly large magnetization that gradually diminishes with increasing H , similar to α-Co and Ni(dca)2 . This suppression is attributed to spin canting. The complex ac susceptibilities show peaks at TN in addition to significant χ (T ) components. Hysteretic behavior was observed with Hcr less than 100 Oe. The field-dependent M(H ) response rises very rapidly, typical of a ferromagnet, but then begins to increase slowly with no sign of saturation up to 50 kOe. This also suggests the presence of competing antiferromagnetic interactions. Effects due to single-ion anisotropy likely play a role, rendering it difficult to quantify the exchange interactions for these materials.

3.5 Polymeric 2D (cat)M(dca)3 cat = Ph4 As, Fe(bipy)3

87

3.5 Polymeric 2D (cat)M(dca)3 cat = Ph4 As, Fe(bipy)3 3.5.1

(Ph4 As)[Ni(dca)3 ]

The 2D anionic network consists of a (4, 4) connectivity [36] identical to that found in (Ph4 P)M(dca)3 {M = Mn, Co} [37, 38]. One-D M–(N≡C–N–C≡N)2 –M ribbons are cross-linked by singly-bridged M–N≡C–N–C≡N–M chains, Figure 3.15, and the bulky cations reside between the layers. The singly-bridged Ni· · ·Ni distance is 8.67 Å while the doubly-bridged chains have an average separation of 7.37 Å [36]. The magnetic properties were found to be strikingly similar to those of parent Ni(dca)2 . Ferromagnetic ordering occurs below 20.1 K [compared to 21 K for Ni(dca)2 ], as denoted by a sharp peak in χ (T ). Use of Ph4 P in place of Ph4 As yielded an identical result. The magnetic data appear to be inconsistent with that of neat Ni(dca)2 , as shown by physical mixtures of (Ph4 As)[Ni(dca)3 ] containing 1% Ni(dca)2 . The magnetization isotherms display markedly different behavior, more characteristic of a soft magnet. At present the origin of the magnetic ordering in this system is unclear, although these findings have been reproduced by other research groups [39]. Similar studies on the Mn- and Co-analogs revealed no evidence for 3D magnetic ordering, only very weak exchange interactions and/or single ion anisotropy.

Fig. 3.15. 2D layered structure of (Ph4 P)M(dca)3 {M = Mn, Co} that is analogous to (Ph4 As)Ni(dca)3 . The cations have been omitted for clarity. Shaded, filled and open spheres represent M, C and N, respectively.

88


3.5.2

[Fe(bipy)3 ][M(dca)3 ]2 {M = Mn, Fe}

Replacement of the tetrahedral cations in the previous example with D3 -symmetric ones leads to a novel 2D anionic hexagonal array, Figure 3.16 [40a]. Each M2+ ion in the layers is bridged by three pairs of dca anions via the nitrile nitrogen atoms to three other M ions. The cations reside within the large hexagonal windows as opposed to between the layers and successive layers are offset relative to one another. It is worth noting the similarity of this system to that of the well-known metal-oxalate networks [40b]. In the M-oxalates, the cations sit between the layers. Although no long range magnetic ordering was observed in this series, this is yet another example that demonstrates the utility and coordination chemistry of the dca anion. As with other µ-bonded M–N≡C–N–C≡N–M materials, the exchange interactions are just too weak to allow 3D magnetic ordering. The [Fe(bipy)3 ]2+ cation is low-spin S = 0 and thus magnetically inert. Murray and co-workers are currently engaged in replacing this cation with magnetically active ones, such as those that show spin crossover behavior [40a].

Fig. 3.16. Anionic 2D hexagonal array displayed by [Fe(bipy)3 ][Fe(dca)3 ]2 . The cations have been omitted for clarity. Shaded, filled and open spheres depict Fe, C and N, respectively.

3.6 Heteroleptic M(dca)2 L Magnets Of great interest and importance to the scientific community is the ability to systematically manipulate crystal structures in an effort to design and control cooperative magnetic properties. One strategy involves the use of ancillary organic ligands that can simultaneously organize metal centers into specific patterns or arrays. In this regard, several research groups have explored various combinations of dca− and organic Lewis bases such as pyrazine (pyz), pyrimidine (pym), pyridine (py), 4,4 bipyridine (4,4 -bipy), 2,2 -bipyridine (2,2 -bipy), and 4-amino-3,5-bis(pyridin-2-

3.6 Heteroleptic M(dca)2 L Magnets

89

yl)-1,2,4-triazole (abpt). Table 3.2 provides an extensive list of the structurally known metal-dca compounds, including diamagnetic systems.

3.6.1

Mn(dca)2 (pyz)

The crystal structure consists of two interpenetrating ReO3 -like frameworks that are assembled from 2D Mn(dca)2 square-like grids which are cross-linked by pyz ligands along the a-axis, Figure 3.17 [41, 42]. Similar layered motifs have been observed in some other systems such as Mn(dca)2 (H2 O)2 ·H2 O [12], Mn(dca)2 (2,5Me2 pyz)2 (H2 O)2 [43] (see Section 3.6.2) and Mn(dca)2 (EtOH)2 ·Me2 CO [12]. At 198 K, the material crystallizes in the monoclinic space group P 21 /n with a = 7.3514 (11), b = 16.865 (2), c = 8.8033 (12) Å, β = 90.057 (2)◦ and V = 1091.4 (3) Å3 , according to X-rays for a twinned crystal [41b]. In another report, Murray and co-workers indicated that the compound is orthorhombic, Pnma, between 223 K and room temperature and attribute the structural change to dynamic disorder of the dca anions [42]. The nuclear structure was also determined at 1.35 K (which is in the magnetically ordered phase) using neutron diffraction [a = 7.3248 (2), b = 16.7369 (4), c = 8.7905 (2) Å, β = 89.596 (2)◦ and V = 1077.65 (7) Å3 ]. At 1.35 K, the high-spin Mn2+ center is quite distorted with four Mn–Neq bond distances ranging from 2.14 (1) to 2.24 (1) Å and two slightly longer Mn–Nax distances of 2.27 (1) and 2.29 (1) Å while the N-Mn–N bond angles reflect a slight deformation from the ideal geometries. The significance of this distortion will be shown to have a profound effect on the magnetism. The shortest metal-metal distance is that between interpenetrating lattices, which is 6.42 Å. Furthermore, the other first-row transition metal ions form isostructural networks and a second β-phase has also been identified for M = Co, Ni, Cu, and Zn [42, 44].

Fig. 3.17. Interpenetrating ReO3 -like network structure of Mn(dca)2 (pyz) emphasizing the two individual lattices. [2]

a (Å)

10.080(7) 8.756(4) 9.7989(2) 9.6800(3) 9.448(3) 8.6469(5) 8.4618(5) 7.5401(7) 6.4242(3) 6.6769(3) 22.378(6) 6.684(3) 6.374(2) 17.5112(4) 17.5814(7) 17.8642(2) 17.768(7) 16.8243(8) 17.1243(2) 17.0863(6) 13.579(6) 8.825(3)

Space Group P 21 /n P 21 /c P 21 /c P 21 /c P1 P bca P1 P 21 /n P1 C2/c I ba2 C2/c P 21 /n P nma P nma P nma P 21 /n C2/c P 42 /mbc P 42 /mbc C2/c P 21 /n

Compound

Cu(dca)(tcm)(phen)2 (i) Cu(dca)2 (phen)2 (i) Mn(dca)2 (phen)2 (i) Zn(dca)2 (phen)2 (i) Ni(dca)2 (4-Meiz)4 (i) Cu(dca)(BF4 )(2,2 -bipy) (i) Fe(dca)2 (abpt)2 (i)

Mn(dca)2 (py)2 (ii) Mn(dca)2 (DMF)2 (ii) Mn(dca)2 (2,2 -bipy) (ii) Mn(dca)2 (4,4 -bipy)·H2 O (ii) Mn(dca)2 (bpym) (ii) Mn(dca)2 (4-bzpy)2 (ii) Mn(dca)2 (bpym)·H2 O (i,ii) Fe(dca)2 (bpym)·H2 O (i,ii) Co(dca)2 (bpym)·H2 O (i,ii) Mn(dca)2 (NITpPy)4 (ii) Mn(dca)2 (NH2 -pyz)1.5 H2 O (ii) Co(dca)2 (2-NH2 -pym) (ii) Ni(dca)2 (2-NH2 -pym) (ii) Cu(dca)2 (2-NH2 -pym)2 (ii) Mn(dca)(NO3 )(terpy) (ii)

13.2643(4) 7.4907(4) 17.2008(2) 22.517(5) 17.213(7) 7.584(2) 11.9955(4) 11.9453(5) 11.9216(2) 7.368(4) 7.5106(3) 17.1243(2) 17.0863(6) 15.453(5) 13.928(4)

12.972(7) 14.611(6) 15.0160(5) 15.0697(7) 9.918(3) 17.8651(8) 9.6086(3)

b (Å)

α (◦ )

Molecular 19.874(13) 90 18.979(8) 90 17.7189(5) 90 17.7166(8) 90 15.173(5) 107.85(2) 28.7434(15) 90 9.6381(7) 83.661(4) 1D chains 8.6973(9) 90 8.4034(4) 103.021(3) 13.0142(4) 90 13.519(5) 90 13.042(5) 90 26.766(5) 90 7.4684(2) 90 7.3292(3) 90 7.2860(2) 90 21.404(8) 90 24.8192(12) 90 7.3816(1) 90 7.3099(2) 90 7.570(7) 90 14.650(4) 90

c (Å)

114.954(2) 106.485(4) 90.110(2) 90 90.27(2) 91.87(2) 90 90 90 92.78(2) 107.287(2) 90 90 92.03(5) 96.05(3)

100.22(6) 101.21(4) 104.595(2) 104.628(2) 93.67(2) 90 86.642(5)

β (◦ )

90 99.390(4) 90 90 90 90 90 90 90 90 90 90 90 90 90

90 90 90 90 104.74(2) 90 65.821(4)

γ (◦ )

788.65(11) 366.46(3) 1494.65(8) 6812(3) NR 1293.3(6) 1568.77(9) 1539.24(11) 1551.71(4) 2799(2) 2994.5(2) 2164.59(5) 2134.1(1) 1596.7(17) 1790.7(9)

2557.4(28) 2381.7(18) 2523.04(12) 2500.64(18) 1293.1(7) 4440.2(4) 710.44(7)

V (Å3 )

33 12 33,63 33 62 63 64 64 64 65 43 66 66 67 68

57 58 59 59 60 61 3

Ref.

Table 3.2. X-ray structural data for numerous dia- and paramagnetic M-dca complexes arranged according to lattice dimensionality. Unless otherwise noted, all structures were determined at or near room temperature. The corresponding M-dca bonding mode (see Scheme 3.1) is given in parentheses following the compound name.

90 3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes

8.795(3) 13.925(3) 7.5684(3) 7.5761(3) 13.016(3) 11.457(1) 6.565(4) 3.601(2) 3.612(2) 29.979(4)

7.574(2) 7.266(2) 23.3789(10) 29.5142(7) 10.174(2) 21.603(1) 17.644(9) 3.601(2) 16.133(8) 12.977(3) 12.409(1) 12.2247(7) 11.316(1) 7.3165(2) 16.111(3) 16.1684(5) 16.203(3) 8.384(2) 9.8389(3) 9.7659(8) 7.1189(2) 7.6209(4) 6.178(3) 13.4354(10) 13.3903(6)

P1 P bca C2/c C2/m C2/m C2/c P nam P 31 21 P nma P nma C2/m C2/m C2/c P 21 /n P nma P nma P nma P 21 /n P 21 /c C2/m Cmmm P nma P 21 /c P 2/n P 2/n

Mn(dca)2 (terpy)(H2 O) (ii) Cu(dca)2 (3-OHpy)2 (i,ii) (PPh4 )2 Co(dca)4 (ii) Cu2 (dca)2 (bipy)1.5 (MeCN)2 (ii) Ru2 (O2 CMe)4 (dca)·MeCN (ii) Zn3 (O2 CMe)4 (dca)2 (bipy)3 (ii) (Me)3 Sn(dca) (ii) Ag(dca) (ii) Ag(dca) (ii) κ-(BEDT-TTF)2 [Cu(dca)Cl]

Mn(dca)2 (MeOH)2 (ii) Fe(dca)2 (MeOH)2 (ii) Mn(dca)2 (EtOH)2 ·(CH3 )2 CO (ii) [Mn(dca)2 (H2 O)2 ]·H2 O (ii) [Ni2 (dca)4 (bpym)]·H2 O (ii) [Co2 (dca)4 (bpym)]·H2 O (ii) [Fe2 (dca)4 (bpym)]·H2 O (ii) [Fe2 (dca)4 (bpym)(H2 O)2 (ii) Cu(dca)2 (phen) (ii) β-Cu(dca)2 (pyz) (ii) β-Zn(dca)2 (pyz) (123 K) (ii) Zn(dca)2 (ii) (Me)2 Sn(dca)2 (ii) (PPh4 )Mn(dca)3 (ii) (PPh4 )Co(dca)3 (ii)

7.481(1) 7.3921(5) 11.358(1) 11.6229(5) 12.755(2) 12.9860(3) 13.122(3) 9.223(2) 11.2975(5) 6.8787(7) 9.6994(4) 7.5958(4) 11.265(10) 7.4426(5) 7.5745(3)

b (Å)

Space a (Å) Group

Compound

Table 3.2. (Continued.) α (◦ )

14.948(6) 78.16(3) 30.327(6) 90 28.3778(12) 90 11.3905(4) 90 7.0750(14) 90 17.798(1) 90 7.684(3) 90 22.868(22) 90 5.983(4) 90 8.480(2) 90 2D layers 6.528(1) 90 6.4610(4) 90 12.488(1) 90 11.3590(5) 90 10.455(2) 90 10.4207(3) 90 10.438(2) 90 13.983(3) 90 14.2340(5) 90 7.3870(5) 90 7.3988(3) 90 12.0477(7) 90 6.860(6) 90 14.1556(10) 90 14.3935(6) 90

c (Å)

119.979(3) 120.119(1) 96.918(3) 103.241(5) 90 90 90 90.95(3) 100.988(2) 95.254(7) 90 90 99.56(5) 101.087(1) 99.663(2)

79.73(3) 90 105.621(1) 106.141(2) 101.83(3) 104.245(4) 90 120 90 90

β (◦ )

90 90 90 90 90 90 90 90 90 90 90 90 90 90 90

81.80(2) 90 90 90 90 90 90 90 90 90

γ (◦ )

524.93(11) 505.03(5) 1593.4(2) 940.28(6) 2148.4 2187.96(11) 2219(1) 1081.1(7) 1553.17(10) 494.15(6) 510.88(3) 697.65(7) NR 1389.06(17) 1439.15(10)

953.1(6) 3068.5(12) 4835.7(3) 2446.5(1) 917.0(3) 4269.6(5) NR NR 348.8(1) 3299(1)

V (Å3 )

12 12,76 12 12 77 64 78 78 79 44 42 30 72 37,38 37

68 56 37 69 70 71 72 73 74 75

Ref.

3.6 Heteroleptic M(dca)2 L Magnets 91

7.5841(1) 14.7418(3) 14.8711(2) 7.3046(3) 7.3703(2) 12.5280(3) 12.4011(3) 12.5231(2) 7.7296(2) 15.2140(5) 18.5279(9) 10.0447(3)

13.3943(4) 13.6963(5) 13.5777(4) 14.2441(8) 14.2905(4) 28.7821(7) 28.8799(6) 28.8625(5) 13.0351(4) 7.3835(1) 3.8969(1) 8.2104(3) 7.3514(11) 7.1848(4) 7.0965(4) 24.2549(7) 18.5410(10) 7.396(3) 7.5609(9) 7.446(4) 7.5743(2) 7.4129(3) 7.1884(3) 12.917(1)

P 2/n P 2/n P 2/n P 21 /c P 21 /c F dd2 F dd2 F dd2 P nma P na21 P 21 /c P1 P 21 /n P 21 /n P 21 /n Pn C2/c P 21 /c P 21 /c P 21 /c Ama2 Ama2 Ama2 P nma

(AsPh4 )Mn(dca)3 (ii) (AsPh4 )Ni(dca)3 (ii) (AsPh4 )Co(dca)3 (ii) (AsPh4 )2 [Ni2 (dca)6 (H2 O)]·H2 O (ii) (AsPh4 )2 [Co2 (dca)6 (H2 O)]·H2 O (ii) [Fe(bipy)3 ][Mn(dca)3 ]2 (ii) [Fe(bipy)3 ][Fe(dca)3 ]2 (ii) [Ni(bipy)3 ][Mn(dca)3 ]2 (ii) Cu(dca)(MeCN) (ii) α-Cu(dca)(bpe) (ii) Cu(dca)(Me4 pyz)0.5 (ii) Cu4 (dca)4 (4,4 -bipy)3 (MeCN)2 (ii)

Mn(dca)2 (pyz) (198 K) (ii) α-Fe(dca)2 (pyz) (173 K) (ii) α-Co(dca)2 (pyz) (123 K) (ii) α-Cu(dca)2 (pyz) (ii) Mn(dca)2 (2,5-Me2 pyz)2 (H2 O)2 (ii) Mn2 (dca)4 (bpym) (ii) Cu2 (dca)4 (bpym) (ii) Zn2 (dca)4 (bpym) (ii) Mn(dca)2 (H2 O) (iv) Co(dca)(tcm) (173 K) (iv) Cu(dca)(tcm) (iv) Fe(dca)2 (pym)·EtOH (ii)

16.865(2) 16.6920(13) 16.6139(9) 6.8571(2) 11.9929(7) 11.498(7) 11.477(42) 11.478(4) 17.4533(7) 17.0895(6) 17.6983(7) 12.0440(6)

b (Å)

Space a (Å) Group

Compound

Table 3.2. (Continued.) α (◦ )

14.3076(4) 90 14.1266(5) 90 14.1776(4) 90 29.057(2) 90 28.9937(8) 90 23.7374(4) 90 23.5140(3) 90 23.9239(3) 90 6.1895(2) 90 12.1963(4) 90 9.9978(5) 90 13.9494(4) 98.995(2) 3D networks 8.8033(12) 90 8.6952(6) 90 8.6342(5) 90 24.6445(7) 90 11.7793(5) 90 12.349(9) 90 11.792(2) 90 12.064(4) 90 5.6353(2) 90 5.5991(2) 90 5.7395(3) 90 9.2575(8) 90

c (Å)

90.057(2) 90.041(5) 90.047(3) 91.023(2) 126.195(2) 106.61(5) 106.565(6) 107.75(2) 90 90 90 90

99.893(1) 103.315(1) 102.196(1) 102.404(2) 102.207(1) 90 90 90 90 90 92.039(3) 93.178(2)

β (◦ )

90 90 90 90 90 90 90 90 90 90 90 90

90 90 90 90 90 90 90 90 90 90 90 101.633(2)

γ (◦ )

1091.4(3) 1042.80(12) 1017.98(10) 4098.2(2) 2113.8(2) 1006.3(1) 971.6(1) 982.0(7) 744.97(4) 709.31(5) 730.19(6) 1440.2(2)

1431.81(6) 2775.6(2) 2798.1(1) 2952.7(3) 2984.7(1) 8559.3(3) 8421.4(3) 8647.2(2) 623.63(3) 1370.04(7) 721.40(5) 1108.43(6)

V (Å3 )

41b 42 42 44 43 62 62 77 35 35 35 47

38 36 36 36 36 40 40 40 69 69 69 69

Ref.

92 3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes

12.8586(4) 12.5520(5) 16.9221(7) 9.8655(3) 9.8222(3) 9.7889(5) 13.9593(3) 12.2904(3) 6.5015(5) 6.739(3)

P nma P nma P nma P 21 /n P 21 /n P 21 /n P 21 21 21 Cc Pbnm P 21 /c

Co(dca)2 (pym)·EtOH (ii) Cu(dca)2 (pym)·MeCN (ii) Co(dca)2 (4,4 -bipy) (ii) Mn(dca)2 (apo) (ii) Co(dca)2 (apo) (ii) Ni(dca)2 (apo) (ii) (PPh3 Me)Mn(dca)3 (123 K) (ii) β-Cu(dca)(bpe) (ii) β-Na(dca) (v) (Me)2 Tl(dca) (v)

11.9268(4) 11.6557(3) 11.4251(4) 12.1640(4) 11.8553(4) 11.7071(6) 17.2000(2) 44.675(1) 14.951(2) 11.830(7)

b (Å) 9.2126(2) 9.4003(4) 8.6147(3) 10.5046(3) 10.4718(4) 10.5283(4) 20.8587(3) 14.6413(3) 3.6050(3) 9.891(7)

c (Å) 90 90 90 90 90 90 90 90 90 90

α (◦ ) 90 90 90 94.795(2) 94.866(2) 94.610(3) 90 93.004(2) 90 117.81(3)

β (◦ ) 90 90 90 90 90 90 90 90 90 90

γ (◦ ) 1412.86(7) 1375.29(9) 1665.4(6) 1256.18(7) 1214.99(7) 1202.64(10) 5008.2(2) 8028.1(3) 350.42(5) NR

V (Å3 )

47 49 80 81 81 81 38 69 15 16

Ref.

Abbreviations: NR = not reported, phen = 1,10-phenanthroline, Meiz = methylimidazole, abpt = 4-amino-3,5-bis(pyridin-2-yl)-1,2,4-triazole, bipy = bipyridine, DMF = N,N -dimethylformamide, bpym = bipyrimidine, bzpy = 4-benzoylpyridine, NITpPy = 2-(4-pyridyl)-4,4,5,5,tetramethylimidazoline-1-oxyl-3-oxide, pyz = pyrazine, pym = pyrimidine, terpy = 2,2 :6 ,2 -terpyridine, Me = methyl, Et = ethyl, apo = 2-aminopyridine-N-oxide, bpe = 1,4-bis(4-pyridyl)ethene.

a (Å)

Space Group

Compound

Table 3.2. (Continued.)

3.6 Heteroleptic M(dca)2 L Magnets 93

94


A comprehensive dc magnetization, ac susceptibility, specific heat, neutron diffraction, and electronic structure study has been reported [41a]. Susceptibility data show a sharp maximum at 2.7 K while Cp (T ) shows a λ-anomaly at 2.5 K that is indicative of 3D magnetic ordering, Figure 3.18. The 2–300 K magnetic data can be very well described by an S = 5/2 1D Heisenberg hamiltonian which afforded g = 2.01 (1) and J /kB = −0.27 (1) K. This exchange coupling is attributed to the Mn–pyz–Mn intrachain interaction and is consistent with theoretical calculations. The zero-field magnetic structure consists of Mn2+ moments [M = 4.45 (10) µB ] that are aligned parallel to the ac-diagonal owing to a competition between the single-ion anisotropy and the dipolar field manifested by the second interpenetrating lattice [45]. From the magnetic order parameter, it was possible to deduce TN = 2.53 (2) K and β = 0.38, which is expected for a 3D Heisenberg antiferromagnet. Field-dependent M(T ), M(H ) and Cp (H ) display features characteristic of spin flop, Hsf , and paramagnetic, Hc , phase transitions at 4.3 and 28.3 kOe, respectively, Figure 3.19. These results have been recently confirmed by neutron diffraction which shows no superlattice reflections above Hc , 0.70

ac

12 10 8 6 4 2 0

C (J/mol-K)

0.60 0.55

p

χ ' (emu/mol)

0.65

0.50

1 1.5 2 2.5 3 3.5

T (K)

0.45 0.40 0.35 0.30 0

TN = 2.53 K

2

4

6

8

10

T (K)

Fig. 3.18. Low-T ac susceptibility acquired for Mn(dca)2 (pyz) showing the cusp associated with long range magnetic ordering. The inset shows Cp (T ) taken in zero-field on a small pellet.

0.7

χ' ac (emu/mol)

0.6 0.5 0.4 0.3 0.2 4.3 kOe

28.3 kOe

0.1 0 0

10

20

30

H (kOe)

40

50

Fig. 3.19. H -dependence of χac for Mn(dca)2 (pyz) obtained at 2 K (Hac = 1 Oe, ω = 10 Hz) [41a].


95

indicating a ferromagnetic-like spin configuration [46]. Complete saturation occurs at 100 kOe (2 K) reaching a value of 4.87 NµB . Mn(dca)2 (pyz) is the only compound in the series shown to undergo long range magnetic ordering, presumably due to its large effective spin value of 5/2. By comparison, a considerably stronger 1D exchange coupling strength of −3.90 K was found for α-Cu(dca)2 (pyz) [44b].

3.6.2

Mn(dca)2 (2,5-Me2 pyz)2 (H2 O)2

The extended structure of this compound is polymeric and consists of slightly puckered 2D Mn(dca)2 (H2 O)2 layers that reside in the bc-plane, Figure 3.20 [43]. The layers are held together by hydrogen bonding interactions between the coordinated H2 O and the nitrogen atoms of the 2,5-Me2 pyz molecules, Figure 3.21. Every other MnN4 O2 chromophore is rotated 5.3◦ with respect to its nearest neighbor and the Mn–Neq and Mn–O bond distances are all very similar [2.198 (2), 2.212 (2) and 2.218 (2) Å]. The intralayer Mn· · ·Mn separation is 8.405 Å while the interlayer Mn–OH2 · · ·2,5–Me2 pyz· · ·OH2 –Mn interaction affords a longer distance of 11.475 Å. (T ) near 1.8 K which suggests a long Ac susceptibility shows a maximum in χac range magnetic ordering of the spins [43]. At the maximum, a very sharp spike was observed that is often attributed to a spontaneous magnetization induced by spin canting, Figure 3.22. Similar behavior was observed in the parent Mn(dca)2 compound [6, 8, 12]. The T -dependent magnetic susceptibility could be modeled

Fig. 3.20. Portion of the crystal structure of Mn(dca)2 (2,5-Me2 pyz)2 (H2 O)2 depicting only the 2D Mn(dca)2 (H2 O)2 layers. Hydrogen atoms have been omitted for clarity purposes.

96


Fig. 3.21. Hydrogen-bonded 3D network of Mn(dca)2 (2,5-Me2 pyz)2 (H2 O)2 . Hydrogen bonding interactions are shown as dashed lines. 0.78

χ' ac (emu/mol)

0.76 0.74 0.72 0.70 0.68 0.66 1.5

T = 1.78 K N

1.75

2

2.25

2.5

2.75

3

T (K) (T) for Mn(dca) (2,5-Me pyz) (H O) showing the sharp spike that arises from Fig. 3.22. χac 2 2 2 2 2 noncollinear antiferromagnetic ordering of the Mn2+ moments.

by a 3D spin hamiltonian which gave g = 2.00 (1) and J /kB = −0.175 (1) K. The weak exchange interaction is typical of a large number of µ-bonded metal-dca solids that contain Mn2+ ions. M(H ) at 1.9 K indicates that saturation magnetization is not quite obtained although a large value of 4.93 NµB is reached, which is very close to the expected value of 5 µB .

3.6.3

Mn(dca)2 (H2 O)

The crystal structure is isomorphous to M(dca)(tcm) as described in Section 3.4 which has a self-penetrating 3D architecture [35]. Because a symmetry-imposed mirror plane lies perpendicular to the chain axis, the dca·H2 O moiety is disordered over two positions, Figure 3.23. At first glance, this disordered group appears geometrically equivalent to tcm, hence tcm can also be readily substituted into this system. The Mn–Namide distance is unusually long at 2.417 (4) Å, suggesting a very weak coordination.


97

Fig. 3.23. Segment of the crystal structure of Mn(dca)2 (H2 O) illustrating the disorder of the dca and H2 O moities. Dashed lines represent hydrogen bonds.

Mn(dca)2 (H2 O) is a canted antiferromagnet (weak ferromagnet) below TN = 6.3 K, as indicated by a sharp peak in χ (T ) [35]. At 300 K, the magnetic moment is consistent with high-spin Mn2+ and gradually decreases upon cooling, as a result of antiferromagnetic correlations between spin centers. At TN , an abrupt increase occurs due to the formation of a spontaneous magnetization, reaching moments as large as 10.9 µB (Hdc = 20 Oe). External fields in excess of ∼200 Oe essentially saturate the canted moment yielding magnetic behavior more typical of a collinear antiferromagnet. Hysteresis experiments at 2 K showed a coercive field of 250 Oe and a remnant magnetization, Mr , of 112 emu Oe mol−1 . Complete saturation magnetization was not observed up to fields of 5 T (2 K) which display a linear M(H ) response consistent with a spin canted system. A considerably reduced magnetization value of 1.7 µB was obtained at 5 T, well below the anticipated value of 5 µB for Mn2+ .

3.6.4

Fe(dca)2 (pym)·EtOH

Three-dimensional scaffolds similar to Mn(dca)2 (pyz) can also be prepared using pyrimidine (pym) which is 1,3-diazine. This scheme, however, only seems to work for M = Fe, Co, and Cu [47] but not Mn or Ni [48, 49]. Ishida and co-workers recently described a preliminary account of the synthesis and characterization of Fe(dca)2 (pym)·EtOH [47]. The crystals were found to contain 0.5–1.0 ethanol per formula unit. The polymeric structure consists of puckered 2D Fe(dca)2 sheets in the ac-plane that are connected together by bridging pym ligands along the b-axis, Figure 3.24. Structural disorder occurs for each of the bridging dca ligands [47a]. The Fe2+ center is slightly elongated with four Fe–Neq distances ranging between 2.138 (4) and 2.142 (4) Å and two Fe–Nax distances of 2.202 (4) Å. The intralayer Fe· · ·Fe separation is 7.9458 (5) Å while the intrachain distance is 6.0220 (3) Å. The magnetic behavior was measured between 2 and 300 K and fitted to the Curie–Weiss expression, giving C = 4.40 emu K mol−1 (θ = −7.0 K) and C = 1.73 emu K mol−1 (θ = −4.4 K) for the Fe and Co-analogs, respectively [47a]. In an external field of 5 kOe, χ T (T ) decreases continuously down to ∼8 K

98


Fig. 3.24. Three-dimensional framework structure of Fe(dca)2 (pym)·EtOH viewed parallel to the (010) direction. The ethanol molecules have been omitted for clarity purposes. Fe, C and N atoms are represented by shaded, filled and open spheres, respectively.

and then increases abruptly to reach a peak at 3.6 K. Below this the data decrease (T ) showed a sharp peak at 3.2 K again as a result of likely saturation effects. χac due to long range magnetic ordering. Similar behavior was found for the Co-analog but a lower Tc was observed near 1.8 K. Low-field M(T ) in the region near TN give strong indications for canted antiferromagnetism. According to M(H ) at low temperatures, both compounds exhibit an initial rapid increase in the magnetization due to the spontaneous moment. At higher fields, the magnetization becomes approximately linear up to the highest field measured of 90 kOe. Such behavior is generally associated with spin-canted systems. It is worth noting that Co- and Fe(dca)2 (pym)·EtOH join an ever increasing library of canted/weak ferromagnets.

3.6.5

Fe(dca)2 (abpt)2

Materials comprised of Fe2+ ions have received much interest over the years because of their ability to show spin-crossover behavior which can be provoked by light, temperature or pressure [50]. Systems such as these usually involve FeN6 coordination spheres although some exceptions occur. In contrast to the aforementioned polymeric materials, Fe(dca)2 (abpt)2 exists as discrete mononuclear entities, Figure 3.25 [3]. Two abpt ligands chelate to the Fe2+ center to occupy all four equatorial sites. The remaining axial positions are occupied by monodentate dca anions. This structural arrangement contrasts with that of Fe(o-phenanthroline)2 (NCS)2 which adopts a cis-conformation [51]. The crystal packing of Fe(dca)2 (abpt)2 con-

3.7 Dicyanophosphide: A Phosphorus-containing Analog of Dicyanamide

99

Fig. 3.25. Room temperature molecular structure of Fe(dca)2 (abpt)2 . Scheme 3.1 Possible dicyanamide coordination modes.

sists of chains that lie along the [001] direction. Relatively strong intermolecular contacts exist so as to define two-dimensional sheets in the [101] plane. While this material does not exhibit long range magnetic order, it is included here because the spin-crossover phenomenon is a cooperative effect. Fe(dca)2 (abpt)2 is the first example of a spin-crossover complex that contains dca− . Magnetic susceptibility data show an incomplete two-step spin transition. Tsc , the temperature at which 50% of the spin conversion occurs, is ∼86 K, one of the lowest temperatures observed for a Fe2+ spin-crossover material. Further details of this study can be found in Ref. [3].

3.7 Dicyanophosphide: A Phosphorus-containing Analog of Dicyanamide As noted in this chapter, the chemistry of dicyanamide, especially with regard to metal complexes, has been extensively investigated. However, little is known about its phosphorus-containing analog. Dicyanophosphide (dcp), [P(CN)2 ]− , was first reported in the literature in 1977 [52]. Shortly thereafter, it was structurally characterized and shown to have a molecular structure similar to dca [53]. The same authors published a limited report on the reactivity of dcp [54]. Because phosphorus has d orbitals available for bonding, the metal ion complexes with dicyanophosphide would be of great interest with respect to their differences in magnetic coupling. Magnetically ordered M(dca)2 complexes are readily prepared in aqueous media using the water soluble Na(dca), but unfortunately the analogous synthesis with dcp is not possible as it is hydrolytically unstable [55]. Re-

100


actions of dicyanamide with divalent metal ions in non-aqueous media produce 1D and 2D network structures with no magnetic ordering [37]. Hence, M(dcp)2 complexes have eluded their rational preparation [55]. Ultimately, a comparison of the magnetic properties of M(dca)2 and M(dcp)2 materials is desired, provided a non-aqueous route to these materials can be achieved.

3.8 Conclusions and Future Prospects It has been demonstrated that the coordinative versatility of the dicyanamide ligand leads to a large variety of structural and magnetic properties. In the examples shown, it is clear that the µ3 -bonded dca configuration (scheme (iv)) stabilizes the strongest exchange coupling between spin-bearing metal sites. This is in marked contrast to µ-bonding via the nitrile N-atoms that affords a five-atom superexchange pathway and thus very weak magnetic interactions. Conceivably, it may be possible to achieve µ-bonding via the amide nitrogen and one of the nitrile substituents that would provide a shorter three-atom pathway and significant exchange interactions. With all of the now known metal-dca compounds, bonding scheme (iii) remains elusive. Individually, the structures described in this chapter contain only one type of dca bonding mode and new topologies may arise if multiple bonding modes can coexist in a single material. Recently reported Cu(dca)2 (3-OHpy)2 {OHpy = hydroxypyridine} does in fact feature two coordination modes, mono- and µbonded dca− [56]. Mixed-anion species such as the tcm/dca combination discussed in Section 3.4 afford interesting hybrid structures with somewhat reduced TN s relative to neat M(dca)2 . Other possible alternatives that can be envisioned include N3 − /dca− , NCS− /dca− , NCO− /dca− , other pseudohalides, and perhaps carboxylate derivatives. Additional complexity stemming from the use of organic co-ligands is also anticipated. Such efforts will require clever synthetic strategies to ensure phasepure materials that contain the desired ingredients. Furthermore, the vast majority of metal-dca materials contain divalent (or diamagnetic) transition metal ions while trivalent ions such as rare earth, Fe3+ , Cr3+ , Mn3+ , etc. have yet to be explored. Ferrimagnetic materials consisting of dca- anions have not been realized owing to the difficulty in preparing appropriate building blocks. Alternatively, it should be possible to create solid solutions that will allow tunability of the desired magnetic properties such as Tc , remnant magnetization, and coercivity. Likewise, attention must be paid to prevent multi-phase materials.

References

101

Acknowledgments It is a great pleasure to acknowledge the following people for their significant contributions to this work: D.N. Argyriou, A.M. Arif, G.M. Bendele, H.N. Bordallo, L. Chapon, J.E. Crow, A.J. Epstein, R. Feyerherm, U. Geiser, E. Goremychkin, J. Gu, Q.-Z. Huang, C.D. Incarvito, C.R. Kmety, D.W. Lee, L. Liable-Sands, A. Loose, J.W. Lynn, S.R. Marshall, J.S. Miller, S. Pagola, F. Palacio, J.W. Raebiger, D.H. Reich, A.L. Rheingold, J.A. Schlueter, P.W. Stephens, and M.B. Stone.

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4 Molecular Materials Combining Magnetic and Conducting Properties Peter Day and Eugenio Coronado

4.1 Introduction Planar organic donors or acceptors such as TTF derivatives and TCNQ derivatives, (Scheme 4.1) have been extensively used in the synthesis of molecular conductors and superconductors. For example, when TTF reacts with TCNQ a partial electron transfer occurs from the donor to the acceptor giving rise to the charge transfer salt [TTF]δ+ [TCNQ]δ− which shows metallic properties. Its structure consists of uniform segregated chains of the donor and the acceptor which stack in the solid state giving rise to delocalised electron energy bands due to overlapping between the π-orbitals of adjacent molecules. Electron delocalisation is also obtained in the solids formed by the ion-radicals resulting from oxidation (or reduction) of one of these two kinds of molecules and a charge-compensating counterion. In this context, cation-radical salts of organic donors formulated as [Donor]m Xn have provided the best examples of molecular conductors and superconductors. Typically, the − − counterion X is a simple inorganic monoanion of the type Cl− , Br− , I− 3 , PF6 , AsF6 , − − − BF4 , ClO4 , NO3 , . . . The structures of these salts consist of segregated stacks of the planar radical cations interleaved by the inorganic anions (Figure 4.1). A way to incorporate localised magnetic moments in these materials is to use magnetic anions as charge-compensating counterions. Inorganic chemistry provides a wide choice of metal complexes of various nuclearities and dimensionalities that can be used with this aim. They range from simple mononuclear complexes of the type [MX4 ]n− (M = Fe(III), Cu(II); X = Cl, Br); [M(C2 O4 )3 ]3− (M = Fe(III), Cr(III)), [M(CN)6 ]3− (M = Fe(III)), to cluster-type complexes (polyoxometallates), to chain complexes as the substituted dithiolates [M(mnt)2 ]− (mnt = maleonitriledithiolate, M = Ni, Pt and Pd), to layered structures as the bimetallic oxalate complexes [M(II)M(III)(ox)3 ]− (M(II) = Mn, Co, Ni, Fe, Cu; M(III) = Fe, Cr). Most of the examples so far reported of hybrid molecular materials combining a conducting component with a magnetic component are based on the above organic/inorganic combination [1, 2]. In this chapter we will focus especially on the achievements so far reported in these materials. Before doing so, however, we will introduce the main reasons that justify the intense effort devoted to this kind of molecular material.

106

4 Molecular Materials Combining Magnetic and Conducting Properties S

S

S

S

TTF

NC

CN

NC

CN

TCNQ

S

S

S

S

S

S

S

S

S

S

S

S

TM-TTF Se

Se

Se

Se

TM-TSF

BEDT-TTF or ET Se

S

S

Se

Se

S

S

Se

BEDSe-TTF or BEST S

Se

Se

S

S

Se

Se

S

BEDT-TSeF or BETS S

perylene (per)

S

S

S

S

BET-TTF or BET

S

Scheme 4.1

Fig. 4.1. Schematic arrangement of an organic–inorganic composite compound.

4.2 Interest of Conducting Molecular-based Magnets From a physical point of view hybrid materials formed by two molecular networks are interesting because they can exhibit a coexistence of the two distinct physical properties furnished by the two networks, or novel and improved properties with respect to those of the two networks due to the interactions established between them. In the particular case of the materials combining magnetic and conducting properties a quite interesting case of coexistence we can look for is that

4.2 Interest of Conducting Molecular-based Magnets

107

of ferromagnetism with superconductivity. These two cooperative properties are considered as mutually exclusive. Their coexistence has been the subject of long debate in solid state physics and has been investigated from both theoretical and experimental points of view in extended inorganic lattices [3]. A second reason for examining the interplay of the localised moments normally found in molecularbased magnetic materials with conduction electrons lies in the possibility that it will provide a further mechanism for exchange interaction through the so-called RKKY interaction.

4.2.1

Superconductivity and Magnetism

The fundamental difference between superconductivity and normal metallic conduction lies in the fact that in the former the current carriers are pairs of electrons (Cooper pairs), while in the latter, to a first approximation, the electrons move independently. Interaction between electrons and lattice vibrations is the most common means of overcoming the Coulomb repulsion, creating a modest attractive potential. However, the presence of a magnetic field can overcome the pairing energy and return the superconductor to the normal state. Thus superconductors are characterised by critical field as well as critical temperature. However, not only externally applied fields are effective; in a ferromagnet there is the internal field due to the ordered moments, while even in antiferromagnets or paramagnets there are local fields. It has therefore been pointed out, with justice, that magnetism and superconductivity are inimical to each other. Ginzburg [4] first pointed out that co-existence between superconductivity and ferromagnetism was impossible. In conventional superconductors, even a few percent of paramagnetic impurity atoms in the lattice are sufficient to suppress superconductivity [5]. The first compounds in which long range magnetic order and superconductivity both figured were discovered in the 1970s, with the ternary lanthanide Rh borides and Chevrel phases LnMo6 S8 [6, 7] On lowering the temperature the former first become superconducting (e. g. Tc2 is 8.9 K for the Er compound), but then return to the normal state (Tc2 ∼ 0.9 K in ErRh4 B4 ) when they become ferromagnetic. There is even a narrow temperature range just above Tc2 over which the two states co-exist, although the magnetic order is not collinear ferromagnetic, but sinusoidal [8, 9]. It is certainly significant that in both series of compounds the source of the magnetic moments is the 4f lattice of lanthanide ions, while the superconductivity comes from conduction bands formed mainly from the 4d orbitals of the transition metal. Any exchange interaction is undoubtedly very weak, because of the large distance between the two kinds of ion and small f–d orbital overlap. Similar considerations are likely to apply in the magnetic molecular charge transfer salts, where cations and anions are widely separated. One recent example of an oxide superconductor is even more spectacular: RuSr2 GdCu2 O8 has a layer structure reminiscent of the high temperature cuprate superconductors, with double CuO4 layers alternating with layers

108

4 Molecular Materials Combining Magnetic and Conducting Properties

of corner-sharing RuO6 octahedra interspersed with Gd and Ba. It becomes ferromagnetic at 132 K and superconducting at 40 K, without loss of ferromagnetism [10]. The astonishing lack of impact of the magnetic order on the superconductivity has been ascribed to a fortuitous effect of crystal symmetry, ensuring that nodes in the conduction electron density occur exactly at the magnetic centers. Several of the LnMo6 S8 phases become antiferromagnetic rather than ferromagnetic at low temperature, and in these cases the superconductivity is not suppressed [11, 12]. For example, Tc and TN are, respectively, 1.4 and 0.8 K for GdMo6 S8 . This is because the localised magnetic moments vanish when averaged over the scale of the superconductivity coherence length of around 100 Å. However, the critical field is influenced by the onset of long range antiferromagnetic order, being decreased below TN in LnMo6 S8 (Ln = Gd, Tb, Dy) but enhanced in SmRh4 B4 . The advantage of molecular materials compared to the extended inorganic solids is that the interactions between the two molecular networks can be made very weak, since the intermolecular contacts are of the Van der Waals type or hydrogen bonds. The drawback is the high difficulty in designing and crystallising such hybrid materials. The usual combination of a discrete magnetic anion with an oxidised organic donor may be appropriate to obtain a material exhibiting conductivity or even superconductivity, but the magnetic network will most probably behave as a paramagnet. A rational strategy to introduce ferromagnetism in the material is to use, as inorganic anion, an extended magnetic layer, as for example the bimetallic oxalato-complexes. However, this novel approach requires the formation of the layered network at the same time that the organic donor is oxidised. As we can imagine, the crystallisation of such a hybrid is not an easy task. Furthermore, even if one succeeds in getting crystals from such a combination, that does not guarantee the superconductivity in the organic network as no control on the packing and oxidation state of the donor is possible. Thus, the design of such materials remains a chemical challenge.

4.2.2

Exchange Interaction between Localised Moments and Conduction Electrons

The second point of interest arises from the interaction between the two networks as it may result in an exchange coupling between the localised magnetic moments through a mechanism that resembles the so-called RKKY-type of exchange proposed in the solid state to explain the magnetic interactions in transition and rare-earth metals and alloys [13]. This kind of indirect interaction is of long range, in contrast to the superexchange one, and presents an oscillatory behavior which can give rise to ferro- or antiferromagnetic coupling, depending on the distance between the moments. In the lanthanide metals for example, the partially filled 4f shells give rise to strongly localised magnetic moments which do not have overlapping orbitals. Therefore, the spin coupling between these f-electrons occurs via

4.2 Interest of Conducting Molecular-based Magnets

109

the conducting electrons (mainly of s-type) which are strongly coupled with the f-electrons. Thanks to this intra-atomic f–s coupling, the f-electrons of a given site are able to strongly polarise the spins of the conduction electrons which are in the vicinity. This local polarisation leads to a modulation of the electron densities in the band which is different for the up and down spins. A second magnetic ion situated at a certain distance from this ion will be informed by the conduction electrons of its spin direction. As a result, these two localised magnetic moments will be coupled by an effective coupling Jind . The sign and magnitude of this indirect coupling is given by the following expression: 2 n 2 9π Jdir F (2kF R) (4.1) Jind = 2 EF N where Jdir is the direct interaction between localised and itinerant spins, Nn is the √ number of conduction electrons per magnetic site and kF = 2me EF / is the momentum of the electron at the Fermi level, EF (Fig. 4.2). Therefore, this indirect interaction is expected to be proportional to the direct interaction between localised and itinerant spins. Its strength decreases as 1/R 3 , where R is the distance between the magnetic sites, in the same way as a dipolar

Fig. 4.2. Oscillating exchange interaction with distance between two localised moments in the RKKY model.

110


interaction. Its sign is determined by the oscillating function F (x) which can give either ferromagnetic or antiferromagnetic coupling between the magnetic sites, depending on their separation R. The period for these oscillations depends on the concentration of conduction electrons, n, since in the free electron model kF = (3/8πn)1/3 . In molecular conductors containing discrete magnetic anions, an indirect exchange interaction between the magnetic moments via the conduction electrons is, in principle, possible. However, its strength is expected to be quite small as the direct interaction between the two networks via a coupling between the itinerant π-electrons and the d-electrons of the magnetic center, is also very weak. Still, the physics associated with this exchange interaction may differ in several aspects from that predicted by the RKKY model. Thus, the model assumes that the conduction electrons can be described by the free electron model. In molecular conductors this model is too crude as the electrons are strongly correlated; furthermore, these systems have low dimensional electronic structures. On the other hand, while in classical metals the direct interaction involves an intra-atomic coupling between the unpaired electrons of the metal (d or f) and the s-electron carriers, in the magnetic synthetic metals this interaction involves an intermolecular π–d coupling. These important differences justify the effort currently being devoted to preparing and physically characterising this novel type of molecular material. To conclude this section, it is worth mentioning that the association between cation-radicals and magnetic anions is not the only way to obtain molecular materials having conducting electrons and localised magnetic moments. Materials formed by a single network can also provide examples of this kind. An illustrative example is the compound [Cu(pc)]+0.33 [I− 3 ]0.33 (pc = phthalocyanine) [14, 15].

J s-d

J d-d

LOCAL MOMENTS

s-electron carriers

Fig. 4.3. Coupling between −0.33 . [Cu(Pc)]+0.33 (I− 3)

Cu2+

moments

in

4.3 Magnetic Ions in Molecular Charge Transfer Salts

111

The compound is a one-dimensional metal formed by columnar stacks of partially oxidised Cu(pc) units separated by a distance of 3.2 Å. The electron delocalisation occurs through the overlap between the π -molecular orbitals of aromatic rings of adjacent phthalocyanine molecules. The paramagnetic Cu(II) ions are embedded in this “Fermi sea” of itinerant electrons. Owing to the large Cu–Cu distance, the Cu2+ ions are expected to be magnetically uncoupled. However, coupling between the Cu2+ local moments (represented as Jd–d in Figure 4.3) of ca. 4 cm−1 has been detected by EPR, NMR and magnetic susceptibility studies. It has been proposed that such coupling occurs through the conduction electrons which are strongly coupled to the local magnetic moments (Jπ –d coupling).

4.3 Magnetic Ions in Molecular Charge Transfer Salts Over the last 15 years there have been many attempts to introduce magnetic centers into conducting molecular lattices by synthesising charge transfer salts with transition metal complexes as anions. Because of the great diversity of metals, ligands, connectivity and structure types it is difficult to present a unified picture of what has been accomplished, but since the primary interest in the present chapter concerns the magnetic species, the following sections are organised from the point of view of the metal-containing complexes. These may be monomeric with monoatomic or polyatomic ligands, discrete clusters or polymeric structures infinite in one or two dimensions. The different organic molecules used to form such hybrid organic/inorganic materials are summarised in Scheme 4.1.

4.3.1 4.3.1.1

Isolated Magnetic Anions Tetrahalo-metallates

Following the discovery of the first molecular charge transfer salts that behaved as superconductors, many attempts have been made to synthesise analogous compounds containing paramagnetic moments inside the lattice. The so-called Bechgaard salts [16] of TTF, TMTTF and TMTSF contain diamagnetic tetrahedral and octahedral anions such as [ClO4 ]− and [PF6 ]− so it was natural to seek examples with tetra- and hexa-halometallates. These examples are summarized in Table 4.1. The first such compound whose structure was determined, (TMTTF)[FeCl4 ], however, not only has a different stoichiometry from the 2:1 Bechgaard salts but a completely different packing of the donor molecules, which form stacks but with alternate long axes orthogonal and no significant interaction between them, although there are several S· · ·Cl contacts of less than the sum of the van der Waals radii [17].

Electrical Properties

β donor layers; MnCl4 layers semiconductor (σRT = 25 S cm−1 ; Ea = 0.04 eV)

PM = Paramagnetic; AFM = antiferromagnetic

(BEDT-TTF)3 [MnCl4 ]2

semiconductor (σRT = 0.5 S cm−1 )

(BEDT-TTF)[CoCl4 ]0.3–0.4 No structure

semiconductor (σRT = 15 S cm−1 ; Ea = 0.1 eV)

semiconductor (σRT = 0.15 S cm−1 ; Ea = 0.2 eV) semiconductor (σRT = 0.15 S cm−1 ; Ea = 0.2 eV)

semiconductor (σRT = 0.17 S cm−1 ; Ea = 0.12 eV) semiconductor

semiconductor (σRT = 0.5 S cm−1 )

No structure

Stacks of donor tetramers; anions in pairs Stacks of donor tetramers; anions in pairs TTF trimers and monomers; isolated anions Same as Mn salt

Orthogonal linear stacks; insulator (σRT > 10−5 S cm−1 ) isolated anions Two independent linear stacks, – isolated anions

Packing

(BEDT-TTF)[MnCl4 ]0.3–0.4 No structure

(TTF)[MnCl3 ]∼0.75

(TTF)14 [CoCl4 ]4

(TTF)14 [MnCl4 ]4

(Perylene)3 [FeBr4 ]

(Perylene)3 [FeCl4 ]

(TMTSF)[FeCl4 ]

(TMTTF)[FeCl4 ]

Compound

AFM below 4 K; C = 4.2 emu K mol−1 θ = −7.5 K Dimers of FeCl− 4; J = −1.26 K Dimers of FeBr− 4; J = −3.72 K PM; C = 1.14 emu K mol−1 ; θ = −4 K PM; C = 0.657 emu K mol−1 ; θ = −4 K AFM Mn2+ chain C = 3.50 emu K mol−1 ; θ = −14 K PM; C = 1.30 emu K mol−1 ; θ = −1 K PM; C = 0.87 emu K mol−1 ; θ = −1.3 K –

PM; θ = −5 K

Magnetic Properties

Table 4.1. Structures and physical properties of charge transfer salts containing tetra- and hexa-halogeno-metallate anions.

39

38

38

36

36,37

36,37

27

27

19

17

Ref.

112 4 Molecular Materials Combining Magnetic and Conducting Properties

α-stacked layers; planar CuBr2− 4 non-planar TTMTTF2+ λ donor stacks; anions layers κ donor stacks; anions layers κ donor stacks; anion layers 2 types of donor layers; isolated anions

(BEDT-TTF)3 [CuBr4 ]

(TTMTTF) [CuBr4 ] (BETS)2 [FeCl4 ]

(BETS)2 [FeCl4 ] (BETS)2 [FeBr4 ] (BET-TTF)2 [FeCl4 ]


Layers of dimerised stacks; layers of anions Donors dimerised; no stacks (BEDT-TTF)[FeBr4 ] (BEDT-TTF)3 [CuCl4 ]·H2 O Layers of stacked trimerised donors; layers of anions Layers of stacked trimerised (BEDT-TTF)3 [NiCl4 ]·H2 O donors; layers of anions (BEDT-TTF)2 [ReCl6 ]·C6 H5 CN Layers of a-stacked donors; layers of ReCl6 and C6 H5 CN 3D lattice of donor dimers and (BEDT-TTF)2 [IrCl6 ] anions

(BEDT-TTF)2 [FeCl4 ]

Packing

Compound


20 40

PM PM –

PM; C = 1.10 emu K mol−1 ; 57 θ = −0.14 K 57 PM; C = 0.234 emu K mol−1 ; θ = −0.37 K

insulator metal metal–insulator transition 100 K semiconductor (σRT = 3 S cm−1 ; Ea ∼ 0.07–0.15 eV) semiconductor (σRT = 10−2 S cm−1 ; Ea = 0.23 eV)

54

35 34 42

55 28

49,55

Ref.

20

Magnetic Properties

semiconductor (σRT = 0.25 Scm−1 ; AFM; Ea = 0.07 eV) C = 2.77 emu K mol−1 θ = −140 K; 1st order transition 59 K −10 −1 insulator (σRT = 10 S cm ) PM; θ = −0.5 K metal–insulator transition 8.5 K; AFM; TN = 8.5 K superconducting > 3.2 kbar superconducting: Tc = 0.1 K AFM; TN = 0.45 K superconducting: Tc = 1.1 K AFM; TN = 2.5 K metal–insulator transition ∼20 K PM; Fe· · ·Fe AFM dimers at low temperature (J = −0.22 K) semiconductor: Ea = 0.21 eV PM; θ = −4 K


4.3 Magnetic Ions in Molecular Charge Transfer Salts 113

114


Both this salt, and one containing [MnCl4 ]2− , are semiconductors and paramagnets with small negative Weiss constants. The corresponding Se salt (TMTSF)[FeCl4 ] was shown to contain two kinds of columnar stacks, one with the long molecular axes parallel, and the other orthogonal, as in the TMTTF salt [18]. Curiously, this structure was reported again, quite independently and without reference to the earlier work [19]. The magnetic properties are dominated by the Fe, with χT at room temperature reaching 4.2 emu K mol−1 (cf. 4.375 for S = 5/2). The [FeCl4 ]− are well isolated, though like the TMTTF salt, there are Se· · ·Cl close contacts. There is a small negative Weiss constant (−7.5 K) but significantly, the susceptibility becomes anisotropic below 4 K, suggesting the onset of antiferromagnetism [19]. The tetrahaloferrate(III) salts of the extended electron donor BEDT-TTF present a fascinating contrast [20]. Electrochemical synthesis under the same conditions yielded different chemical stoichiometries for the salts containing [FeCl4 ]− and [FeBr4 ]− . The structure of (BEDT-TTF)2 [FeCl4 ] consists of dimerised stacks of BEDT-TTF molecules by the sheets of tetrahedral [FeCl4 ]− anions. The anions are situated in an ‘anion cavity’ formed by the ethylene groups of the BEDT-TTF molecules, which are arranged in the sequence · · ·XYYXXYYX· · · (Figure 4.4). Adjacent molecules of the same type (XX and YY ) stack uniformly on top of each other but with a slight displacement between neighbors along the long in-plane molecular axis. On the other hand, the long in-plane molecular axes of adjacent molecules of different type (XY and YX ) are rotated relative to one another. Furthermore, X and X (or Y and Y ) are closer to each other (≈ 3.60 Å) than X and Y (3.81 Å). The shortest distances between BEDT-TTF molecules are shorter than the sum of the van der Waals radii of two sulfur atoms (3.60 Å), thus suggesting the possibility of a quasi-one-dimensional interaction along the a direction. On the other hand, in (BEDT-TTF)[FeBr4 ], there are no stacks but planes of closely spaced BEDT-TTF, in marked contrast to most of the compounds containing this donor molecule. The only short S· · ·S distances ( 8 K) and the Bleaney–Bowers dimer model (T < 8 K).

124


TTF1.5+ )2 [IrCl]3− 6 ]. The formulation as an Ir(IV) salt is confirmed by the S = 1/2 Curie–Weiss magnetic behavior of the anion, combined with an exceptionally high intra-dimer exchange constant of 670 cm−1 , fitted with the Bleaney–Bowers model [48].

4.3.1.3

Pseudohalide-containing Anions

Apart from the high symmetry octahedral and tetrahedral halogeno-complexes of transition metals, a variety of other monomeric anions have been incorporated into charge transfer salts of TTF and its derivatives, in the search for combinations of conducting and magnetic properties. Some are complexes of pseudo-halide ligands such as CN− and NCS− , while others are of lower symmetry with mixed ligands (see Table 4.2). Among the latter are the first examples of long range ferrimagnetic order in an organic–inorganic charge transfer salt, where one of the sublattices is furnished by the pπ electrons of a molecular radical cation and the other by the delectrons of the transition metal complex anions. In a number of cases, the anions have been designed specifically to promote interaction between the organic and inorganic components of the lattice by building into them S atoms of the molecular donor. The first hexacyanometallate salt of TTF was formulated as (TTF)11 [Fe(CN)6 ]3 ·5H2 O, an unusual stoichiometry that indicates a particularly complex structure [59]. Eight of the TTF are present in dimerised stacks, and are assigned a charge of +1 from the bond lengths. The remaining ones have their molecular planes perpendicular to the stacks, two being neutral and the remaining one +1. Close contacts are indeed found between the [Fe(CN)6 ]3− and the TTF (N· · ·S 3.09 Å), but there is no report of cooperative magnetic properties, though the compound is a semiconductor. In contrast, BEDT-TTF salts with [M(CN)6 ]3− (M = Fe, Co, Cr) have more conventional structures with alternating layers of cations and anions. Thus β-(BEDT-TTF)5 [M(CN)6 ]·10H2 O (M = Fe, Co) have the β-packing mode, albeit with a pentamer rather than the more usual tetrameter repeat unit [60]. Both compounds are semiconductors, although apparently there is appreciable Pauli paramagnetism in the Co salt, suggesting the presence of conduction electrons. A further series, κ-(BEDT-TTF)4 (NEt4 )[M(CN)6 ]·3H2 O (M = Fe, Co, Cr) has κpacking mode, and at room temperature all the BEDT-TTF have the same charge of − +0.5, as found in the superconducting salts with diamagnetic anions I− 3 , Cu(NCS)2 , etc. [61]. Nevertheless, they are reported to be semiconducting in the neighborhood of room temperature. The magnetic susceptibility corresponds to the sum of contributions from the paramagnetic [Fe(CN)6 ]3− and the organic sublattice, with no evidence for interaction between them. At 140 K, a sharp drop in susceptibility arises from a charge disproportion among the dimers in the κ-structure, so that one consists of BEDT-TTF+ and another of neutral molecules. The spin susceptibility measured by EPR confirms the presence of the same transition in the isostructural

Packing


Dimerised Stacks orthogo- semiconductor nal monomers (σRT ≈ 10−3 S cm−1 ) β-donor packing; semiconductor (BEDT-TTF)5 [Fe(CN)6 ]·10H2 O pentamers (σRT ≈ 0.02 S cm−1 ) β-donor packing; semiconductor (BEDT-TTF)5 [Co(CN)6 ]·10H2 O pentamers (σRT ≈ 0.5 S cm−1 ) semiconductor (BEDT-TTF)4 NEt4 [Fe(CN)6 ]·3H2 O κ-donor layers (σRT ≈ 0.2 S cm−1 ) semiconductor (BEDT-TTF)4 NEt4 [Co(CN)6 ]·3H2 O κ-donor layers (σRT ≈ 10 S cm−1 ) semiconductor (BEDT-TTF)4 NEt4 [Cr(CN)6 ]·3H2 O κ-donor layers (σRT ≈ 0.15 S cm−1 ) β-donor packing semiconductor (BEST)4 [Fe(CN)6 ] (σRT ≈ 11 S cm−1 ; Ea = 0.025 eV) interpenetrated layers of semiconductor (BEST)3 [Fe(CN)6 ]2 ·H2 O cations 2+ and anions. (σRT ≈ 10−6 S cm−1 ) κ-donor layers semiconductor (BET-TTF)4 (NEt4 )2 [Fe(CN)6 ] (σRT ≈ 11.6 S cm−1 ; Ea = 0.045 eV) (BEDT-TTF)2 Cs[Co(NCS)4 ] α-donor layers metal-insulator transition at 20 K (σRT = 14 S cm−1 ) α-donor layers semiconductor (BEDT-TTF)4 [Cr(NCS)6 ]·PhCN (σRT ≈ 5 × 10−3 S cm−1 ; Ea = 0.26 eV) semiconductor (BEDT-TTF)5 NEt4 [Cr(NCS)6 ]·THF β-donor layers (σRT ≈ 10 S cm−1 )

(TTF)11 [Fe(CN)6 ]3 ·5H2 O

Compound

60 60

PM Pauli paramagnet

62,63

62,63 63

PM

PM PM

67,68 PM; C = 1.7 emu K mol−1 67,69 |D| = 7.3 cm−1

PM

60

PM

64

60

PM

PM; C = 1.3 emu K mol−1 60

59

Ref.

–

Magnetic Properties

Table 4.2. Structures and physical properties of charge transfer salts containing pseudohalide complex anions.


β-donor layers

(BEDT-TTF)5 [Cr(NCS)6 ]·(DMF)4



semiconductor (σRT ≈ 5 S cm−1 ) β-donor layers semiconductor (BEDT-TTF)5.5 [Cr(NCS)6 ] (σRT ≈ 2 S cm−1 ; Ea = 0.03 eV) Cation and anion layers semiconductor (BEDT-TTF)4 [Fe(NCS)6 ]·CH2 Cl2 (σRT = 7 × 10−3 S cm−1 ; Ea = 0.7 eV) orthogonal semiconductor (BEDT-TTF)4 [Fe(NCS)6 ]·(pip) dimers/monomers (σRT = 4.2 S cm−1 ; Ea = 0.25 eV) β-donor layers semiconductor (BEDT-TTF)5 NEt4 [Fe(NCS)6 ] (σRT = 4.0 S cm−1 ; Ea = 0.03 eV) (BMDT-TTF)4 [Cr(NCS)6 ] – – (BEDT-TTF)2 [Cr(NCS)4 (NH3 )2 ] Dimerised, donor layers; semiconductor anion layers (σRT = 30 S cm−1 ; Ea = 0.056 eV) (BEDT-TTF)2 [Cr(NCS)4 bipym]0.25H2 O No π -stacking of anions and semiconductor cations (σRT = 0.015 S cm−1 ; Ea = 0.3 eV) Donor dimers insulator (TMTTF)[Cr(NCS)4 phen] (TMTSF)3 [Cr(NCS)4 phen No close cation–anion semiconductor contacts (σRT = 0.022 S cm−1 ; Ea = 0.16 eV)

Packing

Compound


71

72 70

73

–

– PM

PM; C = 1.82 emu K mol−1 θ = −0.26 K AFM: TN = 3.0 K PM; C = 3.57 emu K mol−1 θ = −3.82 K

75 75

71

68,69

PM; |D| = 4.7 cm−1

70

69

PM; |D| = 2.8 cm−1

PM; C = 4.926 emu K mol−1 θ = −0.19 K –

Ref.

Magnetic Properties



127

salt with diamagnetic Co(CN)3− 6 as anion, indicating further that the anion plays little part [60]. Three different salts of [Fe(CN)6 ]3− with the organic donors BEST-TTF and BET-TTF (Scheme 4.1) have also been reported: β-(BEST-TTF)4 [Fe(CN)6 ], (BEST-TTF)3 [Fe(CN)6 ]2 ·H2 O and κ-(BET-TTF)4 (NEt4 )2 [Fe(CN)6 ] [62, 63]. In the 3:2 phase the structure shows an unusual interpenetration of the donor molecules and the anions. This fact may be due to the +2 charge of BEST-TTF (very unusual in any TTF-type donor and unprecedented with BEST-TTF). The magnetic properties of this salt correspond to the paramagnetic [Fe(CN)6 ]3− anions as the organic sublatice does not contribute. The 4:1 salt of the BET-TTF donor presents the typical alternating layers of anions and donors. The organic layers are formed by only one BET-TTF molecule, with a charge of 1/4, packed in a κ-phase. The room temperature conductivity is very high (11.6 S cm−1 ) although the thermal behavior shows that this salt is a semiconductor with a low activation energy of 0.045 eV. The high electron delocalisation of this salt is confirmed by the EPR studies on a single crystal that show a Dysonian line when the magnetic field is parallel to the organic layers [63]. Because specific non-bonding interactions between chalcogen atoms in neighboring molecules are such a common feature of the solid state chemistry of the Group 16 elements, one strategy for promoting interaction between cation and anion sublattices in TTF-type charge transfer salts is to incorporate Group 16 atoms in the anion, preferably in a terminal position. The most convenient ligand for this purpose is NCS− , which fortunately is bound to most transition metals through N. A salt of BEDT-TTF with tetrahedral [Co(NCS)4 ]2− has the α-packing motif [64], and is isostructural with the series of α-(BEDT-TTF)2 M[Hg(SCN)4 ] (M = NH4 , K, Rb), which has been much studied by physicists because of the interplay between superconducting and antiferromagnetic ground states [65, 66]. Nevertheless, the compound α-(BEDT-TTF)2 Cs[Co(NCS)4 ] is a metal, but undergoes a metal– insulator transition at 20 K, and in the crystal structure there are no close BEDTTTF· · ·SCN contacts. Such contacts are indeed found in several salts of BEDT-TTF prepared with the paramagnetic anions [Cr(NCS)6 ]3− and [Fe(NCS)6 ]3− . With the Cr(III) anion a 4:1 phase: (BEDT-TTF)4 [Cr(NCS)6 ]·PhCN, two 5:1 phases: β(BEDT-TTF)5 [Cr(NCS)6 ](DMF)4 and β-(BEDT-TTF)5 (NEt4 )[Cr(NCS)6 ](THF) and a 5.5:1 phase: β-(BEDT-TTF)5.5 [Cr(NCS)6 ] have been prepared. Curiously, this last phase is closely related to the two other 5:1 phases since the extra half BEDT-TTF molecule is located in the anion layer, replacing the solvent molecules of the other 5:1 phases [67]. All these salts are semiconductors with high room temperatures conductivities in the range 1–10 S cm−1 . The magnetic properties correspond to the sum of both sublattices with zero field splittings in the range 2.8– 7.3 cm−1 in the Cr(III) ion [68, 69]. With the Fe(III) anion two 4:1 phases: (BEDTTTF)4 [Fe(NCS)6 ]·CH2 Cl2 [70] and (BEDT-TTF)4 [Fe(NCS)6 ]·(piperidine) [71] and one 5:1 phase (BEDT-TTF)5 (NEt4 )[Fe(NCS)6 ] [71] have been prepared. The Cr(III) anion has also been used with the bis(methylene)dithio-TTF (BMDT-TTF)

128


donor in the salt (BMDT-TTF)4 [Cr(NCS)6 ] [72]. Most of these salts present short anion–cation S· · ·S contacts despite having a layer structure with alternating anions and cations. There are also close contacts between NCS groups on neighboring anions, but despite these features the Fe(III) compounds remain paramagnetic to 1.5 K (as the Cr(III) salts) with very small Weiss constant (−0.19 K in the (BEDTTTF)4 [Fe(NCS)6 ]·CH2 Cl2 salt). Of much greater interest from a magnetic point of view are charge transfer salts based on partially substituted pseudohalide complexes, of which the Reinecke’s anion trans-[Cr(NCS)4 (NH3 )2 ]− is a prototype. The salt of Reinecke’s anion itself, (BEDT-TTF)2 [Cr(NCS)4 (NH3 )2 ], which contains alternating layers of (BEDT-TTF)+ 2 and anions, has magnetic properties dominated by the latter [70], but again no transition to long range magnetic order above 2 K, despite the presence of several cation–anion S· · ·S contacts less that 4 Å. When the NH3 is replaced with an aromatic amine, however, the situation is transformed, because in favorable cases the planar amines form stacks with the donor cations, in addition to the S· · ·S cation–anion contacts. Under those circumstances bulk ferrimagnetic order is established, the first such case in charge transfer salts. That π–π cation–anion stacking is important for observing bulk magnetic order in this class of compound is demonstrated in a negative sense by the example of (BEDT-TTF)2 [Cr(NCS)4 (2,2 -bipyrimidine)]·0.25H2 O. Despite containing an aromatic amine the structure does not have any π-stacking of the cations and anions, although S· · ·S cation–anion contacts are present [73]. It is paramagnetic down to 2 K, with a very small Weiss constant (−0.26 K). The first ferrimagnetic charge transfer salts with a donor pπ and an anion 3d sublattice were based on the Reinecke’s anions with isoquinoline (C9 H7 N) as the base [74]. In this case the anion [M(NCS)4 (C9 H7 N)2 ]− (with M = Cr or Fe) has the trans-configuration. Charge transfer salts with 1:1 stoichiometry are formed with BEDT-TTF (M = Cr, Fe) and TTF (M = Cr), the bulk magnetic properties in every instance being classically those of a ferrimagnet, showing full long range order below a critical temperature Tc . The temperature dependence of χm T has a shallow minimum decreasing from a room temperature value close to that of donor spin SD = 1/2 and anion SA = 3/2 (for Cr3+ ). Below the minimum χm T rises rapidly towards saturation at Tc , after which χm remains constant so that χm T decreases linearly. Below Tc the isothermal magnetisation saturates at 2NµB for the Cr salt, corresponding to an antiferromagnetically alignment between SA and SD ; there is also a modest hysteresis. Typical magnetic data for these compounds are shown in Figure 4.12, and the magnetic parameters are listed in Table 4.3. When the isoquinoline is replaced by 1,10-phenanthroline, the anion necessarily has the cis-configuration, but TTF, TMTTF and TMTSF salts have also been obtained [75]. The TTF salt of [Cr(NCS)4 phen]− is a ferrimagnetic insulator with Tc = 9 K (IV in Table 4.3), while the TMTTF salt is an antiferromagnetic insulator (TN = 3 K). In both compounds there are close intermolecular contacts between


129

Fig. 4.12. Magnetic data for the ferrimagnetic salt (BEDTTTF)[Cr(NCS)4 (C9 H7 N)2 ]. (a) −1 verχm T (filled squares) and χm sus temperature T (the inset shows the minimum in χm T at 10 K); (b) magnetisation versus field (inset shows the hysteresis). Table 4.3. Magnetic parameters for ferrimagnetic charge transfer salts D[M(NCS)4 B2 ].

Tc /K χm T (at 330 K)/emu K mol−1 Minimum χ − mT /emu K mol−1 Minimum T /K Coercive field/Oe Remanent M/NµB Msat at 7 T /NµB I: II: III: IV:

D BEDT-TTF TTF BEDT-TTF TTF

M Cr Cr Fe Cr

B C9 H7 N C9 H7 N C9 H7 N phen

I

II

III

IV

4.2 2.26 1.7 9.9 338 0.42 2.0

8.9 2.18 0.99 16.9 75 0.74 2.1

4.5 4.75 3.97 14.8 18 0.38 4.3

9.0 2.22 1.2 17.5 ∼0 ∼0 1.7

Ref. 74 74 74 75

130


Fig. 4.13. Crystal structures of (a) (TTF)[Cr(NCS)4 phen]; (b) (TMTTF)[Cr(NCS)4 phen].

Fig. 4.14. Cation–anion π–π stacking in A[Cr(NCS)4 phen]; I, A = TTF; II, A = TMTTF.

the phenanthroline and the donor as well as S· · ·S contacts between the cations and anions. The difference in the bulk magnetic properties appears to be the result of the larger steric requirement of TMTTF, because the latter salt consists of dimerised cations while in the TTF one there are stacks of alternating cations and anions (Figure 4.13). The π -interaction between cations and anions is also disrupted in the TMTTF compound compared to the TTF one (Figure 4.14) [76].


4.3.2

131

Metal Cluster Anions

One strategy for exploring the subtle structure–property relationships in molecular charge-transfer salts by chemical means is to compare isostructural and isosymmetrical series. Furthermore, forming solid solutions could also help to achieve systematic variations of structure and properties, for which purpose it is of interest to identify anion types that facilitate chemical doping. In this respect, metal cluster anions show promise in forming extended isostructural series with TTF and BEDT-TTF. The anion size may be finely tuned by substituting the terminal and capping groups and, in addition, different solvent molecules may nest in the cavities between the cluster anions without greatly altering the structure of the anion layer. Finally, metal cluster salts are promising candidates for testing the feasibility of anion layer doping, since the effects of structural and electrostatic disorder are expected to be small when the dopant is embedded within a thick anion layer. Potential doping mechanisms include mixed solvents (with the additional possibility of including cations or anions in the cavity between the clusters) and mixed anions.

4.3.2.1

Dimeric Anions

In the quest for compounds exhibiting magnetic exchange interactions between metal ions situated within the anion layers, it is logical to look for groups that will bridge neighboring metal centers and transmit superexchange between them. Ambidentate ligands like NCS− and (C2 O4 )2− are simple examples, and we begin by mentioning a few charge transfer salts in which these ligands bridge discrete pairs of metals. The dimeric anion [Fe2 (C2 O4 )5 ]4− , which contains high spin FeIII ions bridged by one C2 O2− 4 has been incorporated in TTF [77], TMTTF [77] and BEDT-TTF [78] salts. In every case the magnetic behavior is dominated by the magnetic anion. In the TTF salt, which has the stoichiometry (TTF)5 [Fe2 (C2 O4 )5 ]·2PhMe·2H2 O, there are chains of donors surrouded by the dimeric anions and orthogonal TTF dimers while in the TMTTF salt (TMTTF)4 [Fe2 (C2 O4 )5 ]·PhCN·4H2 O there are segregated stacks of donors and anions in a “checkerboard” arrangement. In the BEDT-TTF salt (BEDT-TTF)4 [Fe2 (C2 O4 )5 ] there are closely spaced cation dimers, so that the overall structure resembles the “checkerboard” arrangement found in (BEDT-TTF)2 [Ge(C2 O4 )3 ]·C6 H5 CN [79]. The dimers of spin-paired monopositive cations therefore do not contribute to the magnetic properties, neither are there layers of alternating anions and cations. The antiferromagnetic exchange between the FeIII is quite comparable in magnitude to that found in other oxalate-bridged FeIII dimers. Likewise containing oxalate-bridged dimeric anions are (BEDTTTF)5 [MM (C2 O4 )(NCS)8 ] where MM is either CrFe or CrCr [80]. Here the presence of NCS− is especially noteworthy because of the opportunity it presents for cation–anion S· · ·S interactions. The latter compound does have a layer lattice of

132


alternating cations and anions, the former being related to (but crucially different from) the κ-arrangement of orthogonal dimers. In this case the dimers are interleaved by monomers, which are assigned charges close to zero by band structure calculations. In agreement with those calculations the compounds are semiconductors, albeit with relatively high room temperature conductivity and low activation energy. From the standpoint of magnetism, the principal features of interest is a ferromagnetic intradimer exchange interaction in the CrFe compound, leading to the S = 4 dimer ground state expected for S = 3/2 (Cr) and 5/2 (Fe). For the CrCr anion a metallic 8:1 phase with BEDT-TTF has also been reported: (BEDTTTF)8 [Cr2 (C2 O4 )(NCS)8 ] [81]. The room temperature conductivity for this salt is 0.1 S cm−1 and increases with decreasing temperature to reach a value of 1 S cm−1 at 180 K [81]. The magnetic properties are dominated by the antiferromagnetic behavior of the Cr–Cr dimer, as in the 5:1 phase. Dimeric anions containing only NCS− were first synthesised many years ago in the form of [Re2 (NCS)10 ]n− (n = 2, 3) [82]. The structures of their BEDT-TTF salts are quite different, although the anions themselves only vary slightly in geometry with changing charge [83]. The structure of the n = 3 compound consists of layers containing both cations and anions with several very short S· · ·S contacts between them, but no continuous network of closely interacting BEDT-TTF (Figure 4.15).

Fig. 4.15. The crystal structure of (BEDT-TTF)3 [Re2 (NCS)10 ] ·2CH2 Cl2 ; (a) along the BEDT-TTF long axes; (b) along the a-axis.


133

The total susceptibility is modelled best as the sum of Curie–Weiss and dimer contributions, the former attributed to the anions and the latter to one of the cations, whose spin remains impaired while those of the remaining two cations in the unit cell are paired. A special case of dimeric anion appears in the semiconducting salts (TTF)2 [Fe(tdas)2 ] and (BEDT-TTF)2 [Fe(tdas)2 ] (tdas = 1,2,5-thiadiazole-3,4dithiolate). The structures of both salts show the typical layered structure with dimerised chains in the anionic layer and β or α packings in the TTF [84] and BEDT-TTF [85] salts, respectively. Both salts are semiconductors with room temperature conductivities of 3 × 10−2 and 1 S cm−1 and activation energies of 0.18 and 0.10 eV, respectively. Due to the dimerisation of the [Fe(tdas)2 ]2− anions, the Fe(III) ion has a square pyramidal coordination. Therefore, it has an S = 3/2 ground spin state as has been confirmed by magnetic measurements and Mössbauer spectroscopy in the NBu+ 4 salt of this anion [86, 87]. The magnetic data for both salts are consistent with the formation of antiferromagnetic dimers (J /k = −154 K for the TTF salt and −99 K for the BEDT-TTF salt). In the BEDT-TTF salt besides the contribution of the Fe(III) dimers, there is a magnetic contribution from the BEDT-TTF molecules that have been reproduced with a model of interacting antiferromagnetic S = 1/2 chains [85]. There is also a 3:2 TTF salt with this anion although the structure is not known and the magnetic properties show a Curie type behavior, suggesting that in this case the anions are not dimerised [88]. 4.3.2.2

Polyoxometallate Clusters

Polyoxometallates (POMs) have been found to be extremely versatile inorganic building blocks for the construction of organic/inorganic molecular materials with unusual electronic properties. A general review that provides a perspective of the use of POMs in this area can be found in Ref. [89]. In the context of the present article, these bulky metal-oxide clusters possess several characteristics that have made them suitable and attractive as magnetic counter ions for new TTF-type radical salts in which localised and delocalised electrons can coexist: 1. They are anions that can be rendered soluble in polar organic solvents. 2. They can incorporate one or more magnetically active transition metal ions at specific sites within the cluster. 3. Their molecular properties, such as charge, shape and size, can be easily varied. In particular, it is possible to vary the anionic charge while maintaining the structure of the POM. A drawback of these bulky anions is that, although they often stabilise unusual new packing arrangements of the organic ions, their high charges tend to localise the charges of the organic sublattice, making it difficult to achieve high electrical conductivities and metallic behavior for these materials. All the known radical salts with magnetic POMs are based on the organic donor BEDT-TTF. The POMs used

134


Fig. 4.16. Types of magnetic polyoxometallates used as inorganic counter-ions for BEDT-TTFtype radical salts: (a) Non substituted α-Keggin anions [Xn+ W12 O40 ](8−n)− (X = CuII , CoII , FeIII ,. . .); (b) Mono-substituted α-Keggin anions [Xn+ Zm+ (H2 O)M11 O39 ](12−n−m)− (X = PV , SiI V ; M = MoV I , WV I ; Z = FeIII , CrIII , MnII , CoII , NiII , CuII ); (c) The Dawson–Wells anion [P2 W18 O62 ]6− ; (d) The mono-substituted Dawson–Wells anion [ReOP2 W17 O61 ]6− ; (e) The magnetic anions [M4 (PW9 O34 )2 ]10− (MII = Co, Mn).

to prepare these materials are depicted in Figure 4.16. The magnetic and electrical properties of these materials are summarized in Table 4.4.

Keggin anions α-Keggin anions of the type [Xn+ W12 O40 ](8−n)− (abbreviated as [XW12 ]; Figure 4.16(a)) were first combined with BEDT-TTF molecules to provide an extensive series of radical salts having the general formula (BEDT-TTF)8 [XW12 O40 ](solv)n (solv = H2 O, CH3 CN). Here, the central tetrahedral XO4 site may contain a diamagnetic heteroatom (2(H+ ), ZnII , BIII and SiI V ) [90, 91] or a paramagnetic one (CuII , CoII , FeIII ,. . . ) [91]. The compounds crystallise in two closely related structure types, α1 and α2 , consisting of alternating layers of BEDT-TTF molecules with an α packing mode, and the inorganic Keggin anions forming close-packed pseudohexagonal layers in the ac plane (Figure 4.17). In the organic layers there are three (α1 phase) or two (α2 phase) crystallographically independent BEDTTTF molecules which form two types of stacks: a dimerised chain and an eclipsed one. The shortest interchain S· · ·S distances, ranging from 3.46 to 3.52 Å, are significantly shorter than the intrachain ones (from 3.86 to 4.04 Å), emphasising the two-dimensional character of the packing. Another important feature of this structure is the presence of short contacts between the organic and the inorganic layers which take place between the S atoms of the eclipsed chains and some terminal O atoms of the polyoxoanions (3.15 Å), and via hydrogen bonds between the ethylene groups of the BEDT-TTF molecules and several O atoms of the anions (3.13 Å). From the electronic point of view, an inhomogeneous charge distribution in the organic layer was found by Raman spectroscopy, in which the eclipsed chain is formed by almost completely ionised (BEDT-TTF)+ ions, while the dimerised chain contains partially charged BEDT-TTFs. This charge distribution accounts for the electrical and magnetic properties of these salts. All of them exhibit semi-

Packing Layers of donors (α-packing) made of regular and dimerized stacks Layers of donors (α-packing) made of regular and dimerized stacks Layers of donors (α-packing) made of regular and dimerized stacks; Chains of polyoxometallates Layers of donors (β-packing)

Unknown

Compound

ET8 [MW12 O40 ] M = CoII , CuII , FeIII

ET8 [XW11 M(H2 O)O39 ] M = CoII , CuII , NiII , FeIII , CrIII ; X = PIII , SiIV

ET8 [PM11 Mn(H2 O)O39 ] M = W, Mo

ET11 [ReOP2 W17 O61 ]

ET6 H4 [M4 (PW9 O34 )2 ] M = CoII , MnII

Regular AF chains of BEDT-TTF alternating with dimerized AF chains in coexistence with paramagnetic manganese (II) ions

Semiconductors σRT = 0.1 S cm−1 Ea ∼ 100 meV

Insulator

Metallic. σRT = 11.8 S cm−1 ; M-I transition at ≈200 K. Ea = 27 meV

The magnetic behavior corresponds to that of the ferromagnetic CoII cluster or to the antiferromagnetic MnII cluster

Paramagnetic behavior coming from noninteracting Re ions (S = 1/2)

93

Regular AF chains of BEDT-TTF (J = −80 cm−1 ) alternating with dimerized AF chains (J = −280 cm−1 ), in coexistence with paramagnetic metal ions

Semiconductors; σRT = 0.15–0.03 S cm−1 Ea = 0.094–0.159 eV

96

94

93

91

Regular AF chains of BEDT-TTF (J = −60 cm−1 ) alternating with dimerized AF chains (J = −310 cm−1 ) in coexistence with paramagnetic metal ions

Semiconductors; σRT = 0.15–0.03 S cm−1 Ea = 0.094–0.159 eV

Ref.

Magnetic Properties


Table 4.4. Structures and physical properties of BEDT-TTF charge transfer salts containing polyoxometallate anions.


136


Fig. 4.17. (a) Structure of the radical salts (BEDT-TTF)8 [XW12 O40 ] showing the layers of Keggin polyoxoanions and the two types of chains, eclipsed and dimerized, in the organic layers; (b) Projection of the organic layer showing the structural relationship between the three crystallographic α-phases.

conducting behavior (σRT ≈ 10−1 –10−2 S cm−1 and Ea ≈ 100–150 meV), independent of the charge in the organic sublattice (see inset in Figure 4.18). As far as the magnetic properties are concerned, the localised electrons in the eclipsed chain (one unpaired electron per BEDT-TTF) account for the chain antiferromagnetism, and the delocalised electrons in the mixed-valence dimeric chain, account for the


0.014

137

14 12 10 L ρ n

0.012

8 6 4

0.010

2 2

3

4

5 6 7 1000/T (K-1)

8

9

0.008 0.006 0

50

100

150 T (K)

200

250

300

Fig. 4.18. Plot of the magnetic susceptibility (χm ) vs. T for the (BEDT-TTF)8 [BW12 O40 ] radical salt (filled circles). Open circles correspond to the corrected magnetic susceptibility (after subtracting a paramagnetic Curie-type contribution. Solid lines represents the best fit to a model that assumes an antiferromagnetic Heisenberg chain behavior (with J ∼ −30 cm−1 ; the exchange hamiltonian is written as −2J Si Sj ) for the eclipsed chain, and an activated magnetic contribution (with J ∼ −150 cm−1 ) coming from the dimeric chain. Inset: Semilogarithmic plot of the electrical resistivity ( cm) vs. reciprocal temperature.

presence of an activated magnetic contribution at high temperatures and for a Curie tail contribution at low temperatures (Figure 4.18). For those salts containing magnetic polyanions, the isolation of the magnetic center (situated in the central tetrahedral cavity of the Keggin structure) precludes any significant magnetic interaction with the organic spin-sublattice. In fact, the electron paramagnetic resonance (EPR) spectra show both the sharp signal of the radical cation and the signals associated with the paramagnetic metal ions. These salts represent the first examples of hybrid materials based on polyoxometallates in which localised magnetic moments and itinerant electrons coexist in the two molecular networks. A salt containing the one-electron reduced polyoxometallate [PMo12 O40 ]4− has also been reported [92]. It crystallises in the α1 structure, although some structural disorder has been found. From the electronic point of view, this compound may be of special interest as it contains delocalised electrons in the mixed-valence inorganic sublattice. However, the magnetic properties of this compound, in particular the EPR spectroscopy, indicate that these “blue” electrons do not interact with those of the organic sublattice. With the aim of bringing the magnetic moments localised on the Keggin polyanions closer to the π-electrons placed on the organic molecules monosubstituted

138


Keggin anions having one magnetic ion at the polyoxometallate surface have been used [93]. These are of the type [Xn+ Zm+ (H2 O)M11 O39 ](12−n−m)− (X = PV , SiI V ; M = MoV I , WV I ; Z = FeIII , CrIII , MnII , CoII , NiII , CuII , and ZnII ), (abbreviated as [XZM11 ]; Figure 4.16(b)). They can be considered as derived from the non-substituted Keggin anions [Xn+ M12 O40 ](8−n)− by simply replacing one of the external constituent atoms and its terminal oxygen atom by a 3d-transition metal atom, Z, and a water molecule, respectively. This series of the semiconducting BEDT-TTF radical salts maintains the general stoichiometry (8:1) and the structural characteristics of the previous family. In fact, most of them crystallise in the α2 structure (Z = FeIII , CrIII , CoII , NiII , CuII and ZnII ). However, an unexpected arrangement of the Keggin anions has been observed in the Mn derivatives (BEDT-TTF)8 [PMnII M11 O39 ] (M = W, Mo). Here a related structure namely α3 has been found in which the BEDT-TTFs are packed in the same way as in the other two phases, while the Keggin units are linked through a bridging oxygen atom in order to give an unprecedented chain of Keggin anions that runs along the c axis of the monoclinic cell (Figure 4.19). The organic stacking remains nearly unchanged for the three crystalline α-phases.

Fig. 4.19. Structure of the {(BEDT-TTF)8 [PMnW11 O39 ]}n radical salt showing the chains formed by the Keggin units.


139

The magnetic properties of this series are similar to those observed in those with non-substituted Keggin anions. No magnetic effects arising from the d–π interaction between these localised d-electrons and the itinerant π-electrons are detected down to 2 K, even though the two sublattices are closer than in the salts of the nonsubstituted Keggin anions. For example in the FeIII derivative the magnetic behavior shows a decrease in the magnetic moment on cooling, which must be attributed, as before, to antiferromagnetic interactions in the organic sublattice, approaching the behavior of isolated paramagnetic metal ions at low temperature (Figure 4.20(a)). On the other hand, 4 K EPR measurements show signals characteristic of the two sublattices in all cases: a narrow signal at g ≈ 2 with line width of 25–40 G arising from the BEDT-TTF radicals, plus broad signals that closely match those observed in the t-Bu4 N+ salts of the corresponding paramagnetic Keggin anions (Figure 4.20(b)). 6.0 BEDT-TTF NBu4

5.5

a

4.5

. . o

χm(T 1)

5.0

4.0 0

50

100 150 200 250 300 T (K)

b

BEDT-TTF

x10

x10 NBu4

0

2500 H (G) 5000

Fig. 4.20. Magnetic properties of the (BEDT-TTF)8 [SiFeIII (H2 O)Mo11 O39 ] compared to the tetrabutylammonium (NBu4 ) salt of the [SiFeIII (H2 O)Mo11 O39 ]5− anion: (a) Plot of the χmT product vs. T ; (b) Comparison between the EPR spectra performed at 4 K. In the spectrum of the ET salt we observe the coexistence of the signal associated with the radical (sharp signal centered at 3360 G, g = 2), with the low field signals coming from the FeIII ion (centered at 750 G (g = 8.9) and 1640 G (g = 4.1)).

140


The Dawson–Wells anion [P2 W18 O62 ]6− The Dawson–Wells anion [P2 W18 O62 ]6− has also been used to prepare radical salts. In this anion 18 WO6 octahedra share edges and corners leaving two tetrahedral sites inside, which are occupied by PV atoms. Its external appearance shows two belts of six octahedra capped by two groups of three octahedra sharing edges (Figure 4.16(c)). Electrochemical oxidation of BEDT-TTF in the presence of this polyanion leads to the new radical salt (BEDT-TTF)11 [P2 W18 O62 ]·3H2 O [94]. The structure of this compound consists of layers of anions and BEDT-TTFs alternating in the ac plane of the monoclinic cell (Figure 4.21(a)). Parallel chains of BEDTTTF molecules form the structural arrangement of the organic layer. The organic molecules of neighboring chains are also parallel, leading to the so-called β-phase (Figure 4.21(b)). What is remarkable in this structure is the presence of six crystallographically independent BEDT-TTF molecules (noted as A, B, C, D, E and F in Figure 4.21(c)) in such a way that each chain is formed by the repetition of groups of 11 BEDT-TTF molecules following the sequence . . .ABCDEFEDCBA. . . stacked in an exotic zigzag mode. These unusual structural features illustrate well the ability of polyoxometallates to create new kinds of packing in the organic component. But the most attractive characteristic of this salt concerns its electrical conductivity; it shows a metallic-like behavior in the region 230–300 K with an increase in

Fig. 4.21. (a) Structure of the radical salt (BEDT-TTF)11 [P2 W18 O62 ]·3H2 O showing the alternating organic and inorganic layers. (b) View of the organic layer showing the β-packing mode. (c) View of the organic stacking showing the six different BEDT-TTFs (A–F).


141

the conductivity from ca. 5 S cm−1 at room temperature to 5.5 S cm−1 at 230 K. Below this temperature the salt becomes semiconducting, with a very low activation energy value of 0.013 eV (Figure 4.22(a)). In view of this high conductivity, attempts to prepare a related compound containing a magnetic center on the surface of the Dawson–Wells polyanion have been carried out. As a result, a novel 12

a

σ (S . cm−1)

10

[ReOP2W17O61]6-

8 6 4

[P2W18O62]6-

2 0 0

b

50

100

100 K 50 K 40 K 30 K 25 K 20 K 15 K 10 K 4.5 K

1000 2000 3000 4000 5000 H (G)

150 T (K)

200

250

300

300 K 280 K 260 K 240 K 220 K 200 K 180 K 160 K 140 K 120 K 100 K 80 K 60 K 50 K 40 K 30 K 25 K 20 K 15 K 3300 3350 3400 3450 3500 H (G)

Fig. 4.22. (a) Thermal variation of the d.c. electrical conductivity σ for (BEDTTTF)11 [P2 W18 O62 ] · 3H2 O and (BEDT-TTF)11 [ReOP2 ReW17 O61 ] ·3H2 O showing the high conductivity at room temperature and the metallic behavior above 230 K; (b) EPR measurements at 4 K for the ReVI derivative.

142


compound that contains a rhenium(VI) ion replacing a W in the Dawson–Wells structure has been obtained ([ReOP2 W17 O61 ]6− , Figure 4.16(d)). It is isostructural with the non-magnetic one and its electrical properties are also very close to those observed in that compound (Figure 4.22(a)). From the magnetic point of view, no evidence of interactions between the two electronic sublattices has been observed, despite the fact that there are strong intermolecular anion–cation contacts. In fact, the magnetic properties have indicated the presence of the spin S = 1/2 of the ReVI , and EPR measurements show a spectrum very similar to that observed in the tetrabuthylammonium salt of the polyoxometallate (Figure 4.22(b)). This novel compound constitutes an illustrative example of a hybrid salt showing coexistence of a high electron delocalisation with localised magnetic moments.

The magnetic anions [M4 (PW9 O34 )2 ]10− (M = Co2+ , Mn2+ ) Polyoxometallates of higher nuclearities have also been associated with organic donors. Thus, the magnetic polyoxoanions [M4 (PW9 O34 )2 ]10− (M2+ = Co, Mn), which have a metal nuclearity of 22, give black powders with TTF [95] and crystalline solids with BEDT-TTF [96]. These polyoxoanions are of magnetic interest since they contain a ferromagnetic Co4 cluster or an antiferromagnetic Mn4 cluster encapsulated between two polyoxotungstate moieties [PW9 O34 ] (see Figure 4.16(e)). This class of magnetic systems is currently being investigated since polyoxometallate chemistry provides ideal examples of magnetic clusters of increasing nuclearities in which the exchange interaction phenomenon, as well as the interplay between electronic transfer and exchange, can be studied at the molecular level [97]. The electrochemical oxidation of BEDT-TTF in the presence of these magnetic anions affords the isostructural crystalline materials (BEDTTTF)6 H4 [M4 (PW9 O34 )2 ] which have four protons to compensate the charge. The six BEDT-TTFs are completely charged (+1) and the compounds are insulators. The magnetic properties of these salts arise solely from the anions. No influence coming from the organic component on the magnetic coupling within or among the clusters is detected down to 2 K. For example, in the Co derivative the χT product shows a sharp increase below 50 K upon cooling and a maximum at ca. 9 K, which is analogous to that observed in the K+ salt and demonstrates that the ferromagnetic cluster is maintained when we change K+ to BEDT-TTF+ . This also indicates a lack of interaction between the two components. This conclusion is supported by the EPR spectra performed at 4 K that show the same features for both salts: a very broad and anisotropic signal which extends from 1000 to 4000 G centered around 1620 G (g = 4.1) characteristic of the Co4 cluster. No signal from the organic radical is observed, indicating a complete pairing of the spins of the (BEDT-TTF)+ cations in the solid.


143

The two above compounds have demonstrated the ability of the high nuclearity polyoxometallates [M4 (PW9 O34 )2 ]10− to form crystalline organic/inorganic radical salts with the BEDT-TTF donor. As such, they constitute the first known examples of hybrid materials containing a magnetic cluster and an organic donor. To conclude this part we can say that the combination of magnetic polyoxometallates with TTF-type organic donors has witnessed rapid progress in the last few years. This hybrid approach has provided a variety of examples of radical salts with coexistence of localised magnetic moments with itinerant electrons. This is the critical step towards the preparation of molecular materials combining useful magnetic and electrical properties. Thus far, however, the weak nature of the cation/anion contacts as well as the low conductivities exhibited by most of the reported materials have prevented the observation of an indirect interaction between the localised magnetic moments via the conducting electrons.

4.3.3

Chain Anions: Maleonitriledithiolates

Planar metallo-complex anions of the type metal-bisdichalcogenelene tend to form one-dimensional packings in the solid state when they are combined with a suitable cation. In the context of the molecular conductors, the metalbismaleonitriledithiolates [M(mnt)2 ]− (M(III) = Ni, Cu, Au, Pt, Pd, Co and Fe) (Figure 4.23) have been combined with perylene (see Scheme 4.1) to form the charge-transfer solids Per2 M(mnt)2 . This organic molecule is one of the oldest donors used in the preparation of highly conducting solids. Due to the absence of any chalcogen atoms in the perylene molecule, all known charge-transfer salts based on this donor have a strong one-dimensional character, which is at the origin of the electronic instabilities exhibited by these salts. This feature contrasts with the two-dimensional layered structures adopted by the BEDT-TTF derivatives. A recent review that discusses the different perylene based compounds can be found in Ref. [98]. The structures and properties of the Per2 M(mnt)2 salts are summarised in Table 4.5. They are all essentially isostructural and show similar lattice parameters and diffraction patterns. In several cases (at least for M = Ni, Cu and Au) the crystals have been obtained in two distinct crystallographic forms denoted as α and β. The structure consists of segregated stacks of perylene and [M(mnt)2 ]− complexes running along the b axis. In the α-phase each stack of [M(mnt)2 ]− is surrounded

NC

S

S

CN

S

CN

M NC

S

Fig. 4.23. Metal-bismaleonitriledithiolate complexes [M(mnt)2 ]− (M(III) = Ni, Cu, Au, Pt, Pd, Co and Fe).

α-Per2 M(mnt)2 M = Ni, Cu

α-Per2 M(mnt)2 M = Au, Cu, Co

α-Per2 Fe(mnt)2

α-Per2 Ni(mnt)2


Magnetic Properties

Ref.

Segregated stacks of per and [Pt(mnt)2 ]− Metallic behavior along the stack- AF interactions between the spins 99, 100 complexes. Lattice distortion (tetrameriza- ing axis (σRT = 700 S cm−1 ) M–I S = 1/2 of the [Pt(mnt)2 ]− units tion of the per chain and dimerization of transition at Tc = 8.2 K (J ∼ −10 cm−1 ). the inorganic chain) below the metal-toχ vanishes below Tc

Packing

Metallic behavior along the stack- AF interactions between the spins 98 ing axis (σRT = 300 S cm−1 ) M–I S = 1/2 of the [Pd(mnt)2 ]− units transition at Tc = 28 K (J ∼ −50 cm−1 ). χ vanishes below Tc Same as Pt salt Metallic behavior along the stack- AF interactions between the spins 101, 102 ing axis (σRT = 700 S cm−1 ) M–I S = 1/2 of the [Ni(mnt)2 ]− units transition at Tc = 25 K (J ∼ −100 cm−1 ). χ vanishes below Tc Segregated stacks of per and [M(mnt)2 ]− Metallic behavior along the stack- AF interactions between the spins 98 complexes. Lattice distortion (tetrameriza- ing axis (σRT = 200 S cm−1 ) M–I S = 3/2 of the [Fe(mnt)2 ]− units tion of the per chain) observed below the transition at Tc = 58 K (J ∼ −150 cm−1 ). metal-to-insulator transition Same as Fe salt Metallic behavior along the stack- Weak Pauli paramagnetism that 100, 101, 102 ing axis (σRT = 700 S cm−1 for Au vanishes below Tc and Cu; 200 S cm−1 for Co); M–I transition at Tc = 12.2 K (Au), 32 K (Cu) and 73 K (Co) Segregated stacks of perylene and Semiconductors with Larger susceptibility than the α- 101, 102 [Pd(mnt)2 ]− complexes. Structural dis- (σRT = 50 S cm−1 ) phases. χ follows a T −α law with order in the perylene chains. α = 0.75 (Ni) and 0.8 (Cu) that suggest random exchange AF interactions in the perylene chains

insulator (M–I) transition α-Per2 Pd(mnt)2 Same as Pt salt

α-Per2 Pt(mnt)2

Compound

Table 4.5. Structures and physical properties of perylene charge transfer salts.



145

Fig. 4.24. The crystal structure of α-(Per)2 [M(mnt)2 ].

by six stacks of perylene molecules (Figure 4.24). The structure of the β-phase is probably similar, although a full structural refinement does not exist due to the presence of structural disorder. From the electronic point of view, the α-phase produced the first examples of one-dimensional molecular metals where delocalised electron chains coexist with chains of localised spins. In this respect it has been noticed that some of the properties of these compounds resemble those of Cu(Pc)I, a case where, as we have mentioned in the Introduction, the delocalised electrons belonging to the Pc chain interact with the paramagnetic Cu(II) ions. The properties of those derivatives containing the paramagnetic metal complexes (M = Ni, Pd and Pt and Fe) are listed in Table 4.5 and compared with those containing diamagnetic metal complexes (M = Au, Cu, Co). The α-compounds are highly conductive along the stacking axis b (∼700 S cm−1 for M = Au, Pt, Ni and Cu; ∼300 S cm−1 for M = Pd; and ∼200 S cm−1 for M = Fe and Co derivatives), showing a metallic regime at higher temperatures. They undergo metal-to-insulator (M–I) transitions at lower temperatures, associated with a tetramerisation of the conducting perylene chains (2kF Peierls transition) (Figure 4.25(a)). It is important to underline that the magnetic character of the [M(mnt)2 ]− chain does not affect the transport properties and the M–I transition occurs in the same way, irrespective of the paramagnetic or diamagnetic nature of the metal complex. As far as the magnetic properties are concerned, those compounds with S = 1/2 [M(mnt)2 ]− units (M = Pt, Pd and Ni) undergo a spin-Peierls dimerisation of the localised spin chains at the same critical temperature where the M–I transition of the perylene chain takes place. Such a dimerisation can be followed by the magnetic susceptibility. Thus, at temperatures well above the transition the susceptibility indicates antiferromagnetic exchange interactions within the chains with exchange constants of −15, −75 and −150 K for Pt, Pd and Ni derivatives, respectively. This paramagnetic contribution vanishes at the M–I transition (Figure 4.25(b)). The fact that a similar M–I transition also occurs in compounds with diamagnetic [M(mnt)2 ]− units indicates that the Peierls instabil-

146

a

4 Molecular Materials Combining Magnetic and Conducting Properties 10-2

Au α Pt α Pd α Ni α Fe α Co α Cu α

b 20

80 Pt

15 10-4

mu.mol -1

resistivity (Ω.m)

10-3

60 Ni

Pd

.

10

40 20

5

10-5

0

0 0

10-6 3

10

30 100 T (K)

50

100

300

150 T (K)

200

250

300

Fig. 4.25. Transport and magnetic properties of the α-(Per)2 [M(mnt)2 ] (M(III) = Ni, Pt, Pd) hybrids.

ity in the perylene chain is the dominant one and the that spin-Peierls transition in the dithiolate chain is triggered by the perylene chain distortion. The existence of an electronic coupling between the two kinds of chains is still controversial. Clearly, the above picture does not require the presence of any exchange interaction between the itinerant electrons and the localised spins, since the structural distortion in the perylene chains can be sufficient to induce the dimerisation in the dithiolate chains. However, there are features in the EPR spectra that suggest the presence of fast spin exchange between the two sublattices [99]. An additional insight is provided by the proton NMR spin–lattice relaxation time in the Au and Pt compounds which is indicative of a coupling of the proton spins of the perylene molecules to the localised spin in the Pt compound [100]. The β-compounds containing the diamagnetic Cu complex and the paramagnetic Ni complex have also been reported [101]. Both are semiconductors with an electrical conductivity at room temperature in the range 50–80 S cm−1 , that is relatively high for semiconductors. They exhibit a significantly larger magnetic susceptibility than the α-phases. Independently of the magnetic character of the metal complexes, both follow a T −α behavior with α < 1, which is typical of a random exchange antiferromagnetic chain. This similarity suggests that the structural disorder of this phase is essentially associated with the perylene cations [102].

4.3.4

Layer Anions: Tris-oxalatometallates

Over the last few years numerous examples have been found of two-dimensional bimetallic layers containing dipositive cations, MII , and tris-Oxalatometallate (III) anions, [MIII (C2 O4 )3 ]3− , in which the oxalato-ion acts as bridging ligand, forming


147

infinite sheets of approximately hexagonal symmetry, separated by bulky organic cations [103, 104]. In view of the unusual magnetic properties of these compounds, the synthesis of compounds containing similar anion lattices but interleaved with BEDT-TTF molecules has been explored. A number of such compounds have been characterised to date, and they prove to have a rich variety of structures and properties. The first series is (BEDT-TTF)4 [AM(C2 O4 )3 ]·solvent (Table 4.6) (A+ = H3 O, K, NH4 ; M(III) = Cr, Fe, Co, Al; solvent = C6 H5 CN, C6 H5 NO2 , C5 H5 N) [105–108]. While the stoichiometry is the same in all the compounds, the structures fall into two distinct series with contrasting physical properties. One which is orthorhombic (Pbcn) is semiconducting with the organic molecules present 0 as (BEDT-TTF)2+ 2 and (BEDT-TTF) , while the other, which is monoclinic (C2/c) has BEDT-TTF packed in the β arrangement [105] and is the first example of a molecular superconductor containing a lattice of magnetic ions [109]. The crystal structures of both series of compounds consist of alternate layers containing either BEDT-TTF or [AM(C2 O4 )3 ]·solvent. The anion layers contain alternating A and M forming an approximately hexagonal network (Figure 4.26). The M are octahedrally coordinated by three bidentate oxalate ions, while the O atoms of the oxalate which are not coordinated to Fe form cavities occupied either by A. The solvent molecules occupy roughly hexagonal cavities in the [AM(C2 O4 )3 ] lattice. Chirality is a further unusual feature of the anion layers. The point symmetry of [M(C2 O4 )3 ]3− is D3 , and the ion may exist in two enantiomers. In the monoclinic superconductors alternate anion layers are composed exclusively of either one or

Fig. 4.26. Schematic view of the anion layer in (BEDT-TTF)4 [AM(C2 O4 )3 ] ·solvent (solvent = C6 H5 CN).

Fe

Co Al Cr

Cr

Fe

Cr

Fe

Fe

Cr

Cr

NH4 NH4 H3 O

H3 O

H3 O

H3 O

H3 O

H3 O

H3 O

Mn

–

CH2 Cl2

C 5 H5 N

C6 H5 NO2

C6 H5 NO2

C6 H5 CN

C6 H5 CN

C6 H5 CN C6 H5 CN C6 H5 CN

C6 H5 CN

Same as above; 1/4 donors disordered Same as above; 1/4 donors disordered β-donor stacks; bimetallic Mn(II)Cr(III) anion layers

Same as above

Same as above

β donor layers anion layers Same as above

Same as above Same as above Same as above

Layers of pseudo-κ donors anion layers Same as above

PM FM (Tc = 5.5 K)

metal (σRT = 250 S cm−1 )

PM

PM

metal–insulator transition at 200 K

superconductor (Tc = 6 K; Hc = 100 Oe) superconductor (Tc = 8.3 K; Hc = 500 Oe) superconductor (Tc = 6 K; Hc = 100 Oe) superconductor (Tc = 4 K; Hc = 50 Oe) metal–insulator transition at 116 K

PM: C = 4.37 emu K mol−1 θ = −0.11 K PM: C = 4.44 emu K mol−1 θ = −0.25 K DM DM PM: C = 1.73 emu K mol−1 θ = −0.88 K PM: C = 1.96 emu K mol−1 θ = −0.27 K PM: C = 4.38 emu K mol−1 θ = −0.2 K PM

K

C6 H5 CN

semiconductor (σRT = 2 × 10−4 S cm−1 , Ea = 0.140 eV) semiconductor (σRT = 10−4 S cm−1 Ea = 0.141 eV) semiconductor (Ea = 0.225 eV) semiconductor (Ea = 0.222 eV) semiconductor (Ea = 0.153 eV)

Fe

117

108

107

114

114

105

119

106 106 106

105

105

Ref.

NH4

Magnetic Properties

M

A


Table 4.6. Structures and physical properties of charge transfer salts containing tris oxalato-metallate anions: (BEDT-TTF)n [AM(C2 O4 )3 ]· Solvent.

Packing


Solvent

148


149

the other, while in the orthorhombic semiconductors the enantiomers are arranged in alternate columns within each layer. Although the anion layers are very similar, the molecular arrangements in the BEDT-TTF layers are quite different in the orthorhombic and monoclinic series. In the monoclinic phases there are two independent BEDT-TTF, whose central C=C bond lengths differ markedly, indicating charges of 0 and +1. The +1 ions occur as face-to-face dimers, surrounded by monomeric neutral molecules (Figure 4.27). Molecular planes of neighboring dimers along [011] are oriented nearly orthogonal to one another, as in the κ-phase structure of (BEDT-TTF)2 X [110], but the planes of the dimers along [100] are parallel. This combination of (BEDT-TTF)2+ 2 surrounded by (BEDT-TTF)0 has also been observed in a BEDT-TTF salt with the polyoxometallate β-[Mo8 O26 ]4− [111]. The (BEDT-TTF)0 describe an approximately hexagonal network, while the (BEDT-TTF)2+ 2 are positioned near the oxalate ions, with weak H-bonding between the terminal ethylene groups and oxalate O. Packing of the BEDT-TTF in the C2/c salts is quite different: there are no discrete dimers but stacks with short S· · ·S distances between them, closely resembling

Fig. 4.27. Packing of the BEDT-TTF in the orthorhombic series (BEDTTTF)4 [AM(C2 O4 )3 ]·solvent.

150


Fig. 4.28. Packing of the organic layers in the monoclinic series (BEDTTTF)4 [AM(C2 O4 )3 ]· solvent showing the β -structure.

the β -structure in metallic (BEDT-TTF)2 [AuBr2 ] [112] and the pressure-induced superconductor (BEDT-TTF)3 Cl2 ·2H2 O [113] (Figure 4.28). While the orthorhombic salts are semiconductors, the monoclinic ones are metals with conductivity of ∼102 S cm−1 at 200 K, the resistance decreasing monotonically by a factor of about 8 down to temperatures between 7–8 K [105] (A = H3 O+ ; M = Fe; solvent = C6 H5 CN) and 3 K [114] (A = H3 O; M = Cr; solvent = C6 H5 NO2 ) where they become superconducting (Figure 4.29(a)). In line with their contrasting electrical behavior the magnetic properties of the two series are also quite different. The susceptibilities of the semiconducting compounds obey the Curie–Weiss law from 2 to 300 K with the M dominating the measured moment. In particular, there is little contribution from the BEDT-TTF, including those molecules whose bond lengths suggest a charge of +1. Hence the (BEDT-TTF)2+ 2 are spin-paired in the temperature range studied (the singlet– triplet energy gap is expected to be >500 K), while the remaining BEDT-TTF do not contribute to the paramagnetic susceptibility, in agreement with the assignment of zero charge. On the other hand, the superconducting salts obey the Curie–Weiss law from 300 to about 1 K above Tc , though with a temperature independent paramagnetic contribution. The measured Curie constants are close to that predicted for M3+ (Cr, Fe), while the Weiss constants (−0.2 K) signify very weak antiferromagnetic exchange between the M(III) moments. However, there is a strong diamagnetic contribution in the superconducting temperature range, returning to Curie–Weiss behavior above 10 K (Figure 4.29(b)). Whilst the EPR spectrum of the semiconducting A = K, M = Fe compound consists of a single narrow resonance,


151

Fig. 4.29. Temperature dependence of (a) the resistivity; and (b) the magnetic susceptibility; of β -(BEDT-TTF)4 [(H3 O)Fe(C2 O4 )3 ]·C6 H5 CN. In (b) the susceptibility of (BEDTTTF)4 [KFe(C2 O4 )3 ]C6 H5 CN is also shown.

that of the A = H3 O, M = Fe compound consists of two resonances: a narrow one assigned to the Fe(III) by analogy with the A = K compound, and a much broader resonance from the conduction electrons. This situation is reminiscent of that found in (BEDT-TTF)3 [CuCl4 ]·H2 O [43]. In the series (BEDT-TTF)4 [AM(C2 O4 )3 ]·solvent, the lattice appears to be stabilised by molecules included in the hexagonal cavities. The oxalato-bridged net-

152


work of A and M provides an elegant means of introducing transition metal ions carrying localised magnetic moments into the lattice of a molecular charge transfer salt. In the case of the A = H3 O, M = Fe compound, it led to the discovery of the first molecular superconductor containing localised magnetic moments within its structure, while the A = K, NH4 compounds are semiconducting. Clearly, it would be advantageous to incorporate other transition metal ions at the A site to create a two-dimensional magnetically ordered array between the BEDT-TTF layers as well as introducing a wider range of metal ions. A first step towards building such an array produced a salt containing alternating layers of TTF and a trinuclear anion containing a central Mn(II) with trans-oxalate-bridges to two Cr(III). The salt (TTF)4 Mn(H2 O)2 [Cr(C2 O4 )3 ]2 14H2 O contains strongly dimerised TTF+ and hence is not metallic. This compound exhibits an unprecedented packing in the TTF layer similar to a κ-phase, although the interdimer distances are different in the two directions. Its magnetic susceptibility is nicely fitted by a Heisenberg exchange model for a linear trimer [115]. Quite similar compounds occur for all the combinations of MII = Mn, Fe, Co, Ni, Cu; MIII = Cr, Fe [116]. The only known salt of TTF with tris-oxalatometallates is a 7:2 phase formulated as (TTF)7 [Fe(C2 O4 )3 ]2 ·4H2 O where the TTFs are packed in chains surrounded by four orthogonal dimers of TTF molecules and four paramagnetic [Fe(C2 O4 )3 ]3− anions [77]. The goal of creating a magnetically ordered array between the BEDT-TTF layers has recently been reached by the synthesis of a BEDT-TTF salt containing both Mn(II) and Cr(III) in the oxalate layer [117]. The compound β-(BEDTTTF)3 [MnCr(C2 O4 )3 ] has a structure related to the paramagnetic superconductors above, but with Mn(II) replacing H3 O+ within the honeycomb anion layer and without incorporating molecules inside the hexagonal cavities. Furthermore, the anion layer is orientationally disordered with respect to the BEDT-TTF layer in which the molecules adopt a roughly hexagonal arrangement with face-to-face stacks in the β-packing mode (Figure 4.30). Having two-dimensionally infinite layers of Mn and Cr bridged by oxalate ions, the compound behaves as a ferromagnet, with Tc of 5.5 K (Figure 4.31(a)), similar to A[MnCr(C2 O4 )3 ] salts where A is a tetra-alkylammonium cation [103]. The saturation magnetisation and coercive field are also similar. In dramatic contrast to the latter, however, which are insulators, the BEDT-TTF salt is a metallic conductor, remaining so down to 2 K without becoming superconducting (Figure 4.31(b)). It remains to be seen to what extent the properties of this remarkable compound can be modified by further fine tuning of the lattice through varying the metal ions, or by generating structures containing other donor packing arrangements more commonly associated with superconductivity in BEDT-TTF salts, such as β or κ. Several new conducting molecular magnets with either [MnCr(C2 O4 )3 ]− or [CoCr(C2 O4 )3 ]− layers and the donors BEDT-TTF, BEST, BETS and BET-TTF (Scheme 4.1) have also been prepared. In the MnCr derivatives the critical temperature is 5.5–6.0 K while in the CoCr ones it is 9–10 K [118].

4.4 Conclusions

153

Fig. 4.30. Packing of (a) the [MnCr(C2 O4 )3 ]− ; (b) the BEDT-TTF; (c) the organic and inorganic layers, in (BEDT-TTF)3 [MnCr(C2 O4 )3 ].

4.4 Conclusions It is clear from this chapter that compounds containing electron donor molecules of the kind that form molecular metals and superconductors can be synthesised with a wide variety of transition metal-containing anions, which introduce localised magnetic moments into the lattice. Correspondingly, whilst many of the compounds consist of alternating layers containing cations and anions alone, they are formed with many different packing motifs of the donor cations. Insulators, semiconductors, metals and superconductors are all represented. Examples also exist where the anions interact with the cations through weak H-bonds, S· · ·S contacts shorter than the Van der Waals distance or π · · ·π stacking contacts. Nevertheless, in the large majority of cases it is fair to say that experimental evidence for exchange interactions between donor π - and metal d-electrons, or metal d-electrons via a delocalised donor π-system, is difficult to identify. Exceptions are (BEDT-TTF)3 CuBr4 [49], (BET-TTF)2 [FeCl4 ] [42] and κ-(BETS)2 FeCl4 [34, 35], but the change in conductivity of the latter when the Fe(III) moments order antiferromagnetically could well be due to magneto-striction. Whilst it is possible, too, that the failure of the

154


30

2.0

25 1.5 20 1.0

15 10

0.5

5 0.0

0 2

3

4

5 T (K)

6

7

8

8 6 4 2 0 -2 -4 -6 -8 -4

-2

0 H (T)

2

4

200

250

0.005 3.0 H=0 H = 1.5 T

0.004 2.9 2.8

0.003 2.7 0.002 2.60

5

10

15

0.001 0.000 0

50

100

150 T (K)

300

Fig. 4.31. Transport and magnetic properties of the (BEDT-TTF)3 [MnCr(C2 O4 )3 ] showing the coexistence of metallic conductivity and ferromagnetism.

4.4 Conclusions

155

metallic compound (BEDT-TTF)3 [MnCr(C2 O4 )3 ] to become superconducting at low temperature may be the result of ferromagnetic order in the anion layer, there is no unambiguous evidence that this is the case [117]. It is true that in those salts where S· · ·S and π · · ·π stacking interactions occur between cations and anions, transitions to long range ferromagnetic order occur, with one sublattice being furnished by the cation π- and the other by the anion d-orbitals. However, in that case the interactions are strong enough to break up the donor cation layers and, since cations and anions are interdigitated, the resulting compounds are semiconductors or insulators. Nevertheless, a rich harvest of novel molecular materials has emerged, such as paramagnetic and antiferromagnetic superconductors, a ferromagnetic metal and ferromagnetic semiconductors. No doubt further synthetic ingenuity will uncover more novelty in the future.

Acknowledgment Financial support of the Spanish Ministerio de Ciencia y Tecnolog´ıa (Grant MAT98-0880) and the European Union (TMR Network on Molecular Magnetism. From Materials to Devices) are acknowledged. The writing of this article was greatly facilitated by discussions with partners within the EC COST D14 003/99 Action. Peter Day thanks the IBERDROLA Foundation for a Visiting Professorship at the University of Valencia, during which this chapter was written. He is also grateful to colleagues in the University of Valencia for their warm welcome.

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4.4 Conclusions 114. 115. 116. 117. 118. 119.

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5 Lanthanide Ions in Molecular Exchange Coupled Systems Jean-Pascal Sutter and Myrtil L. Kahn

5.1 Introduction Molecular coordination compounds of rare earth ions attract increasing interest in material science due to their luminescence and magnetic properties. As far as the magnetic properties are concerned, the rather large and anisotropic moments of most of the lanthanide ions make them appealing building blocks in the molecular approach to magnetic materials. As early as 1976, Landolt et al. [1] used Ln(III) ions for the preparation of a series of Prussian blue analogs which exhibited magnetic ordering and magnetic anisotropy with rather large hysteresis loops. Since, numerous compounds containing a Ln ion associated with paramagnetic species such as transition metal ions or organic radicals have been described [2, 3]. However, with the exception of the 4f 7 ion Gd(III) which has a spin-only ground state, examples of molecular multi-spin systems involving Ln(III) ions are scarce and more generally the magnetic interaction involving Ln ions remains rather poorly understood. The aim of this chapter is to provide general information on the magnetic behavior of molecular compounds where a Ln ion is in exchange interaction with another spin carrier. Special attention is devoted to the Ln ions with a first orbital momentum. But before considering such compounds and how recent advances permit one to gain some insight into their magnetic interactions, it might be worth recalling some generalities concerning the 4f elements.

5.1.1

Generalities

The electronic configuration of the rare-earth elements is (Xe)4fn 5d1 6s2 and the 14 elements of the series differ by a progressive filling of the f orbitals. In molecular compounds, lanthanide ions are generally trivalent but for some elements a divalent (Sm, Eu, and Yb) or a tetravalent (Ce) state can be stable when 4f0 , 4f7 or 4f14 configurations are attained. The coordination number for a Ln(III) ion may vary from 3 to 12 and strong chemical similarity is found along the Ln series. Such behavior underlines the poor participation of f orbitals in chemical bonds. For a

162

5 Lanthanide Ions in Molecular Exchange Coupled Systems

given ligand set, the difference in coordination number or geometry for a compound of a Ln(III) ion from the beginning of the series as compared to one from the end of the series is mainly due to the decrease in the ionic radii with the atomic number. This contraction as electrons are added across the series reflects the inner nature of the 4f orbitals. For the trivalent Ln series, all ions contain unpaired electrons and, consequently, are paramagnetic, excluding La(III) (4f0 ) and Lu(III) (4f14 ) for which the 4f shell is, respectively, empty or filled. For the Ln ions the orbital contribution is not quenched, as is the case for some 3d ions for instance, interaction between the spin angular momentum and the orbital angular momentum takes place. As a consequence of this spin–orbit coupling, J, the quantum number associated with the total angular momentum defined in Eq. (5.1), becomes a good quantum number to describe the paramagnetism of a Ln ion. The expression allowing one to calculate the value of χLn T for the free ion, where χLn stands for the molar magnetic susceptibility for a Ln ion and T for the temperature, is given in Eq. (5.2). The calculated value is usually in good agreement with the room temperature value of χLn T found experimentally for paramagnetic Ln compounds without exchange interactions. In this expression, N is the Avogadro number, k the Boltzmann constant, β the Bohr magneton, and gJ the Zeeman factor given by Eq. (5.3). The value taken by J in the ground state for the ions with a less than half-filled f-shell (f1 –f6 ) is given by J = L − S whereas it is J = L + S for those with a more than half-filled shell (f8 –f13 ). J=L+S χLn T =

(5.1)

NgJ2 β 2 J(J + 1) 3k

gJ = 1 +

(5.2)

J(J + 1) − L(L + 1) + S(S + 1) 2J(J + 1)

(5.3)

The symbol S corresponds to the spin quantum number and L represents the orbital quantum number of the Ln ion. The values taken by S and L depend on the number of unpaired electrons displayed by the ion. For instance, for Dy(III) which has a 4f9 configuration, the distribution of the nine electrons into the f orbitals following Hund’s rules leads to five unpaired electrons (Figure 5.1). Consequently, for this ion S = 5/2 and L = 5 (L = −1+0+1+2+3) yielding an angular momentum number J = L + S = 15/2. The same S and L values are found for Sm(III) which has 4f5 configuration, but for this ion the angular quantum number is J = L − S = 5/2. As l

-3

-2

-1

Dy(III): 4f 9

0

1

S = 5/2 L=5 J = 15/2

2

3

Fig. 5.1. 4f-shell filling for Dy(III) and S and L values associated with the 4f9 configuration.

5.1 Introduction

163

a general trend, the magnitude of the spin–orbit coupling for the Ln ions is larger than for the 3d ions, and increases from the left to the right of the f-series. This orbital contribution and the ligand field have a dramatic effect on the magnetic properties. For the Ln ions displaying spin–orbit coupling the Curie law does not apply. For such an ion the 4fn configuration is split by inter-electronic repulsion, in spectroscopic terms, the one with the highest spin multiplicity (2S + 1) is the lowest in energy. Each of these terms is further split by the spin–orbit interaction into 2S+1 LJ spectroscopic levels, with |L − S| ≤ J ≤ L + S. As already mentioned, for a 4fn configuration with n < 7 the ground level has the lowest J value, but for n > 7 the ground state has the highest J-value. For instance, for the 4f8 Tb(III) ion the ground level is 7 F6 . Each of these levels is further split into Stark sublevels by the ligand field (Figure 5.2). This lifting is much smaller than for the d ions because of the shielding of the 4f orbitals. Only a few hundred of cm−1 usually separate the lowest from the highest sublevel resulting from the splitting of a 2S+1 LJ level. The number of Stark sublevels depends on the site symmetry of the Ln ion. For C1 symmetry, which is often the case in molecular compounds, 2J+1 sublevels are expected when the number of 4f electrons is even and J +1/2 when it is odd [4]. For all paramagnetic Ln(III) ions, except Sm(III) and Eu(III), the ground 2S+1 LJ level is separated by at least 1000 cm−1 from the next level. At room temperature, only the Stark sublevels of the 2S+1 LJ ground state are thermally populated. As the temperature is lowered, a depopulation of these sublevels occurs and consequently χLn T decreases, the temperature dependence of χLn deviates with respect to the Curie law. 4f n-1 5d1

2 .104 cm-1

2S+1

LJ

4f n

104 cm-1

2S+1

L

102 cm-1 Electronic configuration

Spectroscopic terms

Spectroscopic Levels

Stark sublevels

Fig. 5.2. Schematic energy diagram showing the relative magnitude of the interelectronic repulsion, the spin–orbit coupling, and ligand-field effects

164


When the Ln(III) ion is in exchange interaction with another paramagnetic Ln Ln T for the compound (χM stands for species, the temperature dependence of χM the molar magnetic susceptibility) is due to both the variation of χLn T and the magnetic interaction between the Ln(III) ion and the second spin carrier. Consequently, information about the nature of the magnetic interactions between such a Ln(III) ion and the second spin carrier may not be deduced unambiguously from only the Ln T versus T curve. Moreover, theoretical analysis of the magnetic shape of the χM data of such a compound is impeded by the lack of a general theoretical model to describe the χLn behavior of a Ln(III) ion in its ligand field. In the following, we will consider the cases where a Ln ion is associated with another spin carrier. We will highlight the behavior encountered for these ions through examples of molecular compounds reported so far.

5.2 Molecular Compounds Involving Gd(III) Among the lanthanide ions, Gd(III) is unique because of its half-filled f7 configuration. As a consequence this ion has no orbital contribution (L = 0), its ground state is 8 S7/2 , and its magnetic behavior is governed only by the spin contribution. Thus, when this ion is in an exchange interaction with another paramagnetic species it behaves like a 3d ion. Its magnetic behavior can be analyzed by a Heisenberg– Dirack–van Vleck phenomenological spin hamiltonian. The magnetic behavior of an exchange coupled system involving Gd(III) can be considered as straightforward and numerous compounds for which Gd(III) interacts with a second spin carrier have been reported.

5.2.1

Gd(III)–Cu(II) Systems

The pioneering work in this area was performed by Gatteschi et al. who found that in a series of {Cu(II)–Gd(III)} species the interaction between these ions was ferromagnetic, irrespective of the details of the molecular structure [5–7]. The ferromagnetic nature of the {Gd–Cu interaction} has since been confirmed for a large number of compounds comprising discrete molecules based on Schiff’s bases [8–15] and an extended network based on oxamato linkers [16, 17]. Long range magnetic ordering has been reported for {Gd(III)–Cu(II)} coordination polymers, but Tc for these ferromagnets is found at very low temperatures (Tc < 2 K) [18, 19]. For a very few compounds the {Gd(III)-Cu(II)} interaction was found to be antiferromagnetic [20, 21]. To account for the ferromagnetic interaction between these ions, a mechanism involving a charge transfer from Cu(II) to Gd(III) has been proposed [7, 8, 22].

5.2 Molecular Compounds Involving Gd(III)

165

Following this mechanism, a fraction of the unpaired electron is transferred from Cu(II) into an empty 5d or 6s orbital of Gd(III). While the transfer in the Gd orbital takes place, the spin of the electron remains the same as in the starting orbital. According to Hund’s rules, the f electrons are expected to be aligned parallel to that in the 5d or 6s orbital, thus a ferromagnetic interaction is established. A thorough discussion of the theoretical foundations of this mechanism has been developed by Kahn et al. [23] and summarized recently by Gatteschi et al. [3].

5.2.2

Systems with Other Paramagnetic Metal Ions

Compounds for which Gd(III) has exchange interaction with other paramagnetic metal ions are less documented but it seems that the sign of the exchange is mainly governed by the nature of the chemical link between the spin carriers. For instance, in a series of Schiff’s base derivatives where a Gd(III) is linked to transition metal ions through an oxygen atom, ferromagnetic interactions were observed for Mn(III) [24], Fe(II) [25], Co(II) [26], and Ni(II) [27–29]. However, for V(IV) both ferro- and antiferromagnetic interactions were found [30, 31]. Antiferromagnetic interactions were reported for compounds comprised of a Gd(III) ion linked to Cr(III) or Fe(III) by a CN bridge [1, 32–34]. Oxalate or related bridging ligands have been envisaged as well and lead to ferromagnetic {Gd(III)–Ni(II)} interaction [35], whereas for a {Gd(III)-Cr(III)} system the observed interaction was too weak to yield a conclusive result [36]. The case where Gd(III) is interacting with a second f-ion has also been considered. In all cases reported so far the exchange interaction is weak and antiferromagnetic [37–43], except one for which a ferromagnetic Gd(III)–Gd(III) interaction was found [44].

5.2.3

Gd(III)-Organic Radical Compounds

Several compounds for which organic radicals act as ligands for a Gd(III) ion have been reported. The appealing feature of such compounds is the direct contact that exists between the two paramagnetic centers. This is a favorable situation to improve somewhat the strength of the exchange interaction which is weak with the Ln ions. Interestingly, the magnetic behavior appears greatly influenced by the chemical nature of the organic moiety. The adduct formed between Gd(III) and a nitronyl nitroxide radical (Scheme 5.1), an organic S = 1/2 spin carrier, was found to lead to ferromagnetic interaction [45–49]. An example of such a compound where the Gd(III) ion is linked to two nitronyl nitroxide units by means of NO groups is depicted in Figure 5.3. For this compound, {Gd(NitTRZ)2 (NO3 )3 }, the Gd(III) is surrounded by

166


O

N

N

O

R

.

O

N

N

O

R Imino nitroxide radical (Im-R)

t

t

Bu

Bu

t

3,5- Bu-semoquinonato (SQ)

Scheme 5.1

O

N

N

O

X O

.

.

Nitronyl nitroxide radical (Nit-R)

-

.

.

O

N

Gd

Me N Me

N N X X N N

N

O

N Me Me

2

X = K -NO3

Fig. 5.3. View of the molecular structure of {Gd(NitTRZ)2 (NO3 )3 }.

two N,O-chelating nitronyl nitroxide subtituted triazole ligands and three nitrato anions [48]. The magnetic behavior of {Gd(NitTRZ)2 (NO3 )3 } is shown in Figure 5.4 in the form of the χM T versus T plot, χM being the molar magnetic susceptibility. At room temperature, χM T is equal to 8.90 cm3 K mol−1 , which is close to the value of 8.62 cm3 K mol−1 expected for the isolated spins SGd = 7/2 and two Srad = 1/2. For lower temperatures, χM T increases, reaching a maximum at 7 K before decreasing rapidly. The profile of the curve indicates that the {Gd-aminoxyl radical} interactions are ferromagnetic, the decrease in χM T at low temperature was attributed to weak intermolecular interactions among molecules in the crystal lattice. The S = 9/2 ground state for this compound was confirmed by the field dependence of the magnetization recorded at 2 K. The experimental behavior compares well with the theoretical magnetization calculated by the Brillouin function for an S = 9/2 spin (Figure 5.5).


167

11.5

F T ( cm3.K.mol-1 ) M

11.0

10.5

10.0

9.50

9.00 0

20

40

60

80

100

T (K)

Fig. 5.4. Experimental () and calculated (—) χM T versus T curve for {Gd(NitTRZ)2 (NO3 )3 }.

10

6.0

B

M(P )

8.0

4.0 Experimental data Brillouin for S=9/2 Brillouin for S=7/2 + 2 S=1/2

2.0

0.0 0

10

20

30

H ( kOe )

40

50

Fig. 5.5. Field dependence of the magnetization of {Gd(NitTRZ)2 (NO3 )3 } (•) at 2 K. Calculated magnetization for three non-interacting spins (S = 7/2 + 2 × S = 1/2) ( ) and for S = 9/2 ().

The temperature dependence of the magnetic susceptibility for this compound was analyzed using an expression for χM taking into account the intramolecular interaction between the Gd(III) ion and the radicals, J , the intermolecular interaction between the molecules, J , and an intramolecular interaction between the two radicals, J . This latter interaction parameter considers the superexchange occurring between two paramagnetic units linked by a lanthanide ion. This characteristic will be illustrated in Section 5.3. Gadolinium(III) is a 4f7 ion with a 8 S7/2 ground state and thus has no orbital contribution. Moreover the first excited states are very

168


high in energy. Consequently, the spin hamiltonian appropriate to the system may be written as: H = −J Sˆ Gd · Sˆ − J Sˆ Rad1 · Sˆ Rad2 taking Sˆ = Sˆ Rad1 + Sˆ Rad2 and Sˆ = Sˆ + Sˆ Gd , H may be rewritten as J − J J ˆ2 H=− S − 2Sˆ 2Rad − Sˆ 2Gd − Sˆ 2 − 2Sˆ 2Rad 2 2 and the energies E(s,s ) can be expressed as:

(5.4)

(5.5)

E( 29 ,1) = 0 9 E( 27 ,1) = J 2 E( 25 ,1) = 8J 7 E( 27 ,0) = J + J 2 The g(S,S ) Zeeman factors associated with these levels are:

(5.6)

77 22 g( 29 ,1) = gRad + gGd 99 99 7 g( 2 ,1) = gGd 59 4 gRad + gGd g( 25 ,1) = 63 63 10 45 g( 27 ,0) = − gRad + gGd 35 35 The molecular susceptibility is given by: χM =

Nβ 2 F 3kT − J F

(5.7)

(5.8)

where F is given by: F = 8J

9J 105 2 495 2 +2J g +126g 2 5 ,1 exp − 2kT + 2 g 7 ,0 exp − 2kT +126g 2 7 ,1 exp − 7J2kT 2 ( 29 ,1) (2 ) (2 ) (2 )

9J

8J

+2J 10+8 exp − 7J2kT +8 exp − 2kT +6 exp − 2kT (5.9) Least-squares fitting of the experimental data led to a ferromagnetic {Gd(III)aminoxyl} interaction of J = 6.1 cm−1 (gGd and grad were taken equal to 2.00) [48]. As a general trend, the {Gd(III)-nitronyl nitroxide} interaction is ferromagnetic but for a very few compounds weakly antiferromagnetic interactions were found


169

Fig. 5.6. ORTEP view of the molecular structure for {Gd(o-ImnPy)(hfac)3 }. Reproduced from Ref. [52] by permission of The Royal Society of Chemistry.

[49, 50]. When the nitronyl nitroxide radical is replaced by its imino nitroxide counterpart (Scheme 5.1) the {Gd-radical} interaction becomes antiferromagnetic. For {Gd(o-ImPy)(hfac)3 }, where o-ImPy stands for ortho-imino nitroxide substituted pyridine, the paramagnetic moiety is linked to the Gd(III) ion through the N-atom of the radical unit as shown in Figure 5.6. For this compound, a coupling constant of J = −1.9 cm−1 (H = −2J S1 .S2 ) was found while for a related compound an interaction parameter of J = −2.6 cm−1 was reported [51, 52]. Antiferromagnetic interaction was also observed between Gd(III) and semiquinonato radicals [53, 54]. For compound {Gd(Tp)2 (SQ)}, where Tp stands for hydro-trispyrazolyl borate and SQ for 3,5-di-tert-butylsemiquinonato (Scheme 5.1), the {Gd-semiquinone} interaction is characterized by a coupling constant of J = −11.4 cm−1 (H = −2J S1 .S2 ). This substantial interaction has been proposed to reflect a rather strong chemical link between the two paramagnetic centers. As a result, an overlap may now exist between the single occupied f orbitals of the metal center and the radical centered orbital. This would lead to the observed antiferromagnetic {Gd(III)-SQ} interaction. The interaction between Gd(III) and tetracyanoethylene (TCNE) or tetracyanodimethane (TCNQ) radicals is also antiferromagnetic. Interestingly, the ability of the latter paramagnetic ligands to act as bridges between metal ions leads to extended structures, and magnetic order was observed for these compounds at low temperatures [55, 56]. The information gathered so far on the magnetic interaction occurring in molecular compounds between Gd(III) and another spin carrier, either a metal ion or an organic radical, suggests that the magnetic behavior of the compound depends on the chemical link between the active centers. However, except for the Cu(II) derivatives, the number of known compounds remains too limited to draw definite conclusions. Further examples will be required to confirm and refine the present trends.

170


5.3 Superexchange Mediated by Ln(III) Ions When two, or more, paramagnetic moieties act as ligands for a Ln center, a magnetic interaction may exist between these ligands which is superimposed on their magnetic interaction with the Ln ion. Such combined contributions have been observed for both {Gd-Cu} [5–7, 17] and {Gd-organic radical} [45, 48, 54, 57, 58] systems. This superexchange among the paramagnetic ligands of the Ln center is clearly evidenced with diamagnetic Ln ions, i. e. La(III), Lu(III), or Y(III) [46] which is usually associated with the Ln series, as well as for Eu(III) which has a non-magnetic ground state (see below). The magnetic behavior for the La(III) compound, {La(NitTRZ)2 (NO3 )3 }, is depicted in Figure 5.7. The profile of this curve indicates that an antiferromagnetic interaction takes place between the organic radicals, which tends to cancel the magnetic moment of the complex. Similar behavior was found for the corresponding Y(III) derivative. Analysis by a dimer model (H = −J S1 .S2 ) of their magnetic behavior yielded exchange parameters

0.80

0.06

0.60 F M T ( cm 3 K mol -1)

F M T (cm 3 K mol -1)

0.70

. 0.50 . 0.40

0.05

. 0.04 .

0.30

0.03 0.02

0.20

0.01

0.10

0 0

10

20

30

40

50

0.0 0

50

100

150

200

250

T (K) Fig. 5.7. Experimental () and calculated (—) temperature dependence of χM T for {La(NitTRZ)2 (NO3 )3 }; Insert: detail of the variation of χM showing the maximum at 7 K.

5.3 Superexchange Mediated by Ln(III) Ions

171

of J = −6.8 cm−1 and J = −3.1 cm−1 respectively, for the La and Y derivative [48]. The main difference between these two compounds is the nature of the diamagnetic metal centers. The observation of different J values thus corroborates the hypothesis that the Ln ion is involved in the superexchange pathway between the two paramagnetic ligands. The stronger exchange found for the La(III) derivative may be related to the spatially more diffuse orbitals for this ion as compared to Y(III). This next-neighbor interaction is also expected to occur when Ln is a paramagnetic ion. In that case, the sign and the relative magnitude of the {Ln-radical} or {Ln-M} (M stands for a paramagnetic metal ion) interaction compared to the {ligand-ligand} interaction will determine the ground state and the energy level spectrum of the compound [9, 58]. The case of Eu(III) compounds is somewhat peculiar. This 4f6 ion has a nonmagnetic 7 F0 ground state as a result of the canceling of its L and S components having respectively, a value equal to 3. However, its first excited state, resulting from the splitting of the ground term by the spin–orbit coupling, is sufficiently low in energy to be thermally populated even below 300 K. Typical magnetic behavior for a Eu(III) ion is given in Figure 5.8, it corresponds to the behavior of {Eu(Nitrone)2 (NO3 )3 }, a compound where the metal center is surrounded by diamagnetic ligands. At low temperature χEu T is equal to zero but increases with temperature. This increase in the intrinsic magnetism for this ion is the consequence of the population of its first excited state. In the temperature domain usually investigated for molecular compounds, i. e. 2 to 300 K, it is reasonable to assume 1.4

0.0065

1.2 1.0

3

(cm .mol )

0.0055

0.80

Eu

F

0.60

F

Eu

0.005

-1

T (cm3.K.mol-1 )

0.006

0.40 0.0045

0.20 0.0

0.004

0

50

100

150 T (K)

200

250

300

Fig. 5.8. Temperature dependence of χEu ( ) and χEu T () for {Eu(Nitrone)2 (NO3 )3 }, the solid line corresponds to the best-fit of the analytical expression of χEu T (Eq. (5.10) yielding a spin–orbit parameter λ = 371 cm−1 .

172


that only two levels are concerned, the temperature dependence of χEu may thus be analyzed in the free-ion approximation as a function of the spin–orbit coupling parameter, λ [59]. The theoretical expression of χEu as a function of λ is given by Eq. (5.10). The value taken by the g-factor for the ground term is g0 = 5 and for all other terms gJ is equal to 3/2. χEu can thus be written as in Eq. (5.12). The analysis of the experimental magnetic behavior of {Eu(Nitrone)2 (NO3 )3 } (Figure 5.8) by this expression leads to a spin–orbit coupling value of λ = 371 cm−1 .

χEu

6 λJ(J + 1) (2J + 1)χ (J) exp − 2kT J=0 = 6

λJ(J + 1) (2J + 1)χ (J) exp − 2kT J=0

(5.10)

with χ (J) =

Ng 2 β 2 J(J + 1) 2Nβ 2 (gJ − 1)(gJ − 2) + 3kT 3λ

χEu =

Nβ 2 24+(27x/2−3/2)e−x +(135x/2−5/2)e−3x +(189x −7/2)e−6x 3kT x 1+3e−x +5e−3x +7e−6x +9e−10x +11e−15x +13e−21x

+

(5.11)

(405x −9/2)e−10x +(1485x/2−11/2)e−15x +(2457x/2−13/2)e−21x 1+3e−x +5e−3x +7e−6x +9e−10x +11e−15x +13e−21x λ (5.12) with x = kT

When the Eu(III) ion is surrounded by paramagnetic ligands, as for {Eu(NitTRZ)2 (NO3 )3 }, the magnetic behavior of the compound can be attributed to the contribution of the thermal population of the excited state of the Eu(III) ion and the interaction between the paramagnetic ligands. Because the ground state of the f-ion is non-magnetic, the low-temperature magnetic behavior for {Eu(NitTRZ)2 (NO3 )3 } is governed by the intramolecular interaction between the Eu T below 20 K (Figure 5.9) can be attwo radical units. The rapid decrease of χM tributed to the antiferromagnetic interaction between the nitronyl nitroxide groups. The occurrence of this antiferromagnetic interaction is demonstrated by the maxEu at 3 K (insert Figure 5.9), behavior reminiscent to that imum exhibited by χM observed for the corresponding Y(III) and La(III) derivatives. Provided that the interaction between the paramagnetic ligands is weak enough to take place at low temperature and that for this temperature only the nonmagnetic ground state of Eu(III) is populated, the magnetic behavior of such a compound can be analyzed with the expression given in Eq. (5.13). The first term corresponds to the interaction within a pair of S = 1/2 spins whereas χEu refers to the thermal

5.3 Superexchange Mediated by Ln(III) Ions

173

2.5

F M T ( cm 3 K mol -1)

2.0 . 1.5 .

0.14

F M (cm 3 mol -1)

0.12

1.0

.

0.50

0.10 0.080 0.060 0.040 0.020 0.0 0

0.0 0

50

100

5

150 T (K)

10

15

200

20

25

250

30

300

Eu T versus T curve for Fig. 5.9. Experimental () and calculated (—) χM Eu due to the {Eu(NitTRZ)2 (NO3 )3 }; the insert shows the maximum exhibited by χM antiferromagnetic interaction between the paramagnetic ligands.

dependence of the intrinsic magnetic susceptibility of the Eu(III) ion given by Eq. (5.12). Eu χM =

2 2Nβ 2 gRad + χEu J kT 3 + e− kT

(5.13)

The analysis of the magnetic behavior of {Eu(NitTRZ)2 (NO3 )3 } by this expression led to an intramolecular {radical-radical} interaction parameter J = −3.2 cm−1 (Figure 5.9) [60].

174


5.4 Exchange Coupled Compounds Involving Ln(III) Ions with a First-order Orbital Momentum As mentioned above, the magnetic properties of a compound in which a paramagnetic Ln(III) ion displaying spin–orbit coupling interacts with another spin carrier is the superposition of two phenomena. The first originates from the thermal depopulation of the so-called Stark sublevels of the Ln ion, and the second is the result of the magnetic interaction between the magnetic centers. Usually, both become relevant in the same temperature range. The first phenomenon, intrinsic to the Ln ion, is modulated by the ligand field and the symmetry of the compound, and there is no simple analytical model that can reproduce this magnetic characteristic for a given compound. Thus, the analysis of the overall magnetic behavior for such a compound by a theoretical model is not obvious. However, a rather simple experimental approach may permit one to overcome the problem of the orbital contribution and give some qualitative insight into the interactions occurring between a Ln(III) ion displaying spin–orbit coupling and another spin carrier. It is based on knowledge of the intrinsic contribution of the Ln ion in its ligand set, χLn . This approach requires two compounds, one for which the Ln(III) is in exchange interaction with another spin carrier, and an isostructural compound for which the coordination sphere of the Ln center is identical but involves only diamagnetic ligands. The comparison of the magnetic behavior of the two compounds reveals then the ferro- or antiferromagnetic nature of the interaction taking place in the former compound. Moreover, a compound reproducing the intrinsic contribution of the Ln(III) provides access to the crystal/ligand field parameters required to analyze the magnetic behavior of the exchange coupled compound with a theoretical model. Quantification of the interaction thus becomes possible.

5.4.1

Qualitative Insight into the Exchange Interaction

To illustrate this experimental approach, we will consider the investigation of the {Ln(III)-aminoxyl} interaction in a series of isomorphous compounds, {Ln(NitTRZ)2 (NO3 )3 }, comprising a Ln(III) ion (Ln = Ce to Ho) surrounded by two N,O-chelating nitronyl nitroxide radicals. A view of the molecular structure of these compounds is given in Figure 5.3 for the Gd derivative. For each compound, the intrinsic paramagnetic contribution of the Ln ion, χLn , has been deduced from the corresponding {Ln(nitrone)2 (NO3 )3 } derivative where the Ln(III) Ln is surrounded by a diamagnetic ligand set. To allow a comparison between χM and χLn , the ligand field for the compound used to determine χLn has to be the same as for the exchange coupled system. The ligand chosen as a diamagnetic counterpart to the nitronyl nitroxide radical is the N-tert-butylnitrone-substituted triazole derivative, hereafter abbreviated as nitrone (Scheme 5.2). The nitrone

O

N

N

O X O Ln N N X X N N

Me N Me

N

N

N .

.

5.4 Exchange Coupled Compounds Involving Ln(III) Ions

N Me

Me

X

O

N

Ln

H

O

O

N

N N X X N N

Me

Me

175

H N Me

Me 2

2

X = K -NO3

X = K -NO3

{Ln(NitTRZ)2(NO3)3}

{Ln(Nitrone)2(NO3)3}

Scheme 5.2

and the nitronyl nitroxide-substituted triazole ligands are very much the same as far as the moieties which are coordinated to the metal center are concerned, i. e. the nitrogen heterocycle and the N-oxide unit. Moreover, the crystal structures of both {Ln(NitTRZ)2 (NO3 )3 } and {Ln(nitrone)2 (NO3 )3 } compounds display essentially the same geometrical features. The difference between the magnetic Ln and the correspondsusceptibility of the {Ln(NitTRZ)2 (NO3 )3 } compound, χM ing {Ln(nitrone)2 (NO3 )3 } derivative, χLn , then enables the contribution due to the {Ln-aminoxyl} interaction to be revealed. Ho T is found For example, for the Ho(III) compound, {Ho(NitTRZ)2 (NO3 )3 }, χM to decrease increasingly rapidly as the temperature is lowered (Figure 5.10). Ho T results from the superposition of both the variaAs mentioned above, χM tion of the intrinsic susceptibility of the Ho(III) ion, χHo , and the {Ho(III)radical} interaction. The features of this magnetic behavior preclude any conclusion about the nature of the magnetic interaction between the metal center and its paramagnetic ligands. However, when the intrinsic contribution, χHo T , 16

F T ( cm3.K.mol-1 ) M

14 12 10 8.0 6.0 4.0 2.0 0

50

100

150 T (K)

200

250

300

Fig. 5.10. Temperature deHo T () for pendence of χM {Ho(NitTRZ)2 (NO3 )3 } and χHo T (•) for {Ho(nitrone)2 (NO3 )3 }.

176


5.0 6.0 5.0

-1

' F M T (cm 3 K mol )

4.0 M (P B)

. .

4.0

3.0

3.0 2.0

2.0

1.0 0.0 0

1.0

10

20 30 H (kOe)

40

50

0.0 0

50

100

150 T (K)

200

250

300

Fig. 5.11. Result of subtraction of the Ho(III) paramagnetic contribution, χHo T , from Ho T for {Ho(NitTRZ) (NO ) }. Insert: Field dependence of the magnetization at 2 K for χM 2 3 3 {Ho(NitTRZ)2 (NO3 )3 } (), {Ho(nitrone)2 (NO3 )3 } (), and the expected behavior for the uncorrelated spin system (•).

deduced from the {Ho(nitrone)2 (NO3 )3 } derivative, is discounted, it appears that Ho T − χHo T increases at low temperature (Figure 5.11) clearly indiχHo T = χM cating that the {Ho(III)-aminoxyl} interaction is ferromagnetic. This is confirmed by the field dependence of the magnetization of {Ho(NitTRZ)2 (NO3 )3 } which is compared in Figure 5.11 (insert) to what would be the magnetization for the corresponding uncorrelated spin system. The latter was obtained by adding to the magnetization of Ho(III) in {Ho(nitrone)2 (NO3 )3 } the contribution of two S = 1/2 spins, as calculated by the Brillouin function. For any value of the field the experimental magnetization determined for {Ho(NitTRZ)2 (NO3 )3 } is larger than that expected for an uncorrelated system, confirming that in the ground state all the magnetic moments of the magnetic centers are aligned in the same direction [61]. An example of antiferromagnetic interaction is provided by the Ce(III) comCe T − χCe T decreases when pound, Figure 5.12. In this case, χCe T = χM the temperature is lowered, behavior characteristic of an antiferromagnetic {Cenitronyl nitroxide} interaction. The field dependence of the magnetization for {Ce(NitTRZ)2 (NO3 )3 }, {Ce(nitrone)2 (NO3 )3 }, and the non-correlated magnetic centers is shown in Figure 5.13. For any field, the experimental magnetiza-


177

1.4

F T (cm3.K.mol-1) M

1.2 1.0 0.80 0.60 0.40 0.20 0.0 0

50

100

150 T (K)

200

250

300

Fig. 5.12. Temperature dependence Ce T (), χ T (♦), and of χM Ce χCe T (•).

2.5

1.5

B

M (P )

2.0

1.0

0.50

0.0 0

10

20

30

H ( kOe )

40

50

Fig. 5.13. Experimental field dependence of the magnetization for {Ce(NitTRZ)2 (NO3 )3 } (•) and {Ce(nitrone)2 (NO3 )3 } (♦), and calculated magnetization for a non-correlated spin system (+).

tion of {Ce(NitTRZ)2 (NO3 )3 } is lower than that of a non-correlated system. This comparison confirms that the magnetic moment of the ground state of {Ce(NitTRZ)2 (NO3 )3 } results from antiferromagnetic interactions within the compound. This procedure established that the correlation in the {Ln(NitTRZ)2 (NO3 )3 } compounds is antiferromagnetic for the Ln(III) ions with 4f1 to 4f5 electronic configurations, i. e. Ln = Ce, Pr, Nd, and Sm, conversely, this interaction was found to be ferromagnetic for the configurations 4f7 to 4f10 , i. e. Ln = Gd, Tb, Dy, and Ho [48, 60, 61]. Assuming that Hund’s rules dominate the ligand-field effects on the Ln(III) ions, this would suggest that the {Ln-aminoxyl radical} spin-spin exchange interaction is always ferromagnetic.

178


The magnetic interaction between Ln(III) ions and semiquinone, another organic radical, was also investigated. The tropolonate was chosen as the diamagnetic analog for the semiquinone ligand and the first information available suggests that the {Ln-semiquinone} interaction is antiferromagnetic for Ho(III) and ferromagnetic for Yb(III), respectively 4f10 and 4f13 ions [62]. The {Gd-semiquinone} interaction was also found to be antiferromagnetic (see Section 5.2.3) [53]. The same approach has been applied to elucidate the {Ln–M} magnetic interaction between Ln(III) and paramagnetic metal ions in heterometallic compounds. In that case, access to the intrinsic contribution of the Ln center is obtained by replacing the paramagnetic M by a diamagnetic ion. For instance, the {Ln(III)– Cu(II)} interaction has been investigated in a series of Schiff’s base derivatives. By replacement of the paramagnetic Cu(II) by diamagnetic Ni(II) in a square planar environment, the corresponding χLn T contribution was obtained. In this series, the {Ln–Cu} interaction was found to be antiferromagnetic for Ln = Ce, Nd, Sm, Tm, and Yb, and ferromagnetic for Ln = Gd, Tb, Dy, Ho, and Er [63, 64]. The {Ln(III)–Cu(II)} interaction was also studied in coordination compounds containing Ln(III) and Cu(II) ions bridged by an oxamato-type ligand developing in an extended ladder-type structure. The contribution arising from the Ln(III) ions was deduced from the isomorphous compounds where the Cu(II) was replaced by Zn(II) [65]. By comparison of the magnetic data, ferromagnetic {Ln–Cu} interactions could be established for Ln = Gd, Tb, Dy, and Tm whereas for Ln = Ce, Pr, Nd, and Sm an antiferromagnetic interaction is suggested to take place [66]. The same chemical systems were also prepared with paramagnetic Ni(II) instead of Cu(II), which permits one to investigate the {Ln(III)–Ni(II)} interaction in oxamato-bridged systems. Ferromagnetic interactions were established with Ln = Gd, Tb, Dy and Ho and antiferromagnetic interactions are suggested to take place for Ln = Ce, Pr, Nd, and Er. The ferromagnetic {Ln(III)–Ni(II)} interaction for the Ln ions with 4f7 to 4f13 electronic configurations has also been confirmed for an oxygen-bridged system [27]. The use of [Co(CN)6 ]3− as the diamagnetic counterpart to the paramagnetic building block, [Fe(CN)6 ]3− , involved in the preparation of exchange coupled {Ln(III)–Fe(III)} cyano-bridged systems permited to address the question of the nature of the interaction between these ions. This interaction was found to be antiferromagnetic for Ln = Ce, Nd, Gd, and Dy, whereas ferromagnetic interactions were obtained for Ln = Tb, Ho, and Tm [67]. All these experimental determinations of the ferro- or antiferromagnetic nature of the magnetic interaction involving paramagnetic Ln(III) ions with a first-order angular momentum are summarized in Table 5.1. It can be mentioned that this procedure has also been successfully applied to investigate the nature of the interactions between f ions in homodinulear phtalocyanine compounds of paramagnetic Ln(III) ions. The magnetic behavior for an exchange coupled system, {Ln–Ln} was compared to that obtained for the corresponding {Ln–Y} compound where one paramagnetic Ln(III) was replaced by

Ni(II) Fe(III)

Ni(II)

Cu(II)

O

O

O

O

-OCN

-O-

aminoxyl semiquinone Cu(II)

O

N

R

O

N

R

Bridging ligand

Spin carrier

Ln(III)

AF

AF

AF

AF

AF

Ce

AF

AF

AF

Pr

AF

AF

AF

AF

AF

Nd

Pm

AF

AF

AF

Sm

Eu

F AF

F

F

F AF F

Gd

F F

F

F

F

F

Tb

F AF

F

F

F

F

Dy

F F

F

F AF F

Ho

F

AF

F

Er

F

F

AF

Tm

F AF

Yb

27 67

35

66

48, 60, 61 53, 62 63, 64

Ref.

Table 5.1. Nature of the interaction observed in exchange coupled systems involving Ln(III) ions with a first-order orbital momentum (selection). F stand for ferromagnetic and AF for antiferromagnetic interactions.

5.4 Exchange Coupled Compounds Involving Ln(III) Ions 179

180


the diamagnetic Y(III) ion. Their difference revealed that the {Tb–Tb}, {Dy–Dy}, and {Ho–Ho} interactions are ferromagnetic whereas the {Er–Er} and {Tm–Tm} interactions are antiferromagnetic [68]. Finally, the experimental approach has also been applied to investigate the magnetic interaction involving a 5f ion, U(IV), with Cu(II) and Ni(II) [69]. The experimental method provides qualitative information about the nature of the magnetic interaction involving lanthanide ions with a first-order orbital momentum. It also underlines the importance of the ligand field effect in the overall magnetic behavior of these exchange coupled compounds. It is worth recalling that the procedure is reliable only if the ligand-field effect is the same for the compound used to gain access to χLn as for the exchange coupled derivative. A difference would induce significant differences for their respective χLn contributions, especially at lower temperatures, and thus lead to a distorted interpretation of the contribution of the exchange interaction which is also revealed in the low temperature domain.

5.4.2

Quantitative Insight into the Exchange Interaction

Accurate analysis of the magnetic behavior of a molecular compound containing a Ln(III) ion displaying spin–orbit coupling and in exchange interaction with another spin carrier requires that the intrinsic contribution arising from the Ln(III) ion is properly taken into account. All the energy sublevels of the Ln involved in the investigated temperature range have to be considered whem determining the interaction parameter. If the symmetry is high (octahedral, cubic, or rhombic) the crystal field is described by just a few parameters and modeling of the crystal field effect is straightforward [70]. However, molecular compounds usually present low site-symmetry, as a consequence the number of crystal-field parameters is much more important. Moreover, for a Ln ion, the correct quantum number is the total angular momentum, J, while the hamiltonian that has to be considered incorporates operators acting either on the spin momentum, SLn , or on the orbital momentum, LLn . Consequently, the quantitative treatment of this hamiltonian will then require the use of Racah algebra, especially as the ligand-field effects on the Ln ion may lead to the mixing of multiplets and spectral terms. This makes the analysis of the magnetic behavior of compounds for which a Ln(III) ion with a first-order orbital momentum is exchange coupled with another spin carrier more difficult. Such an analysis has been performed for the {Ln(NitTRZ)2 (NO3 )3 } compounds with Ln = Dy(III) and Ho(III), respectively a Kramers and a non-Kramers ion [71]. The purpose here is not to enter into details of the procedure but to briefly comment on the different steps of the analysis and report the results.


5.4.2.1

181

Model and Formalism

The {Ln–radical} or {Ln–M} exchange interactions in molecular compounds are much weaker than the ligand field effects on the Ln ion. There is thus no need to simultaneously diagonalize the corresponding hamiltonians. The approach followed, to analyze the magnetic behavior of {Dy(NitTRZ)2 (NO3 )3 } and {Ho(NitTRZ)2 (NO3 )3 }, consisted of two steps. First, the ligand field effect, i. e. the intrinsic contribution of the rare earth ion, was modeled in order to determine the energy diagram {ELn } of the Stark sublevels for the Ln ions and the associated eigenfunctions {|χLn }. Then the exchange interactions were computed in the tensorial product space {|χLn |SRad1 |SRad2 } of the state functions |χLn of the Ln ion in its ligand field environment with the state functions |SRad1 and |SRad2 of the two radicals with which the Ln ion interacts by exchange.

5.4.2.2

The Ligand-field Effect

The first step of the approach consists in computing the spectrum of the low-lying states of the Ln ion in its ligand environment. Interestingly, both magnetic and optical properties of the Ln ions have their origin in the spectroscopic Stark sublevels. Analytical models of the ligand field describing the optical properties of these ions in different materials exist and they can be adapted to compute the spectrum of the low-lying states of the molecular compounds considered. In the presented case, the semiempirical Simple Overlap Model (SOM) [72] was used to calculate the crystal-field parameters. These were obtained by reproducing the magnetic behavior of the Ln ion, χLn , measured experimentally for the {Ln(nitrone)2 (NO3 )3 } derivative, compound for which only the Ln ion in its crystal field contributes to the magnetism. The energy diagrams of the Stark sublevels determined by SOM for the Dy(III) and Ho(III) compounds, respectively 4f9 and 4f10 ions, are depicted in Figure 5.14. The degeneracy expected for both ions is well reproduced, the Stark sublevels are doubly degenerate for the Kramers ion Dy(III). It can be noticed that for Ho(III) the ground sublevel is just 5.5 K below the first excited state, whereas for the Dy(III) the ground and first excited states are separated by ca. 60 K. The corresponding eigenfunctions and eigenvalues can then be computed taking into account all spectroscopic terms and multiplets of the Ln ion. These were used for the analyses of the {Ln-aminoxyl} interaction.

5.4.3

The Exchange Interaction

The topology of the {Ln(NitTRZ)2 (NO3 )3 } compounds in terms of exchange interactions is shown in Figure 5.15. Two interactions have to be considered: The interaction between the Ln(III) ion and the organic radical, J , and the intramolec-

182


E (K) 561.0 523.7 487.7

468.1 442.8 393.5 ; 398.7 367.8

341.5

287.6 246.7 223.7 ; 224.3 192.8 180.3 110.5 88.4

219.1 145.0 93.1 60.2

5.5 0.0

0.0

Dy(III)

Ho(III)

Fig. 5.14. Energy diagrams of the Stark sublevels for {Dy(NitTRZ)2 (NO3 )3 } and {Ho(NitTRZ)2 (NO3 )3 }.

Ln (S3, L3, J3)

J

Rad1 (S1)

J

J’

Rad2 (S2)

Fig. 5.15. Schematic representation of the exchange interaction in {Ln(NitTRZ)2 (NO3 )3 }

ular exchange interaction between the two organic radicals, J (see Section 5.3). This radical-radical interaction has been taken into account in the analytical model. An exchange interaction takes place only between spin momenta, and the exchange hamiltonian, Hex , corresponding to this topology is as given in Eq. (5.14). The susceptibility measurements were performed with an applied field, therefore the Zeeman effect must also be taken into account (Eq. (5.15)). In this hamiltonian, HZ , the first and second terms correspond to the Zeeman effect acting on the total angular momentum of each paramagnetic species present in the system (one lanthanide ion and two organic radicals). The third term corresponds to the intermolecular interactions introduced in the mean field approximation. In this expression B is the magnetic induction, µB the Bohr magneton, ge the Lande factor for the electron and N the Avogadro number. The matrix elements (Eq. (5.16)) were calculated in the tensorial product space {|Ln |SRad1 |SRad2 }. The main difficulty arises from the evaluation of the matrix elements between states of different SLn , LLn , and J quantum numbers, of the


183

components with respect to a given system of axis, of the spin momentum and of the orbital momentum of the Ln ion. Hex = −J SLn · (SRad1 + SRad2 ) − J SRad1 · SRad2

(5.14)

HZ = −µB B(LLn + geSLn )−µB B(ge SRad1 + ge SRad2 )−N < (LLn + ge SLn ) − µB B(ge SRad1 + ge SRad2 ) > [(LLn + ge SLn ) − µB B(ge SRad1 + ge SRad2 )] (5.15) Ln |SRad1 |SRad2 |Hex + HZ |Ln |SRad1 |SRad2

(5.16)

Indeed, as already mentioned, the good quantum number of a Ln ion is the total angular momentum, J. But, both the Hex and HZ hamiltonians incorporate operators acting either on the spin momentum, SLn , or on the orbital momentum, LLn , of the Ln ion but they never act on J. Consequently, to calculate the matrix elements describing the whole system the formalism described by Judd must be used [73]. This formalism allows one to calculate the matrix elements γ , j1 , j2 , J , M |X|γ , j1 , j2 , J, M where X is an operator (Hamiltonian) acting on both j1 and j2 (but not on J). In other words, X is an operator formed by two operators, each of which acts on two different parts of the system, namely j1 and j2 . Once these matrix elements have been evaluated the Hex and Hz hamiltonians can be used to calculate the matrix elements associated with the magnetic momentum operator, which are required to calculate the magnetic susceptibility. The isothermal susceptibility calculations were made using the Linear Response theory. The isothermal initial magnetic susceptibility, χijT , is given in Eq. (5.17) where Mipq = p|Mi |q and Mjpq = p|Mj |q are the matrix elements of the magnetic moment operator, Mi and Mj , respectively and with j and i the cartesian directions x, y, and z. µ2 e−βEp µ2 −βEp Mipq Mjqp + B β e Mipp Mjpp χjTi = − B Z0 pq Ep − Eq Z0 p =−

µ2B −βEp β e Mipp e−βEq Mjqq 2 Z0 p q

(5.17)

The experimental magnetic behavior for {Dy(NitTRZ)2 (NO3 )3 } and {Ho(NitTRZ)2 (NO3 )3 } was simulated by this expression as a function of the {Ln-aminoxyl} interaction parameter, J , and the {radical-radical} interaction paramater J . The best simulated curve for the Dy derivative was obtained for Dy J = 8 cm−1 and J = −6 cm−1 , it is compared to the experimental χM T behavior in Figure 5.16. For the {Ho(NitTRZ)2 (NO3 )3 } compound the simulation also yields a ferromagnetic {Ho-aminoxyl} interaction parameter J = 4.5 cm−1 and a {radical-radical} interaction J = −6 cm−1 [71].

184

5 Lanthanide Ions in Molecular Exchange Coupled Systems 16

F T (cm3.K.mol-1) M

15

14

13

12

11 0

50

100

150 T (K)

200

250

300

Fig. 5.16. Experimental () χLn T versus T behavior for {Dy(NitTRZ)2 (NO3 )3 } and calculated curve () obtained for J = 8 cm−1 , J = −6 cm−1 .

Some discrepancies exist between the experimental and calculated thermal variation of χM that can be ascribed to the limitations of the SOM in evaluating the ligand field effects. The very low site-symmetry of the Ln ion in molecular compounds leads to a large number of crystal field parameters and it would be clearly illusory to let them vary freely and fit them solely from the variations of χM . Different physical characteristics may be used to determine the crystal-field parameters. Usually optical data provide access to these parameters but magnetic behavior or NMR shifts can also be used [74]. Improvements can be expected from fitting to measurements of the magnetization vector for single crystals, as from this the full static isothermal initial magnetic susceptibility tensor, χijT can be obtained. Quasielastic and inelastic neutron scattering on a powdered sample should also be very useful, as this would allow one to accurately determine the magnetic energy levels of the molecules, provided that deuterated samples are used to avoid the strong incoherent neutron scattering from hydrogen. Another interesting measurement would be that of the magnetic density by polarized neutron scattering measurements on a single crystal. This magnetic density can be computed from the eigenstates {|p } of the molecules. Obviously, all these experimental measurements will essentially allow greater knowledge of the ligand field effects.

References

185

5.5 Concluding Remarks For quite a while, the magnetic interaction between Gd(III) and another spin carrier was thought to be always ferromagnetic. However, several recent examples show that this is not the case, antiferromagnetic interaction with Gd(III) may also be the dominant interaction. Compounds with other paramagnetic Ln(III) ions are much less documented, but the first information available suggests that for all the paramagnetic ions of the 4f series, there is yet no obvious and general trend to explain their magnetic interaction with other spin carriers. These experimental observations are supported by a recent theoretical investigation on the nature of the magnetic interaction between rare-earth ions and Cu(II) ions in molecular compounds. This study concludes that for a given spin system either ferromagnetic or antiferromagnetic interactions may be encountered. The ground state does not depend solely on the filling of the 4f levels of the Ln(III) ion but also on inter-orbital 4f repulsion and crystal field parameters [75]. This strongly suggests that the nature of the magnetic interaction will depend on the chemical system, not solely the spin bearing units but also the chemical link between them. More examples are needed to get a deeper insight into the chemical parameters governing the magnetic behavior of lanthanide ions in molecular exchange coupled compounds. For these compounds, the interpretation of the magnetic behavior is often not obvious but the experimental method described above appears as a rather simple way to characterize the nature of the magnetic interaction. It requires, however, careful consideration of the derivative chosen as model compound to reproduce the intrinsic behavior of the Ln ion in its ligand field. The crystal-field effect is also a key point in numerical analysis of the magnetic interaction of exchange coupled systems. The growing interest in Ln ions in exchange coupled systems will certainly yield numerous new examples of compounds which will provide the required knowledge for a better understanding and rationalization of their magnetic behavior. The elucidation of the pathways for the exchange interaction with these ions is a further question to be addressed. Information on the mechanisms involved will permit rationalization of the design of new molecule-based magnetic materials.

References 1. 2. 3. 4.

F. Hulliger, M. Landolt, H. Vetsch, J. Solid State Chem. 1976, 18, 283. M. Sakamoto, K. Manseki, H. Okawa, Coord. Chem. Rev. 2001, 219, 379. C. Benelli, D. Gatteschi, Chem. Rev. 2002, 102, 2369. J.C.G. Bünzli, in Lanthanide Probes in Life, Chemicals and Earth Sciences: Theory and Practice, Eds. J.C.G. Bünzli, G.R. Chopin, Elsevier, Amsterdam 1989, p. 219.

186 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48.

5 Lanthanide Ions in Molecular Exchange Coupled Systems C. Bencini, C. Benelli, A. Caneschi et al., J. Am. Chem. Soc. 1985, 107, 8128. A. Bencini, C. Benelli, A. Caneschi et al., Inorg. Chem. 1986, 25, 572. C. Benelli, A. Caneschi, D. Gatteschi et al., Inorg. Chem. 1990, 29, 1750. M. Andruh, I. Ramade, E. Codjovi et al., J. Am. Chem. Soc. 1993, 115, 1822. J.L. Sanz, R. Ruiz, A. Gleizes et al., Inorg. Chem. 1996, 35, 7384. J.-P. Costes, F. Dahan, A. Dupuis et al., Inorg. Chem. 1996, 35, 2400. J.-P. Costes, F. Dahan, A. Dupuis et al., Inorg. Chem. 1997, 36, 3429. I. Ramade, O. Kahn, Y. Jeannin et al., Inorg. chem. 1997, 36, 930. K. Manseki, M. Kumagai, M. Sakamoto et al., Bull. Chem. Soc. Jpn. 1998, 71, 379. J.-P. Costes, F. Dahan, A. Dupuis, Inorg. Chem. 2000, 39, 165. M. Sasaki, K. Manseki, H. Horiuchi et al., J. Chem. Soc., Dalton Trans. 2000 259. O. Guillou, P. Bergerat, O. Kahn et al., Inorg. Chem. 1992, 31, 110. O. Guillou, O. Kahn, R.L. Oushoorn et al., Inorg. Chim. Acta 1992, 198-200, 119. F. Bartolomé, J. Bartolomé, R.L. Oushoorn et al., J. Magn. Magn. Mater. 1995, 140-144, 1711. M. Evangelisti, F. Bartolomé, J. Bartolomé et al., J. Magn. Magn. Mater. 1999, 196, 584. J.-P. Costes, F. Dahan, A. Dupuis et al., Inorg. Chem. 2000, 39, 169. J.-P. Costes, F. Dahan, A. Dupuis, Inorg. Chem. 2000, 39, 5994. C. Kollmar, O. Kahn, Acc. Chem. Res. 1993, 26, 259. O. Kahn, O. Guillou, in Research Frontiers in Magnetochemistry, Ed. C. J. O’Connor, World Scientific, Singapore 1993. C. Benelli, M. Murrie, S. Parsons et al., J. Chem. Soc., Dalton Trans. 1999, 4125. J.-P. Costes, J.M. Clemente-Juan, F. Dahan et al., Inorg. Chem. 2002, 41, 2886. J.-P. Costes, F. Dahan, A. Dupuis et al., C.R. Acad. Sci. Paris, t.1, Série IIc, 1998, 417. S.R. Bayly, Z. Xu, B.O. Patrick et al., Inorg. Chem. 2003, 42, 1576. J.-P. Costes, F. Dahan, A. Dupuis et al., Inorg. Chem. 1997, 36, 4284. Q.Y. Chen, Q.H. Luo, L.M. Zheng et al., Inorg. Chem. 2002, 41, 605. J.-P. Costes, F. Dahan, B. Donnadieu et al., Eur. J. Inorg. Chem. 2001, 363. J.-P. Costes, A. Dupuis, J.P. Laurent, J. Chem. Soc., Dalton Trans. 1998, 735. H.-Z. Kou, S. Gao, C.-H. Li et al., Inorg. Chem. 2002, 41, 4756. H.-Z. Kou, S. Gao, B.-W. Sun et al., Chem. Mater. 2001, 13, 1431. B. Yan, H.-D. Wang, Z.-D. Chen, Inorg. Chem. Commun. 2000, 3, 653. M.L. Kahn, P. Lecante, M. Verelst et al., Chem. Mater. 2000, 12, 3073. T. Sanada, T. Suzuki, T. Yoshida et al., Inorg. Chem. 1998, 37, 4712. J.-P. Costes, F. Dahan, F. Nicodème, Inorg. Chem. 2001, 40, 5285. R. Hedinger, M. Ghisletta, K. Hegetschweiler et al., Inorg. Chem. 1998, 37, 6698. J.-P. Costes, F. Dahan, A. Dupuis et al., Inorg. Chem. 1998, 37, 153. J.-P. Costes, A. Dupuis, J.-P. Laurent, Inorg.Cchem. Acta 1998, 268, 125. A. Panagiotopoulos, T.F. Zafiropoulos, S.P. Perlepes et al., Inorg. Chem. 1995, 34, 4918. S. Liu, L. Gelmini, S.J. Rettig et al., J. Am. Chem. Soc. 1992, 114, 6081. P. Guerriero, S. Tamburini, P.A. Vigato et al., Inorg. Chem. Acta 1991, 189, 19. J.-P. Costes, J.M. Clemente-Juan, F. Dahan et al., Angew. Chem. Int. Ed. Engl. 2002, 41, 323. C. Benelli, A. Caneschi, D. Gatteschi et al., Inorg. Chem. 1989, 28, 272. C. Benelli, A. Caneschi, D. Gatteschi et al., Inorg. Chem. 1989, 28, 3230. C. Benelli, A. Caneschi, D. Gatteschi et al., Inorg. Chem. 1992, 31, 741. J.-P. Sutter, M. L. Kahn, S. Golhen et al., Chem. Eur. J. 1998, 4, 571.

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C. Lescop, E. Belorizky, D. Luneau et al., Inorg. Chem. 2002, 41, 3375. C. Lescop, D. Luneau, E. Belorizky et al., Inorg. Chem. 1999, 38, 5472. C. Lescop, D. Luneau, P. Rey et al., Inorg. Chem. 2002, 41, 5566. T. Tsukuda, T. Suzuky, S. Kaizaki, J. Chem. Soc., Dalton Trans.2002, 1721. A. Caneschi, A. Dei, D. Gatteschi et al., Angew. Chem. Int. Ed. Engl. 2000, 39, 246. A. Dei, D. Gatteschi, C. A. Massa et al., Chem. Eur. J. 2000, 6, 4580. J.W. Raebiger, J.S. Miller, Inorg. Chem. 2002, 41, 3308. H. Zhao, M.J. Bazile, J.R. Galan-Mascaros et al., Angew. Chem. Int. Ed. 2003, 42, 1015. C. Benelli, A. Caneschi, D. Gatteschi et al., Inorg. Chem. 1989, 28, 275. C. Benelli, A. Caneschi, D. Gatteschi et al., Inorg. Chem. 1990, 29, 4223. O. Kahn, Molecular Magnetism, VCH, Weinheim 1993. M. L. Kahn, J.-P. Sutter, S. Golhen et al., J. Am. Chem. Soc. 2000, 122, 3413. J.-P. Sutter, M.L. Kahn, O. Kahn, Adv. Mater. 1999, 11, 863. A. Dei, D. Gatteschi, J. Pécaut et al., C.R. Acad. Sci. Paris, Chimie, 2001, 135. T. Kido, Y. Ikuta, Y. Sunatsuki et al., Inorg. Chem. 2003, 42, 398. J.P. Costes, F. Dahan, A. Dupuis et al., Chem. Eur. J. 1998, 4, 1616. M.L. Kahn, M. Verelst, P. Lecante et al., Eur. J. Inorg. Chem. 1999, 527. M.L. Kahn, C. Mathonière, O. Kahn, Inorg. Chem. 1999, 38, 3692. A. Figuerola, C. Diaz, J. Ribas et al., Inorg. Chem. 2003, 42, 641. N. Ishikawa, T. Iino, Y. Kaizu, J. Am. Chem. Soc. 2002, 124, 11440. T. Le Borgne, E. Rivière, J. Marrot et al., Chem. Eur. J. 2002, 8, 774. A.T. Casey, S. Mitra, in Theory and Applications of Molecular Paramagnetism, Eds. E.A. Bordeaux, L.N. Mulay, Wiley-Interscience, New York 1976, p. 271. M.L. Kahn, R. Ballou, P. Porcher et al., Chem. Eur. J. 2002, 8, 525. P. Porcher, M. Couto dos Santos, O. Malta, Phys. Chem. Chem. Phys. 1999, 1, 397. B.R. Judd, Operator Techniques in Atomic Spectroscopy, Advanced PhysicsMonograph, Mc Graw-Hill, New York 1963. N. Ishikawa, M. Sugita, T. Okubo et al., Inorg. Chem. 2003, 42, 2440. I. Rudra, C. Raghu, S. Ramashesa, Phys. Rev. B 2002, 65, 224411.

6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties Joan Cano and Yves Journaux

6.1 Introduction The quest for molecular based magnets [1–3] and high-spin molecules [4–6], in the wider context of molecular crystal engineering, has led to the synthesis of aesthetic extended networks [7] and high-nuclearity metal complexes [8, 9]. These compounds give rise to interesting magnetic properties, such as spontaneous magnetization, or slow magnetic relaxation times and quantum tunnelling phenomena [10–12]. Furthermore, the large majority of compounds belonging to these families of materials often crystallise in novel topologies. In order to establish a correlation between the structure and magnetic behavior of the compounds, it is essential to develop suitable models for the description of the low lying and excited spin energy levels. Unfortunately, the huge (or infinite) number of possible configurations in these systems precludes the calculation of the exact partition function. As a consequence, the derivation of important thermodynamic properties such as the magnetic susceptibility and specific heat capacity cannot be done. This situation is typical of systems studied by statistical physics which deals with systems with many degrees of freedom. Exact analytical theories are available in rare cases and in order to tackle the calculation of thermodynamic properties, physicists have developed approximate methods such as high temperature expansion of the partition function [13], closed chain computational procedure [14, 15] or density matrix renormalization group approach (DMRG) [16, 17]. However, all these approaches are of limited application or lead to uncontrolled errors which make improvement of the accuracy of the results difficult. Monte Carlo simulation is the obvious choice to overcome these problems [18]. The sources of errors are well known and the accuracy of the calculation can be increased, in principle, by using more sample configurations and by expanding the size of the simulated systems [18]. Furthermore, this approach can be used for systems where analytic methods do not work. However, although the Monte Carlo approach can be applied to many magnetic systems with different types of interactions between the magnetic centers, this method remains simple to program and affordable in term of computer power only in the case of the Ising model [19] and the classical spin approximation (S = ∞) [20]. Recent examples

190

6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties

in the literature provide interesting systems where these models can be applied. In order to illustrate the power and the efficiency of Monte Carlo simulation in molecular magnetism we will reduce the scope of this chapter to isotropic systems with spin S = 5/2 for which the classical spin approximation is satisfactory.

6.2 Monte Carlo Method 6.2.1

Generalities

A classical problem in statistical physics is the computation of average macroscopic observables such as magnetization M for a magnetic system. In the canonical ensemble, the average magnetization M is defined as: ∞

M =

Mi e−Ei /kT

i=1 ∞

(6.1) e

−Ei /kT

i=1

It is generally not possible to compute exactly this quantity in Eq. (6.1) due to the mathematical difficulties and the infinite or huge number of configurations. The basic idea of Monte Carlo simulation is to get an approximation of Eq. (6.1) by replacing the sum over all states with a partial sum on a subset of characteristic states: N

M =

Mi e−Ei /kT

i=1 N

(6.2) e

−Ei /kT

i=1

In the limit, as N → ∞, the sum formula of Eq. (6.2) equates to Eq. (6.1). The first possible approach involved the random selection of the states for the subset, i. e. adoption of the simple sampling variant of Monte Carlo simulation. This approach however, has major drawbacks as the rapidly varying exponential function in the Boltzmann distribution causes most of the chosen states to bring a negligible contribution to Eq. (6.2). In order to get sensible results, the ideal situation would be to sample the states with a probability given by their Boltzmann weight. As will be shown below, this can be done by using the importance sampling approach. Comparison between simple and importance sampling can be illustrated by the fictitious system of 40 independent particles allowed to occupy 100 levels equally

6.2 Monte Carlo Method

191

100 80 T=10 K Energy

60 40 20 0 0

1

2 population

3

4

Fig. 6.1. Occupation at 10 K of 100 energy levels equally spaced by 1 K using a random selection (horizontal bars), an importance sampling (dots) and a Boltzmann’s distribution (line).

spaced by 1 K. In Figure 6.1 is depicted the repartition of the independent particles among the 100 levels at 10 K using a random selection and importance sampling approach (Metropolis algorithm [21]). These two repartitions are compared to the Boltzmann distribution. This plot clearly shows that the high energy particles are too numerous in the random sample when compared to the ideal Boltzmann distribution and will bias the calculation of the average quantities. This is not the case for the sample obtained with the Metropolis algorithm. Even with a small number of configurations (900) the repartition in the average sample is very close to the ideal Boltzmann repartition. For a large number of configurations (900,000) the repartition of the 40 particles obtained by the Metropolis approach is indistinguishable from the Boltzmann repartition. The calculated average energies are 10.15 and 10.58 K for the random and the Metropolis samples respectively (E = 10.50 K for the 900,000 configurations sample). The average energy calculated with the simple sampling is a poor approximation to the real average energy E = 10.50 K. On the other hand, the importance sampling approach gives sensible results, therefore it seems essential to use this sampling method in Monte Carlo simulation [18]. In this approach, the calculation of the average physical quantities is done by a simple arithmetic average (Eq. (6.3)) M =

N 1 Mi N i=1

(6.3)

But the configurations used in the arithmetic average are chosen according to their Boltzmann weights. That is, for low temperature there are more low energy configurations than high energy ones. Although the method looks reasonable, it seems difficult to calculate the sampling probability p(Ci ) of a configuration Ci which depends on the partition function (ZN , Eq. (6.5)), that we are unable to calculate e−Ei /kT (6.4) p(Ci ) = ZN

192


ZN =

N

e−Ei /kT

(6.5)

i=1

This tour de force can be accomplished by applying the Metropolis algorithm [21].

6.2.2

Metropolis Algorithm

The idea advanced by Metropolis et al. [21] is to generate each new configuration Cj from the previous one Ci and to construct a so-called Markov chain [18]. The probability of getting Cj from Ci is given by a transition probability W (Ci → Cj ). It is possible to relate this transition probability W (Ci → Cj ) to the probability of a configuration p(Ci ) by considering the dynamics of the process. At the beginning of the process, the probability of a configuration depends on the computer time (number of iteration). Therefore, it is possible to calculate the probability of a configuration Ci at the time t + 1 through the following relation p(Ci , t + 1) = p(Ci , t) + W (Cj → Ci )p(Cj , t) − W (Ci → Cj )p(Ci , t)

(6.6)

Cj =Cj

After several iterations (thermalization process) the probability of a configuration p(Ci , t) must be independent of the computer time, that is p(Ci , t + 1) = p(Ci , t)

(6.7)

One possibility to cancel the second term of Eq. (6.6) is the so-called detailed balance condition W (Cj → Ci )p(Cj , t) = W (Ci → Cj )p(Ci , t)

(6.8)

which can be rewritten in the case of the Boltzmann distribution for p(Ci ) as p(Cj ) e−E(Cj )/kT /ZN e−E(Cj )/kT W (Ci → Cj ) = = −E(C )/kT = −E(C )/kT i i e /ZN e W (Cj → Ci ) p(Ci )

(6.9)

This condition gives a relationship between the ratio of the transition probabilities and the ratio of the configuration probabilities. It is worth noting that Eq. (6.9) is independent of the partition function ZN and that all the quantities in the last ratio of Eq. (6.9) are known or can be calculated. The next step is to give arbitrary values to W (Ci → Cj ) and W (Cj → Ci ) respecting the detailed balance condition. In 1953, Metropolis, Teller and Rosenbluth proposed the simple following choice for W [21] W (Ci → Cj ) = e−E/kT if E > 0 = 1.0 if E ≤ 0 with E = E(Cj ) − E(Ci )

(6.10)


193

This choice satisfies the detailed balance condition and, more importantly, it can be shown by simple arguments that a sequence of configurations generated by this procedure represents a configuration sample according to the Boltzmann distribution [18]. Finally, the last step in a Monte Carlo simulation is to define whether the new configuration is accepted to calculate average quantities from Eq. (6.3). According to the Metropolis algorithm, only the probability of the transition to a new configuration is given, but no more direct information on this condition is provided. So, the success of a transition is ruled by a comparison of its probability with a real random number r uniformly distributed between zero and unity (r ∈ [0, 1]). Thus, only when W (Ci → Cj ) ≥ r is the new configuration accepted. This option is sensible since most of the high-energy configurations will be rejected, especially at low temperatures, where the transition probability W (Ci → Cj ) reaches smaller values than most random numbers r. Although Monte Carlo simulation using the Metropolis algorithm appears to be a simple alternative for the calculation of average quantities, some points are delicate and can lead to unreliable results. The main points to be checked in order to obtain a robust simulation are: the thermalization process, the size of the model, the number of MC iterations and the random number generators.

6.2.3

Thermalization Process

Before calculating a physical observable, it is necessary to check that the memory of the initial state is lost and the equilibrium distribution is reached, that is, the probability of a configuration must be independent of the “computer time” (the number of Monte Carlo steps, MCS) and should only depend on its energy. The necessary time to get closer to the equilibrium can be very large at temperatures lower than that of the magnetic ordering temperature. Sometimes, 3 × 104 MCS site−1 are not enough to reach equilibrium. When a sample is in equilibrium at higher temperatures (300 K) and suddenly cooled, the initial configuration is frozen and a very large time is required to reach equilibrium in the new conditions. Shorter times are required when a gradual decrease in temperature occurs. For example, in a 3D cubic lattice the equilibrium is not completely reached after 105 MCS site−1 at 0.1 K, see Figure 6.2. To avoid this problem of slow relaxation toward equilibrium, two key points must be considered. First, at each temperature, the configurations found at the beginning of the simulation (first Monte Carlo loops) must be excluded in the calculation of the physical observable. Generally, we discard the first 10% of configurations generated by the MC algorithm, where equilibrium has not been reached. Second, starting from a high temperature, a low cooling rate must be chosen according to the following equation: Ti+1 = kTi , with 0.9 ≤ k < 1.0

(6.11)

194

6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties 6

/ ( χT)

eq

2K 1K 0.25 K 0.1 K

(χT)

cal

4 2 0 4

0

2 10

4

4 10 6 10 MCS / site

4

8 10

4

1 10

5

Fig. 6.2. Limit number of MCS to reach equilibrium as a function of the temperature in a 3D cubic lattice when it is suddenly cooled.

From this equation, the points at low temperatures, where the relaxation time is large, get closer. Therefore, in the last Monte Carlo steps, when the sample has reached equilibrium, a configuration is chosen as the initial configuration for the next temperature. So, this configuration is placed close to the equilibrium condition.

6.2.4

Size of Model and Periodic Boundary Conditions

Except in the case of high nuclearity complexes, which have a finite size, it is not possible to simulate real networks. Since the time of calculation is infinite in the last cases, finite models must be considered in order to study the extended network. On the other hand, it is necessary to use systems large enough to avoid finite size or border effects [18]. To illustrate this point, let us take the example of the antiferromagnetic S = 5/2 regular chain, where the exact law for a classical spin approach is known [20]. The results of the MC simulation of χ|J | (magnetic susceptibility) as a function of T /|J | for an increasing number of spins in the chain show that below 100 spins the simulations are not accurate enough, so it is necessary to reach 200 spins to avoid boundary effects at low temperatures (Figure 6.3). 0.040

12

0.035

20

3

χ M / cm mol

-1

4

40 100

0.030

400 Fisher 0.025 0

20

40

60 T/K

80

100

120

Fig. 6.3. χ |J | versus T /|J | plot for a series of linear systems with an increasing number of sites. The results are compared with Fisher’s law for a one-dimensional system of classical spin moments [20].


195

Fig. 6.4. Illustration of how periodic boundary conditions are used to diminish the model size without introducing border effects.

Although it is possible to simulate a chain of 200 spin moments within a reasonable time, it would take too much time to simulate a 3D network on a 200×200×200 model. In fact, the threshold size to avoid finite size effects over a wide range for a 3D system is smaller, but the required size is still too large to allow an affordable calculation time. The periodic boundary conditions (PBC) are used to diminish the model size without introducing border effects [18]. Thus, for instance, the first and last spin moments of a chain are considered as nearest-neighbours and, in consequence, all spin moments become equivalents, see Figure 6.4. These PBC can be extended to 2d and 3d networks as shown below. In a one-dimensional system, the PBC conditions reduce considerably the finite size effects, so 20 spin moments are enough to obtain a nearly perfect simulation of the magnetic behavior (Figure 6.5).

0.035

4 cyclic

FM / cm3mol-1

8 cyclic 20 cyclic 0.030

40 cyclic Fisher

0.025

0.020 0

20

40

60 T/K

80

100

120

Fig. 6.5. χ|J | versus T /|J | plot for a series of cycles with an increasing number of sites. The results are compared with Fisher’s law for a one-dimensional system of classical spin moments [20].

196


In practice, the model size considered in the Monte Carlo simulations is double the minimum size for which border effects are absent.

6.2.5

Random Number Generators

The use of random numbers is the core of Monte Carlo simulations. Thus, finding a good random number generator (RNG) is a major problem. In an ideal situation the random numbers would be generated by a random physical process. In practice, computers are used to carry out this function using mathematical subroutines. Actually, these generated numbers are not random and are referred to as pseudorandom numbers. However, this difference is not very meaningful if a RNG satisfies some important criteria. In general, RNGs supplied with compiler packages are dirty generators, so it is necessary to find a proper subroutine. A good introduction to RNGs is given in Ref. [22]. All mathematical RNGs supply a finite number sequence, which must be reproducible in any computer. The period of this sequence must be long and, at least, very much larger than the required random numbers sequence to simulate a physical property at a certain temperature. On the other hand, the number produced by a RNG must be apparently random, in other words, they must present a homogeneous distribution, avoiding numbers turning up as a series of sequences involving numbers of a similar magnitude. To summarize, these RNGs must satisfy the statistical tests for randomness. Unfortunately, some RNGs fulfil statistical tests but fail on real problems. Thus, it is necessary to check the RNGs on real problems that have already been solved. Some authors suggest testing the RNGs using the MC methods in the calculation of energy for a 2D Ising network [23].

6.2.6

Magnetic Models

Although the nature of the interaction between the magnetic ions is electrostatic, the magnetic data can be well described using effective spin hamiltonians reminding of a magnetic interaction. Theoreticians have justified the use of such hamiltonians for magnetic systems. Most of the studies have been based on the Heisenberg and Ising Hamiltonians, which can be written in general as: y y (6.12) Jij Siz .Sjz + Jij⊥ (Six .Sjx + Si .Sj ) H =− j >i

where Sik are components of the spin vectors Si , and Jij and Jij⊥ are the exchange coupling constants. The Ising and Heisenberg models correspond to cases where Jij⊥ = 0 and Jij = Jij⊥ , respectively. The Ising model is adapted to strongly anisotropic ions, but in spite of its mathematical simplicity nobody has been able


197

to solve it exactly beyond the 2D square lattice [19]. On the other hand, the Heisenberg model is adapted to isotropic systems, but it is not possible to solve it except for some finite systems. However, Monte Carlo simulation is a useful tool to describe the magnetic properties of systems where exact solutions are not known. We have shown that the Metropolis algorithm allows one to sample the configurations according to the Boltzmann distribution. The core of the algorithm is the comparison of a random number with the quantity e−E/kT . In theory, it is necessary to diagonalize the full energy matrix built from the Heisenberg hamiltonian to know the energies of the configurations that allow the calculation of e−E/kT . Thus, apparently, it seems that we have gone back to the starting point. It is possible to overcome this problem by using a Quantum Monte Carlo approach but this is beyond the scope of this chapter [24–27]. There are many interesting compounds that contain ions with spins S ≥ 2 (Mn(II) or Fe(III)), where there is another possibility. It has been shown that these spins can be considered as classical vectors. However, in order to compare the calculated values with experimental observations, the classical spin vectors are scaled according to the following factor: (6.13) Si = Si (Si + 1) With this approximation, the Heisenberg hamiltonian is reduced to H =− Jij · Si (Si + 1) · Sj (Sj + 1) · cos θij

(6.14)

j >i

which allows one to easily calculate the configuration energies requested for the Metropolis algorithm (CSMC method). Thus, this chapter focuses on the S = 5/2 systems, where the classical spin approach can be used.

6.2.7

Structure of a Monte Carlo Program

All the ingredients to write a Monte Carlo program are available. An abstract of this program is shown in Figure 6.6. Two remarks must be made: (a) the initial spin configuration of the network or cluster is chosen randomly, but other choices are possible; and (b) the sites of the network are not explored randomly for the spin orientation update but systematically through a loop. It has been shown that this approach gives good results for equilibrium configurations. After the generation of the sample using the Metropolis algorithm all the thermodynamic quantities can be calculated. It has been shown that the magnetization is calculated as the simple arithmetic average N 1 Mi M = N i=1

And it is also possible to calculate the average energy:

(6.15)

198

6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties Initialisation of the network Random orientation for the spins T=T initial istep = 0

T =Tend

No

istep =istep+1

Tnew = T x K

Yes

site i= 0

STOP

i = i +1 The new spin components S x(i) , S y(i), S z(i) are choosed randomly Calculate 'E 'E ≤ 0

'E > 0 random number R R ≤ e-'E/kT Yes

No

take the new spin orientation

keep the old spin orientation

i = maxsite No

Yes istep > thermalisation steps

calculate average quantities F M Yes

No

memorize configuration No

istep = maxstep

Yes

Fig. 6.6. Flow chart of a Monte carlo program using the classical spin approach.

E =

N 1 Ei N i=1

(6.16)

as well as the magnetic susceptibility and specific heat, which are calculated as the fluctuation of magnetization and energy, respectively. χ = M 2 − M 2 ; Cp = E 2 − E 2

(6.17)

6.3 Regular Infinite Networks

199

6.3 Regular Infinite Networks In order to fully understand and fine-tune the physical properties of magnetic materials, it is necessary to gain as much information as possible, such as the gfactors or the interaction parameter J between the magnetic ions. For a simple system, it is possible to get the values of these parameters by fitting a theoretical model to the experimental data. So, the calculation of the magnetic susceptibility is often combined with a least-square routine allowing the determination of the best parameters. In practice, a least-square fit by Monte Carlo simulation takes a lot of computer time. Nevertheless, for networks with only one or two interaction parameters, empirical laws using reduced variables can be established from Monte Carlo simulations [28]. The magnetic susceptibility can be given by an expansion function J a (6.18) χ = f b + ε(H ) T T When the magnetic field is close to zero the ε(H ) term is negligible and the magnetic susceptibility becomes field independent. In this case, there is only one χ|J | versus T /|J | curve for all J values. So, it is possible to obtain empirical laws from the Monte Carlo simulations which depend on the reduced temperature β = T /|J |. These empirical laws, which have been derived for several regular networks (1D, square and honeycomb 2D and cubic 3D), take the form:

g2 χ |J | = 4

a0 +

k

ai β i

i=1

1+

k+1

(6.19)

bj β j

j =1

The coefficients associated with the highest degree of the polynomials for both the denominator and the numerator are set so that they converge to the Curie law at high temperatures (χ T = 4.375 cm3 K mol−1 , for g = 2). Furthermore, the zero-grade terms in the numerator are fixed so that they converge to the finite χ |J | values obtained by the simulations at low temperature. The exact numerical coefficients associated with the empirical laws derived for cubic, diamond and 3connected 10-gon (10, 3) 3D networks are given in Table 6.1, and those for square and honeycomb 2D networks are shown in Table 6.2. Empirical laws can also be found for alternating systems with different magnetic interactions, but they present a more complicated form. Equations for other systems that are not shown in the present manuscript are available from the authors. A comparison is made with the high temperature series expansion of the partition function (HTE) for 2D honeycomb and square and 3D cubic networks by Stanley

200


Table 6.1. Coefficients of the rational functions providing the thermal variation of the reduced magnetic susceptibility χ |J | as a function of β = T /|J | for simple cubic, diamond and (10, 3) cubic networks (J in K) (Eq. (6.19)) [36]. Coefficient

Cubic

Diamond

(10,3) Cubic

a0 b0

0.0815865 1

0.116 1

0.156 1

a1 b1

0 0

0 0

0 0

a2 b2

1.22599 × 10−5 −2.78782 × 10−3

1.85958 11.7921

1.20777 × 10−4 5.11803 × 10−5

a3 b3

0 0

0 0

0 0

a4 b4

−5.34657 × 10−7 9.71169 × 10−6

324.872 2795.33

6.12417 × 10−4 −2.47313 × 10−4

a5 b5

0 0

0 0

0 0

a6 b6

3.56382 × 10−8 1.37954 × 10−9

2.5012 18.033

−1.0435 × 10−6 −2.32108 × 10−4

a7 b7

0 8.14585 × 10−9

0 0

0 0

a8 b8

0 0

0.264794 0.816704

3.99986 × 106 8.05117 × 10−6

a9 b9

0 0

0 0.0605244

0 9.14253 × 10−7

et al., and Lines et al. and with Fisher’s law for a chain (Figure 6.7) [13, 20, 29– 33]. Agreement between MC simulations and the other approaches is excellent at temperatures higher than that of the maximum value of χ|J |. Nevertheless, below this temperature there is a noticeable discrepancy since the HTE method is not applicable in this region, whereas there is a perfect agreement between the MC simulation and Fisher’s law for a regular chain over the whole temperature range. On the other hand, as expected, the maximum value of χ|J | increases and its position is displaced towards lower temperatures when the dimensionality of the network and the connectivity between the magnetic ions decrease, since the number of spin correlation paths also decrease [28, 34]. It must be noticed that for the 3D system the maximum corresponds to the antiferromagnetic ordering temperature, whereas for the 1D and 2D networks it is well established that there is no magnetic ordering for the Heisenberg model. We have tested the CSMC approach to fit the magnetic data for [N(CH3 )4 ][Mn(N3 )3 ] [35, 36], which crystallizes in a regular cubic network

6.3 Regular Infinite Networks

201

Table 6.2. Coefficients of the rational functions providing the thermal variation of the reduced magnetic susceptibility χ |J | as a function of β = T /|J | for square and honeycomb 2D networks (J in K) (Eq. (6.19)). Coefficient

Square

Honeycomb

a0 b0

−121201.0 −1.05473 × 106

2.82178 −582.803

a1 b1

311085.0 2.72275 × 106

82.6317 3830.22

a2 b2

−289512.0 −2.56424 × 106

−110.786 −8491.63

a3 b3

−117474.0 1.07481 × 106

−248.245 8711.63

a4 b4

−19202.0 −201403.0

626.252 −4401.53

a5 b5

358.413 17648.1

−530.795 982.435

a6 b6

428.864 −275.529

220.820 −34.5723

a7 b7

−73.9798 −39.9761

−47.0672 −12.2174

a8 b8

4.375 −5.4875

4.375 −2.11426

a9 b9

0.000 1.000

0.000 1.000

(Figure 6.8). Its magnetic behavior can be reproduced using J = −5.2 cm−1 and g = 2.025 [36]. These values are close to those found with the HTE method (J = −5 cm−1 ) [35]. It is worth noting that the agreement between the MC simulation and the experimental data is very good, even at low temperatures, confirming the classical behavior for this 3D network. An interesting comparison between the magnetic behavior of three different antiferromagnetic regular 3d networks is shown in Figure 6.9. These 3D systems correspond to primitive cubic, diamond and 3-connected 10-gon (10, 3) cubic networks. As expected, the antiferromagnetic ordering temperature TN /|J | is displaced toward a lower temperature as the connectivity between the magnetic sites decreases [36]. Below TN /|J |, in an ordered phase, our results could be compared to the less accurate mean field approximation. In this approach, as in our MC simulations, the expected limit of the χ |J | value at T /|J | = 0 is equal to 2/3 of its maximum value. So the CSMC method is able to reproduce the physical behavior in the paramagnetic and in the ordered phases, while the mean field approximation

202


0.300

(a)

0.250 (b) -1

(b)

0.200 (c)

3

F|J| / cm mol

(a)

0.150

(d)

0.100

0.050

0

10

20

30

40

50

T / |J|

(c)

(d)

Fig. 6.7. χ |J | versus T /|J | plots obtained by MC simulation for 1D, 2D honeycomb, 2D square and 3D cubic networks in a Heisenberg model. These plots are compared with those obtained by the high temperature expansion method and Fisher’s law [13, 20, 29–33].

0.035

0.025

3

F / cm mol

-1

0.030

0.020

0.015

0.010 0

50

100

150

200

250

300

T/K

Fig. 6.8. Crystal structure and magnetic properties of [N(CH3 )4 ][Mn(N3 )] [35, 36]. The experimental data (circles) and the simulations by Monte Carlo methods (solid line) are shown.

leads to a large overestimation of the ordering temperature and the HTE method is limited to the paramagnetic region [34]. In [FeII (bipy)3 ][MnII2 (ox)3 ], a compound previously described by Decurtins et al. [37], where bipy = 2, 2 -bipyridine and ox = oxalate, the Mn(II) ions are connected via oxalate bridging ligands to build up a three-dimensional 3-connected 10-gon network (Figure 6.10). From CSMC simulations, an antiferromagnetic interaction is found for this compound with J = −2.01 cm−1 [36]. This value is in agreement with those found in the literature for other dinuclear complexes and regular chains incorporating oxalate groups as bridging ligands.

6.4 Alternating Chains

203

0.25

0.20

F |J| /cm mol K

(c)

-1

(b)

3

(a)

0.15

M

(b) 0.10

(a)

0.050 0

(c)

10

20

30

40

50

T / |J|

Fig. 6.9. MC simulations of χ|J | versus T /|J | plots for three different antiferromagnetic regular 3D networks: (a) primitive cubic, (b) diamond and (c) 3-connected 10-gon (10, 3) cubic networks [36]. The line without symbols represents the theoretical curve found by the HTE method.

0.018

M

3

F / cm mol

-1

0.022

0.014

0.010

0

100

T/K

200

300

Fig. 6.10. Crystal structure and magnetic properties of [FeII (bipy)3 ][MnII 2 (ox)3 ] [37]. The experimental data are shown as circles and the Monte Carlo and HTE simulation as bold and normal lines, respectively [36].

6.4 Alternating Chains Alternating S = 5/2 chains with two or more different exchange coupling constants have also been investigated. An interesting example is that of a chain presenting an interaction topology J1 J2 , that is, two different consecutive interactions (J1 and J2 ) that repeat along the chain (. . .J1 J2 J1 J2 J1 J2 . . .). Drillon et al. have derived an exact analytical law in the frame of the classical spin approach to analyse the magnetic behavior of these systems [38]. On the other hand, the versatility in the coordination of the azido ligand led to several interaction topologies. In the [MnII (2pyOH)2 (N3 )2 ]n compound (2-pyOH = 2-hydroxypyridine) the manganese(II) ions are connected by µ-1,3-azido bridging ligands (Figure 6.11) [39]. It is well known

204


Fig. 6.11. Crystal structure and magnetic properties of [MnII (2-pyOH)2 (N3 )2 ]n [39]. The experimental data are shown as circles and the simulations by Monte Carlo method and Drillon’s law as solid and dashed lines, respectively [38].

Fig. 6.12. Crystal structure and magnetic properties of [MnII (bipy)(N3 )2 ]n [40, 41]. The experimental data are shown as circles and the simulations by Monte Carlo method and Drillon’s law as solid and dashed lines, respectively [38].

that this kind of bridge leads to antiferromagnetic interactions. However, a µ-1,1azido bridging ligand is also present in the [MnII (bipy)(N3 )2 ]n compound; so, a ferromagnetic interaction is expected in this case (Figure 6.12) [40, 41]. The experimental data were simulated by the CSMC method and Drillon’s law, and a good agreement is found between both methods and the experimental data (Table 6.3). The compound [Mn(Menic)(N3 )2 ]n (Menic = methylisonicotinate) represents a more complex alternating 1D system. In this chain, a 1:4 ratio for the µ-1,3- and µ1,1-azido bridging ligands connecting the manganese(II) ions is found (Figure 6.13) [42]. Nevertheless, a more complicated interaction topology than J2 J2 J2 J2 J1 is observed for this compound. In this way, as there are two different MnNazido Mn bond angle (α) values for the [Mn2 (µ-1,1-azido)2 ] entities (101.1o and 100.6o , Figure 6.13), a J2 J3 J3 J2 J1 interaction topology must be considered. In a recent paper, Drillon et al. conclude that several alternating ferroantiferromagnetic homometallic one-dimensional systems present similar magnetic behavior to that of the ferrimagnetic chains [43], which are described by

6.4 Alternating Chains

205

Table 6.3. Best parameters obtained by fitting a theoretical model to the experimental data for [MnII (2-pyOH)2 (N3 )2 ]n and [MnII (bipy)(N3 )2 ]n . The fits have been performed using the CSMC method and Drillon’s law [38–41]. Compound

Method

g

J1 /cm−1

J2 /cm−1

[MnII (2-pyOH)2 (N3 )2 ]n

MC Drillon MC Drillon

2.04 2.03 1.98 1.99

−13.2 −13.8 −12.9 −12.9

−12.3 −11.7 +4.9 +5.0

MnII (bipy)(N3 )2 ]n

Kahn as systems that contain two different near-neighbour spin moments antiferromagnetically coupled [15]. [Mn(Menic)(N3 )2 ]n constitutes a beautiful example of these systems. Thus, its χ T versus T experimental curve presents a minimum. Moreover, a maximum is also observed at lower temperature, which is characteristic of this particular interaction topology. Only the J2 J3 J3 J2 J1 model provides a correct description of the magnetic behavior, even at low temperatures (Figure 6.13). A good fit is obtained with the set of parameters J1 = −15.6 cm−1 , J2 = 1.06 cm−1 and J3 = 1.56 cm−1 . These results agree perfectly with those obtained from a proposed exact analytical law [42]. As is known, the J parameter and the α angle are related. Thus, the J2 and J3 values are in agreement with the theoretical magneto-structural correlation found by Ruiz et al. [44], supporting the consideration that two different exchange coupling constants for the [Mn2 (µ-1,1-azido)2 ] entities has a physical meaning and is not the result of a mathematical artifact.

J2

J3

J3

J2

J1

100.6o 101.1o

Fig. 6.13. Crystal structure and magnetic properties of [Mn(Menic)(N3 )2 ]n . The experimental data are shown as circles and the simulations by Monte Carlo method and the exact analytical law proposed by us as solid and dashed lines, respectively. The interaction topology is shown in the picture of the crystal structure [42].

The presence of a minimum and a maximum in the χM T versus T curve, can be explained by considering instant spin configurations at several temperatures provided by the MC simulation process (Figure 6.14) [42]. In this way, the stronger antiferromagnetic coupling promotes an antiparallel spin configuration and the

206


Fig. 6.14. Thermal variation of the spin configuration for an alternating J2 J3 J3 J2 J1 interaction topology. The antiferro- and ferromagnetic interactions are represented by bold and dashed lines, respectively.

χM T product decreases on cooling. At lower temperatures, in spite of the weak character of the ferromagnetic interactions, as they are present in a greater proportion (4:1), the ferromagnetic alignment of the resulting spins becomes efficient. Finally, the strongest antiferromagnetic interaction dominates the magnetic behavior, and χM T increases to reach a maximum then further decreases attaining a zero value at 0 K.

6.5 Finite Systems In a system where the local spin moments have an infinite value (Si = ∞) the number of microstates (Sz values) is infinite, as in a classical spin approach where the spin vector can be placed along infinite directions. Thus, the classical spin approach is less correct when the value of the local spin moment decreases, since the quantum effects become non-negligible. We have verified previously that the classical spin approach can be used to analyse the magnetic behavior of periodic systems. In a real non-periodic system the number of states is limited, especially for small systems with a few paramagnetic centers, and the energy spectrum is far from being a continuum, so the mentioned quantum effects could be more important in these systems. The question is whether the magnetic behavior of these non-periodic systems can be reproduced by MC simulation within the framework of the classical spin approach. In other words, does the applicability of the classical spin approach depend only on the values of the local spin moments or does the size of the network have some influence? Moreover, is it possible to simulate a discrete

6.5 Finite Systems

(b)

(a) J

0.500

J

2

3

0.400

U

1

2

3

3

-1

F|J| / cm mol K

1

207

0.300

J 0.200 0

3

6

9

12

15

T/J

Fig. 6.15. A comparison between the theoretical χ|J | versus T /|J | plots simulated from the exact quantum solution (symbols) and Monte Carlo methods (lines) for a series of small linear models.

spectrum from a continuous energy spectrum? For any system at low temperatures or for very small systems this task can be especially difficult since there are few populated states. In this section, the limits where the classical spin approach can be applied will be established. Thus, from the study of some systems where an exact quantum solution is available (Figure 6.15), it is possible to check the validity of the classical spin approach. In Figure 6.15, the curves for several linear systems obtained by CSMC simulation are compared to those calculated from an exact quantum method. The classical spin approach is not valid at low T /|J | values, due to the small number of populated states, which can be considered as a quantum effect. Also, from Figure 6.15 it can be concluded that the higher the number of paramagnetic centers, the lower the quantum effect. Thus, for any system at T /|J | > 4, the classical approach can be applied, and it is valid for a wider range of T /|J | as the number of paramagnetic centers increases. So, for more extended systems where the exact numerical solutions cannot be calculated, the MC simulation in a classical spin approach will be a powerful tool to study their magnetic behavior. The same comparison between MC simulations and exact quantum numerical solutions has been made for spin topologies presenting more than one coupling constant. Two examples are shown in Figures 6.16 and 6.17, where only interactions of antiferromagnetic nature are present. χT versus T /|J | curves have been simulated for different J /J values. MC simulations are valid for T /|J | values higher than 1.5, for J > J , and similar conclusions as above are reached. Moreover, several real complexes have been studied by a CSMC method. As an example, in Figure 6.18, two interesting clusters containing ten and eighteen iron(III) ions respectively, with a ring structure, named ferric wheels, are shown [45, 46]. From the magnetic point of view, these clusters are beautiful examples of systems that can be used as models for the interpretation of the magnetic prop-

208

6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties 5.000

-1

FT / cm mol K

4.000

3.000

3

J

J'

2.000

D 0.0 0.2 U

1.000

0.4

0.6 z 0.8 S

1.0

0.000 0

5

10

15

20

T/J

Fig. 6.16. A comparison between the theoretical χT versus T /|J | plots as a function of the J /J ratio (α) for the model shown in the picture. The plots have been simulated by exact quantum solution (symbols) and Monte Carlo methods (lines). 8.000

D 0.0 0.2 U

3

-1

J

FT / cm mol K

6.000

J'

0.4

0.6 z 0.8 S

1.0

4.000

2.000

0.000

0

5

10

15

20

T/J

Fig. 6.17. A comparison between the theoretical χT versus T /|J | plots as a function of the J /J ratio (α) for the model shown in the picture. The plots have been simulated by exact quantum solution (symbols) and Monte Carlo methods (lines).

erties of linear chains. (versus T plots have been simulated by a CSMC method, considering magnetic interactions only between nearest neighbours. The obtained values of the coupling constants agree perfectly with those obtained by an exact analytical classical spin law for 1D systems.

6.6 Exact Laws versus MC Simulations In previous sections, it has been shown that the MC method is a high-performance tool to simulate the magnetic behavior of many different systems. Notwithstanding, in some cases exact classical spin (ECS) laws are also available, so experimental data can more easily be processed. Thus, the question arises as to whether to use a

6.6 Exact Laws versus MC Simulations

209

(a) g = 1.98 J = -9.8 cm-1

(b)

…J1 J1 J2…

g = 1.985 J1 = -19.1 cm-1 J2 = -8.0 cm-1

Fig. 6.18. Crystal structure, experimental (circles) and MC simulated (lines) magnetic properties of: (a) [Fe(OCH3 )2 (O2 CCH2 Cl)]10 and (b) [Fe(OH)(XDK)Fe2 (OCH3 )4 (O2 CCH3 )2 ]6 (where XDK is the anion of m-xylylenediamine bis(Kemp’s triacid imide)) [45, 46].

MC method when an analytical law can be applied. At the moment, there are already ECS laws for several 2D networks. It is very important to understand how these laws are elucidated and what are their applicability limits and this is the subject of the present section. First, a method to obtain an ECS law for a 1D system, that is the Fisher’s law [20], is described.

6.6.1

A Method to Obtain an ECS Law for a Regular 1D System: Fisher’s Law

The evaluation of any physical property at a precise temperature requires the solution of two integrals (Eq. (6.1)): (a) the value of this property as the sum of the contributions from each of the possible states, and (b) the normalization factor, that

210


θι

i

i+1

Fig. 6.19. Illustration of the angle between two coupled vectors.

is given by the partition function (ZN ). Considering the spin moments as vectors, the energy of any configuration is given by Eq. (6.14), where θij is the angle between two coupled vectors. In the case of a regular chain, the partition function can be described as N π 1 sin θi e(x cos θi ) dθi (6.20) ZN = 2 0 i=1 x being equal to −J S(S + 1)/T . It must be pointed out that there is a term, sin θ, that takes into account the different arrangements that can be generated at a constant angle θ, that is, from a precession of the second vector referred to the direction of the first one, see Figure 6.19. The next equation is found from solving this integral

sinh(x) N (6.21) ZN = x The magnetic susceptibility in zero field can be calculated from the total spin pair correlation function, which can be defined as the sum of the individual spin pair correlation functions: 2 2 N N g β s z s z (6.22) χ= (4kT ) i=0 j =0 i j These functions, that provide the average arrangement of all spin moments referred to one of them, can be evaluated in a similar way to the partition function. Defining a pair correlation function by 3 z z s s (6.23) ZN i i+1 In a 1D system the integrals may be factorised as before. π 1 cos θi sin θi e(x cos θi ) dθi (6.24) u = si · si+1 = 2 0 This factorisation involves an independent character for the spin pair correlation function concerning only two near-neighbour centers. However, this is not the case si · si+1 =


211

for topologies other than a chain where this methodology cannot be so easily applied. In this way, Langevin’s function is obtained, which describes how one spin moment is placed with respect to its neighbours. 1 (6.25) x Obviously, the spin correlation function of vector i with itself is unity. On the contrary, the neighbouring vector i + 1 is correlated to vector i by Langevin’s function (u). On the other hand, the neighbouring vector i + 2 is correlated to i through vector i +1. Thus, the spin pair correlation function of vectors i +2 and i is u2 . From the summation in Eq. (6.22) and considering the obtained individual spin pair correlations, the series shown in Eq. (6.26) is constructed. The factor 2 that appears in some of the terms of the equation comes from the fact that an infinite chain grows in the two directions of the chain axis. By expanding the summation over integer n values, the wellknown Fisher’s law is obtained (Eq. (6.27). ∞ 2 3 n 2u (6.26) χ T = χ Tfree–ion (1 + 2u + 2u + 2u + . . .) = χTfree–ion 1 + u = coth(x) −

χ T = χ Tfree–ion

6.6.2

1+u 1−u

n=1

(6.27)

Small Molecules

The simplest case that can be studied is a system with only two paramagnetic centers. Following the methodology detailed in the preceding section, the next ECS law can be deduced χ T = χ Tfree–ion (1 + u)

(6.28)

The χ |J | versus T /|J | plots obtained from Eq. (6.28), from a CSMC simulation and from the exact quantum solution are shown in Figure 6.20. A good agreement between the three methods is found, and some discrepancies appear only at low values of T /|J |. The MC method gives a better result than the ECS law for this T /|J | region, since an approach has been made in the calculation of the partition function. In this same way, several comparisons between the three methods have been made for a series of similar models, and it can be concluded that there is a good agreement amongst them. Nevertheless, there is no such agreement in systems where the interaction topology presents closed cycles, as those shown in Figure 6.21. In some of these cases where the exact quantum solution is available, it has been observed that ECS laws do not simulate the magnetic behavior of the system properly. In the simplest case, that is, a triangle, vector 1 is correlated to

212

6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties 0.6 Quantum result ECS law CSMC

-1

F|J| / cm mol K

0.5

3

0.5

0.4

0.4

0.3 0

2

4

6

8

10

T/J Fig. 6.20. Theoretical χ |J | versus T /|J | plots obtained by exact quantum solution, exact classical law and CSMC simulation.

vector 3 either through the left or the right-hand ways, increasing the number of correlation paths. Also, vector 1 can be correlated to itself through a correlation path that involves a whole turn. This turn can be made clockwise or counter-clockwise, but both paths are equivalent, so it must be considered only once in the ECS law, as shown in the next equation. χ T = χ Tfree–ion (1 + 2u + 2u3 + u3 )

(6.29)

Notwithstanding, as vector 1 is correlated to itself through all other vectors, it is not possible to split the spin correlation function in their individual spin pair correlation functions. Thus, this methodology is not useful in these systems, and the derivation of an ECS law is a hard and difficult task. Series 1

Series 2

Fig. 6.21. Systems where the interaction topology presents closed cycles.


a)

213

b) 20.0 5.0

18.0

(T / J)lim

(T / J)lim

16.0 4.0

14.0 12.0

3.0

10.0 8.0 3

4

5

6

7

Cycle size

8

2

3

4

5

6

7

8

Number of cycles

Fig. 6.22. The limit value of T /J for perfect agreement between the exact classical and quantum solutions increasing: (a) the cycle size and (b) the number of cycles (see Series 1 and 2 in Figure 6.21). The condition to control the quality of the agreement is stricter in case (b) than in case (a) in order to facilitate the analysis of the results.

A study has been performed on the series of topologies shown in Figure 6.21. From a comparison of the results of the ECS laws with those from MC simulations it can be deduced that, by decreasing the number of triangular cycles (Series 2) or increasing the size of the cycle (Series 1), the validity range of the ECS laws increases and, consequently, the T /|J | threshold decreases (Figure 6.22). In the first case, this effect is due to a decrease in the number of correlation paths involving one or more closed cycles. In the second case, when the cycle size increases, the value of the spin correlation function involving a closed cycle path becomes lower. Therefore, this kind of correlation path is negligible in an infinite size ring, as a result again obtaining Fisher’s law.

6.6.3

Extended Systems

Two analytical laws have been derived to date for a 2D network. These ECS laws have been deduced by Curély et al. for alternating square and honeycomb networks [47–50], where there is only one magnetic interaction along a chain and a different interchain interaction (Figure 6.23). From these equations, ECS laws can be obtained for the corresponding regular networks. In this way, it could be expected that more complex topologies or 3D networks could be solved, and that it would not be necessary to use MC methods to simulate their magnetic behavior. On the other hand, MC methods allow one to consider as many coupling constants and g-factors as desired for any system, but this is not the only reason for continuing to use MC methods. From an analysis of Curély’s law for an alternating 2D square network it can be observed that the spin correlation function is, surprisingly, the product of the one-dimensional spin correlation functions along each spatial direction [50, 51]. In this topology, when ferromagnetic and antiferromagnetic interactions are present it

214


J

J J' J'

2d square

2d honeycomb

Fig. 6.23. Alternating square and honeycomb networks.

is expected that χ T will reach a zero value at 0 K, whatever the magnitude of these two interactions. Nevertheless, from Curély’s law, in the case of a ferromagnetic interaction stronger than the antiferromagnetic one, the χT product diverges on cooling, and when both interactions are of the same magnitude, χT versus T follows Curie’s law, that is, the system, surprisingly, behaves as if the spin moments do not interact at all. Moreover, the coefficients of the high temperature expansion for Curély’s law do not agree with those obtained by Camp et al. or Lines [30, 33, 51]. These remarks, as some that will be made later, can also be extended to Curély’s law for 2D honeycomb networks. Thus, for instance, [Mn(ox)2 (bpm)]n presents an alternating honeycomb network, where the oxalate (ox) bridging ligand acts as an exchange pathway along one of the directions and the bipyrimidine (bpm) ligand connects the chains (Figure 6.24) [52]. Excellent fits of the model to the experimental data for this compound have been obtained both from MC simulations and from Curély’s law [28, 49]. However, the J constant values obtained from MC

Fig. 6.24. Crystal structure and magnetic properties of [Mn(ox)2 (bpm)]n [52]. The experimental data (circles) and the simulations by Monte Carlo methods (solid line) are shown.


215

simulations agree much better with those found in dinuclear and one-dimensional systems with oxalate or bipyrimidine as bridging ligands [28, 52]. A more detailed analysis of the elucidation of an ECS law for a regular 2D square network will allow one to find the limitations of this methodology. Thus, as in this kind of network all paramagnetic centers are equivalent, only the total spin correlation function referred to one spin moment must be evaluated. As has been previously said, correlation of spin moment A to itself is 1, correlation of spin moment B to A is given by the Langevin’s function (u), and correlation of spin moment C to A is u3 (Figure 6.25). In this way, the summation in Eq. (6.30) is generated, and its resolution leads to Curély’s law.   ∞ ∞ ∞ ∞ ui + 2 uj + 4 ui+j  χ T = χ Tfree–ion 1 + 2 = χ Tfree–ion

j =1

i=1

1+u 1−u

2

i=1 j =1

(6.30)

Notwithstanding, three short correlation paths exist between the A and C spin moments (1, 2 and 3), so the u3 term must be computed three times. An analytical law can easily be deduced from the summation generated by computing all these paths (even for the alternating case), but an infinite number of correlation paths such as 4 and 5, and a finite number such as 6, have been omitted from this reasoning. These longer correlation pathways are not so important for a wide range of T /|J | values, but they are numerous and the contribution from all of them can be significant and must not be disregarded. Therefore, the calculation of ECS laws for more than 1D becomes impossible. In Table 6.4, the number of different spin cor-

B 4 A

C

2

1

A C C

5 C

6 A 3 C

Fig. 6.25. Illustration of correlation paths to spin moments.

216


Table 6.4. Number of individual spin correlation paths (λ) as a function of the correlation path length (n) in a 2D square network, obtained by SPPA method. n

λ

n

λ

n

λ

0 1 2 3 4 5 6 7

1 4 12 36 104 300 848 2392

8 9 10 11 12 13 14 15

6674 18600 51480 142412 391956 1078612 2956928 8105796

16 17 28 29 20

22155058 60555564 165126324 450294176 1225587036

(a)

(b) 0.250

0.300 SPPAO

SPPAO =4 and 5 max SPPAO =10 and 11

=4 and 5

0.200

max

SPPAO

3

=18 and 19

max

CSMC 0.150

0.100

max

F_J| / cm3mol-1K

SPPAO =10 and 11 max SPPAO =14 and 15

-1

F|J| / cm mol K

max

5

10

15

T / |J|

20

25

max

SPPAO

=18 and 19

SPPAO

=24 and 25

max

max

0.200

CSMC

0.150

0.100

0.050

=14 and 15

SPPAO

0.250

5

10

15

20

25

T / |J|

Fig. 6.26. χ |J | versus T /|J | plots as a function of the length of the spin correlation path for two antiferromagnetic regular 2D networks: (a) square and (b) honeycomb. The results are compared with the CSMC simulation (dots).

relation paths as a function of the correlation path length is shown. In Figure 6.26, simulated χ|J | versus T /|J | curves are shown where the number of spin correlation paths considered is limited by a prefixed maximum length of these paths (spin path progressive addition method, SPPA). These curves show better agreement with the MC simulation as this maximum length increases, so in the infinite limit complete agreement is expected. However, many of these spin correlation paths involve one or several loops. Thus, as has been previously shown, these loops do not allow the factorisation of the partition function and the total spin correlation function cannot be developed in individual contributions, which invalidates this methodology [51]. Nevertheless, as these closed paths become relevant only at low T /|J | values, then the simulated curves reach the best agreement with the MC simulation at T /|J | > 8.7 K. The threshold T /|J | value for the applicability of the SPPA method is higher in a honeycomb (6.6 K) than in a square networks, because the number of closed paths is lower for a prefixed correlation path length in the first case. In Table 6.5, the temperature expansion for Curély’s law and for results obtained by SPPA, CSMC and

6.7 Some Complex Examples

217

Table 6.5. Coefficients of the temperature expansion series for 2D square and 2D honeycomb networks obtained by Curely’s law and by SPPA, CSMC and HTE methods [13, 30, 31, 49, 50]. n

Curely’s Law

0 1 2 3 4 5 6

1.00000 2.66667 3.55555 2.84444 1.26420 0.06020 0.28896

Square 2D 1.00000 1.00000 2.66667 2.65737 5.33333 5.22918 9.95556 9.59006 17.69877 16.81410 31.24374 29.8237 53.99729 52.41480

1.00000 2.66667 5.33333 9.95556 16.90864 27.24044 42.21216

0 1 2 3 4 5 6

1.00000 2.00000 1.77778 0.94815 0.63210 0.46655 0.14448

Honeycomb 2D 1.00000 1.00000 2.00000 1.99966 2.66667 2.65477 3.02222 2.98714 3.31852 3.20519 3.67972 3.41378 3.83925 3.56714

1.00000 2.00000 2.66667 3.02222 3.31852 3.67972 3.57587

SPPA

CSMC

HTE

HTE methods are compared. In the CSMC method, the coefficients are obtained from empirical laws presenting maximum terms β 25 and β 27 for the square and honeycomb networks, respectively. These empirical laws are obtained from a fit of the MC simulation data (see Section 6.3), which entails some uncertainties that lead to very small discrepancies in the first coefficients of the expansion series (see Table 6.5). A good agreement is obtained between the SPPA, CSMC and HTE methods, whereas Curély’s law is certainly not efficient at describing the magnetic behavior of 2D systems. The SPPA method diverges from the CSMC and the HTE methods when the path length is long enough to consider loop diagrams. Differences found between CSMC and HTE methods are due to the limitations of this last method at low T /|J | values.

6.7 Some Complex Examples The first example is a one-dimensional system with the formula [{N(CH3 )4 }n ][Mn2 (N3 )5 (H2 O)}n ], which, from a magnetic point of view, can be considered as a chain where there are magnetic couplings between near and second neighbours (Figure 6.27) [53]. The interaction topology of this system has been simplified by considering only two different exchange coupling constants. A

218


Fig. 6.27. Crystal structure and magnetic properties of [{N(CH3 )4 }n ][Mn2 (N3 )5 (H2 O)}n ] [53]. The experimental data (circles) and the simulations by Monte Carlo methods (solid line) are shown.

good agreement between the experimental and simulated data is obtained using two different sets of parameters: g = 2.001, J1 = 1.57 cm−1 and J2 = 0.29 cm−1 or g = 2.007, J1 = 0.66 cm−1 and J2 = 1.07 cm−1 . However, a careful analysis of the structure (angles, bond lengths), as already done in Section 6.4, does not reveal the set of parameters with the best physical meaning. Furthermore, the determination of ferromagnetic interactions is always fairly inaccurate and the use of a simplified interaction topology does not permit unambiguous assignment [53]. Compound Csn [{Mn(N3 )3 }n ] is a 3D solid where three different magnetic interactions occur (Figure 6.28) [53]. Regarding the interaction topology, this system can be described as a stacking of alternating honeycomb planes. The magnetic behavior has been simulated using the set of parameters: g = 2.029, J1 = 0.76 cm−1 , J2 = −4.3 cm−1 and J3 = −3.3 cm−1 . The J values found for the interaction through a µ-1,1- or µ-1,3-azido bridge are similar to those found in simpler systems [42, 53]. As in a previous example, the values of the J constants are corroborated by the theoretical magneto-structural correlation performed by Ruiz et al. from DFT calculations [44].

Fig. 6.28. Crystal structure and magnetic properties of Csn [{Mn(N3 )3 }n ] [53]. The experimental data (circles) and the simulations by Monte Carlo methods (solid line) are shown.

6.7 Some Complex Examples 64

J2

M

M

3

J3

55

50

F T

F T / cm K mol

-1

M

F T

60

J1

219

40

62

(a)

60

40

0

(b)

30

60

T/K

25 0

T/K

1400

30 0

100

200

300

T/K

Fig. 6.29. Crystal structure, interaction topology and magnetic properties of [Fe10 Na2 (O)6 (OH)4 (O2 CPh)10 (chp)6 (H2 O)2 (MeCO)2 ] [54]. The experimental data (circles) and the simulations by Monte Carlo methods (solid line) are shown.

Compound [Fe10 Na2 (O)6 (OH)4 (O2 CPh)10 (chp)6 (H2 O)2 (MeCO)2 ] (chp = 6chloro-2-pyridonato) is an example of a high-nuclearity molecule (Figure 6.29) [54]. This system is too big to be studied considering quantum spin moments, but the CSMC method allows one to accurately simulate its magnetic behavior using the coupling constant values: g = 2.0, J1 = −44 cm−1 , J2 = −13 cm−1 and J3 = −10 cm−1 . Cano et al. rationalize the values of the the four coupling constants taking into account the different bridging ligands, structural parameters and some other data found in the literature. They conclude that the values found for the four constants have a physical meaning. Compound {[(tacn)6 Fe8 (µ3 -O)2 (µ2 -OH)12 ]Br7 (H2 O)}Br·H2 O (tacn = 1,4,7triazacyclononane) is one of a few examples of a single molecule magnet (Figure 6.30) [12, 55–57]. There are many interesting potential applications of these systems. Although the study of the magnetic behavior of these systems is very important, in some cases it is not yet possible to perform. This system is situated at the limit where exact quantum solutions can be found. The simulated and experimental χ T versus T curves are shown in Figure 6.30. The theoretical curves 50.0

J2 J1

CSMC simulation

FT / cm3mol-1K

J3

J4

Quantum result

40.0 O

Experimetnal data

30.0

20.0

0

50

100

150

200

250

300

T/K

Fig. 6.30. Crystal structure, interaction topology and magnetic properties of {[(tacn)6 Fe8 (µ3 O)2 (µ2 -OH)12 ]Br7 (H2 O)}Br·H2 O [12, 55–57]. The experimental data (circles), the CSMC simulation (solid line) and quantum solution (dashed line) are shown.

220


have been obtained from the exact quantum solutions and from the CSMC method using, in both cases, the same parameter values. In the CSMC simulation, in order to better describe the magnetic behavior at very low temperatures, an extra parameter (θ) has been added to consider the magnetic intermolecular interaction (g = 2.0, J1 = −20 cm−1 , J2 = −120 cm−1 , J3 = −15 cm−1 , J4 = −35 cm−1 and θ = −2.2 cm−1 ).

6.8 Conclusions and Future Prospects In this chapter it has been established that the classical spin approach allows proper analysis of the magnetic behavior of systems with high local spin moments (S ≥ 2). Nevertheless, this approach cannot easily be applied to a great variety of systems. In these cases, it is possible to accomplish this objective using Monte Carlo methods, which appears as a powerful tool in numerical integration to evaluate physical properties. Thus, the Monte Carlo methods applied to a classical spin Heisenberg model (CSMC) are able to study any system, whatever its complexity, and the only limitation of this method is due to the classical spin approach. Unfortunately, the simple CSMC method cannot be applied to systems that present small local spin moments (S < 2). For such cases, it is possible to use alternative methods although they are far more complicated. Among these methods are the Density Matrix Renormalization Group and Quantum Monte Carlo. However, this is another story, too long to be told in detail, and beyond the scope of the present chapter.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

S. Ferlay, T. Mallah, R. Ouahès et al., Nature 1995, 378, 701. O. Kahn, Y. Pei, M. Verdaguer et al., J. Am. Chem. Soc. 1988, 110, 782. J.S. Miller, J.C. Calabrese, H. Rommelmann et al., J. Am. Chem. Soc. 1987, 109, 767. G. Christou, in Magnetism: a Supramolecular Function, Ed. O. Kahn, Kluwer Academic Publishers, Dordrecht, 1996, p. 383. A. Scuiller, T. Mallah, M. Verdaguer et al., New. J. Chem. 1996, 20, 1. R. Sessoli, H.L. Tsai, A.R. Schake et al., J. Am. Chem. Soc. 1993, 115, 1804. S.R. Batten, R. Robson, Angew. Chem. Int. Ed. Engl. 1998, 37, 1460. A. Müller, E. Krickemeyer, J. Meyer et al., Angew. Chem. Int. Ed. Engl. 1995, 34, 2122. A. Müller, C. Serain, Acc. Chem. Res. 2000, 33, 2. R. Sessoli, D. Gatteschi, A. Caneschi, Nature 1993, 365, 141. D. Gatteschi, A. Caneschi, L. Pardi et al., Science 1994, 265, 1054. D. Gatteschi, A. Caneschi, R. Sessoli et al., Chem. Soc. Rev. 1996, 101.

References

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13. R. Navarro, in Magnetic Properties of Layered Transition Metal Compounds, Ed. L.J.D. Jongh, Kluwer Academic Publishers, Dordrecht, 1990, p. 105. 14. E. Coronado, M. Drillon, R. Georges, in Research Frontiers in Magnetochemistry, Ed. C. O’Connor, World Scientific Publishing, Singapore, 1993, p. 27. 15. O. Kahn, Molecular Magnetism, VCH, New York, 1993. 16. S.R. White, R.M. Noack, Phys. Rev. Lett. 1992, 68, 3487. 17. S.R. White, Phys. Rev. Lett. 1992, 69, 2863. 18. K. Binder, D.W. Heermann, Monte-Carlo Simulation in Statistical Physics, SpringerVerlag, Berlin, 1988. 19. L. Onsager, Phys. Rev. 1944, 65, 117. 20. M.E. Fisher, Am. J. Phys. 1964, 32, 343. 21. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth et al., J. Chem. Phys. 1953, 21, 1087. 22. W.H. Press, S.A. Teukolsky, W.T. Vetterling et al., Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd edn., Press Syndicate of the University of Cambridge, Cambridge, 1996. 23. H. Gould, J. Tobochnik, An Introduction to Computer Simulations. Applications to Physical Systems, Addison-Wesley, New York, 1996. 24. M. Suzuki, in Quantum Monte Carlo Methods, Ed. M. Suzuki, Springer-Verlag, Heidelberg, 1986. 25. M. Suzuki, Prog. Theor. Phys. 1976, 56, 1454. 26. M. Suzuki, Phys. Rev. 1985, 31, 2957. 27. S. Yamamoto, Phys. Rev. B 1996, 53, 3364. 28. J. Cano, Y. Journaux, Mol. Cryst. Liq. Cryst. 1999, 335, 685. 29. G.S. Rushbrooke, P.J. Wood, Mol. Phys. 1958, 1, 257. 30. W.J. Camp, J.P.V. Dyke, J. Phys. 1975, C8, 336. 31. H.E. Stanley, Phys. Rev. 1967, 158, 546. 32. H.E. Stanley, Phys. Rev. Lett. 1967, 20, 589. 33. J.E. Lines, J. Phys. Chem. Solids 1970, 31, 101. 34. A. Herpin, Théorie du Magnétisme, INSTN, Saclay, 1968. 35. F.A. Mautner, R. Cortés, L. Lezama, T. Rojo, Angew. Chem. Int. Ed. 1996, 35, 78. 36. E. Boullant, J. Cano, Y. Journaux et al., Inorg. Chem. 2001, 40, 3900. 37. S. Decurtins, H.W. Schmalle, P. Schneuwly et al., J. Am. Chem. Soc. 1994, 116, 9521. 38. R. Cortés, M. Drillon, X. Solans et al., Inorg. Chem. 1997, 36, 677. 39. A. Escuer, R. Vicente, M.A.S. Goher et al., Inorg. Chem. 1998, 37, 782. 40. G. Viau, M.G. Lombardi, G.D. Munno et al., Chem. Commun. 1997, 1195. 41. R. Cortés, L. Lezama, J.L. Pizarro et al., Angew. Chem. Int. Ed. Engl. 1994, 33, 2488. 42. J. Cano, Y. Journaux, M.A.S. Goher et al., New. J. Chem., accepted. 43. M.A.M. Abu-Youssef, M. Drillon, A. Escuer et al., Inorg. Chem. 2000, 39, 5022. 44. E. Ruiz, J. Cano, S. Alvarez et al., J. Am. Chem. Soc. 1998, 120, 11122. 45. K.L. Taft, C.D. Delfs, G.D. Papaefthymiou et al., J. Am. Chem. Soc. 1994, 116, 823. 46. S.P. Watton, P. Fuhrmann, L.E. Pence et al., Angew. Chem. Int. Ed. Engl. 1997, 36, 2774. 47. J. Curély, J. Rouch, Physica B 1998, 254, 298. 48. J. Curély, Physica B 1998, 254, 277. 49. J. Curély, F. Lloret, M. Julve, Phys. Rev. B 1998, 58, 11465. 50. J. Curély, Europhys. Lett. 1995, 32, 529. 51. Y. Leroyer, Europhys. Lett. 1996, 34, 311. 52. G. DeMunno, R. Ruiz, F. Lloret et al., Inorg. Chem. 1995, 34, 408.

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6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties M.A.S. Goher, J. Cano, Y. Journaux et al., Chem. Eur. J. 1999, 6, 778. C. Benelli, J. Cano, Y. Journaux et al., Inorg. Chem. 2001, 40, 188. C. Delfs, D. Gatteschi, L. Pardi et al., Inorg. Chem. 1993, 32, 3099. Y. Pontillon, A. Caneschi, D. Gatteschi et al., J. Am. Chem. Soc. 1999, 121, 5342. C. Sangregorio, T. Ohm, C. Paulesn et al., Phys. Rev. Lett. 1997, 78, 4645.

7 Metallocene-based Magnets Gordon T. Yee and Joel S. Miller

7.1 Introduction A wide variety of magnetically ordered solids derived from organic and organometallic building blocks have been characterized in the past few years [1, 2] These reports of bulk ferro-, ferri-, and antiferromagnetism follow those of superconductivity in organic solids [3] and extend the types of cooperative phenomena observed in molecule-based materials. The great strength of this class of compounds is that modification of their physical properties via conventional synthetic organic and inorganic methods may lead to future generations of molecule-based electronic devices including so-called ‘smart’ materials and systems [4]. The best examples of this concept include the organic light emitting diode flat panel displays, organic photoconductors and liquid crystal displays. One attractive approach to the generation of new magnetically interesting phases is the synthesis of electron transfer (ET) salts with a general formula of [donor]+ [acceptor]− , abbreviated D+ A− .1 This strategy has produced not only isolated examples of magnets but families of structurally and electronically related compounds from which systematic relationships are being deduced. An important feature of this class of compounds is that the spin coupling between the building blocks is thought to be exclusively “through-space” as there are no covalent bonds between D+ and A− . Also, the large anisotropy in these solids permits the separate treatment of the relatively strong intrachain interactions and the weaker interchain coupling. Understanding the mechanism of through-space interactions is one of the most challenging problems in this field, and all but the three-dimensional coordination polymers probably require some degree of this type of coupling to achieve magnetic order, because magnetic ordering cannot occur for a 1D system [5]. In the role of the donor, decamethylmetallocenes, MCp*2 , where Cp* = decamethylcyclopentadienyl and M = principally Cr, Mn and Fe (Scheme 7.1) are unsurpassed. The reasons for this are manifold and not altogether understood, but 1 Also called “charge-transfer salts” in the literature.

224

7 Metallocene-based Magnets

Fe

Scheme 7.1 Decamethylferrocene, FeCp*2 .

certainly include the electrochemical reversibility of their 0/+1 couples, their tendency to π stack and the fact that their monocations all possess at least one unpaired electron. They are also commercially available, which has facilitated their exploration as a building block. The acceptor is generally an organic molecule with an extended π system, substituted with electron withdrawing groups, especially nitriles and likewise is typically commercially available. However, in recent years, much of the progress has been in synthesizing additional acceptors. This chapter summarizes the magnetic properties of the known ET salts based on decamethylmetallocenium cations and related species paired with paramagnetic anions. Electrochemical and magnetic properties of the neutral metallocenes are summarized to introduce the subject. This is followed by families of ET salts grouped according to the acceptor with olefinic acceptors treated first, quinonebased acceptors second, and metal complex acceptors third. Magnetostructure– property correlations will be discussed and the current state of theoretical models will be considered. The chapter concludes with a brief examination of the research opportunities that exist in this field. One group of paramagnetic acceptor anions, namely, metal dithiolate complexes, will not be extensively reviewed herein as they are the subject of Chapter 1.

7.2 Electrochemical and Magnetic Properties of Neutral Decamethylmetallocenes and Decamethylmetallocenium Cations Paired with Diamagnetic Anions Metallocenes, MCp2 , where M is a first row transition metal in the 2+ oxidation state and Cp is cyclopentadienide, and to an even greater extent, decamethylmetallocenes, MCp*2 , where Cp* is pentamethylcyclopentadienide, can be easily and reversibly oxidized [6] (Figure 7.1) making them suitable as donors for electron transfer salts. In general, the substitution of each H with Me on the periphery of the Cp ring shifts the one-electron reduction potential more negative by about 0.05 V. Except for ferrocenes, all the neutral donors shown in Figure 7.1 are easily oxidized in the air, and Schlenk apparatus and/or glove box methods need to be rigorously employed.

7.2 Electrochemical and Magnetic Properties of Neutral Decamethylmetallocenes Fe (C5MeH4)2 FeCp2

C4 (CN)6 DClDQ

FeCp* 2

Fe(C5Me 4H)2

0.5 V

225

MnCp* 2

0V

NiCp* 2

CrCp* 2

- 0.5 V

DCNQ TCNQ/TCNE

- 1.0 V

CoCp* 2

- 1.5 V

DMeDCF

Me 2DCNQI

Fig. 7.1. Electrochemistry (vs. SCE) of some donors and acceptors (see text for abbreviations).

The spin states, S, of metallocenium cations are a consequence of unpaired electrons in metal d orbitals split by either the D5h or D5d ligand field.2 Vanadocenes are 15 electron species and very reactive, hence relatively unexplored. Decamethylcobaltocenium is an 18 electron species and hence diamagnetic. This leaves, as the most important species, those based on chromium, manganese and iron, for reasons explained below. Based on the information in Table 7.1, the Landé g values for [MnCp*2 ]+ and [FeCp*2 ]+ are expected to be different from the free electron value (2.0023), due to an orbital contribution to the magnetic moment. In fact, for M = Fe(III) the g value is very anisotropic (g > 4; g⊥ ∼ 1.25) [7]. The anisotropic g values for decamethylmanganocenium have not been determined because the S = 1 species does not give an EPR signal. However, average g values from powder magnetic measurements have placed it at between 2.2 and 2.4. Anisotropy is important to the manifestation of hysteresis, a characteristic of some ferromagnets. It is also the source of some of the variation in the values of magnetic properties of compounds reported in the literature. For instance, due to anisotropy, two samples

Table 7.1. Electronic Ground State and Spin State (S), for MCp*2 , [MCp2 ]+ , MCp*2 , and [MCp*2 ]+ . M

V

Ground state, MCp2 S, MCp2 Ground state, [MCp2 ]+ S, [MCp2 ]+ Ground state, MCp*2 S, MCp*2 Ground state, [MCp*2 ]+ S, [MCp*2 ]+

4A

Cr 2g

3/2 3E 2g 1 4A 2g 3/2 3E 2g 1

3A

2g

1 4A 2g 3/2 3A 2g 1 4A 2g 3/2

Mn

Fe

Co

Ni

6A

1g

1A 1g

2E 1g

3A 2g

5/2 3E 2g 1 2E 2g 1/2 3E 2g 1

0 2E 2g 1/2 1A 1g 0 2E 2g 1/2

1/2 1A 1g 0 2E 1g 1/2 1A 1g 0

1 2E

1g

1/2 3A 2g 1 2E 1g 1/2

2 The point group symmetry is D 5h when the rings are eclipsed and D5d when they are

staggered. Both geometries are found.

226


of the same compound, nominally randomly oriented, can exhibit different room temperature values of χ T , if they are not truly random, but partially aligned to different degrees.

7.3 Preparation of Magnetic Electron Transfer Salts 7.3.1

Electron Transfer Routes

The synthesis of ionic electron transfer salts typically involves the reaction of a neutral donor capable of reducing a neutral organic acceptor. Fortunately, solution electrochemistry may be used as a guide to predict reactivity. A distinct advantage of the electron transfer strategy over other methods of preparing molecule-based magnets [8] is that, with only this electrochemical constraint, the donor and acceptor may be varied independently to produce additional candidate magnets. Furthermore, by-products from this procedure, in general, are minimized. This translates to the ability to investigate an array of related compounds from each new acceptor by pairing it with all available donors with which it is predicted to react. If 0 0), it must be paired with a a newly synthesized acceptor is weak (i. e. E0/−1 strong donor to enable the pair to satisfy the electron transfer criterion. As a rule of thumb, every acceptor on the scale above (Figure 7.1) will react by outer-sphere electron transfer with every donor located to the right of it to yield an ionic product. So, although TCNE reacts with both decamethylferrocene, FeCp*2 , and ferrocene, FeCp2 , to give 1:1 complexes, only the former is a paramagnetic ionic salt at room temperature. One caveat is that the solvent can play a role in the driving force for this reaction and the structural phase obtained from this method and the metathetical route described below. In some cases, incorporation of the solvent into the crystal lattice leads to additional phases. For example, the reaction of FeCp*2 and TCNE in THF yields [FeCp*2 ][TCNE], whereas in acetonitrile it yields [FeCp*2 ][TCNE]·MeCN. Furthermore, as is the case with FeCpCp* and TCNE, more complex materials, i. e. [FeCpCp*]2 [TCNE]3 ·x(solvent) form [9].

7.3.2

Metathetical Routes

An alternative way to synthesize ET salts involves the reaction of the cationic oxidized donor and a reduced acceptor anion. Careful selection of the counter anion and counter cation, respectively, allows the tuning of the solubilities and reactivities of the components to a much greater degree, but at the sacrifice of simplicity. For

7.4 Crystal Structures of Magnetic ET Salts

227

instance, this approach was used in the preparation of [MnCp*2 ][TCNQ] from solutions of [MnCp*2 ]PF6 and NH4 [TCNQ] [10]. In some cases it is the only route available if the neutral donor and/or acceptors are not available. This was the case for the synthesis of the metal bis(dicyanodithiolate)metal-based (M[S2 C2 (CN)2 ]− 2, M = Ni, Pd, Pt) family of solids [11].

7.4 Crystal Structures of Magnetic ET Salts All magnetically ordering electron transfer salts crystallographically characterized to date have been shown to adopt an alternating · · ·D+ A− D+ A− · · · structure in the π stacking direction to form 1D chains in the solid state [12a, 13b, d, 14], Figure 7.2. This arrangement gives rise to the dominant magnetic interaction, which is intrachain (Jintra ), and usually ferromagnetic for this class of materials. The unit cell typically contains four such chains (arranged as two pairs of two chains, Figure 7.3, top) giving rise to four unique nearest-neighbor pairwise interchain interactions. Within each pair the adjacent chains are in-registry with respect to each other. The two pairs are out-of-registry with respect to each other. While some of the various Jinter values might be similar in magnitude, it is important to note that there is strong evidence that they are not all positive (i. e. not all indicate ferromagnetic coupling). The effects of the competition between ferromagnetic and antiferromagnetic coupling are evident in the results presented below in the type of ordering phenomenon observed.

Fig. 7.2. Segment of the alternating D+ A− D+ A− linear chain structure observed for [FeCp*2 ][TCNE] · MeCN [12a], and most other magnetic ET salts.

228


Fig. 7.3. Packing diagram for β and γ-[FeCp*2 ][TCNQ]. View down the chain axis showing the inter chain interactions between chains I, II, III, and IV, top, and view parallel to the in-registry chains I–II, and out-of-registry chains I–III and I–IV for ferromagnetic γ -[FeCp*2 ][TCNQ] (right hand side) and metamagnetic β-[FeCp*2 ][TCNQ] (left hand side). Other ET salts exhibit similar structures.

7.4 Crystal Structures of Magnetic ET Salts

Fig. 7.3. (Continued.)

229

230


7.5 Tetracyanoethylene Salts (Scheme 7.2) NC

CN

NC

CN

7.5.1

Scheme 7.2 Tetracyanoethylene, TCNE.

Iron

The first electron transfer salt demonstrated to have a ferromagnetic ground state was decamethylferrocenium tetracyanoethenide, [FeCp*2 ][TCNE] [14]. Single crystal X-ray studies of [FeCp*2 ][TCNE]·MeCN and [FeCp*2 ][TCNE] have been reported [14a]. Both pseudopolymorphs are composed of parallel chains of alternating [FeCp*2 ]+ cations and [TCNE]− radical anions as illustrated in Figure 7.2. Monoclinic [FeCp*2 ][TCNE]·MeCN is a well-determined structure as it lacks disorder, but does have layers of MeCN solvent separating the parallel chains along the c-axis. In contrast, the structure of orthorhombic [FeCp*2 ][TCNE] is not completely resolved due to disorder of the [TCNE]− anions. The intrachain Fe· · ·Fe separation is 10.415 Å for [FeCp*2 ][TCNE]·MeCN and 10.621 Å for [FeCp*2 ][TCNE] [14a]. Nonetheless, due to the lack of solvent the interchain separations are shorter for [FeCp*2 ][TCNE] than for [FeCp*2 ][TCNE]·MeCN. Attempts to determine the structure of the former at low temperature to minimize, if not eliminate, the disorder in the structure were thwarted by two phase transitions [14a, 46c] (Figure 7.4) that lead to the destruction of the crystals. A variety of physical measurements have confirmed that magnetic order exists below a critical ordering temperature, Tc , of 4.8 K [14, 15] and its paramagnetic properties above Tc have also been thoroughly examined. The high temperature susceptibility of powder samples of [FeCp*2 ][TCNE] fits the Curie–Weiss expression with θ = +30 K indicating dominant ferromagnetic interactions [14]. The calculated and observed room temperature susceptibility and saturation magne-

Fig. 7.4. Excess heat capacity, [Cp (T )], for [FeCp*2 ][TCNE] [41c] Showing two structural phase transitions occurring below room temperature.

7.5 Tetracyanoethylene Salts (Scheme 7.2)

231

Table 7.2. Summary of magnetic properties of ferromagnetic [FeCp*2 ][TCNE]. Formula Formula mass Structure Solubility Critical/Curie temperature Curie–Weiss Constant, θ Spontaneous magnetization Magnetic susceptibility (290 K) ( to 1D chains) Magnetic susceptibility (290 K) (⊥ to 1D chains) Saturation magnetization (290 K) ( to 1D chains) Saturation magnetization (290 K) (⊥ to 1D chains) Intrachain exchange interaction ( to 1D chains) Intrachain exchange interaction (⊥ to 1D chains) Coercive field, Hcr (2 K)

C26 H30 N4 Fe 454.4 Da 1-D . . .D+ A− D+ A− . . . chains Conventional organic solvents (e.g. MeCN, CH2 Cl2 , THF) 4.8 K +30 K Yes, in zero applied field 0.00667 emu mol−1 (observed) 0.00640 emu mol−1 (calculated) 0.00180 emu mol−1 (observed) 0.00177 emu mol−1 (calculated) 16,300 emu-G mol−1 (observed) 16,700 emu-G mol−1 (calculated) 6,000 emu-G mol−1 (observed) 8,800 emu-G mol−1 (calculated) 27.4 K (19 cm−1 ) 8.1 K (5.6 cm−1 ) 1000 Oe

tization are in excellent agreement (Table 7.2) [14]. Spontaneous magnetization is observed for polycrystalline samples below 4.8 K in the Earth’s magnetic field [14] that is 36% greater than iron metal on a per iron atom basis. Hysteresis loops characteristic of ferromagnetic materials are observed featuring a coercive field of 1 kOe at 2 K, Figure 7.5, [14]. Preliminary studies of the pressure dependence of

Fig. 7.5. M(H ) for [FeCp*2 ][TCNE] at 2 K.

232


Tc reveal that it increases with applied pressure by 0.21 K kbar−1 and reaches 7.8 K at 14 kbar applied pressure [16].

7.5.2

Manganese

The synthesis of [MnCp*2 ][TCNE] was more challenging because the solid is not stable at room temperature unless completely dry and kept under an inert atmosphere. For this reason, it must be synthesized and isolated at −40◦ C utilizing Schlenk techniques [17]. [MnCp*2 ][TCNE] orders ferromagnetically at 8.8 K and, although no single crystal structure analysis has been performed, IR (νCN = 2143, 2184 cm−1 ) and powder diffraction have been used to relate it to its iron analog. Like [FeCp*2 ][TCNE], [MnCp*2 ][TCNE] exhibits hysteresis with a Hcr = 1.2 kOe at 4.2 K. Based on the McConnell model II (vide infra), this compound should also exhibit ferromagnetic coupling, as is observed (θ = +22.6 K). There is evidence, in the form of frequency dependent ac susceptibility data, that this compound exhibits glassiness indicating that the compound is not fully long-range ordered [18].

7.5.3

Chromium

[CrCp*2 ][TCNE] was independently prepared by the groups of Hoffman and Miller. It was reported to order ferromagnetically at 2.1 [19] and 3.65 K [20], respectively, but does not exhibit hysteresis above 2 K. This is ascribed to the lack of anisotropy at the Cr(III) center. The difference in Tc is thought to be due to different phases of the material, with only the latter CH2 Cl2 -grown magnet being structurally characterized. This material is not isomorphous to either [FeCp*2 ][TCNE] or [FeCp*2 ][TCNE]·MeCN [12a], and belongs to the P 21 /n space group. Furthermore, the 2.1 K Tc magnet was made from MeCN and may contain some solvent. Application of the aforementioned McConnell model II to [CrCp*2 ][TCNE] {and [CrCp*2 ][TCNQ] (vide infra)} leads to the expectation of antiferromagnetic coupling leading to ferrimagnetic behavior; however, ferromagnetic order, as evidenced by the value of the saturation magnetization, is observed.

7.5.4

Other Metals

[NiCp*2 ][TCNE] has been prepared from the reaction of NiCp*2 and TCNE. It exhibits antiferromagnetic coupling with θ = −10 K [21]. The CoIII analog, [CoCp*2 ][TCNE], with S = 0 [CoCp*2 ]+ has also been prepared and exhibits essentially the Curie susceptibility anticipated for S = 1/2 [TCNE]− (θ = −1.0 K) [12a]. Attempts to prepare [MnIII Cp*2 ]+ (M = Ru, Os) salts of [TCNE]− have yet to lead to suitable compounds for comparison with the highly magnetic FeIII

7.5 Tetracyanoethylene Salts (Scheme 7.2)

233

phase [22]. Formation of [RuCp*2 ]+ is complicated by rapid disproportionation to diamagnetic RuII Cp*2 and diamagnetic [RuIV Cp*(C5 Me4 CH2 )]+ [23]. The Os analog has led to the preparation of a low susceptibility salt with TCNE; however, crystals suitable for single crystal X-ray studies [22] have not as yet been isolated, limiting progress in this area.

7.6 Dimethyl Dicyanofumarate and Diethyl Dicyanofumarate Salts Two olefinic acceptors that are electronically very similar to each other and to TCNE, dimethyl and diethyl dicyanofumarate (DMeDCF and DEtDCF, respectively), Scheme 7.3, have been investigated. Given the related geometry of these acceptors, the intrachain interactions in the resulting magnetic salts were theorized to be similar and thus, any differences in bulk magnetic properties would be due to modifications in interstack separations only, due to the additional ∼2–3 Å in the lateral direction from the alcohol portions of the diester. O RO

CN R = Me, Et NC

OR O

Scheme 7.3 Dialkyl dicyanofumarate, DRDCF.

The synthesis of these molecules was previously reported by Ireland and coworkers [24] who used the oxidative dimerization of commercially available αcyanoesters. Mulvaney and co-workers showed that they exhibit reversible oneelectron reductions at approximately −0.22 V vs. SCE [25]. As such, both decamethylmanganocene and decamethylchromocene react with each of these acceptors to give well-defined 1:1 ET salts, but decamethylferrocene is not sufficiently reducing to react to give an ionic product.

7.6.1

Manganese

Like their TCNE analog, neither [MnCp*2 ][DMeDCF] nor [MnCp*2 ][DEtDCF] is stable at room temperature when wet with solvent and so each must be prepared and isolated at low temperature. Both are synthesized in dichloromethane and appear as shiny brown-gold needles. Careful attempts to grow large single crystals have been unsuccessful.

234


The bulk magnetic properties of the DMeDCF salt are reminiscent of the corresponding TCNE salt. Dominant ferromagnetic coupling (θ = +15 K) gives rise to apparent ferromagnetic order below Tc = 10.5 K, including well-formed rectangular hysteresis loops with Hcr = 7 kOe at 1.8 K [26]. Ac Susceptibility measurements on the compound show significant frequency dependence, indicative of glassiness. The structure of this compound is believed to be isomorphous with its chromium analog (vide infra) by powder diffraction. As expected, θ for [MnCp*2 ][DEtDCF] is also 15 K, consistent with similar intrachain coupling (Jintra ) in the π stacking direction [26]. In contrast, however, as the temperature is decreased, [MnCp*2 ][DEtDCF] undergoes a 3D antiferromagnetic phase transition at approximately 12 K. The nature of this transition is indicated by low temperature ac susceptibility and magnetization vs. applied field measurements. At 9 K, this compound is a metamagnet with critical field, Hc = 500 Oe. Upon further cooling, this compounds appears to undergo a transition to a re-entrant spin glass state that is accompanied by a large coercive field approaching 10 kOe. Structure elucidation of the chromium analog suggests that the magnetic data reported for this compound are on a crystallographically disordered solid due to loss of solvent (vide infra).

7.6.2

Chromium

[CrCp*2 ][DMeDCF] is stable at room temperature in acetonitrile, permitting its crystallization [27]. It exhibits the usual mixed stack structure (Figure 7.2). Above 50 K, the χ −1 vs. T data can be fitted to the Curie–Weiss law with θ = 23 K. It also orders as a ferromagnet below 5.7 K, which is higher than its TCNE and TCNQ analogs. Presumably because of the 4 A ground state of the cation, the compound shows no hysteresis and the saturation magnetization (Msat =∼ 22,000 emuG mol−1 ) is the value expected for four unpaired electrons with g = 2. In contrast to the Mn analog, it does not exhibit frequency-dependent ac susceptibility [27] and hence, lacks glassy behavior. As expected, [CrCp*2 ][DEtDCF] is magnetically similar to its dimethyl analog, but only up to a point. It exhibits Curie–Weiss behavior with θ = +22 K, again showing that the intrastack interactions strengths are similar [28]. However, instead of a ferromagnetic phase transition, there appears to be an antiferromagnetic phase transition (peak in χ (T )) at 5.4 K, which is identified by a lack of a χ (T ) ac signal. This suggests that, like its manganese analog, increasing the separation between the stacks decreases the interchain ferromagnetic coupling, causing a change from ferromagnetic to antiferromagnetic order. Instead of going to zero as the temperature is lowered still further, as expected for an antiferromagnet, χ (T ) then begins to rise again, suggesting the onset of some sort of frustration and glassiness. At 1.8 K and 5000 Oe, the magnetization

7.7 2,3-Dichloro-5,6-dicyanoquinone Salts and Related Compounds

235

is only ∼70% of its expected saturation value, in marked contrast to the behavior of the dimethyl analog, which is fully saturated in this field. A crystal structure of this latter ET salt as its dichloromethane solvate, [CrCp*2 ][DEtDCF] ·2CH2 Cl2 , which complicates the above analysis, was reported recently [28]. That is, although the stacked . . .D+ A− D+ A− . . . motif is retained as expected, the added methylenes in the acceptor create just enough space between the stacks for two solvent molecules to flank each donor. These additional dichloromethane molecules act as spacers, changing the interstack interactions in ways that are not yet understood. All of the above magnetic data on DEtDCF-based salts were obtained on desolvated samples, implying that they possess intrinsic structural disorder. No crystal structures of the desolvated salt have been reported.

7.7 2,3-Dichloro-5,6-dicyanoquinone Salts and Related Compounds The effect of a subtle alteration in the structure on the magnetic properties has been probed with the study of the isomorphous 2,3-dihalo-5,6-dicyanoquinone (DXDQ; X = Cl, Br, I, Scheme 7.4)3 electron transfer salts of decamethylferrocene. At −70◦ C there are minimal differences in their respective solid state structures [16] and in the observed θ values which range from +10 to +12 K [21, 29] None of these compounds exhibits ordering above 2 K. As Tc in a mean field model is proportional to S(S + 1), [MnCp*2 ][DClDQ] was prepared anticipating that Tc might occur at a higher and thus experimentally more accessible temperature [30]. The magnetic susceptibility of [MnCp*2 ][DClDQ] can be fitted by the Curie–Weiss expression with θ = +26.8 K This strong ferromagnetic interaction between adjacent radicals within each chain coupled with a net weak antiferromagnetic interaction between the chains leads to metamagnetic behavior below TN = 8.5 K [31]. Below ∼4 K anomalous behavior with large hysteresis and remanent magnetization is observed [31]. Similar complex metamagnetic behavior was observed for [MnCp*2 ][DXDQ] (X = Br, I) at lower temperatures [21]. X

X

O

O

NC

CN

Scheme 7.4 2,3-Dihalo-5,6-dicyanoquinone, DXDQ (X = Cl, Br, I).

3 Usually DDQ in the literature, but DClDQ here to avoid ambiguity with other halogen-

substituted acceptors.

236


7.8 2,3-Dicyano-1,4-naphthoquinone Salts The one-electron acceptor, 2,3-dicyano-1,4-naphthoquinone, DCNQ, Scheme 7.5, has previously been explored in the context of organic metals [32]. Cyclic voltammetry indicates that its reduction potential is between that of DDQ and TCNQ. DCNQ is readily prepared from commercially available 2,3-dichloro-1,4naphthoquinone by cyanation with potassium cyanide and acid, followed by oxidation of the resulting naphthohydroquinone with nitric acid [32]. O CN

CN

Scheme 7.5 2,3-Dicyano-1,4-naphthoquinone, DCNQ.

O

7.8.1

Iron

DCNQ readily reacts with decamethylferrocene to form an air-stable crystalline electron-transfer salt that possesses the typical mixed stack architecture with both in-registry and out-of-registry chains [33]. The magnetic properties of [FeCp*2 ][DCNQ], Figure 7.6, are characteristic of a metamagnet with Hc of approximately 3 kOe. The magnetic order is believed to be ferromagnetic within the chains with both ferromagnetic and antiferromagnetic coupling between the chains. However, this compound is unusual as in the nominally antiferromagnetically ordered state, the moments are canted so that there is a net moment and hysteresis observed that is centered about zero. Such an organization is known as a weak

Magnetization (emu-G/mol)

10000

5000

0 -30000 -20000 -10000

0

10000

20000

30000

-5000

-10000 Applied field (Oe)

Fig. 7.6. M(H ) for [FeCp*2 ][DCNQ] at 1.8 K [33].

7.8 2,3-Dicyano-1,4-naphthoquinone Salts

237

ferromagnet or canted antiferromagnet [34]. This phase persists up to 4 K, from M(T ) measurements, where a transition to a paramagnetic state occurs. Mössbauer spectroscopy confirms the presence of a magnetic phase transition [33].

7.8.2

Manganese

The plot of magnetization vs. applied field determined at 1.8 K, Figure 7.7, indicates that [MnCp*2 ][DCNQ], like its iron analog, is also a metamagnet [35]. The critical field, Hc , at this temperature is also approximately 3 kOe. In the nominally antiferromagnetically ordered state, the compound exhibits a coercive field of approximately 1000 Oe and remanence of 500 emu-G mol−1 at 1.8 K. These data show that, like [FeCp*2 ][DCNQ], the moments in this compound are also canted slightly, again producing a weak ferromagnet. It is this condition that gives rise to hysteresis centered at zero and a non-zero out-of-phase component to the ac susceptibility (χ (T )). At 40 kOe, the magnetization is ∼13,000 emu-G mol−1 , approaching the expected value (18,400 emu-G mol−1 , assuming g = 2.3 for the decamethylmanganocenium cation) consistent with ferromagnetic coupling of the unpaired electrons. The low value of the saturation magnetization might indicate canting in the ferromagnet-like state, as well. The ac susceptibility data obtained in zero dc bias are also consistent with weak ferromagnetism. The peak in χ (T ) is accompanied by the onset of a small non-zero χ (T ) component that is associated with the presence of hysteresis, not characteristic of an uncanted (collinear) antiferromagnet. The ordered state persists up to 8 K. However, unlike [FeCp*2 ][DCNQ], [MnCp*2 ][DCNQ] exhibits additional hysteresis centered near the antiferromagnetic to ferromagnet-like transition. At ±Hc the sample does not switch back reversibly from ferromagnet-like to antiferromagnetic order as the field is decreased from a high value toward zero [35].

Magnetization (emu-G/mol)

15000 10000 5000 0 -40000

-20000

-5000

0

20000

40000

-10000 -15000 Applied field (Oe)

Fig. 7.7. M(H ) for [MnCp*2 ][DCNQ] at 1.8 K [35].

238


7.8.3

Chromium

The magnetic properties of the chromium analog are consistent with ferromagnetic coupling (θ = +6 K) within the chain and metamagnetism with a vanishingly small critical field [35]. A peak in the ac and dc susceptibility at 4 K marks an antiferromagnetic phase transition. There is almost no out-of-phase ac signal, consistent with the result that, unlike the iron and manganese analogs, there is essentially no hysteresis. This is attributed to the absence of an orbital contribution to the magnetic moment, and hence a source of anisotropy. The magnetization in an applied field of 40 kOe is 20,400 emu-G mol−1 , approaching the expected spin-only saturation value (22,340 emu-G mol−1 ).

7.9 7,7,8,8-Tetracyano-p-quinodimethane Salts 7.9.1

Iron

The reaction of FeCp*2 and TCNQ (TCNQ = 7,7,8,8-tetracyano-p-quinodimethane, Scheme 7.6) has been shown to yield three magnetic phases. Reaction in acetonitrile at room temperature leads to the formation of the thermodynamic phase, α-[FeCp*2 ][TCNQ], which contains [TCNQ]2− 2 dimers and is better formu[36, 37], and a kinetic phase, β-[FeCp*2 ][TCNQ] lated as {[FeCp*2 ]+ }2 [TCNQ]2− 2 possessing a 1D structure [36, 38] of the type illustrated in Figure 7.2. Electrochemical synthesis also leads to α-[FeCp*2 ][TCNQ] [39]. Reaction in acetonitrile at −40◦ C [38] leads to the formation of γ -[FeCp*2 ][TCNQ] [40], which also possesses a 1D structure of the type illustrated in Figure 7.2. α-[FeCp*2 ][TCNQ] is a paramagnet with one spin per [FeCp*2 ][TCNQ] repeat unit, while both βand γ -[FeCp*2 ][TCNQ] have two spins per repeat unit and magnetically order. β-[FeCp*2 ][TCNQ] is a metamagnet4 with Tc = 2.55 K and critical field, Hc , of 1 kOe at 1.53 K, while γ -[FeCp*2 ][TCNQ] is a ferromagnet with Tc = 3.1 K [40]. β- and γ -[FeCp*2 ][TCNQ] are structurally similar, differing only slightly in key intra- and interchain interactions, Figure 7.3. The most significant of which is the nearest N. . .N distance for TCNQ-TCNQ pairs that is 4.08 Å for the metamagNC

CN

NC

CN

Scheme 7.6 7,7,8,8-Tetracyano-p-quinodimethane, TCNQ.

4 A metamagnet is an antiferromagnet in zero applied field that switches to ferromagnet-like

alignment upon application of a sufficiently large magnetic field.

7.10 2,5-Dimethyl-N, N -dicyanoquinodiimine Salts

239

netic β phase and 4.34 Å for the ferromagnetic γ phase. This is consistent with the proposed antiferromagnetic coupling associated with this interaction [12a]. Specific heat data on β-[FeCp*2 ][TCNQ] reveal a sharp peak at 2.54 K consistent with ordering. The low temperature data suggests an energy gap of 6.5 K and like [FeCp*2][TCNE] is Ising-like [41c].

7.9.2

Manganese

[MnCp*2 ][TCNQ] was synthesized by Hoffman and coworkers utilizing a metathetical route involving the mixing of solutions of [MnCp*2 ]PF6 and NH4 [TCNQ] [10] The structure as determined by single crystal X-ray diffraction, was reported to consist of the usual 1-D stacks (Figure 7.2) with four formula units per unit cell. As predicted, the compound exhibits magnetic properties consistent with strong ferromagnetic coupling in the stacking direction (θ = +10.5 ± 0.5 K) and a phase transition to a three-dimensionally ordered solid at 6.2 K. [MnCp*2 ][TCNQ] also exhibits significant coercivity of 3.6 kOe at 2 K.

7.9.3

Chromium

The chromium analog [CrCp*2 ][TCNQ] was synthesized [42] by combining equimolar solutions of the neutral donor and acceptor in acetonitrile. Crystals grown from acetonitrile are isomorphous with the manganese analog. This compound displays ferromagnetic coupling (θ = +11.6 K) and a transition to a ferromagnetically ordered state below 3.1 K. From a historical perspective, this compound is important because it provided the first counterexample to the McConnell model that, in its original incarnation, predicted antiferromagnetic coupling for this compound.

7.10 2,5-Dimethyl-N, N -dicyanoquinodiimine Salts 7.10.1

Iron and Manganese

[FeCp*2 ][Me2 DCNQI] and [MnCp*2 ][Me2 DCNQI], where Me2 DCNQI is 2,5dimethyl-N, N -dicyanoquinodiimine, Scheme 7.7, have been prepared [43]. Both exhibit ferromagnetic coupling with θs of +10.8 K and +15.0 K, respectively. However, neither exhibits evidence for long-range ordering above 2 K. Rabaça and coworkers [44] have recently re-examined [FeCp*2 ][Me2 DCNQI] and report a single crystal structure as well as somewhat different magnetic properties. The structure confirms the presence of the expected 1D chains. For their

240

7 Metallocene-based Magnets CH3 CN

N

N

NC CH3

Scheme 7.7 2,5-Dimethyl-N, N -dicyanoquinodiimine, Me2 DCNQI.

sample, θ = +3.2 K and a transition to an antiferromagnetically ordered state at occurs at 3.9 K. This state is metamagnetic with Hc = 5.5 kOe at 1.7 K.

7.11 1,4,9,10-Anthracenetetrone Salts [FeCp*2 ][ATO] where ATO is 1,4,9,10-anthracenetetrone, Scheme 7.8, has been prepared [45]. This acceptor is unusual because it supports magnetic order, but does not contain a nitrile functional group. The as-prepared solid is a dark-green microcrystalline materials, but above 0◦ C, it slowly changes to a red-brown powder, presumably due to loss of solvent. Although there is dominant ferromagnetic coupling (θ = 10 K) the bulk magnetic properties of this ET salt, as determined by ac susceptibility, are those of a glassy canted ferromagnet with Tg ∼ 3 K, reflecting the disorder caused by partial desolvation. A second transition at about 5 K appears to be antiferromagnetic (no (χ (T )) and a small amount of hysteresis is observed at 1.8 K. O

O

O

O

Scheme 7.8 1,4,9,10-Anthracenetetrone, ATO.

7.12 Cyano and Perfluoromethyl Ethylenedithiolato Metalate Salts Planar four coordinate metal dithiolate complexes of principally Ni, Pd and Pt, Scheme 7.9, have also been investigated as radical anions. Although formally metal(III) species, these complexes, as monoanions (n = 1), possess one unpaired electron that is delocalized over the π system and the metal.

7.12 Cyano and Perfluoromethyl Ethylenedithiolato Metalate Salts

241

n– R

S

S

R R = CN, CF3

M R

S

S

M = Ni, Pd, Pt R

Scheme 7.9 [M(S2 C2 R2 )2 ]n− , also [M(mnt)]n− when R = CN.

7.12.1

Iron

Although bulk magnetic order is not observed in any of the members of the decamethylferrocenium family of these acceptors where R = CN or CF3 , some 1:1 bis(dithiolato)metallate salts of decamethylferrocenium studied to date exhibit ferromagnetic magnetic coupling with θ constants as high as +27 K (Table 7.3). Of the compounds studied only [FeCp*2 ]{M[S2 C2 (CF3 )2 ]2 } (M = Ni and Pt) have a 1D chain structure reminiscent of other molecule-based ferromagnets (Figure 7.2). The Pt analog with θ = +27 K possesses 1D . . .D+ A− D+ A− . . . chains whereas the Ni analog with α = +15 K possesses zig-zag 1D chains and longer M. . .M separations (11.19 Å vs. 10.94 Å for the Pt analog). Thus, the enhanced magnetic coupling appears to arise from the stronger intrachain coupling. Data on the palladium analog have not been reported. In contrast, [FeCp*2 ]{Ni[S2 C2 (CN)2 ]2 } or [FeCp*2 ][Ni(mnt)2 ] where mnt2− = maleonitrilodithiolate, possesses isolated D+ A22− D+ dimers, akin to α[FeCp*2 ][TCNQ], and is paramagnetic with θ ∼ 0 [11]. This is consistent with one spin per repeat unit. Intermediate between the 1D chain and dimerized chains structures are the α- and β-phases of [FeCp*2 ]{Pt[S2 C2 (CN)2 ]2 } which have 1D + . . .D+ A− D+ A− . . . strands in one direction and . . .D+ A2− 2 D . . . units in another direction. For these materials, the magnetic properties are consistent with the presence of one-third of the anions having a singlet ground state. Data on the palladium analog have not been reported.

7.12.2

Manganese

With these two anions, the analogous salts of decamethylmanganocenium exhibit 3D cooperative magnetic order. For example, [MnCp*2 ]{M[S2 C2 (CF3 )2 ]2 } (M = Ni, Pd, Pt) [46], all exhibit very similar metamagnetic behavior with Tc = 2.5 ± 0.3 K and θ = +2.8 ± 0.9 K (Table 7.3). Critical fields of approximately 800 Oe at 1.85 K are observed. Since the iron and manganese complexes are isomorphous, greater ferromagnetic coupling (predicted in a mean field model) would be expected for Mn as Tc ∝ S(S + 1) [47]. It is possible that [FeCp*2 ]{Ni[S2 C2 (CF3 )2 ]2 } is also metamagnetic, but with a Tc below 2 K and thus a phase transition has yet to be observed.

242


Table 7.3. Weiss constants, θ , and critical temperatures, Tc , of ferromagnetic coupled and magnetically ordered decamethylmetallocenium-based magnets. Compound

θ (K)a

Tc (K)b

Magnetic Behaviorf

Hc or Hcr (T, K)c

[CrCp*2 ][TCNE] [CrCp*2 ][TCNE] [MnCp*2 ][TCNE] [FeCp*2 ][TCNE] [FeCp*2 ]0.955 [CoCp*2 ]0.045 [TCNE] [FeCp*2 ]0.923 [CoCp*2 ]0.077 [TCNE] [FeCp*2 ]0.915 [CoCp*2 ]0.085 [TCNE] [FeCp*2 ]0.855 [CoCp*2 ]0.145 [TCNE] [NiCp*2 ][TCNE] [FeCpCp*][TCNE] [Fe(C5 Me4 H)2 ][TCNE] [Fe(C5 Et5 )2 ][TCNE] [CrCp*2 ][DMeDCF] [MnCp*2 ][DMeDCF] [CrCp*2 ][DEtDCF] [MnCp*2 ][DEtDCF] [CrCp*2 ][C4 (CN)6 ] [MnCp*2 ][C4 (CN)6 ] [FeCp*2 ][C4 (CN)6 ] [MnCp*2 ][DClDQ] [FeCp*2 ][DClDQ] [MnCp*2 ][DBrDQ] [FeCp*2 ][DBrDQ] [MnCp*2 ][DIDQ] [FeCp*2 ][DIDQ] [CrCp*2 ][DCNQ] [MnCp*2 ][DCNQ] [FeCp*2 ][DCNQ] [FeCp*2 ][DCID] [CrCp*2 ][TCNQ] [MnCp*2 ][TCNQ] [FeCp*2 ][TCNQ] [FeCp*2 ][TCNQ] [Fe(C5 Me4 H)2 ][TCNQ] [Fe(C5 Et5 )2 ][TCNQ] [FeCp*2 ][TCNQCl2 ] [FeCp*2 ][TCNQBr2 ] [FeCp*2 ][TCNQI2 ] [FeCp*2 ][TCNQMe2 ] [FeCp*2 ][TCNQ(OMe)2 ] [FeCp*2 ][TCNQ(OPh)2 ] [FeCp*2 ][TCNQMeCl]

+22.2 +12.2 +22.6 +16.9 n.r. n.r. n.r. n.r. −10 +3.3 −0.3 +7.5 +23 +16 +22 +15.5 +13.8 +18 +35 +26.8 +10.3 +20 +19 +19 +12 +6 +11 +4.0 +1 +12.8 +10.5 +3.8 +12.3 +0.8 +6.1 +4.3 +0.1 +9.5 −6.2 +2.1 −1.5 +0.1

3.65 2.1 8.8 4.8 4.4 3.8 2.75 0.75

FM FM FM FM FM FM FM FM

∼0 Oe (2 K) ∼0 Oe (n.r.) 1.2 kOe (2 K) 1.0 kOe (2 K) n.r. n.r. n.r. n.r.

5.7 10.6 5.4 12

FM FM MM MM

8.5

MM MM MM

4.0 8.0 4.0

MM MM MM

3.1 6.5 c 3 2.55

FM FM FM MM

Ref.

20 19 17 12a 69 69 69 69 21 9 61 60 0 −86.4 +24.6 +10.6 +10 e −0.3 +6 −4 +3 +3

Tc (K)b

Magnetic Behaviorf

Hc or Hcr (T, K)c

3.9 3

MM FM

5.5 kOe (1.7 K) 1 kOe (1.8 K)

2.4

MM

∼800 Oe (1.85 K)

2.8 2.3

MM MM

800 Oe (1.85 K) ∼800 Oe (1.85 K)

2.3

MM

200 Oe (2 K)

3.2

MM

4 kOe (2 K)

+2.5

FM

n.r.

2.1

MM

60 Oe (2 K)

Ref. 43 43 44 45 21 21 21 11 21 21 46 11 46 46 21 53 48 48 48 48 48 48 48 48 52 51 51 50 51 50 54 54 54 56 63 63 63 66 66

n.r. Not reported. a For polycrystalline samples. b Tc determined from a linear extrapolation of the steepest slope of the M(T) data to the temperature at which M = 0. c Hcr = coercive field, Hc = critical field. d Does not obey Curie–Weiss law. e Modeled coupling constant. f FM = ferromagnet; MM = metamagnet.

244


7.13 Benzenedithiolates and Ethylenedithiolates Da Gama and co-workers have reported ET salt families utilizing the acceptor radical anions [Ni(bdt)2 ]− , where bdt2− = benzenedithiolate, [Ni(edt)2 ]− where edt2− = ethylenedithiolate, Scheme 7.10, and [Ni(tcdt)2 ]− where tcdt2− = tetrachlorobenzenedithiolate and several donor decamethylmetallocenes [48]. Both 1D and layered structures are observed in these compounds. All exhibit dominant antiferromagnetic coupling with θ values of between −2.4 and −28.5 K (Table 7.3). Two compounds, [FeCp*2 ][Ni(edt)2 ] and [MnCp*2 ][Ni(bdt)2 ] are found to order as metamagnets at Tc = 3.2 and 2.3 K, respectively. Critical fields at 2 K for these solids are reported to be 4 kOe and 200 Oe, respectively [48].

a)

b) n–

n– H

S

H

S

S

H

S

S M

M S

H

S

S

Scheme 7.10 (a) [M(edt)2 ]n− , (b) [M(bdt)2 ]n− .

In a follow-up study of the above, the compounds [MCp*2 ][Ni(edt)2 ] where M = Cr and Fe, have been examined. A single crystal structure of the latter showed it to possess 1D chains and an arrangement of donors and acceptors similar to that shown in Figure 7.3. The former compound is isostructural, based on powder diffraction. θ values are reported to be −6.7 and −5 K, respectively, and the latter orders as a metamagnet with TN = 4.2 K with Hc = 14 kG. It also exhibits a poorly resolved Mössbauer hyperfine field of approximately 350 kG (vide infra) [49]. The nickel complex of the analogous benzenediselenolate ligand, bds2− , has also been explored [50]. The [FeCp*2 ]+ salt, synthesized via a metathetical route, crystallizes in two-dimensional stacks of D+ D+ A− repeat units where the donors are side-by side. These charged stacks are separated from each other by planes of A− anions in the perpendicular direction. The magnetic properties of this solid are consistent with ferromagnetic coupling down to the lowest measured temperature (1.5 K), but no evidence for spontaneous magnetization or hysteresis was observed. A value of θ was not reported.

7.14 Additional Dithiolate Examples

245

7.14 Additional Dithiolate Examples The anion, bis(2-thioxo-1,3-dithiole-4,5-dithiolate)nickel(III), [Ni(dmit)2 ]− , Scheme 7.11, has been investigated as an acceptor anion. From a metathetical route, [FeCp*2 ][Ni(dmit)2 ] forms unusual stacks arranged as D+ D+ A− A− where stacks of side-by-side cations alternate with face-to-face pairs of anions [50]. The magnetic properties of this compound are consistent with dominant but weak ferromagnetic coupling followed at low temperature by antiferromagnetic interactions that lead to a low moment state. The analogous manganese compound [MnCp*2 ][Ni(dmit)2 ] exhibits ferromagnetic coupling and a transition to a ferromagnetic state below 2.5 K [51]. The structure of this latter compound has not been determined.

n– S

S

S

S

Ni

E S

S

E S

S

Scheme 7.11 [Ni(dmit)2 ]− (E = S), [Ni(dmio)2 ]− (E = O).

The iron analog of the above acceptor, bis(2-thioxo-1,3-dithiole-4,5dithiolate)iron(III), whose ET salt is formulated as [MnCp*2 ][Fe(dmit)2 ] has also been reported. It exhibits evidence of antiferromagnetic coupling but no signs of ferrimagnetic order that might be expected based on S = 1 Mn(III) and S = 3/2 Fe(III). Neither the structure, nor the value of θ was reported [51]. The related oxo species, [Ni(dmio)2 ]− where dmio2− = 2-oxo-1,3-dithiole-4,5dithiolate, Scheme 7.11, has been investigated as an acceptor radical anion and its decamethylferrocenium salt prepared [52]. [FeCp*2 ][Ni(dmio)2 ] is ferromagnetically coupled (θ = +2.0 K) with weak antiferromagnetic interactions superimposed at low temperature. Long-range order was not reported. The complex structure consists of mixed anion-cation layers and anionic sheets. One of the few examples of non-planar anions is a tris(dithiolato)metallate salt of decamethylferrocenium, namely [FeCp*2 ]{Mo[S2 C2 (CF3 )2 ]3 } [53]. The salt only possesses parallel out-of-registry 1D · · ·D+ A− D+ A− · · · chains with intrachain Mo. . .Mo separations of 14.24 Å. The θ value is reduced to +8.4 K, which probably reflects the reduced spin-spin interactions due to the bulky CF3 groups. 3D ordering is not observed down to the lowest temperature studied (2 K) as expected for the weak ferromagnetic intra- and interchain interactions. This salt-like structure is to date the only structural motif that does not have parallel chains in-registry, avoiding nearest neighbor antiferromagnetic A− /A− interactions.

246


7.15 Bis(trifluoromethyl)ethylenediselenato Nickelate Salts In an effort to promote stronger intermolecular magnetic interactions, selenium has been utilized in place of sulfur to form a homologous square planar diselenate. Utilizing a metathetical route, the family of ET salts [MCp*2 ][Ni(tds)2 ], Scheme 7.12, were prepared, where M = Cr, Mn and Fe and tds = bis(trifluoromethyl)ethylenediselenato [54]. The three compounds are isostructural, as determined by single crystal X-ray diffraction, consisting of 1-D . . .D+ A− D+ A− . . . chains. The Mn and Fe compounds exhibit dominant ferromagnetic coupling, while the Cr compound shows strong antiferromagnetic coupling. The data for the Fe salt have been fitted well by a 1D Ising model, but no evidence for order has been found. In contrast, the Mn salt orders as a metamagnet with Tc = 2.1 K (Table 7.3). n– F3C

Se

Se

CF3

Se

CF3

Ni F3C

Se

Scheme 7.12 [Ni(tds)2 ]n− .

7.16 Other Acceptors that Support Ferromagnetic Coupling, but not Long-range Order above ∼2 K The reactions of either 2,3,5,6-tetrachloroquinone (chloranil), Scheme 7.13, or 2,3,5,6-tetrabromoquinone (bromanil) with decamethylferrocene also give ferromagnetically coupled solids. The θ s for these compounds are +13.5 and +19.0 K, respectively, although neither has been observed to exhibit ordering above 2 K. No structural information has been reported, although the usual 1-D stack (Figure 7.2) has been presumed [21].

Cl

Cl

O

O

Cl

Cl

Scheme 7.13 2,3,5,6-Tetrachloroquinone, chloranil.

7.16 Other Acceptors that Support Ferromagnetic Coupling

247

2,5-Iodo-7,7,8,8-tetracyano-p-quinodimethane, TCNQI2 ,55, Scheme 7.14, has been investigated as an electron acceptor paired with decamethylferrocene. Structural characterization of this compound revealed D+ A− D+ A− stacking but where the anion is significantly non-planar, perhaps due to the steric bulk of the iodine. Multiple close N· · ·I interstack interactions between adjacent acceptors are observed. This compound exhibits Curie–Weiss behavior with θ = +9.5 K, but does not show evidence of a phase transition to a ferromagnetic state. However, Mössbauer spectroscopy at low temperature reveals hyperfine splitting that suggests insipient magnetic order. Related compounds utilizing TCNQCl2 , TCNQBr2 , TCNQMe2 , TCNQ(OMe)2 , TCNQ(OPh)2 and TCNQMeCl have also been reported with weak magnetic interactions and no evidence of magnetic order (Table 7.3) [55]. I NC

CN

NC

CN

Scheme 7.14 2,5-Iodo-7,7,8,8-tetracyano-p-quinodimethane, TCNQI2 .

I

Hoffman and coworkers have reported [FeCp*2 ][Co(HMPA-B)] [56] where HMPA-B = bis(2-hydroxy-2-methylpropanamido)benzene, Scheme 7.15. This ET salt adopts the D+ A− D+ A− structure and, interestingly, has two unpaired electrons on the acceptor, in contrast to all other metallocene-based magnets. The data were fitted to a model that revealed significant zero-field splitting (D = +65 K) and weak ferromagnetic intrastack interactions (J ∼ +10 K) precluding a magnetically ordered ground state. 1–

O

N

N

O

Co O

O

Scheme 7.15 [Co(HMPA-B]− .

Hexacyanobutadiene, Scheme 7.16, was investigated quite early as a higher homolog of TCNE. [FeCp*2 ][C4 (CN)6 ] 57 is found to adopt a 1D chain structure with strong ferromagnetic coupling. The anion is disordered over two positions involving rotation about the central C–C bond. The corresponding Cr and Mn ET

248


salts similarly exhibit ferromagnetic coupling, but evidence for long-range order is lacking [21]. These compounds need to be re-investigated. NC

CN

NC CN

Scheme 7.16 Hexacyanobutadiene, C4 (CN)6 .

CN

NC

[FeCp*2 ][C3 (CN)5 ] with S = 0 [C3 (CN)5 ]− exhibits essentially the Curie susceptibility anticipated for isolated S = 1/2 [FeCp*2 ]+ (θ = −1.2 K) [12]. 2,3,4,5-tetrakis(trifluoromethyl)cyclopentadienone, Scheme 7.17, was investigated as a possible acceptor and forms the desired one-dimensional chains in reactions with FeCp*2 resulting in the expected ferromagnetic coupling (θ = +15.1 K). However, this ET salt does not order above 2 K [21]. F3C

CF3

F3C

CF3

Scheme 7.17 2,3,4,5-Tetrakis(trifluoromethyl)cyclopentadienone.

O

An acceptor that is isomeric with DCNQ (vide supra) is 2-dicyanomethyleneindan-1,3-dione (DCID), Scheme 7.18. Its relationship to DCNQ allows a comparison of essentially isostructural, but electronically different acceptors. DCID reacts with FeCp*2 to give a structurally characterized ET salt that exhibits only very weak ferromagnetic coupling (θ ∼ +1 K) and no evidence of order above 1.8 K. The arrangement of donors and acceptors in the solid state consists of the usual mixed stacks. O CN

CN O

Scheme 7.18 2-Dicyanomethyleneindan-1,3-dione.

Parallel 1D chains of alternating radical [FeCp*2 ]+ cations and singly deprotonated 2,5-dichloro-3,6-dihydroxy-1,4-benzoquinone (HCA− ) anions,

7.17 Other Metallocenes and Related Species as Donors

249

Scheme 7.19, is reported for [FeCp*2 ]+ [HCA]− ·H2 O, however, the magnetic properties for this compound were not reported [58]. Due to the diamagnetic nature of the anion, magnetic ordering is not expected to occur. This work has been extended to include the synthesis and structural characterization of the analogous bromanilic and cyananilic acids [59]. HO

Cl

O

O

Cl

OH

Scheme 7.19 2,5-dichloro-3,6-dihydroxy-1,4-benzoquinone, H2 CA.

7.17 Other Metallocenes and Related Species as Donors 1,2,3,4,5-Pentamethylferrocene, and decaethylferrocene maintain the five-fold symmetry necessary to form a cation with degenerate partially occupied molecular orbitals and a Kramers doublet (2 E) ground state as reported for decamethylferrocenium. FeCpCp* is a sufficiently strong donor to reduce TCNE and the simple (1:1) 1D salt as well as three other phases were prepared [9]. This 1:1 phase exhibits weak ferromagnetic coupling, as evidenced from the fit of its susceptibility to the Curie–Weiss expression with θ = +3.2 K, but cooperative 3D magnetic ordering is not observed down to the lowest temperature studied (∼2 K). A linear chain structure is proposed for [Fe(C5 Et5 )2 ][TCNE], which also exhibits ferromagnetic coupling, as evidenced from the fit of its susceptibility to the Curie–Weiss expression with θ = +7.5 K. It also did not exhibit cooperative 3D magnetic ordering [60]. To test the necessity of a 2 E ground state, the TCNE electron-transfer salt with the lower- symmetry Fe(C5 Me4 H)2 donor was prepared [61]. The magnetic susceptibility can be fitted by the Curie–Weiss expression with θ ∼ 0 K. The absence of either 3D ferro- or antiferromagnetic ordering above 2.2 K in [Fe(C5 Me4 H)2 ][TCNE] contrasts with the behavior of [FeCp*2 ][TCNE]. The 57 Fe Mössbauer data are in accord with the absence of significant magnetic coupling among the radical ions, and show only nuclear quadrupole splitting for the [Fe(C5 Me4 H)2 ]+ salts and not the zero-field Zeeman splitting observed for ordering solids such as [FeCp*2 ][TCNE] [12a]. The lack of magnetic ordering is attributed to poorer intra- and intermolecular overlap within and between the chains, leading to substantially weaker magnetic coupling for [Fe(C5 Me4 H)2 ][TCNE], and suppressing the ordering temperature.

250


Alternatively, due to the essentially C2v symmetry of [Fe(C5 Me4 H)2 ]2+ the lowest lying virtual charge transfer excited state may be a singlet, not a triplet, and the admixture of a singlet excited state (a la McConnell II) should lead to antiferromagnetic, not ferromagnetic, coupling [61, 62] Since significant antiferromagnetic coupling was also absent for [Fe(C5 Me4 H)2 ][TCNE], perhaps a reduced overlap with neighboring radicals is the more important effect of modification of the cation. Bis(heptamethylindenyl)iron(II), [Fe(η5 -C9 Me7 )2 ], has also been investigated as a donor [63]. This sandwich compound also lacks a five-fold axis and so will, at best, possess accidentally degenerate metal d orbitals. ET salts pairing this donor with TCNE, TCNQ and DDQ have been reported. Each forms a 1:1 complex with one unpaired electron associated with the donor and one with the acceptor. The TCNE and DDQ salts exhibit weak antiferromagnetic interactions, but the TCNQ compound shows intriguing evidence of ferromagnetic coupling (θ = +6 K), in contrast to predicted antiferromagnetic coupling based on the McConnell II mechanism (vide infra). [Fe(η5 -C9 Me7 )2 ][TCNQ] has been structurally characterized by X-ray diffraction and found to possess · · ·D+ A− D+ A− · · · chains (Figure 7.2) and the usual in-registry and out-of-registry interchain interactions characteristic of solids that order magnetically. However, although the magnetization saturates faster than predicted by the Brillouin function, no evidence of order was observed above 2 K. Electron transfer salts and charge transfer (CT) complexes have been prepared from octamethylferrocenyl thioethers, Fe(η5 -C5 Me4 SMe)2 , Fe(η5 -C5 Me4 St Bu)2 , and Fe(η5 -C5 Me4 S)2 S, and various acceptors. The latter CT complexes, characterized by non-integral charge transfer such as for [Fe(η5 -C5 Me4 SMe)2 ]3 [TCNQ]7 , exhibit complex crystal structures and significant degrees of electrical conductivity, but are not the subject of this chapter [64]. Ionic ET salts with 2,3,5,6-tetrafluoro7,7,8,8-tetracyano-p-quinodimethane, TCNQF4 , exhibit dimerization of the radical anion to give a diamagnetic dianion [64], as has been seen before with the analogous FeCp*2 salt [65]. One-to-one ET salts derived from [Fe(η5 -C5 Me4 SMe)2 ]+ or [Fe(η5 C5 Me4 St Bu)2 ]+ and [M(mnt)]− (where M = Co, Ni and Pt) vide supra) have been characterized [66]. For most of these, θ values that were zero or slightly negative were found. The exceptions were [Fe(η5 -C5 Me4 St Bu)2 ][M(mnt)] where M = Ni and Pt, which form isomorphous . . .D+ A− D+ A− . . . chains and which exhibit θ = +3 K, indicating weak ferromagnetic coupling, also in conflict with the McConnell model prediction (vide infra). The reaction of 1, 1 -bis[(octamethylferrocenylmethyl)ferrocene, A (M = M = Fe), Scheme 7.20, with TCNE leads to the isolation of − (θ = −0.8 K) {Fe(C5 H4 CH2 )2 [Fe(C5 Me4 )(C5 Me4 H)]}2+ 2 {[TCNE] }2 − − [TCNE] [C (CN) [67] and {Fe(C5 H4 CH2 )2 [Fe(C5 Me4 )(C5 Me4 H)]}2+ 3 5] 2 (θ = +0.1 K) [67, 68] while reaction of A (M = Fe, M = Co) forms − {Co(C5 H4 CH2 )2 [Fe(C5 Me4 )(C5 Me4 H)]}3+ 2 {[TCNE] }3 (θ = −5.8 K) [67]. The structures of these compounds have been reported.

7.19 Mössbauer Spectroscopy

M

M'

251

M

Scheme 7.20 1,1 -Bis[(octamethylferrocenylmethyl)ferrocene (M = M = Fe), A

7.18 Muon Spin Relaxation Spectroscopy The static and dynamic magnetic properties of [FeCp*2 ][TCNE] have been studied via the muon-spin-relaxation technique [70]. Spontaneous order is observed in the ferromagnetic ground state below 5 K, while the muon spin relaxation rate in the paramagnetic phase displays a gradual variation with temperature, indicating that a slowing down of spin fluctuations occurs over a wide temperature range. The temperature dependence of spin fluctuations between 8 and 80 K shows the thermally activated behavior expected in a spin chain with Ising character.

7.19 Mössbauer Spectroscopy The 57 Fe Mössbauer spectra of magnetically ordering electron transfer salts containing decamethylferrocenium cations give insight into the development of the local internal magnetic fields. Well above Tc , an unresolved quadrupole doublet characteristic of [FeCp*2 ]+ is observed with an isomer shift of ∼ 0.5±0.1 mm s−1 . Evolution of this signal to an atypical six-line Zeeman split spectra is observed in zero applied magnetic field at low temperature as the compounds become longrange magnetically ordered, either ferromagnetically or antiferromagnetically. For example, a Zeeman split spectrum with an internal field (Hint ) of 379 kG is observed for the [DCNQ]− salt at 1.63 K (Figure 7.8). These internal fields are substantially greater than the expectation of 110 kG/spin/Fe [12a]. Mössbauer data for several decamethylferrocenium ET salts are collected in Table 7.4.

252


Fig. 7.8. Mossbauer spectra of [FeCp*2 ][DCNQ] above and below Tc [33]. Table 7.4. Summary of 57 Fe Mössbauer parameters for [FeCp*2 ][acceptor] magnets. Acceptor

Isomer Shift, δ, mm s−1

Internal Field, kG (at T , K)

Ref.

TCNE C4 (CN)6 DDQ β-TCNQ TCNQI2 Me2 DCNQI DCNQ Ni(edt)2

0.58 0.51 0.6 0.53 0.47 0.43 0.45 0.48

424.6 (4.23) 448 (4.34) 440 (1.7) 404,449 (1.4) 270 (1.5) 448.5 (2.24) 379 (1.63) ∼350 (3.5)

12a 57 29b 71 55 43 33 49

7.21 Dimensionality of the Magnetic System and Additional Evidence for a Phase Transition

7.20 Spin Density Distribution from Calculations and Neutron Diffraction Data The spin density on [FeCp*2 ]+ has been determined by neutron diffraction at low temperature. Experiments on [FeCp*2 ]+ paired with a diamagnetic polyoxotungstate anion reveal that the iron atom carries 2.0 µB of spin density, the ring carbons carry −0.005 ± 0.001 µB and the methyl carbons carry 0.008 ± 0.001 µB . These values have been described as roughly consistent with ab initio DFT calculations [71].

7.21 Dimensionality of the Magnetic System and Additional Evidence for a Phase Transition The single crystal susceptibility can be compared with different physical models to aid our understanding of the microscopic spin interactions. For samples oriented parallel to the field, the susceptibility above 16 K fits a 1D Heisenberg model with ferromagnetic exchange of Jintra = +27 K (+19 cm−1 ) [12c]. Variation of the low field magnetic susceptibility for an unusually broad temperature range above Tc [χ ∝ (T − Tc )−γ ], magnetization with temperature below Tc [M ∝ (Tc − T )−β ], and the magnetization with magnetic field at Tc (M ∝ H 1/δ ) enabled determination of the β, γ and δ critical exponents as 0.50, 1.2 and 4.4, respectively. These values are consistent with a mean-field-like 3D behavior. Thus, above 16 K 1D nearest neighbor spin interactions are sufficient to understand the magnetic coupling, but near Tc 3D spin interactions are dominant. At higher temperatures the anisotropic magnetic susceptibility shows the dominance of 1D, Heisenberglike ferromagnetic exchange behavior in accord with the linear chain structure. A fourth critical constant, α, obtained from heat capacity, Cp (T ), studies (Figure 7.9), Cp ∝ (T − Tc )−α , gives α = 0.09 ± 0.02 [41a], consistent for an Ising-like system as the excess entropy is approximately 2R ln 2 (R = gas constant) in value [41c]. The low value of the 3D ordering temperature, Tc = 4.8 K, compared to the 1D exchange interaction (as indicated by Jintra = +27 K) for [FeCp*2 ][TCNE], suggests the applicability of quasi-one-dimensional models governing the onset of 3D cooperative ordering. For example, for a tetragonal lattice with interacting nearest neighbor chains [72], √ 1.556 Jintra Jinter (7.1) Tc = kB Solving this for Jinter using the above data gives a ratio of Jintra /Jinter = 77. Thus, [FeCp*2 ]+ [TCNE]− and most of the other metallocene electron transfer salts are in the 1D limit.

253

254


Fig. 7.9. Low temperature Cp (T ) for [FeCp*2 ][TCNE] [41a].

To further test the applicability of the one-dimensional models, spinless S = 0 [CoCp*2 ]+ cations were randomly substituted for the cation in the [FeCp*2 ]+ [TCNE]− structure. This leads to a solid solution of [FeCp*2 ]x [CoCp*2 ]1−x [TCNE] that possesses finite magnetic chain segments punctuated, at random, by isostructural, but diamagnetic interruptions [69]. This results in the dramatic reduction of Tc with increasing [CoCp*2 ]+ content (Table 7.3) and is in excellent agreement with theoretical models [74].

7.22 The Controversy Around the Mechanism of Magnetic Coupling in ET Salts Because of the many related examples of ET salts, several efforts to model the magnetic properties have been made, though all have met with mixed success and this remains a key unsolved problem. The first attempt, commonly known as the McConnell-II model, involved the application of configurational mixing of the lowest energy virtual charge transfer excited state with the ground state [75]. It makes the prediction that if the donor and acceptor each have non-degenerate partially occupied molecular orbitals, then only antiferromagnetic coupling will be observed, but that degeneracy can permit ferromagnetic interactions. Using this approach, it is possible to rationalize the ferromagnetic intrastack coupling observed in [FeCp*2 ][acceptor] and [MnCp*2 ][acceptor] families of compounds. Extension of this simple model in the other two dimensions would, in principle,

7.23 Trends

255

support bulk ferromagnetic order. However, for the analogous [CrCp*2 ][acceptor] compounds, antiferromagnetic coupling is predicted and ferromagnetic coupling is observed, casting doubt on the validity of this mechanism. Kollmar and Kahn [76] have also argued that consideration of only the lowest CT excited state for configurational mixing is an oversimplification for determining the preferred spin state of the ground state and have challenged the general validity of this model. Kahn and coworkers have suggested that positive spin density on the metal can induce negative spin density on the Cp rings via configurational mixing. Subsequent overlap of regions of negative spin density on the Cp ring with regions of positive spin density on the TCNE radical gives rise to significant net ferromagnetic coupling between the metal and TCNE. Neutron diffraction, presented above, directly addresses the appropriateness of this model, which only considers intrachain interactions. However, the predictive ability of this mechanism, known as McConnell I, has recently been called into question based on calculations on diradical paracyclophanes [77]. Again, a theoretical understanding of ET salt magnets has not yet been achieved.

7.23 Trends Although there is as yet no comprehensive theoretical treatment of the magnetic behavior in this class of compounds, it is clear that there are trends that suggest such an understanding is achievable. For example, with the exception of a few poorly characterized cases of substituted TCNQs, when the acceptor is a purely organic molecule and the donor is a Cr, Mn or Fe decamethylmetallocene, θ is positive, indicating the dominant interaction, intrachain coupling, is always ferromagnetic (for approximately 30 compounds). It is also the case that in all of the five known families of ET salts that exhibit magnetic order utilizing the same acceptor with two or more different decamethylmetallocenes, the critical temperature is always highest for the [MnCp*2 ]+ salt and, where the data is available, roughly equal for the [CrCp*2 ]+ and [FeCp*2 ]+ salts. It is interesting that Figure 7.10 includes data from both ferromagnetic and antiferromagnetic (metamagnetic but well below Hc ) phase transitions. Although not shown in Figure 7.10, it has also been noted that, consistent with this trend, there are examples of [MnCp*2 ]+ salts that exhibit magnetic order but where the corresponding [FeCp*2 ]+ salt does not and it has been assumed that Tc for the latter is simply too low to be experimentally accessible (i. e. below about 1.8 K, vide supra). These results show that critical temperature does not scale in any simple way with S (which increases from left to right in the plot) as would be expected based on a mean field model (i. e. Tc ∝ S(S + 1)). But it also seems clear that the bulk magnetic properties are not so critically dependent on the subtle variations of the crystal structures as to be beyond understanding.

256


Critical Temperature, T c, K

12.5

[DEtDCF] •[DMeDCF] •-

10.0

7.5

[TCNE]•5.0

[DCNQ] •-

[TCNQ]•-

2.5 0.5

1

Fe

Mn S

1.5

Cr

Fig. 7.10. Trends in critical temperature for magnetic ordering ET Salts with the same anion and different decamethylmetallocenium cations. Solid lines denote ferromagnets, dashed lines, metamagnets.

7.24 Research Opportunities The quest for s/p-orbital based ferromagnets remains the focus of intense interest worldwide. The growth of this area of metallocene-based ET salts depends critically on the identification of new donor and acceptor building blocks. Candidates need to have favorable electrochemical and structural properties, including reversible electrochemistry and probably π electrons for mediating coupling. The synthesis of additional donors, other than decamethylmetallocenes, remains a vexing problem, particularly because some of the evidence above seems to indicate that high symmetry is an important consideration. We conclude this chapter with a series of questions that we hope will spur additional research, which, we have argued above, ET salts are well-suited to address. Can the question of the mechanism of the intrachain magnetic coupling, and through space coupling in general, be answered? A more subtle question, because its strength is orders of magnitude smaller, concerns the nature of interchain coupling. Why is the net interchain coupling sometimes antiferromagnetic and sometimes ferromagnetic? It seems quite likely that Tc is intrinsically limited by weak interstack coupling. Can this be increased? Finally, this problem becomes one of crystal structure engineering. Is there something special about the “usual” structure of these compounds? And if not, can other structural classes be discovered and can structure be controlled? Can the magnetic properties be predicted based on knowledge of the building blocks? As molecular solids, these compounds are highly compressible. How does Tc vary with

References

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applied pressure? Although this was not specifically addressed, structural disorder appears to contribute to spin glass behavior in some of the above examples. Is this related to the known occurrence of glassiness in dilute metal alloys or is it an example of new physics?

Acknowledgments The authors gratefully acknowledge partial support by the Department of Energy Division of Materials Science (Grant Nos. DE FG 03-93ER45504 and DE FG 02-86BR45271). We deeply thank our numerous co-workers, especially Arthur J. Epstein and his group at The Ohio State University, for the important contributions they have made over the years enabling the success of some of the work reported herein.

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B.B. Kaul, W.S. Durfee, G.T. Yee, J. Am. Chem. Soc 1999, 121, 6862. B.B. Kaul, R.D. Sommer, B.C. Noll et al., Inorg. Chem. 2000, 39, 865. G.T. Yee, B.B. Kaul, J. Solid State Chem., 2001, 159, 420. (a) E. Gerbert, A.H. Reis, J.S. Miller et al., J. Am. Chem. Soc. 1982, 104, 4403; (b) J.S. Miller, P.J. Krusic, D.A. Dixon et al., J. Am. Chem. Soc. 1986, 108, 4459. J.S. Miller, R.S. McLean, C. Vazquez et al., J. Mater. Chem. 1991, 1, 479. K.S. Narayan, O. Heres, A.J. Epstein et al., J. Magn. Magn. Mater. 1992, 110, L6. M.R. Bryce, S.R. Davies, M. Hasan et al., J. Chem. Soc., Perkin Trans. II, 1989, 1285. G.T. Yee, M.J. Whitton, R.D. Sommer et al., Inorg. Chem. 2000, 39, 1874. R.L. Carlin, Magnetochemistry, Springer-Verlag, Berlin, 1986, pp. 154-159. G.T. Yee, unpublished data. J.S. Miller, J.H. Zhang, W.M. Reiff et al., J. Phys. Chem. 1987, 91, 4344. J.S. Miller, A.H. Reis, Jr., E. Gerbert et al. J. Am. Chem. Soc. 1979, 101, 7111. G.A. Candela, L. Swartzendruber, J.S. Miller et al., J. Am. Chem. Soc. 1979, 101, 2755. M.D. Ward, personal communication. W.E. Broderick, D.M. Eichorn, X. Liu et al., J. Am. Chem. Soc. 1995, 117,3641. (a) A. Chackraborty, A.J. Epstein, W.N. Lawless et al., Phys. Rev. B, 1989, 40, 11422; (b) M. Nakano, M. Sorai, Chem. Phys. Lett. 1990, 169, 27; (c) M. Nakano, M. Sorai, Mol. Cryst. Liq. Cryst. 1993, 233, 161. W.E. Broderick, B.M. Hoffman, J. Am. Chem. Soc. 1991, 113, 6334. J.S. Miller, C. Vazquez, R.S. McLean et al.,Adv. Mater. 1993, 5, 448. S. Rabaça, R. Meira, L.C.J. Pereira et al., J. Organomet. Chem. 2001, 632, 67. B.B. Kaul, G.T. Yee, Polyhedron, 2001, 20, 1757. W.E. Broderick, J.A. Thompson, B.M. Hoffman, Inorg. Chem. 1991, 30, 2958. D.A. Dixon, A. Suna, J.S. Miller et al., in NATO ARW Molecular Magnetic Materials, Eds. O. Kahn, D. Gatteschi, J.S. Miller et al. 1991, E198, 171. V. de Gama, D. Belo, I.C. Santos et al., Mol. Cryst. Liq. Cryst. 1997, 306, 17. See also Ref. [54]. V. de Gama, D. Belo, S. Rabaça et al., Eur. J. Inorg. Chem. 2000, 2101. W.E. Broderick, J.A. Thompson, M.R. Godfrey et al., J. Am. Chem. Soc. 1989, 111, 7656. C. Faulmann, A.E. Pullen, E. Riviere et al., Synth. Met. 1999, 103, 2296. M. Fettouhi, L. Ouahab, E. Codjovi et al., Mol. Cryst. Liq. Cryst. 1995, 273, 29. W.B. Heuer, D. O’Hare, M.L.H. Green et al., Chem. Mater.1990, 2 , 764. V. de Gama, S. Rabaça, C. Ramos et al., Mol. Cryst. Liq. Cryst. 1999, 335, 81. J.S. Miller, J.C. Calabrese, R.L. Harlow et al., J. Am. Chem. Soc. 1990, 112, 5496. D.M. Eichhorn, J. Telser, C.L. Stern et al., Inorg. Chem. 1994, 33,3533. J.S. Miller, J.H. Zhang, W.M. Reiff, J. Am. Chem. Soc. 1987 ,109, 4584. M.B. Zaman, M. Tomura, Y. Yamashita et al., CrystEngComm 1999, 9. Md. B. Zaman, M. Tomura, Y. Yamashita, Inorg. Chem. Acta 2001, 318, 127. K.-M. Chi, J.C. Calabrese, W.M. Reiff et al., Organometallics 1991, 10, 688. J.S. Miller, D.T. Glatzhofer, D.M. O’Hare et al., Inorg. Chem. 1989, 27, 2930. J.S. Miller, A.J. Epstein, J. Am. Chem. Soc. 1987, 109, 3850. V.J. Murphy, D. O’Hare Inorg. Chem. 1994, 33, 1833. S. Zürcher, J. Petrig, V. Gramlich et al., Organometallics 1999, 18, 3679. D.A. Dixon, J.C. Calabrese, J.S. Miller, J. Phys. Chem. 1989, 93, 2284. S. Zürcher, V. Gramlich, D. von Arx et al., Inorg. Chem. 1998, 37, 4015. S. Barlow, V.J. Murphy, J.S.O. Evans et al., Organometallics, 1995, 14, 3461.

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8 Magnetic Nanoporous Molecular Materials Daniel Maspoch, Daniel Ruiz-Molina, and Jaume Veciana

8.1 Introduction The exceptional characteristics of nanoporous materials have prompted their application in different fields such as molecular sieves, sensors, ion-exchange and catalysis. In this context, zeolites have been the predominant class of open-framework materials. However, in the last two decades, the number of approaches to obtain new porous materials that behave as zeolites has shown a spectacular increase. In 1982, Flanigen and coworkers initiated the synthesis of the first zeolite analogs, the microporous aluminophosphate solids [1]. Immediately, this fascinating family stimulated the discovery of new inorganic porous materials, most of them based upon phosphates, nitrides [2], sulfates [3], sulfides [4], selenides [5], halides [6] and cyanides [7] and a large list of metal ions (gallium [8], tin [9], iron [10], cobalt [11], vanadium [12], indium [13], boron [14], manganese [15] and molybdenum [16], among others). Together with the rapid development of inorganic-based porous solids, a crucial innovation appeared at the beginning of the 90s, the introduction of organic molecules as direct constituents of the porous structures. In essence, this approach uses multifunctional organic linkers to connect “inorganic” frameworks. According to the dimensionality of the inorganic network, Férey has classified these new porous materials into four different categories [17]: starting from a pure inorganic framework (3-D inorganic system) [18] such as that shown in Figure 8.1a, the introduction of organic moieties can induce pillaring between inorganic 2D layers (Figure 8.1b) or they can act as linkers between 1-D inorganic chains (Figure 8.1c) [19]. Both, inorganic 1-D and 2-D structures are usually referred to as hybrid inorganic-organic materials. Finally, organic ligands may arrange around discrete clusters, containing one or several metal ions, as shown in Figure 8.1d. These 0-D structures, as far as the inorganic part is concerned, will be referred to from now on as coordination polymers [20, 21]. At this point, it has to be mentioned that beyond the discovery of new openframework topologies and structures, development of new porous solids with openshell metal ions introduced the possibility of obtaining nanoporous materials with additional magnetic properties. The synergism of both magnetic properties and the

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Fig. 8.1. Classification of the nanoporous structures as a function of the dimensionality of the inorganic subnetwork. (a) 3-D pure “inorganic”-based framework; (b) Pillared 2-D “inorganic” layers through multitopic organic linkers (hybrid materials); (c) 1-D “inorganic” chains linked through multitopic organic linkers (hybrid materials); (d) “Inorganic” clusters or metal ions connected through multitopic organic linkers (coordination polymers).

exceptional characteristics of nanoporous materials opens a new route to the development of low-density magnetic materials, magnetic sensors and multifunctional materials on the nanometer scale. For instance, magnetic zeotype structures offer excellent conditions to encapsulate different functional materials with conducting, optical, chiral and NLO properties, among others. Here, we will give a short overview of the different types of magnetic nanoporous materials, although, due to the large number of examples so far described in the literature, we will mainly focus on the analysis and study of magnetic nanoporous coordination polymers, i.e., 0-D zeotype systems according to Férey’s classification. Finally, indications and prospects for further investigations based on magnetic nanoporous materials will be given.

8.2 Inorganic and Molecular Hybrid Magnetic Nanoporous Materials

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8.2 Inorganic and Molecular Hybrid Magnetic Nanoporous Materials Before 1996, only a few examples of the magnetic properties of porous materials based on vanadium [22], cobalt [23], copper [24] and molybdenum phosphates and diphosphonates [25] had been described, most of them antiferromagnets with ordering temperatures in the 2–50 K range. Then, important advances were introduced by Férey, Zubieta and their coworkers who reported an extensive family of porous iron (III) fluorophosphates and phosphates with antiferromagnetic ordering in the temperature range 10–37 K [26] and iron phosphates with a three-dimensional antiferromagnetic order at 12–30 K [27]. These results represented an important breakthrough that was followed by an exponential increase in scientific publications devoted to the study and understanding of magnetic properties on porous solids. Indeed, since then, new nanoporous systems that exhibit not only antiferromagnetic ordering [28] but also interesting ferri-/ferromagnetic ordering [29], spin-crossover [30] and metamagnetic [31] properties, among others, have been reported. For instance, the magnetic properties of several new 3-D inorganic magnetic porous materials such as metal sulfates [3, 32] metal cyanides [33], oxochlorides [34], fluorides [35] and selenites [36] have been described. Another important result in this field was reported by Long et al, who obtained a microporous cobalt cyanide magnet of composition Co3 [Co(CN)5 ]2 showing long-range magnetic ordering with a critical temperature of 38 K [33]. Moreover, its microporosity was confirmed by dinitrogen sorption measurements, with a Type I sorption isotherm after dehydration at 100 ◦ C under vacuum and a calculated surface area of 480 m2 g−1 (see Figure 8.2). Important contributions of 2-D and 1-D hybrid materials have also been achieved. In 2003, Kepert et al. discovered a hybrid porous material formed by a cobalt hydroxide layer structure pillared with trans-1,4-cyclohexanedicarboxylate ligands that orders magnetically below 60.5 K, and has small one-dimensional channels (3.7 × 2.3 Å2 ) that represent 13.4% of the crystal volume [37]. In the field of porous antiferromagnets, the ordering temperature has been increased to 95 K for a hybrid vanadium carboxylate complex [38]. Finally, the hybrid nickel glutarate open-framework shown in Figure 8.3, which behaves as a pure ferromagnet below a temperature of 4 K, has been recently described [39]. All the examples previously mentioned belong to 3-D, 2-D and 1-D hybrid inorganic–organic systems. However, one of the approaches that has been more intensively explored in the last few years is the preparation and characterization of 0D nanoporous coordination polymers. The advantage of this approach is threefold. First, the endless versatility of molecular chemistry provides chemists with a huge variety of polyfunctional ligands, most of them carboxylic-based and nitrogenbased molecules. Second, these ligands have been proved to be good superexchange

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Fig. 8.2. (a) Dinitrogen sorption isotherm for evacuated Co3 (Co(CN)5 )2 at 77 K, where (◦) and (•) indicate the absorption and desorption, respectively. (b) Field-cooled magnetization data for evacuated Co3 (Co(CN)5 )2 at H = 10 G. Inset, magnetic hysteresis loop at 5 K. (Reprinted with permission from [33]. Copyright 2002 American Chemical Society.)

pathways for magnetic coupling. And, last but not least, it may profit from crystal engineering techniques to arrange transition metal ions within a wide variety of open-framework structures that favor magnetic exchange interactions, since they coordinate in a predictable way.

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Fig. 8.3. (a) Illustration of the nanoporous structure of [Ni20 (C5 H6 O4 )20 (H2 O)8 ]·40H2 O. (b) Temperature-dependence of the χ T value, showing ferromagnetic ordering at 4 K. (Reproduction with permission from [39].)

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8.3 Magnetic Nanoporous Coordination Polymers As previously mentioned, the design of coordination polymers may profit from crystal engineering techniques to yield a large variety of open-framework structures, since organic ligands coordinate to transition metal ions in a more or less predictable way. This situation is very advantageous where the challenge is often to increase and modulate the pore sizes for selective adsorption and other applications. For instance, Yaghi et al. have already described a systematic approach (reticular synthesis) based on the use of different dicarboxylic acids for the design of open-framework structures with controlled pore sizes and functionalities [40]. In this section we will review representative examples of magnetic nanoporous coordination polymers. All these examples combine relevant magnetic properties (the presence of strong magnetic exchange interactions and/or any type of magnetic ordering) and a contrasted porosity. First, examples of magnetic nanoporous frameworks based on carboxylic ligands and different transition metal ions will be reviewed. The second section will be devoted to metal-organic open-framework structures based on N,N -ligands and the third to a new approach, developed in our group, based on the use of paramagnetic organic radicals as polytopic ligands.

8.3.1

Carboxylic Ligands

Although 1,3,5-benzenetricarboxylic or trimesic acid (BTC) has been widely used to obtain open framework structures, it was not until 1999 that Williams et al. reported for the first time the magnetic properties of an open-framework structure based on the BTC ligand, the [Cu3 (BTC)2 (H2 O)3 ]n complex (referred to as KHUST-1; see Figure 8.4) [41]. Structurally, KHUST-1 is composed of typical paddle-wheel Cu(II) dimers connected by BTC ligands along the three crystallographic directions to create a three-dimensional network of channels with fourfold symmetry and dimensions of 9 × 9 Å2 . Water molecules that fill the channels can be easily removed at a temperature of 100 ◦ C without loss of structural integrity. Resulting voids give a surface area of 917.6 m2 g−1 , a calculated density of 1.22 g cm−3 and an accessible porosity of nearly 41% of the total cell volume. Interestingly, additional experiments with the non-hydrate KHUST-1 form showed that it is possible to induce chemical functionalization without losing the overall structural information. The structural porosity of KHUST-1 is accompanied by interesting magnetic properties [42]. As shown in Figure 8.4, this porous coordination polymer shows a minimum in its χ vs. T plot at around 70 K and an increase at lower temperatures. Fitting to the Curie-Weiss law gave a Weiss constant of 4.7 K. This magnetic behavior can be explained by the presence of strong antiferromagnetic interactions within a Cu(II) dimer and weak ferromagnetic interactions between Cu(II) dimers.

8.3 Magnetic Nanoporous Coordination Polymers

267

Fig. 8.4. [Cu3 (BTC)2 (H2 O)3 ]n (HKUST) open-framework coordination polymer. (a) Paddlewheel CuII dimeric building-block. (b) Secondary building unit (nSBU). (c) Illustration of the channel-like HKUST-1, showing nanochannels with fourfold symmetry. (d) Temperature dependent magnetic susceptibility of as-synthesized HKUST-1 (•) and HKUST treated with dry pyridine to give [Cu3 (BTC)2 (py)3 ]n ( ). (Reproduction with permission from [41] and [42].)

The paddle-wheel Cu(II) dimer motif (see Figure 8.5a) was also used by Zaworotko et al. to obtain a molecular nanoporous Kagomé lattice [43]. In this case, the authors proposed the use of such building blocks as molecular squares 120◦ linked by 1,3-benzenedicarboxylate ligands (BDC) to generate two different porous frameworks, according to the self-assembly of the building units. The first of such structures was: [(Cu2 (py)2 (BDC)2 )3 ]n [43], generated from the self-assembly of the Cu(II) dimers with a triangular bowl-shaped topology to yield a Kagomé lattice with hexagonal channels and dimensions of 9.1 Å (see Figure 8.5b). The second structure [Cu2 (py)2 (BDC)2 ]n [44] was generated from the self-assembly of Cu(II) dimers with a square bowl-shaped topology to give a two-dimensional network with channels formed by narrowed windows (1.5 × 1.5 Å2 ) and large cavities with maximum dimensions of about 9.0 × 9.0 × 6.5 Å3 (see Figure 8.5c).

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Fig. 8.5. Crystal structure of [(Cu2 (py)2 (BDC)2 )3 ]n and [(Cu2 (py)2 (BDC)2 )4 ]n . (a) Paddlewheel CuII dimeric building block. (b) A schematic representation of the triangular nSBU and its arrangement in the Kagomé lattice, followed by a space-filling illustration of this openframework structure. (c) A schematic representation of the square nSBU and its arrangement in the square lattice, followed by a space-filling view of this nanoporous structure. (Reproduction with permission from [43] Wiley-VCH)

As for KHUST-1, the Kagomé lattice shows a high rigidity in the absence of solvent guest molecules and pyridine ligands, which can be removed at a temperature of 200 ◦ C without loss of the crystalline character. From a magnetic point of view, its most interesting feature is remnant magnetization [45]. Indeed, the χ vs. T plot shows a maximum just below 300 K and a minimum at around 60 K, increasing again at lower temperatures (see Figure 8.6). Fitting of magnetic data to the Bleaney-Bowers model confirmed a strong intradimer antiferromagnetic interaction of −350 cm−1 , typical of discrete Cu(II) dimers [46], and weaker interdimer antiferromagnetic interactions of −18 cm−1 . Even though interdimer interactions are antiferromagnetic, their triangular lattice arrangement leads to a magnetic spin frustration with a canted arrangement of spins and, therefore, to a geometrically frustrated antiferromagnetic ordering. This is the origin of the unusual remnant magnetization. In contrast, the two-dimensional framework with a square-like arrangement of the dimeric units does not present any remnant magnetization due to the lack of any geometrical frustration. In such a context, its magnetic behavior is very similar to that observed for KHUST-1, with an intradimer antiferromagnetic interaction of −380 cm−1 and interdimer interactions of −85 cm−1 .


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Fig. 8.6. Temperature dependence of the susceptibility (smooth line indicates the fitting to the Bleaney-Bowers law) for (a) square [(Cu2 (py)2 (BDC)2 )4 ]n lattice and (c) triangular (Kagomé) [(Cu2 (py)2 (BDC)2 )3 ]n lattice, respectively. Field-dependent magnetization for (b) square lattice and (d) triangular lattice, respectively, showing the hysteresis loop for the latter. (Reproduction with permission from [45])

Another rare example of spin-frustration is a vanadocarboxylate complex with a magnetically frustrated framework described by Riou et al. [47]. Complex [V(H2 O)]3 O(O2 CC6 H4 CO2 )3 ·(Cl·9H2 O) exhibits a three-dimensional framework built up from octahedral vanadium trimers joined via the isophthalate anionic linkers to delimit cages where water molecules and chlorine atoms are occluded. Although the trimeric clusters are connected along three directions, the 120◦ triangular topology of V(III) ions in each cluster induces a spin-frustration of their magnetic moments and, therefore, a lowering of the temperature for magnetic ordering. Finally, Kobayashi et al. have recently reported a 3-D nanoporous magnet [Mn3 (HCOO)6 ]·(MeOH)·(H2 O) with a diamond framework containing bridging formate ligands (see Figure 8.7) [48]. This is a short ligand with a small stereo effect beneficial for the formation of coordination magnetic frameworks. The resulting diamondoid framework exhibits one-dimensional channels of 4×5 Å2 (32% of the total cell volume), where each node is occupied by a MnMn4 tetrahedral unit

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where the central Mn(II) ion is connected to four Mn(II) through six formate ligands with one bidentate oxygen atom binding the central Mn(II) and one apical Mn(II) and the other oxygen atom binding one neighbouring apical Mn(II) ion. This 3-D network is thermally rigid up to 260 ◦ C, even after evacuation of guest molecules, and exhibits a rich guest-modulated magnetic behavior. Indeed, magnetic measurements of the as-synthesized or evacuated samples show characteristic ferrimagnetic

Fig. 8.7. [Mn3 (HCOO)6 ]·MeOH·H2 O diamantoid open-framework structure. (a) Mn-centered MnMn4 tetrahedron. (b) Topological representation of the porous diamantoid framework formed by the tetrahedral units as nodes sharing apices. (c) Temperature-dependent magnetic susceptibility for as-synthesized and desolvated sample. ([48] – Reproduced by permission of the Royal Society of Chemistry.)


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behavior and long-range magnetic ordering with critical temperatures close to 8 K. Additional measurements of the magnetization (M) as a function of T indicate a saturated magnetization close to 5 µB without a hysteresis loop, indicative of a soft magnet. Fascinatingly, this critical temperature can be modulated at will from 5 to 10 K by the absorption of several kinds of guests molecules, thanks to the porosity characteristics of this material.

8.3.2

Nitrogen-based Ligands

Although carboxylic ligands have been more extensively used, the use of polytopic nitrogen-based ligands has also generated some nice examples of magnetic openframework structures. For instance, Kepert et al. recently reported a nanoporous spin crossover coordination material based on the use of trans-4,4 -azopyridine (azpy) as a ditopic ligand [49]. The crystal structure of the resulting complex [Fe2 (azpy)4 (NCS)4 ·EtOH]n consists of double interpenetrated two-dimensional grid layers built up by the linkage of Fe(II) ions by azpy ligands (see Figure 8.8). As a result, two kinds of one-dimensional channels running in the same direction, filled with ethanol molecules and exhibiting openings of 10.6 × 4.8 Å2 and 7.0 × 2.1 Å2 , are created. The evacuation of ethanol guest molecules takes place at 100 ◦ C and

Fig. 8.8. Schematic representation of the guest-dependent spin-crossover nanoporous [Fe2 (azpy)4 (NCS)4 ·(EtOH)]n . X-ray crystal structures of the as-synthesized material at 150 K and the evacuated sample at 375 K; and the temperature-dependent magnetic moment of (◦) the as-synthesized [Fe2 (azpy)4 (NCS)4 ·(EtOH)]n , () the evacuated [Fe2 (azpy)4 (NCS)4]n and (♦) [Fe2 (azpy)4 (NCS)4 ·(1-PrOH)]n (evacuated structure exposed to 1-propanol). (Reprinted with permission from [49]. Copyright 2002 AAAS.)

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is accompanied by several structural changes. The most significant modification consists in an elongation and constriction of the one-dimensional channels, the new dimensions being 11.7 × 2.0 Å2 . Furthermore, crystal changes by −6, +9, +3% along the a, b and c axes, respectively, can also be macroscopically detected. Interestingly, these structural modifications are accompanied by changes in the macroscopic magnetic properties. The as-synthesized sample exhibits a constant effective magnetic moment of 5.3 µB between 300 and 150 K. Below this temperature, the magnetic moment decreases, reaching a constant value of 3.65 µB due to a spin-crossover interconversion coming from a fraction of the Fe(II) ions. On the contrary, the evacuated sample does not show spin-crossover behavior, exhibiting a constant magnetic moment of around 5.1 µB , corresponding to two crystallographic high-spin Fe(II) ions. Surprisingly, spin-crossover is recovered after re-absorption of guest solvent molecules. Indeed, when an evacuated crystalline sample was immersed in methanol, ethanol or propanol solvent, the magnetic properties were similar to those observed for the as-synthesized sample. The use of the structural versatility of coordination polymers to obtain magnetic nanoporous molecular materials was once again demonstrated by You et al. who reported a family of Co(II) imidazolates (im) complexes showing a variety of open-framework structures with different magnetic behaviors [50]. In this case, the rational use of solvents and counter-ligands plays a key role in obtaining a collection of polymorphic three-dimensional nanoporous Co(II) structures: [Co(im)2 ·0.5py]n , [Co(im)2 ·0.5Ch]n , [Co(im)2 ]n , [Co(im)2 ]n and [Co5 (im)10 ·0.4Mb]n (where py, Ch and Mb refer to pyridine, cyclohexanol and 3-methyl-1-butanol, respectively). Complexes [Co(im)2·0.5py]n and [Co(im)2·0.5Ch]n are isostructural and formed by Co(II) centers linked into boat- and chairlike six-membered rings connected in an infinite diamond-like net. This conformation originates one-dimensional channels with dimensions 5.3 × 10.4 Å2 and 6.6 × 8.4 Å2 , respectively. The influence of the reaction solvent and structure-directing agents was also evident in the other three Co(II) imidazolate coordination polymers. The crystal structure of one of the two compounds with formula [Co(im)2 ]n is formed by the self-assembly of fourmembered ring Co(II) units, which are doubly connected to wavelike or double crankshaft-like chains. These chains intersect with those running along the perpendicular axis by means of the common four-rings at the wave peaks. Three such frameworks are interwoven and linked by the imidazolates at the Co(II) ions. The resulting 3-D framework shows one-dimensional helical channels with dimensions 3.5×3.5 Å2 . Similarly, the complex [Co(im)2 ]n is also formed by the self-assembly of identical units connected into chains. These chains are linked to each other by the imidazolate ligands along the other two directions to give a 3-D framework with a pore opening of 4.0×4.0 Å2 . The fact that both structures crystallize in the absence of solvent guest molecules gives them a highly structural rigidity up to 500 ◦ C. Of special interest is the second complex [Co(im)2 ]n . In all polymorphous frameworks the imidazolates transmit the antiferromagnetic coupling between the cobalt(II) ions. However, the uncompensated antiferromagnetic couplings arising from spin-


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canting phenomena are sensitive to the structures: compound [Co(im)2 ·0.5py]n is an antiferromagnet with TN = 13.11 K; [Co(im)2 ·0.5Ch]n shows a very weak ferromagnetism below 15 K, [Co(im)2 ]n exhibits a relatively strong ferromagnetism below 11.5 K and a coercive field (HC ) of 1800 Oe at 1.8 K, and [Co(im)2 ]n displays the strongest ferromagnetism of the three cobalt imidazolates and demonstrates a TC of 15.5 K with a coercive field, HC , of 7300 Oe at 1.8 K. However, compound [Co5 (im)10 ·0.4MB]n seems to be a hidden canted antiferromagnet with a magnetic ordering temperature of 10.6 K.

8.3.3

Paramagnetic Organic Polytopic Ligands

Magnetic coupling between transition metal ions in coordination polymers generally takes place through a superexchange mechanism involving the organic ligand orbitals, a mechanism that is strongly dependent on their relative orientation and, especially, on the distance between interacting ions. Therefore, the difficulty in obtaining nanoporous materials with increasing pore size dimensions and simultaneous long-range magnetic properties remains a challenge. To overcome such inconvenience, in our group we have developed a new efficient and reliable synthetic strategy based on the combination of persistent polyfunctionalized organic radicals, such as polytopic ligands, and magnetically active transition metal ions. The resulting structures are expected to exhibit larger magnetic couplings and dimensionalities in comparison with systems made up from diamagnetic polyfunctional coordinating ligands, since the organic radical may act as a magnetic relay. This so-called metal–radical approach [51] (combination of paramagnetic metal ions and pure organic radicals as ligating sites) has already been used successfully by several groups working in the field of molecular magnetism. However, even though a large number of metal–radical systems have been studied, this is the first occasion that this approach has been used to obtain magnetic nanoporous materials. Organic radical ligands must fulfil a series of conditions. Obviously, they must have the correct geometry to induce the formation of open-framework structures. Second, they must exhibit high chemical and thermal stability and, third, they have to be able to interact magnetically with transition metal ions, which is an indispensable condition to enhance the magnetic interactions of the nanoporous material. To fulfil all three conditions we have chosen the tricarboxylic acid radical (PTMTC) [52], shown in Figure 8.9. First, the conjugated base of the PTMTC radical can be considered as an expanded version of the BTC ligand, where the benzene-1,3,5-triyl unit has been replaced by an sp2 hybridised carbon atom decorated with three four-substituted 2,3,5,6-tetrachlorophenyl rings. Therefore, in accord with their related trigonal symmetries and functionalities, PTMTC is also expected to yield similar openframework structures Second, polychlorinated triphenylmethyl (PTM) radicals have their central carbon atom, where most of the spin density is localized, sterically

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Fig. 8.9. Plot and crystal structure of the tricarboxylic perchlorotriphenylmethyl radical (PTMTC).

shielded by encapsulation with six bulky chlorine atoms that increase astonishingly the lifetime and thermal and chemical stability [53]. Third, a recently reported family of monomeric complexes using a similar PTM radical with only one carboxylic group (PTMMC) has confirmed the feasibility of this type of carboxylic-based radicals to magnetically interact with metal ions [54]. Following this strategy, we have recently reported the first example of a metalradical open-framework material [Cu3 (PTMTC)2 (py)6 (EtOH)2 (H2 O)] (referred to as MOROF-1) that combines very large pores with magnetic ordering at low temperatures [55]. As shown in Figure 8.10, crystal structure of MOROF-1 reveals a two-dimensional honeycomb (6,3) network with the central methyl carbon of the PTMTC ligand occupying each vertex, similar to those observed for some openframeworks obtained with the trigonal BTC ligand and a linear spacer [56]. In our case, the linear spacer is composed of Cu(II) centers with a square pyramidal coordination polyhedron formed by two monodentate carboxylic groups, two pyridine ligands and one ethanol or water molecule. The correct arrangement of the honeycomb planes leads to the presence of very large one-dimensional hexagonal


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Fig. 8.10. Illustration of the nanochannel-like structure of MOROF-1. The correct arrangement of the honeycomb (6,3) layers creates large nanopores of dimensions 3.1 and 2.8 nm between opposite vertices.

nanopores, each composed of a ring of six metal units and six PTMTC radicals, which measure 3.1 and 2.8 nm between opposite vertices (see Figure 8.10). To our knowledge, this is one of the largest nanopores reported for a metal–organic open-framework structure. Moreover, complex MOROF-1 shows square and rectangular channels in a perpendicular direction with estimated sizes of 0.5 × 0.5 and 0.7 × 0.3 nm2 , respectively. Both pore systems give solvent-accessible voids in the crystal structure that amount to 65% of the total unit cell volume. Paramagnetic Cu(II) ions are separated by long through-space distances of 15 Å within the layers and 9 Å between them, for which non-magnetic coupling between metal ions should be expected. However, each open-shell PTMTC ligand is able to magnetically interact with all three coupled Cu(II) ions and, therefore, to extend the magnetic interactions across the infinite layers. As shown in Figure 8.11, the smooth decrease in the χ T value below 250 K is a clear sign of the presence of antiferromagnetic coupling between nearest-neighbour Cu(II) ions and PTMTC ligands within a 2-D layer. The minimum of χT corresponds to a short-range or-

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Fig. 8.11. (a) A honeycomb (6,3) layer showing the distribution of the copper ions (sphere) and the central methyl carbon, which has the most spin density, of the PTMTC radicals (dark sphere); (b) Value of χ T as a function of the temperature for as-synthesized (filled circle) and evacuated (open circle) MOROF-1.

der state where the spins of adjacent magnetic centers are antiparallel, provided that there is no net compensation due to the 3:2 stoichiometry of the Cu(II) ions and PTMTC radical units. The huge increment in χT at lower temperatures indicates an increase in the correlation length of antiferromagnetically coupled units of Cu(II) and PTMTC as randomising thermal effects are reduced, either via in-plane


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long-range antiferromagnetic coupling and interplane dipolar–dipolar magnetic interactions. The magnetization curve at 2 K exhibits a very rapid increase, as expected for a bulk magnet, although no significant hysteretic behavior was observed. The magnetization value increases much more smoothly at higher fields up to a saturation value of 1.2 µB , which is very close to that expected for an S = 1/2 magnetic ground state. Thus, this molecular material can be considered as a ferrimagnet with an overall magnetic ordering at low temperatures (∼2 K), which shows the behavior of a soft magnet. A second remarkable feature is the reversible “shrinking–breathing” process experienced by MOROF-1 upon solvent uptake and release. Indeed, when MOROF-1 is removed from solution and exposed to air, the crystalline material loses ethanol and water guest molecules very rapidly, even at room temperature within a few seconds, becoming an amorphous material with a volume decrease of around 30% (see Figure 8.12). Even more interesting, the evacuated sample of MOROF-1 experiences a mechanical transformation, recovering its original crystallinity and up to 90% of its original size after exposure to liquid or vapor EtOH solvent.

Fig. 8.12. Real images of a crystal of MOROF-1 followed with an optical microscope. The top series represents the “shrinking” process, in which a crystal of MOROF-1 exposed to the air exhibits a volume decrease of around 30%. In the down series, the same crystal exposed again to ethanol liquid begins to swell. The scheme represents the structural changes of MOROF-1 in contact or not with ethanol or methanol solvent. (Reproduction with permission from [57].)

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This chemical and structural reversibility is also accompanied by changes in the magnetic properties that are macroscopically detected. Magnetic properties of an evacuated amorphous sample of MOROF-1 show similar magnetic behavior to that shown by the as-synthesized crystals of MOROF-1, with two main differences: (a) the displacement of the χ T minima from 31 K for as-synthesized to 11 K for the evacuated MOROF-1 samples and (b) the magnetic response of the filled MOROF1 sample at low temperature, where the long-range magnetic ordering is attained, results in a much larger (up to one order of magnitude) magnetic response than that of the evacuated MOROF-1 material. From these results it was inferred that the effective strength of the magnetic interactions for the evacuated sample of MOROF-1 was less than that observed for the as-synthesized crystals. Thus the most striking feature exhibited by MOROF-1 is that the structural and chemical evolution of the material in the process of solvent inclusion can be completely monitored by the magnetic properties. When MOROF-1 is re-immersed in ethanol solvent, a fast recovery up to 60% of the signal can be seen during the first minutes, whereupon, the recovery of magnetic signal seems to be linear with the logarithm of time (see Figure 8.13).

8.4 Summary and Perspectives The use of organic ligands has been shown to be an efficient methodology for the preparation of magnetic nanoporous materials due to the chemical versatility of organic ligands, their capability to be good superexchange pathways for magnetic coupling and the possibility of benefiting from crystal engineering techniques to arrange transition metal ions within a wide variety of open-framework structures. The synergism of magnetic properties and nanoporous materials, together with the molecular characteristics of coordination polymers, opens a new route to the development of Multifunctional Molecular Materials. For instance, magnetic zeotype structures offer excellent conditions to encapsulate different functional materials with conducting, optical, chiral and NLO properties, among others. In consequence, the resulting material combines the magnetic properties of the framework and the inherent properties and applications of the protected functional molecules. Another field of research where this type of material will have an enormous interest in the near future is magnetic sensors. Throughout this chapter, different examples of nanoporous materials whose magnetic properties can be modulated by the presence of guest molecules within the channels have been shown. From amongst them, special mention of the complex MOROF-1 is deserved. The enhanced magnetic response of a filled sample when compared to that exhibited by an evacuated sample of MOROF-1, together with the reversible solvent-induced structural changes experienced by this sponge-like material, open the door to the possible development

8.4 Summary and Perspectives

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Fig. 8.13. (a) Powder X-ray diffractograms (XRPD) of MOROF-1, showing the steps of the transformation of the amorphous, evacuated phase in contact with ethanol vapor: a, amorphous phase; b, 0; c, 4.5; d, 5; e, 6; f, 8; g, 10; h, 26; i, 28; j, 52 h. Inset, XRPD of the as-synthesized MOROF-1. (b) and (c) Reversible temperature-dependent χT value behavior of the amorphous, evacuated phase in contact with ethanol liquid at 1000 and 10,000 Oe, respectively. (d) Reversible field-dependent magnetization of the amorphous, evacuated phase in contact with ethanol liquid. In (b), (c) and (d), amorphous phase (open circle), amorphous phase in contact with ethanol for 5 min (), 12 min (), 30 min (), 15 days () and assynthesized MOROF-1 (filled circle).

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of magnetic sensors based on open-framework molecular magnets. Moreover, from more than 15 different solvents so far used, including several alcohols, such reversible behavior has only been observed for EtOH and MeOH solvents; a fact that enhances the selectivity of the sponge-like magnetic sensor. Also one can imagine molecular (drug) delivering devices activated by external magnetic fields. But before all this potentiality becomes a reality, much work has to be done by chemists in the near future to develop new synthetic methodologies that overcome the inherent difficulties of this type of system: (1) the ultimate design is never obvious; (2) the final products are often poorly crystallized and prevent one from obtaining structural information; (3) the overall thermal stability is generally limited to the intrinsic thermal stability of the organic ligand and, therefore, is lower than some inorganic-based porous materials like zeolites and (4) since “Nature hates a vacuum”, many structures collapse in the absence of the guests.

Acknowledgments We want to thank our collaborators in the development of magnetic nanoporous molecular materials based on organic radicals, both in our institute (C. Rovira) and abroad (K. Wurst from Innsbruck University and J. Tejada and N. Domingo from UB).

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9 Magnetic Prussian Blue Analogs Michel Verdaguer and Gregory S. Girolami

9.1 Introduction Magnetic solids have numerous and important technological applications: they find wide use in information storage devices, microwave communications systems, electric power transformers and dynamos, and high-fidelity speakers [1–3]. By far the largest application of magnetic materials is in information storage media, and the annual sales of computer diskettes, compact disks, optical disks, recording tape, and related items exceed those of the celebrated semiconductor industry [3–5]. The demand for higher bit-density information storage media and the emergence of new technologies such as magneto-optic devices make it crucial to expand the search for entirely new classes of magnetic materials [2, 3]. In response to the increasing demands being placed on the performance of magnetic solids, over the last decade or so there has been a surge of interest in molecule-based magnets [6–20]. In such solids, discrete molecular building blocks are assembled, with their structures intact, into 0-, 1-, 2-, or 3-dimensional arrays. One of the attractive features of molecular magnets is that, by choosing appropriate building blocks, the chemist can exert considerable control over the connectivity and architecture as well as the resulting magnetic properties of the array. The local exchange interactions, which can be specifically tailored through judicious choice of appropriate molecular building blocks, dictate the bulk magnetic behavior of the solid. By choosing molecular building blocks whose singly occupied molecular orbitals (magnetic orbitals) are of specific symmetries, and by linking the building blocks into arrays with favorable geometric relationships between the building blocks, the synthetic chemist can exert powerful control over the properties of new molecule-based magnetic materials. Although the high molecular weights and low bulk densities observed for essentially all molecule-based magnets preclude their use as permanent magnets, they are potentially useful as magnetic recording media [21] or quantum computing devices [22]. More significantly, however, some molecule-based magnets exhibit bulk properties quite unlike those of conventional magnetic solids. For example, some are optically transparent, and others are non-magnetic in the dark but magnetic in

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9 Magnetic Prussian Blue Analogs

the light. Until quite recently, the magnetic ordering temperatures of these unusual solids were too low ( 0) aligns the magnetic moments and provides a long-range magnetic order. We shall see that ferromagnetic interactions are rare in Prussian Blue analogs. Finally, case (d) represents a very appealing situation, in which the usual antiferromagnetic interaction gives rise to a nonzero resultant spin, if the two spins S1 and S2 are different in absolute value. Unfortunately, the spin Hamiltonian does not provide insights into how to control the sign or magnitude of J . For this, we needed to find the proper orbital strategy. JAF

SA SB (a)

JF

SA SB = 0 SA (b)

JF

JAF

SA SB (c)

SA SB (d)

Fig. 9.6. Spin arrangements in Prussian Blues: (a) antiferromagnetic interaction between identical neighboring spins; (b) ferromagnetic interaction through a diamagnetic neighbor (double exchange in Prussian Blue); (c) ferromagnetic interaction between identical neighboring spins; (d) antiferromagnetic interaction between different neighboring spins: ferrimagnetism.

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9.3.2.1

Mean Field, Ligand Field and Exchange Models

The most successful model for understanding the magnetic properties of insulating magnetic solids is the “mean field model,” which was originally suggested by Weiss and refined by Néel [76]. Here, we briefly give the basic elements of this model. Consider an insulating two-component magnetic solid AB in which A and B are interpenetrating subnetworks, each of which consists of a set of identical spin centers. The mean field model assumes that all the spins within each subnetwork are oriented in the same direction. It further postulates that the interaction between the two subnetworks A and B can be described by the molecular field coefficient W , and that the interaction within each subnetwork can be described by the coefficients WA and WB . The parameter W can be positive (for ferromagnetic interactions) or negative (for antiferromagnetic interactions); the parameters WA , and WB are always positive. The effective local magnetic fields HA and HB acting on the magnetic moments of the sub-networks A and B are: HA = H0 + W MB + WA MA HB = H0 + W MA + WB MB

(9.1)

where H0 is the applied field, and MA and MB are the mean magnetisations of sub-networks A and B. At high temperatures, the magnetisations of subnetworks A and B are proportional to the effective local field, so that: MA = [H0 + W MB + αW MA ] · CA /T MB = [H0 + W MA + βW MB ] · CB /T

(9.2)

where CA and CB are the Curie constants of the spins constituting sub-networks A and B, respectively, and where α = WA /W and β = WB /W . Solving these equations for MA and MB , and then calculating the magnetic susceptibility χ from the definition χ = (MA + MB )/H0 gives the following expression: 1/χ =

γ (T − θa ) − C (T − θ )

(9.3)

where the parameters C, θ , θa , and γ are functions of CA , CB , W , α, and β (see Ref. 75 for the exact form of these functions). The mean field model has not been extensively used for ferromagnets, where fluctuations in the mean field restrict the analysis to the high temperature range and impede analysis of the data close to the magnetic ordering temperature, but the model is well adapted for ferrimagnets (antiferromagnetic interactions between the A and B subnetworks). For such solids, the mean field model predicts that the plot of 1/χ vs. T at high temperatures should be hyperbolic, and this curve is often referred to as a Néel hyperbola.

9.3 Magnetic Prussian Blues (MPB)

295

For a magnetic solid consisting of an array of identical S = 1/2 centers, the magnetisation at low temperature is given by: M = Nµ tanh[µH /kT ]

(9.4)

where N is Avogadro’s constant, µ is the magnetic moment, H is the local magnetic field, and k is Boltzmann’s constant. More generally, for the case in which the solid consists of two subnetworks A and B whose constituent spin centers have spins SA and SB and g values gA and gB , respectively, the magnetisation within the A subnetwork is (β, Bohr magneton): MA = NgA βSA BS [gA SA β(H + hA )/kT ]

(9.5)

where hA = W (εMB + αMA ), BS is the Brillouin function (with its argument in square brackets), and ε equals 1 if W is positive and −1 if W is negative. To obtain this expression, we have assumed that the applied field is negligible compared to the mean field (so that the mean field dominates). We can obtain a similar expression for MB ; the total magnetisation M is equal to (MA + εMB ). Solving the system of two equations for MA and MB (which is usually done numerically rather than analytically) and finding the total magnetisation as a function of temperature gives magnetisation curves that depend on the details of the exact system studied: the results depend on the nature of A and B, on the fraction of occupied sites, on the parameters α and β, and, for ferrimagnetic systems, on the parameters x = µA /µB and y = nA /nB , where µA and µB are the magnetic moments on A and B, and nA and nB are the number of atoms A and B in the unit considered. Depending on the values of x and y, Néel predicted very different shapes for magnetisation curves M(T ) including some that change sign at a certain temperature (called the “compensation temperature”) at which the magnetisations of the sub-networks A and B are exactly equal and opposite in direction [75]. The model was used in a predictive and clever way by Okhoshi et al. in their studies of the compensation points in the magnetisation curves of polymetallic magnetic Prussian Blues (see Section 9.5.2). The ideas developed by Néel in his 1948 paper [75] (see also Herpin [76] and Goodenough [77]) within the frame of mean field theory to interpret the magnetism of perovskite ferrimagnets ABO3 are fully valid for MPBs. In particular, the expression for the susceptibility close to the ordering temperature TC can be used to extract the following very useful relation: (9.6) kTC = Z|J | CA CB /NA g 2 β 2 where Z is the number of magnetic neighbors, |J | is the absolute value of the exchange interaction between A and B, CA and CB are the Curie constants of A and B, weighted by the stoichiometry, NA is Avogadro’s constant, g is a mean Lande factor for A and B, and β is the Bohr magneton. Equation (6) clearly shows that TC can be maximized by increasing the number of magnetic neighbors, by increasing the magnitude of J , and by increasing CA and CB . For the Prussian

296


Blues of stoichiometry Mx A[B(CN)6 ]z ·nH2 O, we can follow several strategies to maximize TC : • Maximize Z by controlling the Prussian Blue stoichiometry. The number of nearest neighbors Z is dictated by the value of z in the Prussian Blue formula. In Prussian Blues with a 1:1 A:B stoichiometry (i.e., lacking vacancies in the [B(CN)6 ] sites), the number of nearest neighbors Z adopts its maximum possible value of 6. In the frequently encountered 3:2 A:B systems (in which z = 2/3 and one-third of the B sites are vacant), the number of nearest neighbors Z is only 4. As the number of vacancies in the MPB structure decreases, TC becomes larger. We shall use these conclusions later. • Maximize |J | by changing the identities of the spin centers A and B in the two subnetworks. We develop this point in the following paragraph. • Maximize the Curie constants CA and CB by proper choice of the metals A and B. This approach to maximize TC proves to be less useful than the other two, as we shall see. Ligand field model

In Prussian Blue magnets, the exchange mechanisms that dictate the magnitude of J involve the delocalization of spin from the metal centers onto the cyanide bridges. The extent of spin delocalization is readily explicable in terms of ligand field theory. In the idealized Prussian Blue structure of stoichiometry Mx A[B(CN)6 ]z ·H2 O, each B atom is surrounded by the carbon atoms of six cyanide ligands and will always experience a large ligand field (with very large octahedral splitting). As a result, the B atoms will be low spin with unpaired electrons (if any) only in the t2g orbitals (Figure 9.7a). It may be noted that the octahedral is sufficiently large (and the antibonding orbitals e∗g so high in energy) that no [B(CN)6 ] complex exists with more than six d-electrons: such complexes are not stable. In contrast, the A atom is surrounded by the nitrogen atoms of six cyanide ligands (when the stoichiometry is z = 1), or by four cyanides and two water molecules (when the stoichiometry is z = 2/3). The A atoms thus experience weak ligand fields, and are usually high-spin (Figure 9.7b and c), although in a few cases [CrII , MnIII , CoII , see below] the A atoms can be low-spin. Because cyanide is a moderate σ -donor, a weak π-donor, and a moderate πacceptor, spin delocalization can occur by means of both σ and π mechanisms. The nitrogen pz orbital mixes with the dz2 orbital of the A ion to which it is directly attached (σ symmetry), and the nitrogen px and py orbitals mix with the dxz and dyz orbitals of the A ion (π symmetry). The singly occupied orbitals (or magnetic orbitals) on both metals are sketched in Figure 9.7: φ(t2g ) magnetic orbitals on the B site, and either φ(t2g ) or φ ∗ (eg ) magnetic orbitals (or both) on the A site. The dotted lines represent the nodal surface of the orbitals on the internuclear axis.


297

Fig. 9.7. Local magnetic orbitals in an isolated (NC)5 –B–CN–A(NC)5 binuclear unit: (a) φ(t2g ) magnetic orbitals in B(CN)6 ; (b) φ(t2g ) magnetic orbitals in A(NC)6 ; (c) φ ∗ (eg ) magnetic orbitals in A(NC)6 .

Previous experimental studies of paramagnetic molecules containing C-bonded cyanide ligands show that there is a small spin density on the carbon atom but a larger spin density on the nitrogen atom. Figure 9.7a closely follows the spin density maps obtained from polarized spin neutron diffraction [78] and solid state paramagnetic NMR studies [79] of [BIII (CN)6 ] salts (B= Fe, Cr). From this simple ligand field analysis, it is possible to draw an important conclusion about the exchange: the empty π ∗ orbitals of the cyanide ligands play an important role in the antiferromagnetic exchange interactions in Prussian Blue analogs. Consequently, we predicted that substituting into the structure metals that have single electrons in high-energy (and more radially expanded) t2g orbitals should afford Prussian Blues with higher magnetic ordering temperatures. Higher-energy d-orbitals are characteristic of the early transition metals in lower oxidation states, owing to the lower effective nuclear charges of these elements. Accordingly, building blocks such as aquated salts of VII and CrII , and hexacyanometalate derivatives of VII , CrII , and CrIII , should afford Prussian Blue compounds with much higher magnetic ordering temperatures. Orbital symmetry and the nature of the magnetic exchange coupling

The relationship between the symmetry of the singly-occupied orbitals on two adjacent spin carriers and the nature of the resulting magnetic exchange interaction is one of the most useful concepts available to the synthetic chemist interested in designing molecule-based magnetic systems with specifically tailored magnetic properties [6–8, 19, 80]. To predict the value of |J |, two different approaches have been used: Kahn’s model, in which the magnetic orbitals are non-orthogonalized, and Hoffmann’s approach, in which the magnetic orbitals are orthogonalized. Both models predict that orthogonal orbitals give rise to ferromagnetism and that non-orthogonal orbitals give rise to antiferromagnetism. Consider the case of two electrons residing in two identical orbitals a and b on two adjacent sites. In Kahn’s model [7, 81–83], the singlet-triplet energy gap, J

298


(= Esinglet − Etriplet ), is given by: J = 2k + 4βS

(9.7a)

where k is the two-electron exchange integral (positive) between the two nonorthogonalized magnetic orbitals a and b; β is the corresponding monoelectronic resonance or transfer integral (negative), and S is the monoelectronic overlap integral (positive) between a and b. In Hoffmann’s model [84], J is given by: J = 2Kab − (E1 − E2 )2 /(Jaa − Jab )

(9.7b)

where Kab is the two-electron exchange integral (positive) between two identical orthogonalized magnetic orbitals a and b ; (E1 − E2 ) is the energy gap between the molecular orbitals 1 and 2 built from a and b , Jaa is the bielectronic interelectronic repulsion on one centre, and Jab the equivalent on two centres. In both Eqs. (9.7a) and (9.7b), the first term is positive and the second term is negative; thus J can be represented as the sum of two components, a positive term JF that favors a parallel alignment of the spins and ferromagnetism, and a negative term JAF that favors an antiparallel alignment of the spins and short-range antiferromagnetism. J = JF + JAF

(9.7c)

When the two a and b orbitals are different, no rigorous analytical treatment is available, but a semi-empirical relation was proposed by Kahn [85]: J = 2k + 2S(2 − δ 2 )1/2

(9.8)

where δ is the energy gap between the (unmixed) a and b orbitals, and is the energy gap between the molecular orbitals built from them. When several electrons are present on each centre, nA on one side, nB on the other, J can be described as the sum of the different “orbital pathways” Jµν , weighted by the number of electrons [86]: Jµν /nA nB (9.9) J = µν

where µ varies from 1 to nA and ν varies from 1 to nB . When only one electron is present per site, the situation is simple: a shortrange ferromagnetic interaction leads to a triplet ground state [86]; a short-range antiferromagnetic interaction leads to a singlet ground state. When each site bears a different number of electrons, the short-range ferromagnetic coupling leads to a total spin ground state which is the sum of the spins: ST = SA + SB ; the short-range antiferromagnetic coupling leads to a total spin ground state which is the difference of the spins: ST = |SA − SB |. Figure 9.6 illustrates these situations. A key point is that antiferromagnetism between two neighbors bearing different spins leads to a non-zero spin in the ground state. For a bulk solid [75], this situation is known as ferrimagnetism.


9.3.2.2

299

Application to Magnetic Prussian Blue Analogs

The Prussian Blues are excellent “textbook” examples of the use of symmetry to analyze the exchange interactions in magnetic solids, because their cubic structures greatly simplify the analysis. Furthermore, magnetic exchange is a short-range phenomenon, and thus we can neglect interactions with second nearest neighbors (which are more than 10 Å away) and with more distant magnetic centers, and consider only the interactions between adjacent metal atoms. The analysis thus reduces to a consideration of the exchange interactions present between two metal centers connected by a cyanide linkage: i.e., in a (CN)5 A−N≡C−B(CN)5 subunit (Scheme 9.1). CN

NC

CN NC

M' NC

C

N

M

z

NC

y

CN CN

x

NC

NC

Scheme 9.1

Suppose that the two adjacent metal centers each carries a single unpaired electron in a d-orbital (we will refer to such orbitals as “magnetic orbitals” after Kahn). If the two magnetic orbitals are orthogonal, then the ground state of the system has parallel electron spins. In contrast, if the two magnetic orbitals are not orthogonal, then the ground state of the system generally has antiparallel electron spins. In other words, orthogonal orbitals lead to local ferromagnetic interactions whereas non-orthogonal orbitals favor local antiferromagnetic interactions. The behavior is simply a two-site analog of Hund’s rule, and has the same quantum mechanical origin. For systems in which the interacting magnetic centers each contain several magnetic orbitals, or that consist of arrays of many spin centers, the symmetry relationship between each magnetic orbital on one spin carrier must be considered with respect to the various magnetic orbitals on the adjacent spin carriers. Mutually orthogonal magnetic orbitals will contribute to the ferromagnetic exchange term, whereas non-orthogonal magnetic orbitals will contribute to the antiferromagnetic term. The net interaction is simply the sum of all the ferromagnetic and antiferromagnetic contributions. In a Prussian Blue compound, the A and B centers are octahedral and connected together by nearly linear A−N≡C−B cyanide bridges. (Even when this linkage is somewhat non-linear, the basic conclusions remain unchanged.) The B atom, which is surrounded by the carbon atoms of six cyanide ligands, is in a large ligand field. As a result, all known [B(CN)6 ] units are invariably low spin and have electrons

300


only in the t2g orbitals. In contrast, the A atom, which is surrounded by nitrogen atoms of cyanide ligands or oxygen from water molecules, is in a weak ligand field and is almost always high-spin. For the A atoms, it is possible for unpaired electrons to be present only in the t2g orbitals (for d2 or d3 ions), only in the eg orbitals (for d8 and d9 ions), or in both the t2g and eg orbitals (for d4 through d7 ions). For the Prussian Blues, therefore, three situations arise: 1. When only eg magnetic orbitals are present on A, all the exchange interactions with the t2g magnetic orbitals present on [B(CN)6 ] will be ferromagnetic. Thus, if a Prussian Blue is prepared by adding a d8 or d9 A cation such as NiII or CuII to a paramagnetic [B(CN)6 ] anion, a ferromagnet should result. The accuracy of this analysis was illustrated by the preparation in 1991 of NiII2 [FeIII (CN)6 ]3 ·xH2 O and CuII 2[FeIII (CN)6 ]3 ·xH2 O, both of which are ferromagnetic as predicted [87]. 2. When only t2g magnetic orbitals are present on A, all the exchange interactions with the t2g magnetic orbitals present on [B(CN)6 ] will be antiferromagnetic. In this case, if the Prussian Blue is prepared by adding a d2 or d3 cation to a paramagnetic [B(CN)6 ] anion, a ferrimagnet should result. The first such compounds were described in 1995 [29] and will be discussed below. 3. When both t2g and eg magnetic orbitals are simultaneously present on A, ferromagnetic and antiferromagnetic interactions with the t2g magnetic orbitals on [B(CN)6 ] coexist and compete. Here, the overall nature of the interaction is not so simple to predict. Usually, the antiferromagnetic interactions dominate and the solid orders ferrimagnetically. For example, Babel’s compound CsMnII [CrIII (CN)6 ]·xH2 O falls into this class and is ferrimagnetic. But this may not always be the case, FeII3 [CrIII (CN)6 ]2 ·xH2 O and CoII3 [CrIII (CN)6 ]2 ·xH2 O are ferromagnetic with low TC s and weak exchange interaction.

9.3.2.3

Molecular Orbital Analysis

Semi-empirical extended Hückel calculations have afforded detailed information about the high energy molecular orbitals directly related to exchange in the (CN)5 A−N≡C−B(CN)5 units. Typical molecular orbitals constructed from linear combinations of the magnetic φ(t2g ) orbitals appear in Figure 9.8 (for clarity, our graphical representation exaggerates the amount of A–B mixing): bonding: ϕ1 = λ+ φt2g (B) + µ+ φt2g (A) (λ+ µ+ ) antibonding: ϕ2 = λ− φt2g (B) − µ− φt2g (A) (λ− µ− )

(9.10a) (9.10b)

The precise contribution of each atomic orbital to these MOs depends on their energies and radial extensions. Nevertheless, the importance of the participation of the cyanide bridge in the exchange phenomenon is clearly apparent.


301

Before mixing, the energy difference between the magnetic orbitals φ(t2g )(A) and φ(t2g )(B) is δ; after mixing the energy gap between ϕ2 and ϕ1 is . The dotted lines display the nodal surfaces in the orbitals along the internuclear axis: there is one nodal surface in the bonding orbital, and two in the antibonding orbital. The situation in the case of orthogonal φ(t2g )(B) orbitals and φ(eg )(A) orbitals is shown in Figure 9.9a. In the insert (Figure 9.9b), we emphasize the spin density borne by the nitrogen in the two orthogonal py and pz orbitals. The overlap density ρ, which is given by the expression: ρ = φ(t2g )(B) · φ(eg )(A)

(9.11)

is strong on the nitrogen and, from this situation, we expect a strong ferromagnetic interaction because the exchange integral k is proportional to ρ 2 [86]. In all the cases, Figures 9.8 and 9.9 display the triplet electronic configuration. The conclusions from Figures 9.8 and 9.9 are straightforward: the t2g (B)–eg (A) pathways lead to ferromagnetic (F) interactions, the magnitude of which is expected to be significant, owing to the electronic structure of the cyanide bridge and the

E

y

ϕ2

z

t2g

B C N

δ

y

∆

z

ϕ1

CN

A

t2g

Fig. 9.8. Molecular orbitals ϕ1 and ϕ2 built from φ(t2g ) magnetic orbitals in the (NC)5 –B– CN–A(NC)5 binuclear unit. E

(a)

y

y z z

B C N t2g

C N A

(b) C

eg N

Fig. 9.9. Orthogonal magnetic orbitals in the (NC)5 –B–CN–A(NC)5 binuclear unit: (a) Orthogonal φ(t2g ) (B) and φ(eg ) (A) orbitals left unchanged in the binuclear unit; (b) Insert: spin density in two orthogonal p orbitals of nitrogen (py and pz ).

302


special role of nitrogen; the t2g (B)–t2g (A) pathways lead to antiferromagnetic (AF) interactions; as the ( − δ) gap becomes larger, so does |J |. 9.3.2.4

Experimental Answers

We can use this orbital analysis to predict the nature of the interaction between various paramagnetic cations with a representative hexacyanometalate ion, [CrIII (CN)6 ], in which the octahedral CrIII center is spin 3/2 with a (t2g )3 electronic configuration. The number and the nature of the exchange pathways are represented in Figure 9.10 and summarized in Table 9.1 for known divalent cations AII of the first period of the transition elements, from VII to CuII . Table 9.1. Curie temperatures as a function of A in AII [CrIII (CN)6 ]2/3 ·xH2 O. AII ion Configuration dn Nature of the transitiona TC /K

V d3 AF 330

Cr d4 AF 240

Mn d5 AF 66

Fe d6 F 16

Co d7 F 23

Ni d8 F 60

Cu d9 F 66

a AF = ferrimagnetic, F = ferromagnetic.

A simple overlap model predicts that A ions with d3 through d7 configurations should couple antiferromagnetically, and those with d8 and d9 configuations should couple ferromagnetically. As Table 9.1 shows, this prediction holds true except for A = Fe and Co; the reasons for these exceptions will be discussed below. If we now look at the results given in Figure 9.11 and Table 9.2 (including Ref. [88–94]), we can check other aspects of the theoretical predictions given above. To begin, comparisons between two particular compounds are especially interesting: Babel’s CsMnII [CrIII (CN)6 ]·H2 O is a ferrimagnet with TC = 90 K, and Gadet’s compound CsNiII [CrIII (CN)6 ]·H2 O is a ferromagnet with the same ordering temperature. The TC values are relatively high for molecule-based magnets, and this fact supports the conclusions of Figure 9.9 about the strength of ferromagnetic pathways. If the J values for the Ni and Mn derivatives are evaluated from formulae (9.1) and (9.4), we find that, if everything is equal, JCrNi ≈ 2|JCrMn | and that jF , the mean coupling of a single ferromagnetic orbital pathway, and jAF , the corresponding antiferromagnetic coupling, are roughly equal in absolute value. Similar conclusions about the importance of ferromagnetic pathways can be drawn from the study of discrete molecular analogs of Prussian Blues, for which J values can be computed using analytical expressions [95]. It is also interesting to compare the TC values of Babel’s and Gadet’s compounds (which have six magnetic neighbors) with the ordering temperatures of related A1 B2/3 systems with the same A and B pairs but with four magnetic neighbors.


303

Table 9.2. Curie temperatures TC of Prussian Blue analogs. Compound Cx A1 [B(CN)6 ]z ·nH2 Oa

Ordering Nature

TC /K

Ref.

K1 VII 1 [CrIII (CN)6 ]1 VII 1 [CrIII (CN)6 ]0.86 ·2.8H2 O K0.5 V1 [Cr(CN)6 ]0.95 ·1.7H2 O Cs0.8 V1 [Cr(CN)6 ]0.94 ·1.7H2 O VII 1 [CrIII (CN)6 ]2/3 ·3.5H2 O V1 [CrIII (CN)6 ]0.86 ·2.8H2 O CrII 1 [CrIII (CN)6 ]2/3 ·10/3H2 O (Et4 N)0.4 MnII 1 [VII (CN)5 ]4/5 ·6.4 H2 O Cs2/3 CrII 1 [Cr(CN)6 ]8/9 ·40/9H2 O Cs2 MnII 1 [VII (CN)6 ]1 (VIV O)1 [CrIII (CN)6 ]2/3 ·4.5H2 O Cs1 MnII 1 [CrIII (CN)6 ]1 Cs1 NiII 1 [CrIII (CN)6 ]1 ·2–4H2 O MnII 1 [CrIII (CN)6 ]2/3 ·5–6H2 O CuII 1 [CrIII (CN)6 ]2/3 ·5–6H2 O NiII 1 [CrIII (CN)6 ]2/3 ·4H2 O (NMe4 )MnII [CrIII (CN)6 ] MnII 1 [MnIV (CN)6 ]1 CsNiII 1 [MnIII (CN)6 ]1 ·H2 O K2 MnII 1 [MnII (CN)6 ]1 ·0.5H2 O CoII 3 [CoII (CN)5 ]2 ·8H2 O MnII 1 [MnIII (CN)6 ]2/3 ·4H2 O Cs1 MnII 1 [MnIII (CN)6 ]1 ·0.5H2 O MnIII 1 [MnIII (CN)6 ]1 NiII 1 [MnIII (CN)6 ]2/3 ·12H2 O MnIII 1 [MnII (CN)6 ]2/3 ·solvent (Me4 N)MnII [MnIII (CN)6 ] VIII 1 [MnIII (CN)6 ]1 CoII 1 [CrIII (CN)6 ]2/3 ·4H2 O NiII 1 [FeIII (CN)6 ]2/3 ·nH2 O CrIII 1 [MnIII (CN)6 ]1 CuII 1 [FeIII (CN)6 ]2/3 ·nH2 O CoII 1 [CrIII (CN)6 ]2/3 ·nH2 O FeII 1 [CrIII (CN)6 ]2/3 ·4H2 O CoII 1 [FeIII (CN)6 ]2/3 ·nH2 O CrII 1 [NiII 2 (CN)4 ]2/3 ·nH2 O MnII 1 [FeIII (CN)6 ]2/3 ·nH2 O FeIII 1 [FeII (CN)6 ]3/4 ·3.7H2 O

Ferri Ferri Ferri Ferri Ferri Ferri Ferri Ferri Ferri Ferri Ferri Ferri Ferro Ferri Ferro Ferro Ferri Ferri Ferro Ferri Ferri Ferri Ferri Ferri Ferro Ferri Ferri Ferri Ferro Ferro Ferri Ferro Ferro Ferro Ferri Ferri Ferri Ferro

376 372 350 337 330 315 240 230 190 125 115 90 90 66 66 53 59 49 42 41 38 37 31/27 31 30 29 28.5 28 23 23 22 20 19 16 14 12 9 5.6

40 88 88 40 40 29 28 31 28 31 89 70 27 36 36 27 74 69 32 30 90 30 30 91 32 91 70 91 36 92 91 87 36 36 87 93 87 94

a The formulae given were adapted from the literature to be related to one A cation – A [B(CN) ] ·nH O. 1 2 6 z We did not include explicitly the vacancies A1 [BIII (CN)6 ]z 1−z ·nH2 O. In the references the same

compound is given different formulations. If we chose for example nickel(II) hexacyanoferrate(III), one can find: NiII 3 [FeIII (CN)6 ]2 1 ·nH2 O, the simplest formula that indicates the neutral character of the precipitate but is not related to a special structural entity; NiII 4 [FeIII (CN)6 ]8/3 4/3 ·4n/3H2 O, which is related to the conventional cell, with 4 nickel(II), in line with the Ludi’s structural model; NiII 1 [FeIII (CN)6 ]2/3 1/3 ·n/3H2 O, for one nickel(II), which is the one we adopted for simplicity; NiII 3/2 [FeIII (CN)6 ]1 ·3n/8H2 O, related to one Fe; this one can be misleading since it suggests that there are no vacancies of [FeIII (CN)6 ] and that part of the NiII are in the centre of the octant (Keggin model).

304


(t2g )3 9 AF

d3

•

•

•

[VII 3CrIII 2 ] 3F 9 AF

•

(t2g )4(eg )2 d4

•

•

•

[CrII 3CrIII 2 ] 6F 3-

[Cr(CN)6]

9 AF

(t2g )4(eg )2 d5

• •

• •

•

[MnII 3CrIII 2 ] •

•

6F

•

6 AF

(t2g )3 d3

(t2g )4(eg )2 6

d

•

• ••

•

•

[FeII 3CrIII 2 ] 6F

(t2g )5(eg )2

3 AF

d7

•

•

•• • •

•

II

III

[Co 3Cr 6F

(eg)2 d8

•

2]

•

•• •• • •

[NiII 3CrIII 2 ] 3F

(eg)1 d9

••

•

•• •• • •

[CuII 3CrIII 2 ] Fig. 9.10. Nature and number of exchange pathways between chromium(III) and the divalent transition metal ions of the first row of the periodic table.

The mean field theory predicts that the latter compounds should have ordering temperatures 4/6 times 90 K, or 60 K. In fact, the prediction is quite accurate: NiII 2 [CrIII (CN)6 ]3 ·xH2 O has TC = 53 K and MnII 2 [CrIII (CN)6 ]3 ·xH2 O has TC = 60 K. A more subtle prediction of the ligand field and exchange models is that early transition metals should give higher exchange interactions thanks to a better interaction of their d orbitals with the π ∗ orbitals of the bridging cyanide. The example of Cs2 MnII [VII (CN)6 ]·H2 O whose synthesis was published by Girolami in 1995 is


305

Fig. 9.11. Variation of the experimental Curie temperatures of a series of MPBs {A1 [B(CN)6 ]z } as a function of Z the atomic number, for different stoichiometries and electronic structures of the A and B transition metal elements: Series 1F: {A1 Fe(CN)6 ]2/3 }; Series 2F and 2af: {A1 Cr(CN)6 ]2/3 }; Series 3af: {Mn1 [B(CN)6 ]1 }; Series 4af: {Mn1 [B(CN)6 ]2/3 }; Series 5F: {Ni1 [B(CN)6 ]2/3 }; Selected compounds: ×, Prussian Blue; §, KV[Cr(CN)6 ]; ∗, CsMn[Cr(CN)6 ]; #, CsNi[Cr(CN)6 ]; elements A or B are shown by their atomic number Z (bottom) and their symbol (top). (See Table 9.2 for numerical values.)

especially revealing [31]. This material is a ferrimagnet with a Néel temperature of 125 K. It can be compared with the two other isoelectronic Prussian Blue analogs, CsMnII [CrIII (CN)6 ]·H2 O and MnII [MnIV (CN)6 ]·xH2 O. All three compounds have high-spin d5 MnII centers in the weak ligand-field sites (N6 coordination environments) and furthermore d3 metal centers in the strong ligand-field sites (C6 coordination environments). The main differences are the oxidation states of B, which increase as the metal changes from VII to CrIII to MnIV , and the energies and the expansion of the B t2g orbitals, which decrease in the same order. The relative magnetic ordering temperatures of 125, 90, and 49 K for these three materials clearly show that incorporation of transition metals with higher-energy and more diffuse t2g orbitals into the strong ligand field sites leads to higher magnetic ordering temperatures. As the backbonding with the cyanide π ∗ orbitals becomes more effective, the coupling between the adjacent spin centers increases, and so does TC .

306


9.3.3

Quantum Calculations

The above qualitative theoretical approach was based on simple symmetry or energy considerations and did not rely on precise quantum calculations. The apparent simplicity of the structure of Prussian Blues (especially the linearity of the A−N≡C−B linkages and the octahedral environments of A and B), and the availability of a large set of experimental data constitutes a favorable situation for theoreticians to compute, reproduce, and predict the magnetic properties of Prussian Blue analogs, including their magnetic ordering temperatures TC . It is therefore not surprising that several theoretical methods at various level of sophistication have been applied to magnetic Prussian Blues. In Volume II of this series, in a chapter entitled “Electronic Structure and Magnetic Behavior in Polynuclear Transition-metal Compounds”, Ruiz, Alvarez and coworkers present different theoretical models of exchange interactions [96]. They point out that the study of the electronic structure of coupled systems is more challenging than that of closed-shell molecules, in large part because the J values are several orders of magnitude smaller than the total energy of the system. They point out that “no single qualitative model [is] able to explain satisfactorily all features of exchanged coupled systems and there are still a number of controversies about the advantages and limits of the various approaches that have been devised.” Other sources of valuable information about theoretical treatments of molecule-based magnets are the books by Kahn [7] and Boca [97]. In the following sections, we focus on some computational studies of Prussian Blues. We start with semi-empirical calculations (extended Hückel), which allow the considerations in the preceeding section to be evaluated semi-quantitatively. Then we present some results obtained from density functional calculations based on the broken symmetry approach [96]. Finally, a perturbative approach by Weihe and Güdel is briefly presented.

9.3.3.1

Extended Hückel Calculations

The antiferromagnetic contribution JAF

We performed extended Hückel calculations on a series of bimetallic dinuclear units [(CN)5 AII −N≡C−BIII (CN)5 ], where A = Ti, V, Cr, Mn, Fe, or Co and B = Ti, V, Cr, Mn, or Fe [36, 98–100]. All of the B ions have (t2g )n electron configurations; the A ions possess no more than seven d-electrons, so that in the high-spin state they also have partly filled t2g orbitals. As a result, there is always at least some antiferromagnetic contribution to the exchange between A and B. All bond distances were kept fixed for all the combinations. As shown previously in Figure 9.8, key features of Prussian Blue analogs are interactions (via the cyanide ligands) of a t2g orbital on one metal center with a t2g orbital on an adjacent metal center. Although in a binuclear model system some of


307

the pairwise t2g –t2g interactions are zero by symmetry, in a three-dimensional Prussian Blue network every t2g orbital can find a related orbital on a neighboring metal center with which it can interact strongly. Owing to the symmetry of the Prussian Blue structure, it is sufficient to analyse the interaction for a single pair of orbitals and to sum all the combinations presented by a three-dimensional network. Two of the possible interactions between t2g and eg orbitals are also shown in Figure 9.9. In this case the overlap is zero and the exchange interaction is strictly ferromagnetic. Although a direct estimation of the strength of this ferromagnetic contribution is not possible in the frame of semi-empirical methods, we will describe below how qualitative estimates can be obtained. From Eq. (9.11), the antiferromagnetic contribution to the coupling J is given approximately by the expression 2S(2 −δ 2 )1/2 , where δ is the energy gap between the (unmixed) a and b orbitals, is the energy gap between the molecular orbitals built from them, and S is the monoelectronic overlap integral between a and b. For each pair of metals in the list above, the values of and δ (Figure 9.8) have been calculated. Some features may be highlighted by decomposing the antiferromagnetic term as (2 − δ 2 ) = ( − δ)( + δ). Indeed, two effects contribute to the tendency of the electrons to pair: (i) a strong interaction between the two magnetic orbitals, which stabilises the bonding molecular orbital (the strength of the interaction is gauged by the term − δ, and (ii) the stabilization of charge transfer states in which an electron is transferred from one magnetic orbital to the other (the importance of this phenomenon is gauged by the term + δ. Therefore, to have a strong antiferromagnetic interaction, it is best if both ( − δ) and ( + δ) are large. It should be noted that there is a non-trivial dependence of on δ. The energy gap after mixing, δ, is equal to the energy gap before mixing, , plus the energy change upon mixing, but the energy change is enhanced when δ is small. Thus, ( − δ) becomes larger as δ becomes smaller, whereas ( + δ) becomes larger as δ becomes larger. Our calculations show that both and δ have similar trends: their values are maximized when metal atoms A and B possess d orbitals of very different energy, and minimized when they are very similar. Such behaviour can be understood with the help of Figure 9.7a and b (and Figure 5 in Ref. [99], not reproduced here). The energies of the t2g orbitals on the A and B metals are affected by interactions with both the low-energy filled CN π orbitals (a destabilizing interaction) and the highenergy empty CN π ∗ orbitals (a stabilizing interaction involving back-donation). As a general rule, the metal–carbon interaction is stronger than the metal–nitrogen interaction, and both interactions are stronger for the early transition metals, which possess higher energy and more diffuse d orbitals (low values of the ζ coefficient). The final energy of the t2g orbitals also depends on the relative energies of the (unmixed) d orbitals on the metallic ions with respect to the energy of the (unmixed) cyanide π and π ∗ orbitals. Our calculations show that the stabilizing interaction with the cyanide π ∗ orbitals dominates (thus lowering the t2g orbital energies) when the A sites are occupied by TiII , VII , or CrII , but that the interactions with the cyanide π and π ∗ orbitals cancel each other out (thus leaving the energies of the

308


Fig. 9.12. Plot of the quantity (2 − δ 2 ) obtained from extended Hückel calculations for a series of binuclear complexes [(CN)5 AII (µ-NC)BIII (CN)5 ] with A = Ti to Co and B = Ti to Fe (see text).

t2g orbitals unchanged) when the A sites are occupied by MnII , FeII , or CoII . This delicate balance affects the composition of the magnetic orbitals and the overlap between them. In Figure 9.12 the corresponding (2 − δ 2 ) values are shown. The higher (2 − δ 2 ) values are seen for the [(CN)5 TiII −N≡C−BIII (CN)5 ] dinuclear units, and the highest value of all is found for the TiII FeIII couple. This result, which at first seems counter-intuitive, is understandable once one recalls the effect of the cyanide π and π ∗ orbitals on the energies of the d orbitals. Indeed, for such a TiII FeIII system, the values ( + δ) and ( − δ) are both maximized: ( + δ) is large because the t2g orbitals on Ti and Fe are so different in energy, and ( − δ) is large because the diffuseness of the d orbital on Ti promotes efficient overlap between the magnetic orbitals. The calculated surface suggests that Prussian Blue compounds containing an early transition metal A cation should always possess strong antiferromagnetic interactions, irrespective of the identity of the B metal ion (this is one of the important qualitative arguments presented in a preceeding section). As predicted by the Néel expression (Eq. (9.9), the TC values of MPB analogs depend not only on the strength of JAF but also on the number of unpaired spins nA and nB on both sites and the number of possible interactions N = nA nB between√them. Taking this effect into account, we multiply (2 − δ 2 ) by the factor nA nB (nA + 2)(nB + 2)/nA nB to obtain the new surface shown in Figure 9.13.

9.3 Magnetic Prussian Blues (MPB) 8

309

TC / a.u.

7 6 5 4 3 2 1 0

Ti V

Fe(CN) 6 Mn(CN) 6

Cr Mn

Cr(CN) 6 Fe

V(CN) 6 Co

Ti(CN) 6

√ Fig. 9.13. Plot of the quantity (2 − δ 2 ) · N [(nA + 2)(nB + 2)/nA nB ] ∝ TC (arbitrary units) (see text).

The surface should mirror the TC values of MPB compounds made with A and B metals from the first transition series. Indeed, these calculated trends agree well with the experimental ones (see Table 9.2), both predicting that the maximum TC value should be found for the VII CrIII pair. The ferromagnetic contribution JF

Although the ferromagnetic contribution to J cannot be explicitly calculated, some information about it can be obtained even from simple extended Hückel calculations. The exchange integral kab is directly proportional to the squared overlap density defined in Eq. (9.11) ρab = |a |b . This contribution to the exchange interaction is always present, and it becomes the only contribution when the overlap Sab between the two orbitals is zero. This is the case for the t2g –eg interactions in MPB analogs, where the overlap is zero by symmetry. The TC values of up to 90 K found for those compounds that solely possess ferromagnetic pathways indicate that the ferromagnetic interaction can be quite strong. To verify the presence of high ρt2g−eg overlap density zones, we began with the results of the extended Hückel calculations described above for the dinuclear model complexes [(NC)5 AII −N≡C−CrIII (NC)5 ], where A = Co, Ni, or Cu, and B = Cr. The product ρt2g−eg could be visualised by plotting projections of the magnetic orbital compositions taken directly from the extended Hückel output. Owing to their influence on the density overlap, both the angular and radial normalisation constants for all the single atomic wavefunctions were carefully checked. Figure 9.14 shows

310


Fig. 9.14. Overlap density in the xz plane between the φ(t2g ) xz-type magnetic orbital centered on Cr and the φ(eg ) z2 -type magnetic orbital centered on Ni.

the overlap density (in the xz plane) between the t2g xz-type magnetic orbital centred on Cr and the eg z2 -type magnetic orbital centred on Ni. The overlap density is symmetric with respect to the z axis. A similar result was obtained for the monoatomic µ-oxo bridge in a Cu–VO complex [87]. Our result is counterintuitive for a diatomic bridge, where the spin density for the atom farthest from the metallic centre is expected to be low. Indeed, it is the strong delocalisation of the spin density on the nitrogen in the [B(CN)6 ] units that allows the strong overlap density and the strong ferromagnetic interaction. In contrast, for a µ-oxalato bridge, where the spin density is spread over the entire molecule, the overlap density is weak and so is the coupling [210]. 9.3.3.2

Density Functional Theory Calculations

Progress in computer speed and memory and in density functional theory (DFT) techniques have now made it possible to carry out calculations on very complex systems. Magnetic Prussian Blues are indeed complex systems to treat computationally. For example, the number of unpaired electrons per formula unit can be as high as 8 (as in a CrIII −MnII system). DFT computations on magnetic Prussian Blues were performed on two model systems, dinuclear complexes [(CN)5 A−N≡C−B(CN)5 ] and ideal face-centeredcubic extended solids. For a system with identical two centres A and B and one electron per centre, the method can be briefly summarized as follows. For two orthogonal orbitals φa and φb , the spin eigenfunctions of the system are: √ (9.12a) S,0 = (1/ 2)(|φa αφb β| − |φa βφb α|) √ √ T,0 = (1/ 2)(|φa αφb β| + |φa βφb α|); T,+1 = (1/ 2)(|φa αφb α|); √ T,−1 = (1/ 2)(|φa βφb β|) (9.12b)


311

Because the singlet state cannot be described by one single configuration, the J value (J = ES − ET ) cannot be computed directly. Noodleman suggested a broken-symmetry (BS) solution [see Ref. 96, 211–213]: BS = |φa αφb β|

or BS = |φa βφb α|

(9.13)

which is a mixed state, combination of S,0 and T,0 √ BS = (1/ 2)[S,0 + T,0 ] (9.14) √ The corresponding energy is EBS = (1/ 2)(ES + ET ) and the coupling is given by: J = 2(EBS − ET )

(9.15)

In the context of DFT calculations, therefore, it is possible to compute J from the energy of the broken symmetry state and the high spin state. Depending on the kind of calculations (HF, UHF, DFT, . . . ) and the existence of “spin-projection” processes [96], other expressions for J have been used, such as: 2 J = 2(EBS − EHS )/SHS

(9.16)

The main conclusion is that J can be obtained in a reasonable computing time from the difference of two energies. The calculation can be extended to systems with more than one electron per metal centre. Dinuclear models

The first DFT papers on dinuclear models of Prussian Blues were published by Nishino, Yamaguchi et al. [101–103]. Their work continues a longstanding theoretical tradition of studying open-shell spin systems [81, 82, 84, 104, 105]. The first two papers deal with very simple A−N≡C−B systems in which there is only one bridge and no other ligands are attached to A and B [101, 102]. The third paper deals with [(CN)5 A−N≡C−B(CN)5 ] units [103]. In all three papers, the symmetry rules that we applied before are used to analyze the d–d orbital interactions. The correct sign of the effective exchange integrals J is found. The authors carried out ab initio unrestricted Hartree Fock (UHF) and DFT calculations to elucidate the nature of the magnetic orbitals. For the unligated VII −N≡C−CrIII and NiII −N≡C−CrIII units, the magnitudes of the calculated exchange integrals were much larger than the experimental values found for real dinuclear systems. We focus therefore on the last paper, which deals with the more realistic situation in which the A and B centres have octahedral coordination environments. Figure 9.15a shows the orbital interaction in the A−N≡C−B entity. Figure 9.15b displays the molecular orbitals φA (HOMO) and φS (LUMO) built from the t2g orbitals of the A and B metals and the π and π ∗ MOs of the cyanide ligand; these molecular orbitals are, respectively, (pseudo)antisymmetric and (pseudo)symmetric relative to a plane bisecting the

312


Fig. 9.15. (a) Orbital interaction schemes in the BCNA entity; (b) symmetric (S) and antisymmetric (A) natural MOs; h(c) magnetic orbitals obtained by mixing the S and A MOs (adapted from Ref. [103]) (see text).

A–B axis. Figure 9.15c represents the magnetic orbitals φa and φb built from φA and φS according to the relations within the UHF and DFT approximations: φa (spin up α) = cos θ φA + sin θ φS φb (spin down β) = cos θ φA − sin θ φS

(9.17a) (9.17b)

(the authors use the Hamiltonian H = −2J SA SB ). Then the authors apply the Heisenberg model to describe the energy gaps between the ferromagnetic (HS) and antiferromagnetic (LS) states and, using the approximate spin projection procedure (AP), find the following expression for the effective exchange integrals Jab with various methods (X = UHF, DFT): JAP−X = (LS EX − HS EX )/[HS S 2 X − LS S 2 X ]

(9.18)

In addition to calculating J values, they also obtained an orbital picture of the exchange phenomenon and values for the atomic spin densities. Using the molecular field approach (Langevin–Weiss–Néel), they also computed Curie temperatures for the solid from the expression: (9.19) TC = ZA ZB |JAB | SA (SA + 1)SB (SB + 1)/3kB where kB is Boltzmann’s constant, ZA and ZB are the numbers of magnetic neighbors of A and B, respectively, and SA and SB the spins of A and B. Some of their results are collected in Table 9.3.


313

Table 9.3. a Comparison of the computed J b and TC c values with experiment. System A–B

SB

SA

Jab /cm−1

TC /K (calc)

TC /K (exp)

NiII –CrIII

3/2

1

NiII –CrIII 2/3 MnII –CrIII MnII –CrIII 2/3

+15.92

3/2

5/2

−7.01

125 102 116 95

90 53 90 60

VII –CrIII 2/3

3/2

3/2

−75.56

815

(315)d

MnII –VII

3/2 3/2

1 5/2

−31.24 −14.49

246 239

(315)d 125

VIII –CrIII

a Adapted from Ref. [103] and Table 9.2. b J is computed in a [(NC) A−C≡N−B(NC) ] 5 5 model. c From Eq. (9.19). d The sample contains both VII and VIII .

The agreement between computation and experiment is not exact, but to obtain a better fit the authors suggest the empirical law: TC (exp) = 1.2TC (calc) − 49.9 K

(9.20)

This expression gives very good agreement between experimental and theoretical values. The very large value for |J | in the VII –CrIII 2/3 system (which is ten times larger than the value found for the MnII –CrIII system) can be related to the strong participation of VII in the φb orbital (Figure 9.15) compared to the MnII , whose orbitals are well localized (Figure 3 in Ref. [103], not shown here). Important Table 9.4. a Atomic spin densities from methods UB2LYP in [(NC)5 A−C≡N−B(NC)5 ] System A–B

2S + 1b

Ac

Cc

Nc

Bc

NiII –CrIII AF NiII –CrIII F MnII –CrIII AF MnII –CrIII F VIII –CrIII AF VIII –CrIII F VII –CrIII AF VII –CrIII F MnII –VII AF MnII –VII F

2 6 3 9 2 6 1 7 3 9

−1.73 +1.73 d –4.75 d +4.76 –2.02 d +2.02 –2.82 d +2.85 –4.74 d +4.76

−0.12 –0.16 –0.17 −0.09 –0.17 −0.05 –0.23 −0.04 –0.14 −0.07

0.07 0.19 0.12 0.11 0.15 0.04 0.19 0.05 0.14 0.15

3.06 3.06 3.05 3.06 3.06 3.06 3.03 3.06 2.63 2.66

a Adapted from Ref. [103]. b Spin multiplicity for the computed states (AF = antiferromagnetic coupling; F = ferromagnetic coupling). c Spin densities of A, C, N, and B; a positive sign means that the magnetic moments are aligned along the field and a negative sign means the reverse. d Spin multiplicities shown in bold italics correspond to the coupling observed experimentally.

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new information provided by these calculations is the atomic spin densities. Some significant results are collected in Table 9.4. From Table 9.4, it can be concluded that (i) the chromium(III) centers bear the spin density foreseen from its +3 valence; in contrast, the spin density of vanadium(II) is significantly decreased by delocalisation; (ii) the carbon atom always bears a negative spin density, an observation that is consistent with Figgis’s spin polarized neutron diffraction study of [CrIII (CN)6 ] salts [78]; this effect is due to spin polarisation (SP) and is represented by the authors by the spin-flip excitation from φS to φA orbitals shown in Figure 9.15; when the spin densities are decomposed into σ and π components, the SP effect is more significant for the π than for the σ network; (iii) there is a significant positive spin density on nitrogen atoms of the bridge; (iv) the spin density on the A ion is always less than expected from the valence, thus suggesting that there is significant spin delocalisation. These calculations provide quantitative information about the mechanism of the exchange interaction through the cyanide bridge. One striking observation of the article is that, without the cyanide bridging ligand, at the same A–B distance, the A–B interaction becomes negligibly small. DFT calculations have also been carried out for the homodinuclear complexes Ln CuII −N≡C−CuII Ln and Ln NiII −N≡C−NiII Ln systems [106] based on the computational procedures described in Ref. [108]. The results are relevant to dinuclear complexes but not to Prussian Blues, and thus this work is outside the scope of the present review. At present, additional computations on various dinuclear models of Prussian Blues are in progress, including a study of the effect of incorporating metals of different oxidation states or from the second row of the d-block, in order to determine whether larger J and TC values than those found in the vanadium–chromium derivatives can be achieved. Indeed, larger |J | values are foreseen [108]. Three-dimensional models

At approximately the same time as the computations on the molecular dinuclear models, three articles appeared on DFT calculations of three-dimensional networks, using computation packages adapted for solids [109–111]. These studies afforded important insights into the band structure and density of states (DOS, spin-polarized or not), the atomic spin density in the solid, and the crystal orbital overlap populations (COOP), a concept introduced by Hoffmann [112]. The first brief paper by Siberchicot was based on a local-spin-density approximation using the augmented spherical wave (ASW) method and including spin– orbit coupling [109]. Two species were studied: the ferromagnet CsNi[Cr(CN)6 ] [27] and the ferrimagnet CsMn[Cr(CN)6 ] [70]. The calculated magnetic moments (spin and total, spin+orbital) were in good agreement with the experimental values. The spin polarized partial densities of states on the chromium and nickel clearly showed semiconducting behavior with a rather large gap at the Fermi level EF , and


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localized d bands near EF . The d band is split in energy by the octahedral ligand field. For both solids, the empty (eg )0↓ levels derived from the CrIII orbitals are above the Fermi level. In CsNi[Cr(CN)6 ], the filling of the d-bands is [NiII ]: [(t2g )3 (eg )2 ]↑ [(t2g )3 (eg )0 ]↓ , [Cr III ]: [(t2g )3 (eg )0 ]↑ [(t2g )0 (eg )0 ]↓ The band structure is consistent with the observed ferromagnetic coupling between NiII and CrIII . In comparison, for CsMn[Cr(CN)6 ] the filling is: [MnII ]: [(t2g )3 (eg )2 ]↑ [(t2g )0 (eg )0 ]↓ , [Cr III ]: [(t2g )3 (eg )0 ]↓ [(t2g )0 (eg )0 ]↑ which agrees with the experimental antiferromagnetic coupling between MnII and CrIII . The same two species were studied in more detail by Eyert and Siberchicot [110]. Again a local density approximation was employed, using augmented spherical waves (ASW) in scalar-relativistic implementations, taking particular care in the optimisation of empty spheres and the Brillouin zone sampling. A new feature was the evaluation of the crystal orbital overlap populations, which permitted an assessment of the chemical bonding in the solid [112, 113]. The electronic structure was analysed by means of two sets of calculations, one non-magnetic and the other magnetic, the first serving as a reference for the discussion of the magnetic configurations. The density of states and COOP analyses suggested the following: in the two compounds, the band structure reflects mainly the strong bonding within the cyanide and the ligand field splitting. In contrast, near the Fermi level (from −1.2 eV to 0.5 eV), the situation is completely changed: in the manganese derivative, the bands mix and split in a way reminiscent to t2g –t2g overlaps in Figure 9.8, whereas in the nickel compound, they do not (as in Figure 9.9, t2g –eg ). This difference has dramatic consequences for the magnetic properties. The spin-polarized calculations demonstrate that the ground state is indeed ferrimagnetic in CsMn[Cr(CN)6 ] and ferromagnetic in CsNi[Cr(CN)6 ] (the ferrimagnetic state of CsNi[Cr(CN)6 ] is computed to be 9.8 mRyd higher in energy than the ferromagnetic state). The computed atomic moments are given in Table 9.5. The spin-polarized densities of states for CsMn[Cr(CN)6 ] are given in Figure 9.17 and beautifully illustrate the opposite polarisations of the metallic bands [Cr(t2g )3 ]↑ (at −1.5 eV) and [Mn(t2g )3 (eg )2 ]↓ (at −2.0 and −0.5 eV). In addition, the polarisations of the bridging carbon and nitrogen atoms in the same energy range help to explain the mechanism of the polarisation. Indeed, a close examination of the spin polarized DOS in the Fermi level region level led the authors to “point out that the overlap of magnetic orbitals already present in the non-magnetic configuration completely fixes the antiferromagnetic coupling while disallowing a ferromagnetic correlation”.

316


a)

b)

Fig. 9.16. Total and partial crystal orbital overlap populations (COOP): (a) in CsMn[Cr(CN)6 ]; (b) in CsNi[Cr(CN)6 ] (from Ref. [110]].

An analogous demonstration results from the spin-polarized densities of states for CsNi[Cr(CN)6 ], given in Figure 9.18, where now the orthogonality of the [Cr(t2g )3 ]↑ and the [Ni(eg )2 ]↓ orbitals leads to identical polarisations of these bands. The densities of states also show that the carbon and nitrogen atoms participate significantly in the exchange mechanism. One important conclusion that can be drawn from this study is that the electronic interactions present in three-dimensional Prussian Blue solids are very similar to those seen in discrete molecular analogs. Furthermore, exchange models such as that proposed by Kahn and Goodenough–Kanamori, involving t2g –t2g overlap and


317

Table 9.5. Local magnetic moments in CsA[Cr(CN)6 ] (A = Mn, Ni).a Atom Cs A Cr C N Cell

µ/µB in CsMn[Cr(CN)6 ] 0.001 −4.200 2.658 −0.061 0.001 −2.000

µ/µB in CsNi[Cr(CN)6 ] 0.001 1.369 2.717 −0.046 0.129 5.000

a Adapted from Ref. [110].

Fig. 9.17. n polarized partial densities of states of ferrimagnetic CsMn[Cr(CN)6 ] (from Ref. [110]].

orthogonality of the t2g and eg orbitals as described in Figures 9.8 and 9.9, do in fact constitute accurate descriptions of the electronic structures of Prussian Blues in the solid state, particularly near the Fermi level. The DFT calculations, however, afford much more quantitative information about the resulting magnetic properties.

318


Fig. 9.18. Spin polarized partial densities of states of ferromagnetic CsNi[Cr(CN)6 ] (from Ref. [110].

Periodic UHF – CRYSTAL calculations

Harrison et al. [111] carried out a study of several Prussian Blue compounds using the periodic unrestricted Hartree–Fock approximation as implemented in the CRYSTAL package. The compounds studied were KA[Cr(CN)6 ] (A = V, Mn, Ni) and Cr[Cr(CN)6 ]. Structural optimisation was performed, and the optimized structures closely resemble those determined experimentally. To compare the energies of the various magnetically ordered states, they obtained self-consistent field solutions, sometimes using a “spin-locking” procedure to constrain the initial total spin. The authors calculated the magnetic ordering energies and the relative contibutions of exchange, kinetic and Coulomb interactions according to Anderson’s model [114], as shown in Table 9.6. The total energies clearly show the strong stabilisation of the ferrimagnetic state in the CrIII and VII compounds (corresponding to high TC s) and of the ferromagnetic state in the NiII derivative. From these results and an analysis of the Mulliken spin populations, the authors conclude that “an ionic picture of the metal–ligand interactions and a superexchange model of the magnetic coupling naturally emerges from first principles calculations of the ordering energetics of bi-metallic cyanides.


319

Table 9.6. Magnetic ordering energies in CrIII [CrIII (CN)6 ] and KAII [CrIII (CN)6 ] models.a A

d configuration

Total b,c

Exchange b

Kinetic b

Coulomb b

CrIII VII MnII NiII

(t2g )3 (t2g )3 (t2g )3 (eg )2 (t2g )6 (eg )2

4.33 4.40 0.79 −1.78

14.70 9.91 14.70 −7.49

−12.57 −2.78 0.29 5.60

2.20 −2.74 −0.75 0.11

a Adapted from Ref. [111]. b Values are in milliHartree. c Positive values favor ferrimagnetic

states; negative values favor ferromagnetic states.

. . . Ferromagnetic coupling [is favoured] for the A(eg )2 –Cr(t2g )3 arrangement as the superexchange integral is dominant. . . Antiferromagnetic coupling is favoured for the A(t2g )3 –Cr(t2g )3 arrangement where the effects of the orthogonality constraint on the metal d-orbitals is dominant. In the antiparallel configuration the orthogonality constraint is relaxed through delocalisation of the metal d-orbitals and concomitant polarisation of the orbitals of the CN group”.

9.3.3.3

Valence Bond Configuration Interaction (VBCI) and Perturbation Theory

Güdel and Weihe have recently applied their valence bond/configuration interaction model to the A−N≡C−B units in materials related to Prussian Blues [115, 116]. They define the interactions between two d orbitals, a and b, and the π and π ∗ MOs of the cyanide as shown in Figure 9.19; the integrals are defined by the following one-electron Hamiltonian h: Va = a|h|π ; Vb = b|h|π ; Va∗ = a|h|π ∗ ; Vb∗ = b|h|π ∗

(9.21)

As shown in Figure 9.20, the exchange splitting is obtained by mixing into the ground configuration selected one-electron excited configurations: ligand-to-metal charge transfer (LMCT) states, metal-to-metal charge transfer (MMCT) states, and metal-to-ligand charge transfer (MLCT) states. The wavefunction for each configuration is obtained and the interaction matrix elements with the ground state are calculated as described in the appendices of Refs. [115] and [116]. The energies

Fig. 9.19. Interactions between p symmetry orbitals in the A–NC–B entity (adapted from Ref. [115]).

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Fig. 9.20. Ground and excited configurations in the A–NC–B entity (adapted from Ref. [116]): Case I: interactions between singly occupied metallic a and b orbitals and π and π ∗ ; Case II: interactions between singly occupied metallic a and b orbitals and π and π ∗ ; Case III: interactions between singly occupied metallic a and b orbitals and π and π ∗ ; from top to bottom: ground, LMCT, MMCT and MLCT configurations. For each configuration the possible spin states and the relative energies are shown (adapted from Ref. [115]).


321

A , B , ∗A , ∗B , and Uab are defined in Figure 9.20. I2 is defined as a one-centre two electron exchange integral. The authors suggest that one can choose a mean value for all the LMCT and MLCT transition energies, a mean value V for all the interaction integrals and a mean value I for the one-centre two-electron exchange integral. After making some other approximations, they arrive at simple expressions for Jcalc that depend on the number of unpaired electrons residing on A and B, Table 9.7. Table 9.7. Calculated magnetic couplings for different A−N≡C−B linkages.a A/B Elect. Config.

Jcalc

Examples (A/B)

d5 /d3 d8 /d3 d3 /d3 d3 /d1 d2 /d3

+32Q/15 b −4Q + W/3 c +32Q/9 +16Q/3 − 2W/3 +8Q/3

MnII CrIII , MnII VII , MnII MnIV NiII CrIII CrIII CrIII , VII CrIII CrIII VOIV CrII CrIII

a Adapted from Ref. [115]. b Q = V 4 /2 U . c W = [1+{(2U +)/U }+2(U +)/]I /U .

The authors made the debatable assumption that the parameters Q and W were constants (i.e., independent of the nature of A or B), and then carried out a leastsquares optimization, with Q and W as adjustable parameters, to fit Jcalc and Jexp . Using an expression similar to Eq. (9.19), the authors calculated the magnetic ordering temperature, obtaining a reasonably linear correlation with experiment. This approach, however, is intrinsically flawed: in the series of Prussian Blues in which the AB pairs are MnII VII , MnII CrIII , and MnII MnIV , the model predicts that Jcalc should be invariant, and TC should equal 280 K for all three compounds, because the electronic configuration of all three species is d5 /d3 . In fact, the experimental Curie temperatures decrease monotonically across this series, from 125 to 90 to 49 K. The authors recognize that in this case the transferability of the parameters Q and W is not a good approximation, in line with the arguments presented earlier that J is strongly dependent on the energies (and diffuseness) of the orbitals on the metal centers, with early transition metals in low oxidation states giving rise to the largest J values. The authors conclude that “according to our calculations ordering temperatures much higher than those already achieved should not be expected for Prussian Blue analogs containing 3d metals,” a conclusion similar to that obtained from semi-empirical calculations. This pessimistic but realistic conclusion leaves open the possibilities provided by the 4d and 5d transition metals. There is still hope for further improvements in TC . We would like to conclude this theoretical survey by mentioning some recent papers that use the Anderson model [114] and particularly the kinetic exchange contributions to explain the ferromagnetism experimentally observed in systems

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where ferrimagnetism might be expected, at first glance. Examples of such systems include certain Prussian Blues that contain the CrIII –FeII pair [117], which is one of the exceptions we quoted before in discussing Table 9.1 and Figure 9.11, and certain non-Prussian Blue solids (constructed from octacyanometalate building blocks) that contain the MoV –MnII pair [118]. In this short review, we can only describe the highlights of the theoretical work on Prussian Blues and related cyanide-bridged model open-shell systems. The reader is referred to the articles cited for additional references to such studies.

9.4 High TC Prussian Blues (the Experimental Race to High Curie Temperatures) We are now in a position to use the theoretical models to guide experiment and enhance the Curie temperature of Prussian Blue analogs. To set the stage, before we began our work, the highest ordering temperature seen for any Prussian Blue analog was TC = 90 K. Because we need interactions in the three directions of space, for the B centre, a d3 , (t2g )3 electronic configuration, S = 3/2, is better adapted than an electronic configuration with S < 3/2: VII , CrIII , MnIV > MnIII > FeIII . Because the ordering temperature is proportional to Z, the number of magnetic neighbors, everything being equal, a MA1 [Cr(CN)6 ]1 stoichiometry with six neighbors should be preferred to a A1 [Cr(CN)6 ]2/3 one with only four neighbors. Because the highest possible ferromagnetic interactions allow one to reach only TC = 90 K [27], a ferrimagnetic strategy must be looked for. Because the interaction between the metallic d orbitals and the cyanide π ∗ MOs increases with earlier transition elements, it should be better to work with chromium, vanadium or titanium, when the chemistry allows. In the Mx Mn1 [M(CN)6 ]1 series (see Section 4.2), starting from 49 K for the Mn1 [MnIV (CN)6 ]1 derivative [69], 90 K is found for Cs1 Mn1 [Cr(CN)6 ]1 , [70] and 125 K for the Cs2 Mn1 [VII (CN)6 ]1 [31] and then 230 K when the sample is optimized [31]. From the MnII derivative of Klenze in 1980 to the VII materials of Girolami in 1995 took 15 years. Because the ferromagnetic exchange pathways are non-negligible, if one wants to enhance the absolute value |J | of a ferrimagnetic system, it is necessary to decrease the ferromagnetic contributions (see Eq. (9.2c)). This means choosing an A ion that has as few eg electrons as possible. Figure 9.10 shows how this goal can be achieved: whereas MnII has two eg electrons, CrII has only one (if high-spin), and VII has none. Furthermore, the use of the early transition ions CrII and VII will enhance the absolute value of the antiferromagnetic interaction by backbonding more effectively with the cyanide π ∗ orbital.

9.4 High TC Prussian Blues (the Experimental Race to High Curie Temperatures)

323

Indeed these approaches have worked pretty well [119]! Whereas MnII [CrIII (CN)6 ]2/3 ·xH2 O has TC = 60 K, CrII [CrIII (CN)6 ]2/3 ·xH2 O has TC = 240 K [28], and VII /CrIII Prussian Blues have TC s that range from 315 K [29] to 376 K [40]. Nevertheless, from the MnII derivative of Babel in 1982 to the amorphous VII analog of Ferlay in 1995 took 13 years. And four years more for Girolami’s crystalline VII compound. The situation deserves some comment.

9.4.1

Chromium(II)–Chromium(III) Derivatives

In 1993, we described the synthesis of two Prussian Blue analogs prepared by adding [Cr(H2 O)6 ]2+ to [CrIII (CN)6 ]3− [28]. In the absence of a source of cesium cations, a light gray precipitate of stoichiometry CrII [CrIII (CN)6 ]2/3 ·10H2 O is isolated. The material has a single C–N stretching band in the IR spectrum at 2194 cm−1 , and this frequency suggests that all of the cyanide ligands are C-bound to CrIII . Magnetisation measurements show that the compound orders ferrimagnetically at 240 K, although interestingly the saturation magnetisation suggests that some CrII centers are low-spin. Relative to the previous record for highest TC for a Prussian Blue, that of 90 K for Babel’s or Gadet’s compound, a TC of 240 K represents a significant step towards room temperature. In an attempt to increase the number of magnetic neighbors by preparing a 1:1 compound, the same reaction was carried out in the presence of Cs+ . Under these conditions a green compound of stoichiometry Cs0.67 CrII 1 [CrIII (CN)6 ]0.9 ·4.5H2 O was isolated [28]. The infrared spectrum of this compound, however, features two cyanide stretching bands, due either to linkage isomerism or to a partial conversion of high-spin CrII centers (S = 2) to low-spin CrII centers (S = 1). The latter hypothesis is supported by the fact that the magnetisation at saturation is well below the expected value calculated assuming that all the CrII centers are highspin [28]. As a result, the magnetic ordering temperature of 190 K, while still high for a Prussian Blue analog, is lower than that of the 3:2 compound. Because the chemistry of the system did not allow further increase in TC by increasing the A:B ratio to 1:1, we tried another approach: we hoped that compressing the solid under pressure would decrease the distances, enhance the orbital overlaps, increase the antiferromagnetic interaction, and thus increase the ordering temperature. Instead, a disaster happened. Compressing the sample under a pressure of 4 kbar causes all of the CrII centers to become low-spin, and the local antiferromagnetic coupling causes the solid to become diamagnetic below its ordering temperature because the spins of the low-spin CrII centers exactly cancel those of the CrIII centers [120]: MT = MCrIII − −MCrII

(9.22a)

with Cr , d , S = 3/2 and high spin Cr , d , S = 2, one obtains: III

3

II

4

MT /µB = |MCrIII − MCrII HS | = |((2/3) × 3) − (1 × 4)| = 2

(9.22b)

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Instead, with CrIII , d3 , S = 3/2 and low-spin CrII , d4 , S = 1, one obtains: MT /µB = |MCrIII − MCrII LS | = ((2/3) × 3) − (1 × 2) = 0!

(9.22c)

This change was shown beautifully by the thermal variation of the magnetisation under pressure. In chemistry, as in Roman history, the Tarpeian rock is close to the Capitol. Three years later, with the same system, Sato, Hashimoto et al. used an electrochemical method and succeeded in getting a derivative with TC = 270 K, which was furthermore switchable from ferrimagnetic to paramagnetic electrochemically [121]. Two years later, with the same electrochemically-synthesized chromium– chromium system, Miller et al. were able to prepare thin layers of materials, either amorphous or crystalline, with TC ranging from 135 to 260 K depending on the oxidation states of the chromium. They observed a robust negative magnetisation in low field that they assigned to single ion anisotropy of chromium(II) [122].

9.4.2

Manganese(II) –Vanadium(III) Derivatives

To check the hypothesis of an improved interaction using early transtion metals led us to replace the [CrIII (CN)6 ]3− precursor by [VII (CN)6 ]4− [32]. We have already commented on the higher TC presented by the ferrimagnet CsI 2 MnII [VII (CN)6 ] (125 K) compared to its homologs CsMnII [CrIII (CN)6 ] (90 K) and MnII [MnIV (CN)6 ] (49 K) (see Section 9.3.2.4). Cs2 MnII [VII (CN)6 ] is prepared in aqueous solution under argon from K4 [VII (CN)6 ] and MnII (OSO2 CF3 )2 (CH3 CN)2 in the presence of Cs(OSO2 CF3 ). It is an air-sensitive green solid. It crystallizes in a face-centered-cubic (fcc) lattice with a = 10.66 Å. Its magnetisation at saturation is in line with an antiferromagnetic coupling between vanadium and manganese. When (NEt4 )2 [VII (CN)6 ] is treated with MnII (OSO2 CF3 )2 (CH3 CN)2 in the absence of Cs(OSO2 CF3 ), the crystalline yellow solid obtained, formulated as (NEt4 )0.5 MnII 1.25 [VII (CN)5 ]·2H2 O is a strongly coupled ferrimagnet with TC = 230 K. The color of the two compounds, green and yellow, the absence of an intervalence band in the near-infrared spectrum indicates that there is no electron transfer between the metallic centres. X-ray powder diffraction shows that the second compound is crystalline but does not adopt a fcc structure. The XRD pattern and the unusual ratio of CN− to V suggest that the structure is more complex. Interestingly, Babel has shown that attempts to substitute cations larger than Cs+ into the Prussian Blue lattice usually gives rise instead to lower dimensional structures with substantially decreased magnetic phase transition temperatures [74]. Even though the large (NEt4 )+ cations prevent the adoption of the cubic structure, the high value of TC suggests that the structure still consists of a 3D array of interacting spin centers, with a very strong antiferromagnetic coupling constant. The magnetisation data of the two compounds are revealing on this point. One of the characteristic features of ferrimagnetic materials is the presence of a minimum in the thermal χM T curve: the higher the temperature of the minimum, the higher the antiferromagnetic


325

coupling constant J . CsI 2 MnII [VII (CN)6 ] presents such a minimum at about 210 K. However, there is no visible minimum in the (NEt4 )0.5 MnII 1.25 [VII (CN)5 ]·2H2 O data: because the saturation magnetisation allows one to rule out a ferromagnetic coupling, it means that the minimum is displaced above the observed temperature range and that |J | is strong. The hypothesis that the back-bonding with the cyanide π ∗ orbitals become more effective with VII ions is fully confirmed. The conclusion of Ref. [31] was: “These two V-based molecular magnets represent an important step in the design of molecular magnets with high TN . Through judicious choice of cations and metal centers, TN values above 300 K should be possible.” The stage was set for another step.

9.4.3

The Vanadium(II) –Chromium(III) Derivatives

Our ultimate success in obtaining Prussian Blues with ordering temperatures above room temperature resulted indeed from the idea to enhance J by maximizing the backbonding of the d orbitals of the metal A with the π ∗ orbitals of cyanide and returning to the idea that increases in TC can be achieved by reducing the number of ferromagnetic pathways. The metal ion best able to accomplish both of these goals is VII . Upon adding the Tutton salt (NH4 )2 V(SO4 )2 ·6H2 O to K3 Cr(CN)6 , a midnightblue solid that has a stoichiometry of V[CrIII (CN)6 ]0.86 ·2.8H2 O precipitates from solution. The magnetic ordering temperature is 315 K. Prepared in this manner, using Schlenk techniques, the expected VII [CrIII (CN)6 ]2/3 stoichiometry is in fact not obtained, and a non-stoichiometric, amorphous, compound results instead, probably because it precipitates very

Fig. 9.21. “A midnight blue solid precipitates from solution . . . ”. Molecule-based magnets can be prepared in mild conditions. They are transparent and low density.

326


1.5

700 600 χ T / cm mol K

H = 30G 1

M

0.5

0 0

50

100 150 200 250 300 350 T/K

(a)

500 400 300

Tmin = 240 K

200 100 0 50

100 150 200 250 300 350 T/K

(b)

Fig. 9.22. Role of the oxidation state in VCr derivatives: thermal variation of (a) the magnetisation of VII α VIII (1−α) [CrIII (CN)6 ]0.86 ·2.8H2 O (α = 0.42); (b) product χM T of VIV O[CrIII (CN)6 ]2/3 .

rapidly and the interstitial sites are occupied by a variety of species. The A sites contain a mixture of VII and VIII , and the formula of the compound is best represented as VII α VIII (1−α) [CrIII (CN)6 ]0.86 ·2.8 H2 O with α = 0.42. The magnetisation at saturation is very weak (0.15 µB ) and fits perfectly with the above formulation. The coercive field corresponds to a very soft magnet (25 Oe at 10 K). The compound is very sensitive to dioxygen. In a comment accompanying the publication [119], Kahn underlined that on the one hand “the synthesis of such a material can be considered as a cornerstone in the field of molecular magnetism” . . . and that V[Cr(CN)6 ]0.86 ·2.8H2 O was “an excellent example on which to learn (or to teach) the basic concepts of molecular magnetism”. On the other hand, Kahn pointed out that [VCr] “is not a molecular compound, but rather an amorphous and non stoichiometric compound”, “the saturation magnetisation is limited to 0.15 µB . . . “, ”the coercive field is only 10 Oe . . . ”. This was the first Prussian Blue system to present a Curie temperature above room temperature, but it is far from perfect.

9.4.3.1

Improving the Magnetic Properties of VCr Room Temperature Molecule-based Magnets

Further improvements in the TC for the VII /CrIII Prussian Blue analogs have been achieved by varying the synthetic conditions so that the solids obtained are crystalline and more nearly stoichiometric. New syntheses were undertaken by our groups and some others, in particular Miller and Epstein, as recently reviewed [17, 18, 123, 124], and Hashimoto and Ohkoshi [25]. It would take too long to detail all the results. The reader is advised to consult the original papers. A set


327

of non-stoichiometric Prussian Blue analogs MI y V[CrIII (CN)6 ]z ·nH2 O (M = alkali metal cation) arose with TC s varying up to 376 K. We give hereunder some information on these new compounds. Many factors affect not only the successful synthesis of the compounds in the VCr series but also the magnetic properties of the resulting solids (Curie temperature, magnetisation at saturation, coercivity . . . ). Particularly important is the crystallinity and/or the magnetic domain size of the particles. The structure of Prussian Blues is rich in void spaces, channels, and (often) vacancies that can accommodate guest species (anions, cations, solvent . . . ). These guest species can either improve or compromise the structural organisation of the material. To convince the reader that this chemistry is indeed not easy, we shall give only three examples in which the role of the solvent and of the starting materials (“innocent” counterions) was investigated: (i) The reaction carried out in H2 O with [V(MeOH)6 ]I2 as the starting material, gives compound {VII 0.58 VIII 0.42 [Cr(CN)6 ]0.77 (I− )0.2 (NBu4 + )0.1 }·5H2 O (TC = 330 K). (ii) The reaction in H2 O as solvent and the Tutton salt K2 VII (SO4 )2 ·6H2 O as the starting material, gives the compound {VII 0.78 VIII 0.22 [Cr(CN)6 ]0.56 (SO4 2− )0.28 (K+ )0.11 }·4H2 O (TC = 295 K). (iii) When the reaction is performed in methanol as solvent and with [V(MeOH)6 ]I2 as the starting material, {V[Cr(CN)6 ]0.69 (I− )0.03 }·1.5MeOH. (TC = 200 K) is obtained. The magnetisation curves can be found in Refs. [99, 125]. The counteranions and the solvents have large effects on the Curie temperatures and also on the magnetisation at saturation. Large size and weak coordinating anions as I− , do not induce disorder in the structures and the magnetic properties are improved. As for the solvent, it can be expected that, when the kinetics of solvent exchange in [V(solvent)6 ]2+ is faster, the substitution of the solvent molecules by cyanides around the V2+ ion is more effective, the structure is better organized, and the number of interactions between Cr and V increases. Among many synthetic attempts, four were successful in improving the situation: changing the VII /VIII ratio to improve the magnetisation [126]; using large counterions and slow precipitation by the sol–gel technique, to improve the regularity of the structure [40]; using alkali metal cations to change the stoichiometry [41]; and using VIII as a catalyst in the synthesis [127, 128]. Changing the VII /VIII ratio to improve the magnetisation [126], relies on the observation that, in a VCr Prussian Blue ferrimagnet, the antiparallel alignment of the neighboring spins in the magnetically ordered phase leads to a resulting total magnetisation MT which is the difference between the magnetisation arising from the subset of chromium ions MCr and that from the subset of vanadium ions, MV : MT = |MCr − MV |

(9.23)

Two situations may arise, one when the larger magnetic moments are borne by the chromium ions and are aligned parallel to an external applied field (MCr > MV ); the other when MV > MCr . In the later case, the sign of the quantity (MCr − MV ) is reversed and the magnetic moments of the vanadium ions now lie parallel

328


to the field. In between, the magnetisation is zero. For example, in the analogs (CI y VII α VIII 1−α [CrIII (CN)6 ]z ·nH2 O, it is easy to find that MT = −(3z − α − 2)

(9.24)

The spin values (magnetisation) of the compounds can be represented in a threedimensional space, in which the value of α varies from 0 to 1 and z varies from 2/3 to 1. The spin values are described by the plane in Figure 9.23. The compound {VII 0.45 VIII 0.53 (VIV O)0.02 [Cr(CN)6 ]0.69 (SO4 )0.23 (K2 SO4 )0.02 }· 3H2 O synthesized in this context [126] has a saturation magnetisation MS = 0.36 NA β. The calculated MT value is positive (MT = +0.36 NA β). On the other hand, {CsI 0.82 VII 0.66 (VIV O)0.34 [Cr(CN)6 ]0.92 (SO4 )0.20 }3.6H2 O, prepared in the presence of Cs and containing vanadyl, presents MS = 0.42 NA β. The calculated MT value is negative (MT = −0.36 NA β). The absolute values are in good agreement with the experimental ones. The crucial difference between the two compounds is the sign of MT , which is influenced by the balance between the values of z (CrIII /V ratio) and the ratio VII /V. Conventional magnetisation measurements give the absolute value of the macroscopic magnetisation but not the local magnetisation. Instead, X-ray magnetic circular dichroism (XMCD), a new X-ray spectroscopy developed with synchrotron radiation, is an element- and orbital-selective magnetic local probe. Direct information is obtained about the local magnetic properties of the photon absorber (direction and magnitude of the local magnetic moment). The signal appears whatever the shape of the sample (crystals, powders . . . ). A chapter of Volume I of this series by Sainctavit, Cartier dit Moulin, and Arrio is devoted VIIICrIII S

S=0

z

α

+

CIVIICrIII

-

A-IVIIICrIII2/3

1 VIICrIII2/3

Fig. 9.23. Variation of the total spin (or magnetisation MT ) in the series CI y VII α VIII 1−α [CrIII (CN)6 ]z ·nH2 O as a function of the vanadium fraction α and of the stochiometry z (MT = −(3z − α − 2). The sign of the magnetisation changes above and below the line S = 0 (see text).


329

to this technique [129]: “Magnetic Measurements at the Atomic Scale in Molecular Magnetic and Paramagnetic Compounds”. Figure 8, p. 146 therein, gives the XMCD spectra at the chromium and vanadium edges and demonstrates: (i) The antiferromagnetic coupling between vanadium and chromium ions (inversion of the dichroic signal at the vanadium and the chromium K edges, for each compound). (ii) The opposite local magnetisation of both chromium and vanadium: for a given edge, the general shape of the dichroïc signal of the first compound is the opposite of that found in the second. Further useful applications of X-ray absorption (EXAFS, XANES at the K and L2,3 edges and XMCD) in the study of Prussian Blues, in particular CsNi[Cr(CN)6 ] and CsMn[Cr(CN)6 ] can be found in Refs. [130–133] For the present discussion, the conclusion is that it is absolutely necessary to control the stoichiometry and the vanadium oxidation states to avoid generating an antiferromagnet or, with complete oxidation of vanadium to vanadyl, the loss of the high TC properties as in the (VIV O)[Cr(CN)6 ]2/3 derivative (TC = 115 K) [89] (Figure 9.22b). Second, we found that precursors with large counterions afford a material that closely resembles the preceding VCr material but whose structure is more regular [40]. Combining aqueous solutions of the triflate salt V(O3 SCF3 )2 with the tetraethylammonium salt [NEt4 ]3 [Cr(CN)6 ] under anaerobic conditions affords a dark blue gel after about 10 min. The gel forms only if the reactant concentrations are above a certain threshold (in our experiments the concentrations were 0.02–0.06 mol l−1 ). After 2 h, the gel becomes less viscous and takes the appearance of a suspension. The suspended solids are collected by centrifugation and washed with water to afford a dark dlue solid of stoichiometry VII 1 [CrIII (CN)6 ]2/3 ·3.5H2 O·0.1[NEt4 ][O3 SCF3 ]. Unlike the material prepared in the presence of K+ , NH4 + and SO4 2− counterions, this material is crystalline, with a fcc cell parameter of a = 10.54 Å. Presumably because it is more highly crystalline, it has a slightly higher magnetic ordering temperature of 330 K. When the sample is heated to 350 K, a change occurs and the ordering temperature is lowered slightly to 320 K. Although the nature of this change is still under investigation, one possibility is that the material simply dehydrates upon heating. Another possibility is that a slight rearrangement (rotation) of the [CrIII (CN)6 ] octahedra leads to a smaller J value (see Scheme 2 below). The next step was clear: change the stoichiometry to 1:1 by adding alkali metal cations [see Figure 9.24, derived from Eq. (9.19)]. If the synthesis is conducted in the presence of 4.5 equivalents of CsO3 SCF3 , the cesium salt Cs0.82 VII 1 [CrIII (CN)6 ]0.92 ·3H2 O·0.1[NEt4 ][O3 SCF3 ] (or Cs0.8 VCr0.9 ) is obtained. A similar reaction with the potassium salt K3 [Cr(CN)6 ] leads to K1 VII 1 [CrIII (CN)6 ]1 ·2H2 O·0.1KO3 SCF3 (or KVCr). Table 9.8 gathers important characteristics of the three compounds. Figure 9.25 gives the X-ray powder diffractogram of KVCr, Figure 9.26 presents the thermal variation of the magnetisation and Figure 9.27 is devoted to the magnetisation vs. applied magnetic field at 5 K. The low value of the magnetisation of KVCr is perfectly understood by looking

330


Table 9.8. Properties of the three crystalline high-TC VCr compounds of Ref. [40]. a

a/Å TC /K TC /K After treatment Msaturation /kG cm3 mol−1 Msat expected /kG cm3 mol−1 Hcoercive /G Mremnant /G cm3 mol−1 TClosing hysteresis loop /K

VII 1 CrIII 2/3

CsI 0.82 VII CrIII 0.94

KI 1 VII 1 CrIII

10.54 330 320 3.5 5.7 10 570 350

10.65 337 337 2.2 1.0 15 750 350

10.55 376 365 0.7 0.0 165 220 380

a Adapted from Ref. [40].

at Figure 9.23: KVCr, with α and z = 1 should have a zero magnetisation (line S = 0). The observed low magnetisation at saturation is indeed the result of a very small departure of stoichiometry z from 1 or of the oxidation state of vanadium from +2. Further data, experimental details, and comments can be found in Ref. [40]. The fourth and last issue we would like to address deals with the role of kinetics in the formation of such compounds. The sol–gel technique above was a first step in this direction. Furthermore, we discovered during our studies that: (i) in a perfect anaerobic atmosphere (glove box, 3 ppm O2 ), the slowly precipitating

TC / a.u. 5.5 4.5

3.5

2.5 1.5 1.0 0.8 0.6

0.5 0.6 0.7

0.4 0.8

z

α

0.2

0.9 1.0 0.0

Fig. 9.24. Variation of the Curie temperature (u.a.) in the series CI y VII α VIII 1−α [CrIII (CN)6 ]z · nH2 O as a function of the vanadium(II) fraction α and of the stoichiometry z.


331

Fig. 9.25. X-ray powder diffraction of KVCr (from Ref. [40]).

Fig. 9.26. Thermal variation of the magnetisation of KVCr (from Ref. [40]).

solid is no longer a room temperature magnet (compound 1 in Figure 9.28), in strong contrast with the results obtained by the Schlenck technique which lead to room-temperature magnets (with uncontrolled amount of oxidized vanadium in solution). (ii) Some oxidation of the vanadium ion during the synthesis is necessary to reach a Curie temperature above ambient (compound 2 in Figure 9.28). Both observations prompted us to look more closely at the role of vanadium(III) in the synthetic process. The results are reported in Ref. [127]. We found that small amounts of VIII during the synthesis (1% < VIII < 4%) (Figure 9.29) led to derivatives which display a stoichiometry close to the V1 Cr2/3 ideal one. The solids are free from VIII . Their structure, obtained from EXAFS, comprised of [CrIII CN)6 ] units linked to octahedral vanadium(II) ions by bent C−N−V units (α = 168◦ ) as shown in Scheme 9.2. In contrast, without VIII , the

332


Fig. 9.27. Field dependence of the magnetisation of the VCr derivatives in Table 9.8. 6000 Compound 2

3

M / cm .G.mol

-1

5000

4000

3000

2000 Compound 1 1000

0 0

50

100

150

200

250

300

350

T/K Fig. 9.28. Thermal dependence of the magnetisation of two compounds prepared with catalytic amounts of V(III) (2, ——) and without (1, —◦—).

structures are disordered with a distribution of α angles and tilts of the [Cr(CN]6 ] octahedra. The observed magnetisation fits well the V1 Cr2/3 stoichiometry (Figure 9.30). The Curie temperatures obtained in this way are not the highest obtained so far but


333

OH2

D Cr C N

N

OH2

N

V

D

C Cr

N

Scheme 9.2 Tilted configuration of [CrIII CN)6 ] and V(NC)4 (H2 O)2 octahedra. 340

T /K C

320

T = 310 K

300

a

280

b

260 240 220 200 0

10

20

30

40

50

60

% V(III) Fig. 9.29. Curie temperatures vs. percentage of VIII in solution during the synthesis under various conditions (see Ref. [127] for details).

they are reproducible and remain constant after heating the samples above TC . The tilted configuration of the [CrIII CN)6 ] octahedra, reminiscent of the situation in distorted perovskites, is therefore a thermodynamically stable one. The structural model with α = 168◦ given in Scheme 9.2 allows a straightforward explanation of the higher TC s of the metastable samples: they adopt a (metastable) structure with α angles closer to 180◦ (corresponding to a smaller tilt of the [Cr(CN)6 ] octahedron) and therefore larger orbital overlaps, |J |, and TC s. Heating the sample and cycling the temperature brings the system to the stable structure with α angles closer to 168◦ and lower TC s. It is particularly significant that the stable TC = 310 K value, reached here directly, is close to that of VII 1 CrIII 2/3 in Table 9.8, synthesized by the sol–gel approach by Girolami after cycling the temperature around TC . The

334

9 Magnetic Prussian Blue Analogs 1 Compound 2

Compound 1

Α

Μ/Ν µ

Β

0,5

0

-0,5

-1 4 -6 10

-4 10

4

-2 10

4

0

4

2 10

4

4 10

4

6 10

H / Oe Fig. 9.30. Field dependence at 5 K of the magnetisation of two compounds prepared with catalytic amounts of V(III) (2, ——) and without (1, —◦—).

key role of VIII can also be demonstrated in the synthesis of VCr Prussian Blue analogs in which the stoichiometry is varied by inserting alkali metal cations (K, Rb, Cs); these materials have stable TC s between 340 and 360 K and magnetisations in agreement with the V1 Cr5/6 stoichiometry [128].

9.4.4

Prospects in High-TC Magnetic Prussian Blues

We list below some directions of research which are currently being explored by the magnetic Prussian Blue community. Among others: magnetic devices, thin layers and magneto-optical properties, dynamic magnetic properties etc.

9.4.4.1

Devices Built from [VCr] Room-temperature Magnets

Once room temperature is reached, it becomes possible to think about applications, and the design of demonstrators and devices. Molecule-based magnets, such as the [VCr] systems, are a useful tool to illustrate easily, near room temperature, what is a Curie temperature. Figures 9.31 to 9.33 show several devices and demonstrators. Figure 9.31 displays a very simple demonstration, in which a disk of [VCr], embedded in a polymer to protect it from air-oxidation, is attracted by a powerful


1

2

3

Water

Water

Water

T - 80 ºC

T - 80 ºC

T - 80 ºC

Permanent Magnet

Holder

Holder

Holder

335

4

RT Magnet Holder

Fig. 9.31. Principle of a “flying” magnet.

permanent magnet located just above (2). The permanent magnet is located at the bottom of a beaker filled with hot water: in contact with the hot bath, the temperature of the [VCr] disk increases (3). When the temperature reaches TC , the disk falls (4). Then, on cooling, it is ready to “fly” again when its temperature drops below TC (1). One can dream of a machine built along the same lines, pumping water by solar energy (free) and an atmospheric temperature bath (free). Figure 9.32 describes an oscillating magnet. The [VCr] compound is sealed in a glass vessel under argon and suspended at the bottom of a pendulum [equilibrium, position (2) in the absence of a permanent magnet]. It is then cycled between its two magnetic states: the 3D-ordered ferrimagnetic state, when T < TC , and the paramagnetic state, when T > TC . The three steps are: (i) the room temperature Image

(1) (2)

RT Magnet

Screen (1)

(3) (2) Holder

Permanent Magnet

Len Light Source, Sun … Fig. 9.32. Principle of an “oscillating” magnet.

336


magnet ([VCr]) is cold (T < TC , ferrimagnetic state). It is attracted (→) by the permanent magnet and deviates from the vertical direction towards position (1). The light beam is focused at this position (1), just above the permanent magnet and heats the sample, the temperature of which increases; (ii) when T > TC , the hot [VCr] magnet is in the paramagnetic state. It is no longer attracted and moves away from the magnet (←) under the influence of its own weight. It is then air-cooled and its temperature decreases; (iii) when T < TC , the cold [VCr] magnet is attracted again by the permanent magnet (→) and returns to position (1). The system is ready for a new oscillation. The demonstrator works well, and millions of cycles have been accomplished without any fatigue. It is an example of a thermodynamical machine working between two energy baths with close temperatures (sun and shadow) allowing the conversion of light into mechanical energy. Figure 9.33a shows a photograph of the demonstrator in use in our laboratory. Figure 9.33b shows another demonstrator that could be used as a magnetic switch or thermal probe: the [VCr] magnet located at the end of a diamagnetic bar, can take two

(a)

(b)

Fig. 9.33. Two demonstrators (a) oscillating magnet transforming light to mechanical energy; (b) magnetic switch and thermal probe (see text).


337

positions: when T < TC , it is in contact with the permanent magnet, the temperature of which is tunable; when T > TC it is repelled by a mechanical couple installed on the rotation axis, hence opening or closing an electric circuit [134].

9.4.4.2

Thin Layers, Electrochromism, Magneto-optical Effects

Magnetic Prussian Blue analogs display bright colors and transparency, among other interesting properties. To exploit these optical properties, it is useful to prepare thin films: a 1 µm thick film of a vanadium–chromium magnet is indeed quite transparent. The best way to prepare thin films of these materials is by electrochemical synthesis or ion-exchange on Nafion membranes. Various films have been prepared from hexacyanoferrates or chromates [135]. To obtain [VCr] thin films, the experimental conditions must be adapted. One actually wants to produce and to stabilise the highly oxidisable VII ion. Thus, strongly negative potentials are applied at the working transparent semiconducting electrode. The deposition of the [VCr] film is realised from aqueous solutions of [CrIII (CN)6 ]3− , and aqueous VIII or VIV O solutions either at fixed potential or by cycling the potential. An interesting property of [VCr] thin films is the exhibition of electrochromism during cycling. The way is open for the preparation of electrochromic room temperature magnets (see Refs. [99, 136–138] for illustrations and details). The magnetisation of a transparent magnetic film, protected by a transparent glass cover, can then be probed by measuring the Faraday effect. Spectroscopic measurements in the ultraviolet–visible range bring information about the magnetisation of the sample and its electronic structure. Observing the Faraday effect at room temperature in these compounds is a first step towards demonstrating that the materials can be used in magneto-optical information storage. Hashimoto [136] and Desplanches [99, 137, 138] succeeded in obtaining from [VCr] room-temperature magnets a magneto-optical signal at room temperature through a transparent semiconducting electrode. The thin films of VCr and CrCr materials presenting high TC s are protected by a patent [139]. Faraday effects are also observed in low-Tc Prussian Blues [140]. Electrochemically prepared films of trimetallic Prussian Blue analogs exhibit second harmonic generation effects [141]. Even if further studies are needed to control the purity and the homogeneity of the air-sensitive layers and to correlate the magneto-optical effects with the local magnetisation of vanadium and chromium, a very promising area is open. To conclude this section, we can state that, of all the Prussian Blue analogs prepared to date, the highest TC s are seen for solids isolated by adding V2+ to [CrIII (CN)6 ]3− , and that the KI 1 VII 1 CrIII material is the current record-holder. New precursors, new bimetallic pairs, are coming, involving metal ions of the second and third period of the transition metal ions, which may change the situation.

338


9.5 Prospects and New Trends Space is lacking in this review to develop further aspects of the chemistry and physics of other magnetic Prussian Blues. Fortunately, many aspects have been reviewed recently and the interested reader will find valuable information in the references quoted below. We would like nevertheless to quote some promising areas of development. They show that besides the problem of high TC much more can be learned from, and done with, Magnetic Prussian Blues.

9.5.1

Photomagnetism: Light-induced Magnetisation

A new field was opened in the magnetic Prussian Blues story and in molecular magnetism when Hashimoto and his team reported the existence of an exciting photomagnetic effect in a Prussian Blue analog formulated K0.4 Co1.3 [Fe(CN)6 ]1 ·5H2 O (or K0.3 Co1 [Fe(CN)6 ]0.77 ·3.8H2 O, close to Co1 Fe2/3 ), that has been known for a long time (Table 9.2) [142]. Starting from aqueous solutions of co(II) and hexacyanoferrate(III), Hashimoto obtained a powder, containing potassium ions, which exhibited photo-induced enhancement of the magnetisation at low temperature and an increase in the Curie temperature: photoexcitation at the molecular level, in the Co−NC−Fe unit, gives rise to a modification of the macroscopic properties of the material, an important feature [143]. The authors suggested the presence of isolated diamagnetic pairs CoIII −FeII in a compound otherwise built from −CoII −NC−FeIII − units and a photo-induced electron transfer from FeII to CoIII through the cyanide bridge. The enhancement of the magnetisation and the increase in the Curie temperature simply follows from the increase in the number of magnetic pairs in the photo-induced state. The publication of this first result gave rise to a an impressive series of findings by several groups. Theoretical studies were carried out by Yamaguchi [144], Kawamoto [145] including a patent for an optical storage element [146] and experimental studies were performed by Bleuzen [147, 148, 214], Gütlich [149], Hashimoto [25, 150–152], Miller [153] and Varret [154, 155], who defined the conditions of appearance of the phenomenon, pointing out the role of the ligand field around the cobalt, the role of the vacancies, the very specific role of the alkali metal cations, the presence of several phases, etc. There is not room here to give an exhaustive survey. Among many beautiful results, the first evidence of a photo-induced diamagnetic–ferrimagnetic transition [25, 147] and magnetic pole inversion [25, 150–152] can be underlined. Epstein and Miller studied the dynamics of the magnetisation and proposed a model of a glass cluster in the ground and photoexcited states, with an increase in spin concentration in the photo-induced phase [153]. Although the Co–Fe systems are still being actively studied [156–159], they are now joined by other systems constructed from octacyanometalates, developed by Hashimoto [25, 160], Mathonière [161, 162],

9.5 Prospects and New Trends

339

Marvaud [163] etc. The field has been reviewed by several authors, emphasizing the importance of optically switchable molecular solids. Varret, Nogues and Goujon in the Chapter entitled “Photomagnetic Properties of Some Inorganic Solids” in Volume I of this series [164], Hashimoto and Okhoshi [25], and more recently Sato [165, 166], cite many references to work in this illuminating field.

9.5.2

Fine Tuning of the Magnetisation

The flexibility of the Prussian Blues, especially the ability to adjust at will the composition, was used to play with the magnetisation of the systems, using the mean field model as a predictive tool (see Section 9.3.2.1). Okhoshi, Hashimoto and coworkers produced an impressive series of new results beginning with the coexistence of ferromagnetic and antiferromagnetic interactions in a Nix Mn(1−x) [Cr(CN)6 ]2/3 a trimetallic Prussian Blue [167–169]. With the same theoretical model, they looked at the compensation temperature and other phenomena predicted by Néel [75]. They used competing ferromagnetic interactions to tune the compensation temperatures in the magnetisation of ferrimagnets and they were able to design systems with two compensation temperatures [170, 171]. They also describe an inverted hysteresis loop combining a spin–flop transition and uniaxial magnetic anisotropy. Finally, they combined their efforts and experience in photomagnetism and magnetisation to characterize photo-induced magnetic pole inversion [172]. The results are reviewed in Refs. [25, 173]. The same authors review the very peculiar magnetic properties of RbMn[Fe(CN)6 ] in Ref. [174].

9.5.3

Dynamics in Magnetic and Photomagnetic Prussian Blues

The AC susceptibility was not systematically exploited in earlier studies of MPBs. Epstein and Miller opened this field. When measuring the alternative susceptibility of different molecule-based magnets, they discovered unexpected new behavior, often assigned to spin–glass behavior, as described before in the photomagnetic CoFe PB analog [153, 175–178]. They found similar behavior in first-row transition metal hexacyanomanganates [179]. Other authors suggested similar conclusions in vanadium hexacyanochromates [180] and gadolinium hexacyanoferrates [181]. It appears that the synthetic conditions, the chemical stability, the crystallinity, the homogeneity and the purity are important issues to control in order to understand the dynamics.

9.5.4

Nanomagnetism

This field is still in its infancy but several papers have recently appeared, showing the interest and the potential of magnetic Prussian Blues for the preparation

340


of magnetic nanosized systems. In the trend to ever higher magnetic information storage densities, obtaining nanosize magnetized particles is an important issue, both for theory and applications. Prussian Blues allow top-down (breaking three-dimensional PB solids) or bottom-up (controlling crystalline growth from molecules in solution) approaches. The chemical flexibility of the PB analogs can be a great advantage in tuning the final properties. In 2000, Gao et al. announced that they were able to get obtain VCr derivatives with TC = 340 K, fcc lattice, a = 11.78 Å, stable in air for days, with an average particle size of 5 nm, presenting long range ferrimagnetic behavior and spin–glass behavior [182]. In 2001 Mann et al. prepared good quality inverse opals of Kx Co4 [Fe(CN)6 ]z from polystyrene or silica colloïdal crystal templates [183]. Then, they used water-in-oil emulsions to synthesize crystalline cobalt hexacyanoferrate, cobalt pentacyanonitrosylferrate, and chromium hexacyanochromate in the form of 12–22 nm particles organized in 100 particle superlattices [184]. They expected that the preparation method would be readily applicable toward the synthesis of other nano-sized molecule-based magnets. It was successful with nickel hexacyanochromate in the hands of Catala et al. who obtained 3 nm sized particles(with a wide distribution) [185]. Zhou adopted an electrodeposition technique in the nanocavities of aluminum oxide films to fabricate highly ordered Prussian Blue nanowire arrays 50 nm in diameter and 4 µm in length [186]. Stiegman used the sol–gel technique competing with arrested precipitation to obtain superparamagnetic nanocomposites: transparent nickel hexacyanochromate and photomagnetic cobalt hexacyanoferrate [159]. Langmuir–Blodgett films, which are known to incorporate Prussian Blue itself [187, 188] are also able to trap MPB nanocubes in a thin film, as shown by Delhaes et al. [189]. The field will most probably expand quickly if the difficult problem of characterisation of the new phases can be solved.

9.5.5

Blossoming of Cyanide Coordination Chemistry

The cyanide ligand has a long history in coordination chemistry and organometallic chemistry. It is known as a very dangerous, but also friendly, ligand. The reviews by Fritz and Fehlhammer [190] in 1993 and by Dunbar and Heintz in 1997 [60] pointed out the revival of cyanide chemistry. Molecular magnetism and MPBs have contributed to the blossoming of cyanide coordination and organometallic chemistry with new ideas, new concepts, new precursors (tetra-, penta-, hexa-, hepta-, octa-cyanometalates), new architectures etc. Work by Ceulemans [191], Decurtins [192, 193], Dunbar [194, 195], Hashimoto [196], Kahn [197], Julve [198], Long [199, 200]], Mallah [201, 202], Marvaud [97], Murray [203], Okawa, Ohba and Inoue [204], Ouahab [205], Rey [206], Ribas [207], Sieklucka [208]. and many others, shows that there is considerable interest in this area.


341

9.6 Conclusion: a 300 Years Old “Inorganic Evergreen” These new directions of development are clear indications that the field of magnetic Prussian Blues is very active, with various lines of development in addition to the problem of reaching high critical temperatures, which was the main subject of the present chapter. The deep color of Prussian Blue was, and remains, a fascination for drapers, artists, and chemists. Magnetic and multifunctional Prussian Blues add a new facet to this attraction, from fundamental quantum mechanics to appealing applications, via solid state chemistry and physics. Ludi [209] was right when he pointed out that Prussian Blue is indeed an “inorganic evergreen”. The statement is especially specially appropriate for its 300th anniversary, celebrated this year.

Acknowledgments The authors dedicate this chapter to the memory of their colleague and friend O. Kahn, whose ideas inspired much of the work presented here. MV wishes to thank Drs. S. Alvarez, E. Ruiz, M. Julve, F. Lloret, B. Siberchicot and V. Eyert for illuminating discussions and suggestions about the theory of the systems. The authors are grateful to their coworkers, without whom these magnetic Prussian Blues studies could not have been done; their names appear in the cited articles. Funding from the Pierre et Marie Curie University at Paris, the Department of Energy through the Frederick Seitz Materials Research Laboratory at the University of Illinois at Urbana-Champaign, CNRS, the European Community (TMR and Marie Curie Programmes), I.C.R.E.A. Barcelona and the European Science Foundation (Molecular Magnets Programme) is sincerely acknowledged.

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10 Scaling Theory Applied to Low Dimensional Magnetic Systems Jean Souletie, Pierre Rabu, and Marc Drillon

10.1 Introduction Since the 1960s, much work has been devoted to phase transitions and the study of critical phenomena in the vicinity of the ordering temperature TC [1]. These studies reveal the existence of striking similarities in the behavior of very different physical systems. Most of the experimental results show that, superconductors apart [2], the behavior of the order parameter is very different from that predicted by Landau theory [3–5], indicating the key role played by fluctuations close to TC . A phase transition is characterized by pre-transitional processes with a variable local order (short-range order) where the system fluctuates between states of close energy. Approaching TC , ordered domains are formed whose mean size is the correlation length ξ . The divergence of ξ and, accordingly, of the related susceptibility, increases when T approaches TC . This description of the phase transition leads to important results. Thus, in the vicinity of TC , the variation of the thermodynamical functions is described by power laws (T − TC )γ where γ is the critical exponent [6]. It is worth noticing that the critical exponents depend only on the spatial extent of the system, d, and on the number of components of the order parameter, n, thus defining classes of universality. This induces two key ideas in the critical phenomena theory, namely the concept of scaling invariance and the concept of universality, as pointed out by Kadanoff [7], and checked by the calculations of critical point behavior by Wilson and Wegner [8]. In that area, magnetic phase transitions have likely been the most investigated, because of the wide variety of compounds exhibiting different spins (Ising, planar or Heisenberg) and lattice dimensionalities [9–12]. In the present chapter, we develop a model of “hierarchical superparamagnetism” which generalizes the idea of scaling by taking advantage of the nonsingular solutions that are introduced, together with the singular ones, when the hypotheses of “critical scaling” are formulated. These non-singular solutions, although they have the same legitimacy, have simply been set aside when the goal was to describe the singularities of phase transitions. They happen to be very useful

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10 Scaling Theory Applied to Low Dimensional Magnetic Systems

when correlations exist, but are not sufficient to trigger a long-range order at a finite TC , either because frustration is strong, near e.g. an antiferromagnetic (AF) order, or because we sit at, or below, a lower critical dimensionality. Model systems, such as the 1D or 2D-Heisenberg systems of spin S = 1/2, 1, . . . ∞ display such behavior. For this reason, much effort has been devoted to performing exact calculations on such finite systems of increasing size, and in trying to infer which type of limit is reached when the size diverges. On the other hand, the progress of chemistry has made it possible to design organometallic clusters, chains or planes, of axial, planar or isotropic spins, which closely approximate the abovementioned systems, and are very appropriate to investigate the properties of interest. We will show with a few examples, some based on the experimental behavior of real compounds and others on theoretical data derived for finite Heisenberg chains, that the model of hierarchical superparamagnetism provides the right framework to approach these problems and suggest a strategy adapted to each case.

10.2 Non-critical-scaling: the Other Solutions of the Scaling Model Let χ T = Nµ2 /3, where µ = [S(S + 1)]1/2 and χT is normalized to g 2 µ2B /k, be the Curie constant of N independent spins, and ξ0 the typical size at the atomic scale. In the presence of interaction, we assume that these spins are correlated in space, and the correlation length ξ(T ) defines the size of the new objects. Their volume is ξ d in space dimension d, and their number N = N0 (ξ/ξ0 )−d . Following Néel in his description of fine magnetic particles, we similarly assume that the moment of each object increases as a power d of ξ , where the dimensionality d characterizes the magnetic order which sets in [13]. Depending on the relation between d and d, we may then characterize different situations: thus, if d = d, we describe a ferromagnet whose moment increases as the volume of the units. By contrast, the moment in an antiferromagnet is accurately compensated within the volume of the units but not, presumably, at the surface, and d = d − 1 or (d − 1)/2 in the presence of disorder at the surface. In the absence of any correlation between the magnetic ordering and the structure, the uncompensated moment increases as ξ d/2 , a situation which occurs in spin glasses. Then, the expression of the χ T product is given by:

χ T ∝ ξ(T )−(d−2d )

(10.1)

We now write that ξ increases when T decreases, and that it is possible, in the spirit of Kadanov’s renormalization scheme, to connect by a “hierarchical recipe” the successive steps of the cascade which relates ξ and ξ0 . Assuming, for example, that ξ is multiplied by b when (J /TC − J /T ) is multiplied by a, then, if n steps

10.2 Non-critical-scaling: the Other Solutions of the Scaling Model

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are needed to relate Tn , where the correlation is ξn , with J , where it reduces to ξ0 [13], one obtains: J /TC − J /Tn = a × (J /TC − J /Tn−1 ) = a × a × a × . . . × (J /TC − 1) = a n × (J /TC − 1) (10.2a) ξn = b × ξn−1 = b × b × b × . . . × ξ0 = bn × ξ0 (10.2b) By eliminating n between Eqs. (10.2a) and (10.2b), one derives the standard relation of static scaling: ξ/ξ0 = (1 − TC /T )−ν = (1 − TC /T )−/TC

(10.3)

with = νTC > 0 in order to ensure that log(ξ/ξ0 ) = 1 + /T + TC /2T 2 + TC2 /3T 3 + . . . is an increasing function of 1/T . For > 0, the sign of TC fixes the curvature in such a way that the Arrhenius law ξ/ξ0 = exp(/T ), corresponding to the TC /T = 0 limit, separates solutions of positive curvature, ξ/ξ0 = (1−TC /T )−/TC , from those whose curvature is negative, ξ/ξ0 = (1 + TK /T )/TK where TC = −TK , which have the same legitimacy (see Figure 10.1). The “static scaling assumption” has measurable consequences. In particular, using Eq. (10.1) and permitting TC to be positive, zero or negative, we find:

for TC > 0 (10.4a) χ T = C × (1 − TC /T )−(2d −d)ν = C × (1 − TC /T )−γ χ T = C × exp((2d − d)/T ) = C × exp(−W/T ) for TC = 0 (10.4b) χ T = C × (1 + TK /T )(2d −d)/TK = C × (1 + TK /T )−γ for TC = −TK (10.4c)

Fig. 10.1. (a) log(ξ/ξ0 ) vs. 1/T and corresponding (b) ∂ log(T )/∂ log(χT ) vs. T diagram showing the typical variations expected for TC positive, zero or negative in the framework of the proposed model.

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The solutions (10.4a) are the familiar power laws appropriate to describe the usual phase transitions, with γ being the critical exponent related to the spin and lattice dimensionalities. Note that because we were careful by using J /T , which cancels when T diverges, rather than T /J to construct the scaling variable (J /TC − J /T ), all Eqs. (10.4) that we obtain have a sensible high temperature expansion. Thus, the Curie–Weiss law χ = C/(T − W ) is recovered, with C = S(S + 1) being the Curie constant (in Ng 2 µ2B /3k units), and W = (2d − d) the Weiss temperature. Let us now focus upon other aspects of the system of Eqs. (10.4) that have, in general, been left aside. First, we observe that the solutions of type (10.4b) or (10.4c) have the same legitimacy as the solutions of type (10.4a) and that they are not forbidden by any thermodynamic rule. They are therefore natural candidates to describe systems, sitting at or below a “lower critical dimensionality”, where spin correlations are significant but no long-range order sets in at any finite temperature. Second, we observe that, for a given positive = νTC , the model provides, depending on the sign of 2d −d, both ferromagnetic solutions where χT increases upon cooling and AF solutions where χ T decreases. We will use hereafter the latter to describe the magnetization of real AF systems, breaking with a tradition whereby it is argued that the usual susceptibility does not contain valuable information, and that the “staggered” magnetization should be considered instead. In order to check these ideas and to decide which expression is more appropriate to describe experiments, we propose to differentiate Eq. (10.4) to obtain the equivalent expression: ∂ log(T )/∂ log(χ T ) = −(T − TC )/γ TC

(10.5)

It appears that ∂ log(T )/∂ log(χ T ) is a linear function of T , in the temperature window where the scaling argument is valid, and that γ −1 and TC are simultaneously deduced from the intersection of the straight line with the axes (see Figure 10.1). In the TC = 0 limit, where χ T is described by Eq. (10.4b), the straight line intersects the axes at their origin. In previous works, we have reported examples where ∂ log(T )/∂ log(χT ) obtained by differentiating the experimental data shows a unique linear regime, giving a TC value that is positive, zero or negative [14, 15]. In some cases, we observe an abrupt crossover, from one regime to the other (e.g. from solutions of type (10.4b) to solutions of type (10.4a)) occurring at a given crossover temperature where the effective space dimensionality changes (e.g. because correlations which are negligible at the scale of atomic distances may become important on large segments). We will hereafter consider yet another situation where two different criticalities seem to coexist in the same temperature range, i.e. where two solutions of type (10.4b) are superimposed in a common temperature window.

10.3 Universality Classes and Lower Critical Dimensionality

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10.3 Universality Classes and Lower Critical Dimensionality As ξ(T ) diverges, it is argued that the physics should not depend on the local defects or the details of the structure. Rather, it reflects the main anisotropies, such as the dimensionality d of space and the dimensionality n of the order parameter, or spin space symmetry, which persist and are dominant at long range. As a consequence, the value of the critical exponent is expected to depend closely on these dimensional features. We have reported in Table 10.1 the values of the critical exponent of χT at the ferromagnetic transition, according to the dimensions of d and n, where n = 1, 2, 3, for Ising, planar and Heisenberg spins, respectively and n = ∞ for the spherical model. A finite number of interesting cases is observed, including two exact solutions, the Ising chain model (n = 1, d = 1) and the Onsager’s solution for the 2D-Ising model (n = 1, d = 2). Table 10.1. Critical exponent of the χT = f (T ) dependence, according to the spin space (n) and lattice (d) dimensionalities. The exponent conserves the mean field value γ = 1 for all n at d ≥ 4. We suggest that γ diverges, for each n, at a lower critical dimensionality, dc (n), which is 1 for the Ising case and is a frontier between the solutions of Eqs. (10.4a) and (10.4c). Our finding for the 1D-Heisenberg case is also included.

d=1 d=2 d=3 d=4 Mean field

n = 1 (Ising)

n = 2 (XY)

n = 3 (Hbg)

n = ∞ (sph.)

∞ 1.75 1.25 1 1

KT 1.32 1 1

−1.23S ∞ 1.387 1 1

2 1 1

Table 10.1 reflects results that bypass, to a large extent, the ferromagnetic transition itself. In particular, it is noticed that: • A ferromagnetic transition occurs in mean field, the solution of which, γ = 1, corresponds to the limit of infinite dimensionality of space. • The mean field solution is available down to an “upper critical dimensionality”, which is d = 4 in the ferromagnetic case. • The long-range order is destroyed if the space dimension is decreased below a “lower critical dimensionality”, dc (n), characterized by a divergence of γ . • In the space dimension between dc (n) and 4, there is still a ferromagnetic transition but γ differs from the mean field value. As a result, we propose that solutions of Eqs. (10.4b) and (10.4c) well describe the situations at and below dc (n), respectively, making possible the determination

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of γ to complete Table 10.1, either by analysing the theoretical results or by an accurate analysis of the experimental data. There are difficulties that we propose to discover in typical examples, together with a strategy inspired by our model of hierarchical superparamagnetism.

10.4 Phase Transition in Layered Compounds Considerable attention has recently been focused on the design and synthesis of ferro- or ferrimagnetic molecular materials [16]. Basically, the exchange interaction in these materials usually has a low-dimensional character, and so they may be considered as good candidates for studying isolated chains or layers. Layered systems with isotropic in-plane interactions are known to show longrange order at T = 0, only. TC becomes finite only if any type of anisotropy (exchange or dipolar-like, magnetocrystalline . . . ) is introduced, as demonstrated for the weak in-plane anisotropy of dipolar origin which induces a 2D ordering [17, 18]. Recently, we have shown that a 3D long-range order might occur at a sizeable temperature in layered compounds made of ferromagnetic layers up to 40 Å apart [19]. Similar results have been observed for chain systems [20, 21] and therefore the combination of in-plane (or in-chain) quantum exchange and inter-plane (or inter-chain) dipolar interaction has been considered. Basically, the strength of the dipolar interaction is weak as far as single ions are concerned and, for a pure dipole system, critical temperatures of a few K, at most, can be expected. However, as the dipolar energy depends on the square of the effective moment, the interaction between high spin correlated units, as for instance temperature dependent domains in low dimensional ferro- or ferrimagnets, can become efficient [22, 23]. The series of hydroxide-based compounds M2 (OH)4−x Ax ·zH2 O (M = Co, Cu and A = n-alkyl carboxylate anion) provides suitable examples of quantum magnetic layers coupled by dipolar interactions. The distance between metal hydroxide layers is controlled in the range 9–40 Å by the length of the organic anions which play the role of spacers (Figure 10.2) [24–26]. The magnetic properties are shown to depend closely on the nature of the metal ions and organic spacers. Thus, the compounds Cu2 (OH)3 (n-Cm H2m+1 CO2 )·zH2 O have a ferrimagnetic character, while the cobalt(II) analogs order generally ferromagnetically with critical temperatures being 10–58 K for m ranging from 1 to 12 [24–26]. From a structural point of view, the above hydroxy carboxylates consist of 2D triangular arrays of CuII ions octahedrally surrounded by oxygen atoms belonging to either hydroxide or long-chain carboxylate anions. The distance between layers varies linearly with the length of the n-alkyl chain (m), according to the relation d(Å) = d0 + 2.54m cos θ available for double organic layers, where θ is the tilt

10.4 Phase Transition in Layered Compounds

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Fig. 10.2. Layered structure of the hydroxy carboxylate-based compounds showing the metal-hydroxide layers well separated in the space by organic chains. The tilt angle (θ) of the chains depends on the metal ion.

angle of the chains [19, 26]. For m = 10 and 12, d is found to be 35.9 Å and 40.7 Å, respectively [19]. The magnetic susceptibility χ (T ) is shown in Figure 10.3 for m = 9, which is representative of the series. M/H recorded by cooling the sample in 1 T increases strongly with decreasing temperature, and exhibits a transition at about TC = 21 K, where ferromagnetic order sets in. The existence of a magnetically ordered state is confirmed by the hysteretic effect observed at very low temperature. In the following, we focus on the high-temperature region, where the correction due to the demagnetizing field is small and can be neglected. Several features point

Fig. 10.3. Variation of χ (T ) and χT (T ) for Cu2 (OH)3 (n-C9 H19 CO2 ). The raw data (circles) are well fitted by a model allowing for the competition of two exponential contributions of the type of Eq. (10.4b).

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towards a ferrimagnetic or a non-collinear spin configuration within the copper(II) layers, such as the presence of a well-marked minimum in the χT vs. T plot well above TC (Figure 10.3). To discuss the results, we have plotted in Figure 10.4 ∂ log(T )/∂ log(χT ) vs. T , as obtained from powder sample measurements in a conventional SQUID magnetometer. First, we observe, that ∂ log(T )/∂ log(χ T ) diverges at two extrema of the χT (T ) dependence. The maximum of χ T , near 20 K, is associated with the ferromagnetic transition, while the minimum, at about 65 K, separates a high temperature window where ∂ log(T )/∂ log(χ T ) is positive, and the system is AF, from a lower temperature regime where ferromagnetic correlations dominate. Trial values of TC , which can be inferred from the regimes away from the singularity, are zero or small enough to be neglected in the temperature range of interest. This leads us to search for a fit above 40 K, by superimposing two exponentials of the type (10.4b), one AF dominant at high temperature and the other, ferromagnetic, which prevails at low temperatures when the former collapses. Note that the latter is fully justified for a 2D Heisenberg ferromagnet, whose low-temperature behavior is given by

Fig. 10.4. Plots of ∂ log(T )/∂ log(χT ) and ∂ log(T )/∂ log(χT )ferro vs. T in Cu2 (OH)3 (nC9 H19 CO2 ). χ Tferro has been obtained by subtracting from the bulk χT data the AF component which dominates the high temperature regime.


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χ T = exp(4π J S 2 /T ), J being the in-plane exchange interaction [16]. We found indeed an excellent fit (see Figure 10.3) over the whole range, with the expression: χ T = C1 exp(αJ /T ) + C2 exp(βJ /T )

(10.6)

where C1 = 0.619, αJ = −99.2 K, C2 = 0.037, βJ = +99.2 K. The driving interaction, responsible for the initial high temperature decay of χ T , is antiferromagnetic (negative αJ ). It concerns most of the moments and is attributed to the dominant in-plane interaction. In turn, the low-temperature increase of χ T is dominated by the second term that is ferromagnetic-like. In order to know more about this ferromagnetic contribution, we have corrected the bulk susceptibility from the AF component, determined above 50 K, to obtain χ Tferro = χ T − C2 exp(W2 /T ). We thought that our knowledge of the AF component, obtained in a domain where it is dominant, was sufficiently good to be extrapolated below 40 K and subtracted from the signal, in order to improve our knowledge of the ferromagnetic component. The comparison of ∂ log(T )/∂ log(χT )ferro with its bulk counterpart, in Figure 10.4, stresses the permanence of the ferromagnetic contribution. It is confirmed that, down to about 30 K, the ferromagnetic component is well described by an exponential solution of the type (10.4b) since ∂ log(T )/∂ log(χ T )ferro is proportional to T . We can, on the basis of this observation, identify the space dimension d = 2 as a lower critical dimension for ferromagnetic Heisenberg systems. The remarkable feature in Figure 10.4 is the abrupt crossover, that occurs at about 29 K, to a distinct regime where ∂ log(T )/∂ log(χT )ferro is still a linear function of T , but aims towards a finite TC with a typical 3D exponent. A direct fit of the data with Eq. (10.4a) in the temperature window 22–30 K, as suggested by Figure 10.5, yields TC = 21.4 K and γ = 1.31, which is close to the theoretical 3D-Heisenberg value. Note that the same analysis for m = 10 gives TC = 21.05 and γ = 1.36. The crossover, once it has been spotted, can be made visible in the data themselves. For example, in the Arrhenius plot of χ T vs. T (Figure 10.6), we notice a change from a high temperature linear variation to a regime of strong positive curvature. The fit with Eq. (10.4), is excellent in either case, and can be made better if we take into account, near TC , the effect of the demagnetizing field, which limits the divergence of the susceptibility. It is possible, by doing so, to minimize and eventually to suppress the rounding the maximum on the ∂ log(T )/∂ log(χT ) vs. T variation. The crossover is not surprising. As the temperature decreases, the 2D correlation length increases leading to larger correlated domains. The interactions between domains of the same plane increase with their perimeter, while the interactions between domains of different planes increase with their surface area, so that sufficiently large plates, even when far apart, will get coupled below some temperature; accordingly, the transition which is observed ultimately is a 3D transition. The existence of a crossover can very seldom be made as visible as it is in Figure 10.5. This alternative representation of the experimental evidence allows

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Fig. 10.5. The plot is an enlargement of Figure 10.4 where the crossover at T = 29 K in the m = 9 system (CuC9), from a 2D regime where TC is zero and γ is infinite to a 3D regime where TC = 21.4 K and γ = 1.31, appears magnified. The same graph shows the behavior of Co2 (OH)3.5 (IMB)0.5 ·2H2 O (Corad1), that undergoes a similar crossover between the same two classes of universality, although the physics involved is different.

Fig. 10.6. Arrhenius representation of log(χT ) and of log(χT )ferro vs. 1/T , for the m = 9 system. At high temperature the ferromagnetic component, (χT )ferro obeys Eq. (10.4b) and is described by a straight line in this plot.


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one, at a glance, to decide the reality of a scaling process, with regard to range and parameters. It is then possible, coming back to the original data, to determine, in this range, the best values of the parameters [15]. The study of the metal-radical compound, Co2 (OH)3.5 (IMB)0.5 ·2H2 O, obtained by aion-exchange reaction in Co2 (OH)3 NO3 with meta-iminonitroxidebenzoate anion [26, 27], is another good illustration of what can be deduced from this particular reading of the experimental data. The structure consists of the stacking of Ising-like Co(II) hydroxide layers and isotropic IMB radicals. Cobalt(II) ions occupy both octehadral and tetrahedral sites, while the basal spacing is found to be 22.8 Å. The χ T product shown in Figure 10.7a is not a monotonic function of temperature, due to the influence of spin–orbit coupling competing with magnetic interactions. The plot of ∂ log(T )/∂ log(χ T ) vs. T is shown in Figure 10.7b, and compared to that of the copper(II) analog in Figure 10.5. Very similar situations

Fig. 10.7. Magnetic behavior of Co2 (OH)3.5 (IMB)0.5 ·2H2 O: (a) temperature dependence of the χT product, (b) plot of ∂ log T /∂ log(χT ) vs. T for raw data (squares) and those corrected for the high temperature contribution, namely χTcorr = χTmeas − 3.16 exp(−6.87/T ) (circles).

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are noticed from the universality class point of view, despite both systems being extremely different from a microscopic point of view. Two singularities are observed at 8 K and 65 K, defining three temperature ranges. These divergences point to extrema of χT = f (T ) occurring when there is a balance between two regimes, as defined in the system of equations (10.4). Thus, the minimum of χ T at 65 K separates a high temperature range where ∂ log(T )/∂ log(χ T ) is positive, with TC small or zero, from a low temperature regime where ferromagnetic correlations dominate and where TC is also small. The fit over the temperature range 15–300 K by using two exponentials gives χ T = 3.16 exp(−68.7/T ) + 2.92 exp(20.46/T ). It is worth noticing that the χ T variation above 65 K does not correspond to AF behavior, but actually to the effect of spin–orbit coupling for octahedral Co(II) ions. There is no real explanation as to why the fit turns out to be so good with a plain superimposition of the two exponential contributions, but it adequately describes the spin–orbit coupling, which stabilizes discrete levels, and the low-temperature divergence of the susceptibility of a 2D ferromagnetic system. In the critical regime, the apparent susceptibility χ must be corrected for the demagnetizing field, which limits the effect of the external field. At the ferromagnetic transition, χ = M/H saturates to a value 1/α, where α is the demagnetizing coefficient. This determination of α allows one to deduce the intrinsic magnetic susceptibility χi = M/(H − αM), and to obtain the actual temperature dependence of χT , illustrated in the Arrhenius plot of Figure 10.8. The best agreement is obtained for χ T ∝ (1 − 7.6/T )−1.40 which is consistent with the value expected for a 3D Heisenberg ferromagnet. It is to be noted that the crossover from a 2D to a 3D regime occurs at about 13 K (see Figure 10.7).

Fig. 10.8. Variation of χ T vs. 1/T for Co2 (OH)3.5 (IMB)0.5 ·2H2 O. The data corrected for the demagnetizing effect are shown as χTcorr and compared to the power law variation (full and dotted lines).


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The compound [Co(CO2 (CH2 )OC6 H5 )2 (H2 O)2 ] also exhibits changes of regime at low temperature, due to the spin–orbit coupling effect and to the magnetic dimensionality [28]. This system can be described as a layered cobalt(II)-diaqua-bis-µ-η1,η1phenoxyacetate polymer, as displayed in Figure 10.9. Each CoII atom is coordinated by six oxygen atoms forming slightly elongated octahedra. The cobalt atoms are interconnected within the layers via carboxylato bridges in a syn-anti conformation, thus forming square planar magnetic arrays separated by a double layer of phenoxy acetate anions (Figure 10.9a). The latter are quasi-perpendicular to the cobalt layers, which are 16.57 Å apart (Figure 10.9b). The temperature dependence of the χ T product shown in Figure 10.10 exhibits a regular decrease from 300 K to 10 K, in agreement with the behavior of a nonsymmetrical ion submitted to spin–orbit coupling [29, 30] It is to be noticed that for isolated octahedral Co(II) ions, a minimum value of χT ≈ 1.8 emu K mol−1 is expected, corresponding to a pseudo-spin S = 1/2 and g ≈ 4.4. Below 10 K, χ T increases abruptly up to 2.81 emu K mol−1 at 2 K, according to the influence of significant ferromagnetic correlations. As deduced from magnetization measurements, no long-range order takes place at this temperature. The saturation moment, Ms = 2.25 µB mol−1 , agrees with the expected value for octahedral high spin Co(II) ions. Ac magnetic measurements were performed on a small platelet-shaped crystal in an ac field of approximately 1 G (frequency 2.1 Hz), parallel to the Co(II) lay-

(a)

(b)

Fig. 10.9. Structure of Co(CO2 (CH2 )OC6 H5 )2 (H2 O): (a) Perspective view showing the square planar arrangement of the cobalt(II) atoms at the center of oxygen octahedra which are interconnected through carboxylato bridges (the H atoms are omitted for clarity); (b) View of two neighboring CoII layers separated by phenoxy acetate moieties arranged in a double layer.

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Fig. 10.10. Variation of the χT product as a function of temperature for Co(CO2 (CH2 )OC6 H5 )2 (H2 O). The magnetization vs. field curve measured at 2 K is plotted in the inset.

Fig. 10.11. Low temperature magnetic susceptibility measured in an ac field of approximately 1 Oe at 2.1 Hz. A sharp peak in the real part of the susceptibility χ is seen just below 0.6 K together with an abrupt increase of the out-of-phase susceptibility χ . The inverse susceptibility 1/χ vs. T shows a positive Curie–Weiss temperature, characteristic of ferromagnetic interactions.

ers (Figure 10.11). The real and imaginary parts of the susceptibility exhibit the characteristic features of long-range ferromagnetic order at 0.57 K, and the plot of the inverse susceptibility vs. T (see inset) confirms that ferromagnetic interactions dominate.


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The field dependent magnetization measured at 90 mK, with the field parallel or perpendicular to the surface of the crystal, agrees with an out-of-plane hard axis of magnetization. The exchange coupling involving a bridging carboxylate ligand in syn-anti conformation is known to favor weak AF interactions between neighboring Co(II) ions [31, 32] contrary to the observed behavior below 10 K. In fact, the structure shows that two well distinct directions of local anisotropy are to be considered between magnetic centers linked through dicarboxylato bridges. As a result, a competition between the local anisotropy field and the exchange coupling likely promotes a non-collinear spin ground-state [33–35]. In order to discuss the magnetic behavior in the critical regime, we have corrected the susceptibility from the influence of the demagnetizing field. From the maximum value χa = 0.39 emu cm−3 at TC , we found the demagnetising factor α = 2.55, which is a reasonable value for a flat disk-shaped sample with the field parallel to the planes. We then deduced the actual temperature dependence of χT , illustrated in the Arrhenius plot of Figure 10.12, and compared it to solution (10.4a) of the static scaling model. The best fit is obtained for [14]: χ T ∝ (1 − 0.57/T )−1.39

(10.7)

which confirms the 3D character of the transition (TC = 0.57 K), and agrees with the value of 1.387 predicted for a Heisenberg system.

Fig. 10.12. Low temperature variation of the χT product vs. 1/T , where χ is the intrinsic susceptibility corrected for demagnetization effects. The solid line is a fit of the nonlinear scaling function χ T = C(1 − TC /T )−γ to the data, giving TC = 0.57 and γ = 1.39.

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Fig. 10.13. Structure of the terephthalate-based compound Co2 (OH)2 (C8 H4 O4 ).

Similarly to the above systems, the actual dimensionality of the terephthalatebased compound Co2 (OH)2 (tp) (with tp = C8 H4 O4 ), was a matter of debate, due to the strong anisotropy of the magnetic carriers. The structure, determined by an ab initio XRPD method, is illustrated in Figure 10.13 [34]. The terephthalates are pillared and coordinated to the cobalt hydroxide layers, thus forming a three-dimensional network. The basal spacing is 9.92 Å. Two crystallographically independent Co(II) ions are found: one (Co1) bound by four hydroxyls and two carboxylic oxygen atoms, the other (Co2) bearing two hydroxyls and four tp oxygen atoms. The temperature dependent magnetic susceptibility of Co2 (OH)2 (tp) agrees with the presence of high-spin Co2+ ion. The χT product exhibits, upon cooling, a smooth minimum at about 100 K, then a strong increase up to a sharp maximum at 47.8 K and a decrease to zero (Figure 10.14a). From ac magnetic susceptibility measurements and neutron diffraction [35], it has been emphasized that this maximum corresponds to a long-range AF order, and that a net moment associated with a canted AF structure is stabilized below 44 K. The plot of ∂ log T /∂ log(χ T ) vs. T (Figure 10.14b) gives a very good agreement between theory and experiment for the parameters TC = 48 K and γ = 1.28. The exponent γ is very close to typical 3D values (γ = 1.32 for the planar form and 1.25 for the Ising model), showing the bulk character of the magnetic transition. This result points to a driving contribution of π electrons in the bridging unit to promote the 3D order, even though dipolar coupling between layers may also be invoked.

10.5 Description of Ferromagnetic Heisenberg Chains

363

Fig. 10.14. Magnetic behavior of Co2 (OH)2 (tp): (a) temperature dependence of the χT product; (b) variation of d log(T )/d log(χT ) vs. T .

From these experimental examples, it appears that worthwhile information, such as the spin space and lattice dimensionalities, and further exchange interaction energy, may quite readily be obtained by using the scaling approach.

10.5 Description of Ferromagnetic Heisenberg Chains In this section, we focus on the magnetic susceptibility of finite ferromagnetic rings of n Heisenberg spins (S = 1/2, 1, 3/2, etc), obtained by the direct diagonalization method, and we show, by using the scaling arguments developed above, that there exists a unique closed form expression describing their magnetic behavior.

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We have been guided by our confidence that: 1. Superparamagnetic scaling should describe the infinite one-dimensional systems. 2. The use of finite rings is allowed if the correlation length is much smaller than the size of the rings. It follows that superparamagnetic hierarchical scaling should be obeyed down to the lowest temperatures for very large rings. The behavior of ferromagnetic quantum Heisenberg chains has been analyzed from the thermodynamical data obtained by exact diagonalization of the spinhamiltonian H = −J Si Si+1 , for S = 1/2, 1 and 3/2, and rings of maximum size n = 14, 10 and 8, respectively. The results are given in Figure 10.15 as ∂ log(T )/∂ log(χT ) vs. T /J S(S +1) for some finite quantum chains together with that of the classical spin chain (S = ∞) which has analytical solution [36]. For a given S, ∂ log(T )/∂ log(χT ) is a linear function of T , which is aiming towards a negative TC = −TK , down to a threshold value TS (n). We observe that this linear plot intercepts the axes at TK and γ −1 , which

Fig. 10.15. Plot of the ∂ log(T )/∂ log(χT ) function vs. T /J S(S + 1) as determined from the theoretical susceptibility of finite ferromagnetic rings of n Heisenberg spins for the spin values S = 1/2 and 3/2.


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stay much the same for different n values. However, the linearity, and accordingly the fit of data by Eq. (10.4c), is better for larger rings, suggesting that the following expression is available for the infinite chain: χ T = C[1 + J S(S + 1)/T ]−γ

for T > TS (∞)

(10.8)

Table 10.2 gives the best values of C, and γ , obtained for S = 1/2, 1 3/2, by fitting the susceptibility data above TS (n), for n = 14 (S = 1/2), 10 (S = 1) and n = 8 (S = 3/2). We observe, in all cases, that the Curie constant is within 1% of the theoretical value S(S + 1). Similarly, we find that −γ = 0.75 within 1%. It can be noted that the data for finite rings depart from the 1D-Heisenberg model at a temperature TS (n) which becomes smaller as the rings become larger. Table 10.2. Best values of the pertinent parameters for 1D-Heisenberg ferromagnetic chains of spins S = 1/2, 1, 3/2. C is the Curie constant in Ng 2 µ2B /3k units, T is the negative critical temperature (in S(S + 1) units), and γ the (negative) exponent characterizing systems in a space dimension below a lower critical dimensionality. S

1/2

1

3/2

C/(S(S + 1)) −γ −γ /S

0.991 0.742 1.222

0.989 0.735 1.232

0.989 0.731 1.164

The data display a negative curvature which signals, in Arrhenius coordinates, a hierarchical scaling described by Eq. (10.4c), and that our model associates with systems below a lower critical dimensionality. Finally, we find, although with less accuracy (within 5%), that γ = −1.23S. This enables us to propose the following expression for χ T by using the reduced temperature t = T /S(S + 1): χ t = [1 + 0.61J /St]1.23S

t > tS

(10.9)

which is clearly more tractable than the polynomial expressions reported for quantum spins S in the literature [30, 37]. From this approach, we can deduce the very low temperature behavior of a ferromagnetic chain, which is illustrated in Figure 10.16 for S = 1/2. In the classical limit (S = ∞), the above expression becomes: χ t = exp(0.75J /t) t > tS=∞

(10.10)

which indeed fits very well the theoretical expression of the magnetic susceptibility for T > J [36]. According to our definition, therefore, d = 1 would be a lower critical dimensionality for classical Heisenberg spins but not for quantum Heisenberg ones, at least for T > J . The latter would belong to the space dimension below dc , since

366


Fig. 10.16. Plot in Arrhenius coordinates of χT vs. J S(S +1)/T for finite ferromagnetic rings of n Heisenberg spins S = 1/2. The infinite 1D-Heisenberg chain is described by a power law (see Eq. (10.9)).

their magnetic susceptibility is described by a finite power law, χ ∼ T −(1.23S+1) , over a very large temperature range.

10.5.1

Application to Ferromagnetic S = 1 Chains

This model has been used to describe the magnetic behavior of Ni2 (O2 CC12 H8 CO2 )2 (H2 O)8 , in which the Ni(II) metal ions are located in slightly distorted octahedral sites and form helical chains (Figure 10.17a) [38]. These ions are connected through a biphenyl-dicarboxylate ligand, the shortest Ni–Ni distance along the chain being 4.94 Å. The chains are moreover connected by inter-chain hydrogen bonds to form planes quasi-perpendicular to the [10-1] direction. The magnetic behavior illustrated in Figure 10.17b agrees with the Curie–Weiss law for T > 100 K, with C = 2.289 emu K mol−1 (two NiII ions per mole), and θ = +1.08 K, pointing to a weak ferromagnetic interaction. Accordingly, the χ T product is nearly constant from room temperature down to ∼150 K, then shows a slight increase to a maximum of 2.49 emu K mol−1 at 16 K and a drop to


367

(a)

Fig. 10.17. (a) View of neighboring Ni(II) helical chains. Intra-chain and inter-chain hydrogen bonds are illustrated as dashed lines (labeled B, C and D respectively); (b) χ(T ) and χT (T ) variation for Ni2 (O2 CC12 H8 CO2 )2 (H2 O)8 . The full line shows the best fit for a ferromagnetic spin-1 chain model.

368


1.69 emu K mol−1 at 2 K. The observed behavior is characteristic of the occurrence of ferromagnetic correlations within the chains, while the drop to zero below 16 K is reminiscent of either AF interchain interactions or a zero-field splitting effect. The magnetisation versus field measurement exhibits a paramagnetic-like behavior with a saturation value of 2µB per nickel. Neither a metamagnetic or spin–flop transition is observed, suggesting that no long range 3D AF order is achieved at this temperature. In order to evaluate the exchange interaction between neighboring nickel(II) ions, the magnetic susceptibility has been fitted in the high temperature region by considering a model of Heisenberg S = 1 ferromagnetic chain and the approach developed in the framework of the scaling theory. It is shown that the analytical expression χ t = 3/8g 2 (1 + 0.61J /St)1.23S

(10.11)

fits the experimental data very well (Figure 10.17), giving g = 2.13 and J = +1.06 K, in agreement with the θ value deduced above. So, from the proposed model and close examination of the crystal structure, we merely deduce the ferromagnetic interaction between magnetic centers that is shown to involve, in the present compound, biphenyl-dicarboxylate ligands and hydrogen bonds.

10.6 Application to the Spin-1 Haldane Chain The AF chain of Heisenberg spins with integer S values is still an object of interest many years after Haldane conjectured that an energy gap separates the singlet ground-state from the first excited state, while half integer spin chains are gapless. After the pioneering work of Botet et al. [39] who solved numerically the spin Hamiltonian for finite rings of n spins S = 1 with n = 6 to 12, further calculations have been performed by means of the quantum Monte Carlo [40] and the density-matrix renormalization group (DMRG) techniques [41] to determine more precisely the energy gap as n diverges. The extrapolated value for the infinite chain was estimated to be ≈ 0.41J [42] where J (> 0 for an AF coupling) is the nearest neighbor exchange interaction. This system displays other fascinating features, for example the ground-state of open chains is characterized by an effective spin S = 1/2 at each end of the chain and the correlation length at T = 0 reaches a finite value ξq = 2J S/, which results directly from spin fluctuation effects. We derive here a simple phenomenological expression for the magnetic susceptibility of AF rings made of an even number n of Heisenberg spins S = 1 which, extrapolated to the thermodynamic limit, captures the main features of the

10.6 Application to the Spin-1 Haldane Chain

369

Haldane chain. The method is based upon scaling arguments [13, 14] developed in Section 10.2, which are applied to the theoretical data deduced for finite quantum rings of size n. The whole procedure provides a new insight into the gap and the finite correlation length at T = 0, and results in a closed expression available for fitting experimental data, as demonstrated for two Haldane chain compounds Y2 BaNiO5 and Ni(C2 H8 N2 )2 NO2 ClO4 . We use here the thermodynamic data of the finite AF rings of n spins S = 1 obtained by exact diagonalization of the spin Hamiltonian H = J Si Si+1 for n up to 10, and by the density-matrix renormalization group (DMRG) technique for n = 16 and 20. Periodic boundary conditions have been imposed to minimize finite size effects, while only even n values have been considered to avoid frustration effects. A standard DMRG procedure was used to construct the spin Hamiltonian matrices in the DMRG basis [43]. It might appear surprising that the DMRG method, in which usually the ground-state and one or two excited states are targeted in each iteration, can provide accurate thermodynamic properties. In fact, it is well known that, at each iteration, the DMRG space, which contains the lowest energy state, has substantial projections from low-lying excited states, so that these can be well described in the chosen DMRG basis. A description of the method is given in Refs. [44, 45]. Figure 10.18 shows ∂ log(T )/∂ log(χ T ) vs. T obtained from the data computed for AF rings of n spins-1, with n = 6 to 20. In both the high and the low-temperature regimes, the data are positive and approach a straight line which intersects the axes near the origin at T = 0. This indicates that an AF exponential solution of the type (10.4b) is relevant in either range. The high temperature solution χT = CHn exp(−WHn /T ) is much the same for all n values, and valid for T > TM where ∂ log(T )/∂ log(χ T ) = 1 (this is where the magnetic susceptibility χ is maximum). The low temperature solution χ T = CLn exp(−WLn /T ) is available for T < Tm where ∂ log(T )/∂ log(χ T ) = 0.5 (this is where χ/T is maximum). The high and low temperature regimes are described by different straight lines for T > TM and T < Tm in the Arrhenius plot of Figure 10.19. The same data are also shown in Figure 10.20 in a more traditional representation of χ vs. T /J . The corresponding Cs and W s are listed in Table 10.3, and their dependence on 1/n is displayed in Figure 10.21. The Curie constant in the high temperature regime is CH ∝ 0.673, within 1% of the expected S(S + 1)/3 value. The associated activation energy, namely the actual Weiss temperature, approaches WH = 1.44 J for all n, which is close enough to the value 4J/3 deduced analytically for a ring of 4 spins. In the low temperature regime, CLn = 2/n, which is the expected value for a singlet–triplet spin configuration well separated from the high-energy states. The associated WLn is precisely the singlet–triplet gap, (n), that is directly deduced by computation for finite chains (see Table 10.3). It decreases as n increases, and its dependence on n is well approximated by the power law 0.421 + 6.5n−1.74 (in J unit). In the n → ∞

370


Fig. 10.18. ∂ log(T )/∂ log(χT ) vs. T /J deduced from exact calculations of the susceptibility of AF Heisenberg rings of n spins S = 1 for n = 6, 16 and 20. Asymptotic behaviors are observed in the high and low temperature regimes, namely above TM and below Tm .

Fig. 10.19. Variation of χT (T ) for finite AF Heisenberg rings of spins S = 1, shown as log(χT ) vs. J /T , for n equal to 6, 8, 10, 16 and 20. At high temperature, we observe a unique Arrhenius regime, whose activation energy is WH ≈ 1.44 J. Below Tm , distinct Arrhenius laws are deduced, whose Curie constant is CL = 2/n and the activation energy WL reflects the Haldane gap.


371

Fig. 10.20. Plot of χJ /Ng 2 µ2B vs. T /J for n equal to 6, 8, 10, 16 and 20. The best values of the coefficients C1n , W1n and C2n , W2n characterizing the low and high-temperature regimes are given in Table 10.3. Table 10.3. Best parameters characterizing the fits of the magnetic susceptibility of AF rings of n Heisenberg spins S = 1. n

1/n

/J

CLn

WLn /J

CHn

WHn /J

C1n

W1n /J

C2n

W2n /J

4 6 8 10 12 14 16 18 20

0.2500 0.1666 0.1250 0.1000 0.0833 0.0714 0.0625 0.0555 0.0500

1.000 0.721 0.594 0.525 0.502 0.486 0.478 0.469 0.457

0.486 0.329 0.248 0.193

0.999 0.720 0.593 0.524

0.680 0.674 0.673 0.673

1.495 1.444 1.438 1.439

0.204 0.178 0.145 0.132

0.769 0.605 0.512 0.475

0.506 0.544 0.558 0.561

2.087 2.090 1.916 1.844

0.162

0.483

0.673

1.437

0.132

0.475

0.561

1.844

0.191

0.523

0.673

1.438

0.128

0.463

0.561

1.819

∞ 0.0000

0.421

0.125

0.451

0.564

1.793

limit, it tends towards a finite value that may be compared to the Haldane gap, /J ∝ 0.41. We have also checked whether two superimposed exponentials could describe the susceptibility at all temperatures (Figure 10.22). The optimization has been achieved with χ (T ) rather than χ T (T ), because more weight is given to the data in the range of the susceptibility maximum where both exponentials contribute a sizeable amount. The best values of the different parameters are given in Table 10.3.

372


Fig. 10.21. Variation of the parameters CLn , WLn , CHn and WHn (in J unit) characterizing the asymptotic low and high-temperature Arrhenius regimes of the χT (T ) product.

Fig. 10.22. Best values of the coefficients C1n , C2n , W1n and W2n (in J unit) characterizing the overall temperature dependence of the susceptibility of AF rings of n Heisenberg spins S = 1 in a fit with two exponentials.


373

Clearly, the C coefficients need to be related by CHn ≈ C1n +C2n and CHn WHn ≈ C1n W1n + C2n W2n to reproduce the main features in the high temperature limit. Similarly, we need CLn ≈ C1n and WLn ≈ W1n in the low temperature regime. These constraints are pretty well realized, as noted in Table 10.3. The resulting fit is very good (Figure 10.20), and even becomes excellent on increasing the number of spins. For all these rings, we propose the following expression of the χT product (normalized to Ng 2 µ2B /k) χ T = C1n exp(−W1n /T ) + C2n exp(−W2n /T ) for T /J > 0.1

(10.12)

For the Haldane chain (n → ∞) limit, the best-fit parameters are C1 = 0.125, W1 = 0.451 J, C2 = 0.564 and W2 = 1.793 J.1 In Ref. 46, the authors have used the above equation to analyze the magnetic data of Y2 BaNiO5 , a typical AF S = 1 chain system. The best fit parameters agree with our prediction, provided that J = 300 K which matches with previous findings (J = 285–322 K) [47]. Note that defects are expected to have very different effects in gapless 1D systems and Haldane chains [48]. In the former, they reduce the correlation length, and the magnetism obeys the Curie-like contribution of the finite segments with an odd number of spins. In turn, for the Haldane spin-1 chain, characterized by a finite correlation length at low temperature, the valence-bond-solid (VBS) model suggests a free spin-1/2 at each end of the segments, giving a staggered susceptibility, but there is no significant change in the gap value. We have extended this analysis to the magnetic behavior of Ni(C2 H8 N2 )2 NO2 ClO4 (denoted NENP) which is the archetype of the Haldane gap systems [49]. A small temperature independent contribution χ0 , which is observed to depend on axial symmetry, has been introduced. The agreement between theory and experiment is excellent for the three crystal axes, as may be observed in Figure 10.23 [50]. We need in this case J = 43 K along both axes to match the paramagnetic Curie–Weiss temperature which is much the same along all axes. The effect of the known anisotropy of this system is that the Haldane gap which we deduce from the fit ranges from 0.53J along the a axis to 0.40J along the b axis when we expect 0.451J for the isotropic crystal. To our knowledge, Eq. (10.12) is the only expression available to describe the behavior of the Haldane chain over the whole temperature range. At high temperature, everything behaves initially as in any system sitting at a lower critical dimensionality: an exponential solution of the type (10.4b) is found, as in the case of the classical Ising chain with nearest neighbor interactions. Note that, in the low temperature regime, gapped AF chains are usually described by the expression χ = AT −1/2 exp(−/T ) [51]. The T −1/2 factor which follows from field-theory mapping [52] is essentially related to the relativistic magnetic 1 In the thermodynamic limit, the coefficients have been deduced by extrapolating the 1/n

dependence of the Cs and W s, using third order polynomials.

374


Fig. 10.23. Fit of the magnetic susceptibility of NENP along two crystallographic axes using Eq. (10.12). From the Weiss constant WH = 1.793J , we deduce J = 43 K.

properties in the nanometric scale magnon dispersion [53], and has further been quantitatively confirmed by Monte-Carlo calculations [54]. Actually, it can be pointed out that this expression, which is dominated by the exponential, does not differ significantly from the proposed approach, even for T /J ranging from 0.2 to 0.05, giving = 0.409 J. Further, it becomes irrelevant at higher temperatures, since little can be inferred from the magnitude of the prefactor, A. In the proposed model, we observe at low temperature the terminal stages of the ordering of a different Ising-like chain, where the Curie constant bas been divided by a factor five and the activation energy by a factor three. Such behavior could be explained by assuming that the n individual moments of the initial chain are not permitted to order completely in a single process where χ (T ) would grow from 0 to ∞ as is described in Section 10.2. The initial chain of n spins, rather, is rearranged as a new chain of N/5 AF segments of five spins each, with an uncompensated spin S = 1, due to the unbalance of the up and down moments in the correlated state of each segment. The Haldane gap would correspond to the renormalized interaction from segment to segment. This implies that some sort of dichotomy occurs, at an early stage, whereby a finite length of five atomic distances is selected for each segment and the ordering is made in two stages: the former accounts for the short range ordering 0 < ξ(T ) < ξq which is responsible for the cohesion of each segment; the latter, ξq < ξ(T ), with the Curie constant divided by five, describes the divergence of the correlation between the newly defined segments. The expression (10.12) displays two simultaneous contributions accordingly. The segmentation length ξq = 5, which comes

10.7 Conclusion

375

from the ratio of the Curie constants, turns out to be of the same magnitude as the finite correlation length ξq = 2J S/ predicted for the Haldane chain in the T = 0 limit [42]. Maybe, it is not much of a surprise, after all, if the susceptibility does not vary very much once we reach rings of n > 10 spins, large enough to contain several segments of size ξq . Interestingly, such rings already contain all the elements which are required for describing the physics of the system.

10.7 Conclusion We have illustrated in this chapter the pertinence of a strategy that extends to the description of correlated systems, in general, the powerful ideas of scaling previously reserved for single phase transitions. Of particular interest, for this purpose, is the plot of ∂ log(T )/∂ log(χ T ) vs. T . This alternative representation of the experimental evidence allows one, in one single process, to establish the existence of a given scaling and to fix the extent of its validity range. It is then possible to comment on the physical justifications of these limits and to determine, within these limits, the pertinent parameters characterizing the particular scaling that is requested. On the basis of the sign and magnitude of these parameters, it seems possible to proceed with the classification sketched in Figure 10.1, and to extend the notion of “universality class” to these systems that stand at or below a lower critical dimension.

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Index

a Alternating chain model 123, 203–206 Anthracenetetrone 240 Azido 200, 203–205, 217–218 b Bis(dithiolato)metallates 131, 143–146, 240–241, 243, 244–246 Bis(dithiolato)metallates, see also Metallocenium bis(dithiolato)metallates Bis(heptamethylindeny)iron(II) 250 c Canted antiferromagnetism 79–81 Chiral magnets 41–68 [Co(C5 Me5 )2 ][TCNE] 232 Cobalt hydroxide carboxylates 263, 354, 356–361 Cobalt imidazolates 272, 273 CoHMPA-B bis(2-hydroxy-2methylpropanimido)benzene 247 Conductivity 105–155 Copper hydroxide layers 266–269, 352–355 [Cr(C5 Me5 )2 ][TCNE] 232, 242 Cr(NCS)4 126–130, 131 Critical constants 77, 82, 347–375 Cu Phthalocyanine 110–111 d Dawson-Wells ions, see Polyoxometallates Decaethylferrocene 249 Dicyanamide, see M[N(CN)2]2 Dicyanofumarate salts 233–235, 242 Dicyanomethylene 248

2,3-Dicyano-1,4-naphthoquinones 236– 238, 243 2,5-Dichloro-3,6-dihydroxy-1,4benzoquinone 248–249 2,3-Dihalo-5,6-dicyanoquinone 235, 243 2,5-Dimethyl-N,N -dicyanoquinodiimines 239–240, 242 Dipolar-dipolar interactions 277, 352, 362 Dzyaloshinsky-Moriya interaction 42 e Electrochromism 337 Exchange between localized moments and conduction electrons, see RKKY model Exchange models 294–300, 306–322 f Faraday effect 44, 62–63 Fe clusters 209, 219–220 [Fe(C5 Me5 )2 ][TCNE] 225, 226–227, 230–233, 242, 249, 250 Hysteresis 231 Mössbauer 251–252 Specific Heat 230, 253–254 Structure 227, 251–256 [Fe(C5 Me5 )2 ][TCNQ] 225, 228–229, 238–239, 242, 247, 250 Structure 228–229 Ferrimagnetic 19 Ferromagnetic 6, 8, 23, 27, 76 Ferromagnetism and superconductivity 107, 153 Fisher chain 194, 200, 202, 209–211 Fisher model 115

380

Index

g Gd(III) and a nitronyl nitroxide radical 165–169, 170–173, 174–177, 180–184 Gd(III) 161, 164–169 Gd(III)-Cu(II) 164–165, 170 h Haldane chain 368–375 Heisenberg Model 78, 196, 197, 200, 253, 348, 351, 358, 361, 363, 366, 368, 370 Hexacyanobutadiene 242, 247–248 Hexacyanometallates 53–68, 105, 124–125, 127 Hexacyanometallates, see also Prussian blue Hexahalohalometallates 122–124 Hexathiocyanatometallates 124–128 i Ising model

189, 196, 253, 351

k Kagomé lattice 72, 267, 268, 269 Keggin ions, see Polyoxometallates l Ladder-type structure 178 Lanthanides 161–185 Light-induced magnetization

338–339

m M(CN)6 ]n− see Hexacyanometallates and Prussian blue M(NCS)6 ]3− see Hexathiocyanatometallates M(ox)3 ]3− see Tris(oxalato)metallate M[C(CN)3 ]2 , 71–73, 76, 85, 86 M[N(CN)2 ]2 , 71–100 magnetic behavior 76–82, 84, 94–98 structure 73–76, 79, 82–84, 87–93, 96, 99 Magnetic semiconductor 121, 122 Magneto-chiral optical effects 48–49 Magneto-optical effects 43–48 Magnetostriction 153 Magnets and conductivity 105–155 Magnets, chiral, see Chiral magnets,

Magnets, chiral, see Nitroxide chiral magnets, Manganese formate 269–271 McConnell model 3, 20, 25, 232–239, 250, 254–255 Mean field approximation 201 Mechanism for magnetic ordering 81, 82 Metallocene 1–38 magnetic properties 4–37 structure 4–37 magnets 223–227 Metallocenium bis(dithiolato)metallates 1–38 Metamagnetic 7, 8, 10, 11, 13, 14, 20, 30, 34, 35, 228–229, 236, 238, 241, 242, 243, 244 [Mn(C5 Me5 )2 ][TCNE] 232–242 [Mn(C5 Me5 )2 ][TCNQ] 227, 242 Mn(hfac)2 49–53 Molecular orbital analysis 300–302, 310–319 Monte Carlo Simulation of Magnetic Properties 189–220, 374 Mössbauer spectroscopy 251–252 Muon spin relaxation 251 [MX4 ]2− see Tetrahalometallates [MX6 ]3− see Hexahalohalometallates n N− 3 see Azido Nanoparticles 339–340 Nanoporous magnetic materials 261–280 Neutron diffraction 78, 94 Ni(C2 H8 N2 )2 NO2 CIO4 369, 373–374 Nickel carboxylate 263, 265, 366–369 NiCp*2 ][TCNE] 232, 242 Nitroxide 357–358 chiral magnets 49–53, 67 o Octamethylferrocene Optical effects 337

249–250

p Pentamethylferrocene 249 Perylene 112, 115, 143–146

Index Polychlorinated triphenylmethyl 273–278 Polyoxometallates (POM) 133–143 POM see Polyoxometallates Porous materials see Nanoporous Prussian blue 43, 53, 60–68, 161, 238–341, 263,264 critical temperatures 302–305 magnets 291–337 structure 385–387 synthesis 384–385, 388–390 r Relativistic magnetic properties 373–384 RKKY Model 107, 108–111, 120 Room temperature magnets 322 s Scaling see Critical constants Semiquinone 169, 178–180, Specific heat 230 Spin coupling mechanism 254–255 Spin crossover 72, 98–99, 271–272 Spin density 20, 26, 27, 253 Spin flop 80 Spin fluctuations 78 Spin frustration 72, 73

381

Superconductivity and magnetism 107–108 Superexchange 82, 170–173, 180–184 Superparamagnetic scaling 364 t TCNE see Tetracyanoethylene TCNQ see 7,7,8,8-Tetracyano-pquinodimethane (TCNQ) Tetracyanoethylene 169 7,7,8,8-Tetracyano-p-quinodimethane (TCNQ) 169, 238, 242 Tetrahalometallates 111–122 Thin layers 337 Tricyanomethanide see M[C(CN)3 ]2 Tris(oxalato)metallates 67, 105, 131, 146, 154, 202, 214–215 TTF–based electron donors 105–106, 111–143 v Valance bond configuration interaction 319–322 Vanadium carboxylates 269 x XY Model

351

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