Magnetoelectronics

Foreword

Scholars, politicians and pundits spoke of the 1950s as the beginning of the “Atomic Age.” The invention and use of atomic weapons were dramatic events during a dramatic time of history. The invention and development of semiconductor electronics and, more generally, of information science and technology have been less dramatic. Nevertheless, the growth of these technologies and their impact on world society is truly remarkable. Some scholars, politicians and pundits refer to the present era as the “information age.” Surely this era began with a whimper rather than a bang. In 1943, Thomas Watson Sr. (Chairman, IBM) proclaimed “I think there is a world market for maybe 5 computers.” In 1977, Ken Olsen, Chairman and founder of Digital Equipment Corp. (DEC), said “There is no reason anyone would want a computer in their home.” DEC is not longer in business, having been acquired by Compaq in 1998. Consider an example that demonstrates the accelerated progress of the field. In the late 1960s, the IBM 360 computer was heralded as a revolution in computing. Model 360/65, available around 1970, came with 1 MB or RAM in the form of magnetic core memory. A typical user might have 200 MB of off-line memory, in the form of a dozen or so tape drives, each the size of an armoire. Characteristic processing speeds were the order of microseconds. Today, an individual can purchase more computing power for roughly $200 in the form of a Personal Digital Assistant (PDA) that fits in your pocket. Its processor will work with clock speeds of nearly 1 GHz (nanosecond times scales). For another $100 one can purchase 200 MB of FLASH RAM in the form of a memory stick the size of your thumb. Analysis of the success of digital electronics often mentions Moore’s law: the number of devices on a semiconductor chip doubles every 18 months. It is perhaps less well known that the magnetic recording industry has also followed Moore’s Law, and for the past few years has sustained progress at a faster pace. During the 1990s, the areal density of bits recorded on a disk drive increased at a rate of about 60% per year, equivalent with a doubling time of about 18 months. From 1999 to 2003, the areal density increased at a rate of about 100% per year. This corresponds to a doubling time of 12 months, which is faster than Moore’s Law. This remarkable success of magnetic storage technology derives from a number of results of basic research over the past two decades. The research has been in the fields of physics, materials science, and device engineering, and has had the common themes of magnetism and conduction electron spin. As research and development continue to progress, those researchers on the leading edge are examining broader applications of these new materials and devices.

viii Foreword

For example, the high areal density of recording media has enabled the production of “mini disk drives” with dimensions of a few centimeters and capacities of nearly 100 GB. These are used for playing MP3 music files, among other applications. However, the time required to find and access any particular bit (or string of bits) of data on a disk drive is a few milliseconds, barely faster than access times twenty years ago. In semiconductor technology, high density nonvolatile FLASH memory is inexpensive, and FLASH is one of the fastest growing segments of the integrated semiconductor market. However, this kind of memory requires relatively long times (and high energies) to erase and write, has limited endurance, and individual bits cannot be addressed. It’s natural to ask if a novel device based on magnetism and using spin polarized conduction electrons can be used to make an integrated memory. At low density and bit count, such a Magnetic Random Access Memory (MRAM) would be superior to nonvolatile semiconductor memory. At high density and bit count, MRAM would avoid the slow access times and reliability problems of read heads and would be superior to magnetic media mass storage. The field known as Magnetoelectronics is based on using these novel materials and devices for integrated digital electronics applications. In a broader view, Magnetoelectronics is a novel kind of union of elements of physics, materials science, and electrical engineering. The goal is to create devices and architectures for digital electronics applications. Magnetoelectronics will never replace complementary metal on oxide semiconductor (CMOS) technology, but it recognizes that CMOS has some vulnerabilities. Magnetoelectronics may become established in a vulnerable area, for example as high performance bit addressable nonvolatile RAM. This feat alone would qualify Magnetoelectronics as a successful technology. If it becomes established in broader memory applications, it will qualify as a successful and important technology. Furthermore, the model of uniting elements from several disparate disciplines may become a paradigm for exploiting other vulnerable areas of CMOS. This book is written to be a resource for scientists, engineers and program managers who are becoming involved in Magnetoelectronics. This is an interdisciplinary field, and important contributions have come from the fields of physics, materials science, and electrical engineering. Contributions to new dimensions of Magnetoelectronics are coming from fields related to biology, biophysics, and biochemistry. Readers are expected to come from a variety of backgrounds and to have very different areas of expertise. This book also may be used as a graduate level text for students in any of the disciplines mentioned above. Much of the first chapter, “Introduction to Magnetoelectronics,” is written at an undergraduate level. This chapter is designed to be accessible to graduate students in one particular field, or to readers with advanced training in some specialized area but with little or no knowledge of Magnetoelectronics. It uses simple pictures and heuristic descriptions to introduce basic ideas of magnetism, the transport of spin polarized electrons, the mechanisms by which several magnetoelectronics devices operate, and basic architectures of MRAM. This chapter also provides some background material on the physics of semiconductors and of metals, also

Foreword ix

written at an undergraduate level. This is for the benefit of readers who may have had an undergraduate course in solid state physics in a long-forgotten past. It is also for readers who may never have had a course on this topic. Some other portions of Chapter 1 are “special topics” that are not treated elsewhere in the book, and are presented at the level of a graduate course. Similarly, all of the other chapters are written at a level appropriate for a graduate course. This is also an appropriate level for professional scientists who are moving into this area. This book is a remarkable anthology because each chapter is written by someone who made historically important contributions to the field. Prof. Bernard Dieny (Chapter 2, SpinValves) was a young Ph. D. scientist at IBM Almaden in the late 1980s and early 1990s, where he was involved with the development of the first spin valves and was first author on several seminal papers. Prof. Dieny is presently the director of the SPIN-TEC laboratory at Grenoble, France. Chapter 2 presents a thorough review of spin valve structures and the giant magnetoresistance (GMR) phenomena. Prof. Robert Meservey (Chapter 3, Spin-polarized Tunneling) can be described as a founding father of the field known as the Physics of Spin-Polarized Transport. His experiments at the Francis Bitter Laboratory at MIT in the early 1970s were the earliest demonstrations of spin-polarized transport in the solid state. These experiments were the beginning of a list of accomplishments and achievements in the field. Dr. Jagadeesh Moodera, also from the Francis Bitter Laboratory, is credited with the development of fabrication techniques for highly stable magnetic tunnel junctions that have large and reproducible values of magnetoresistance. While this is only one of his achievements, it continues to have a lasting impact on the field. Chapter 3 presents a broad review of spin-polarized tunneling phenomena. Magnetic tunnel junctions (MTJs) are an important class of devices and are discussed at length. Dr. James Daughton (Chapter 4, MRAM) can be described as a founding father of magnetic random access memory (MRAM). He was developing MRAM ideas as early as the 1980s, and he moved quickly to adapt MRAM designs to accomodate new spin-valve and MTJ structures. Nevertheless, technologies for MRAM were not developing very rapidly. In the late 1990s, several companies, including Motorola, decided that MRAM was worthy of substantially increased Research and Development. Dr. Saied Tehrani was a leader in the effort to assemble a remarkable group of basic and applied research scientists at Motorola, most of whom had little background in magnetism and magnetic materials. In a few years of dedicated research, this group has succeeded in bringing high performance MRAM chips to market. Chapter 5 discusses all aspects of MRAM technology, including important discussions on scaling for future memory generations. Prof. Paulo Freitas (Chapter 7, Magnetoresistive DNA Chips) has made many contributions to magnetism and magnetic materials. In the late 1990s, Prof. Freitas was one of the first scientists to recognize that biotechnology would be an important applications area for Magnetoelectronics. Similar to the group at Motorola, a relatively short period of a few years of research and development by the group of Prof. Freitas has succeeded in producing several

x Foreword

successful prototype DNA chips. These chips will be brought to market within a short time. Chapter 7 presents the physics and technology of biochips. Of equal importance it also discusses the biochemistry of assay techniques and processes. As for myself (Chapter 1, Introduction to Magnetoelectronics and Chapter 6, Broader Digital Applications of Magnetoelectronics), my Ph. D. thesis work at Cornell with Prof. R. H. Silsbee, who is also a founding father of Spin-Polarized Transport, was the “Spin injection experiment.” Many researchers view our experiment, along with the theoretical framework we developed, as keystones of spin-polarized transport and of Magnetoelectronics. In the early 1990s, I published papers that proposed bit-addressable MRAM and magnetic logic. Around 1992, Dr. Gary Prinz and I had some informal discussions about the fabrication of electronic devices that incorporated a patterned ferromagnetic element, and their use for applications in integrated electronics. We were among the first to used the word “magnetoelectronics,” and perhaps we invented the term. I have a continuing interest in a broad variety of magnetoelctronic device structures and in novel applications. Chapter 6 presents Magnetoelectronics in a perspective of broader applications in digital electronics, discussing topics such as dynamically reprogrammable logic and broad bandwidth analog to digital conversion. Finally, a comment about units should be made. Every research scientist has a preferred system of units. Most conversions between CGS and SI units are familiar, but conversions related to magnetic field may be an exception. The reader may wish to keep in mind the following conversions. In CGS units, an oersted and a gauss are essentially the same and both are commonly used as units of magnetic field. In the SI system, magnetic field is measured in kilo-amperes per meter (kA/m), and the conversion is that 1 kA/m ¼ 4p Oe. If you also remember that 1 tesla is 10,000 gauss, you will probably know all the necessary conversions.

List of Contributors

˚ kerman (231), Freescale Semiconductor, 1300 N Alma School Road, Chandler, AZ 85224, Johan A USA M.D. Amaral (331), Department of Chemistry and Biochemistry, Faculty of Sciences of the University of Lisbon, Campo Grande, 1000 Lisbon, Portugal J.S. Cabral (331), Bioengineering Research Group, Chemical Engineering Department, Instituto Superior Tecnico, R. Rovisco Pais, 1000 Lisbon, Portugal L.A. Clarke (331), Department of Chemistry and Biochemistry, Faculty of Sciences of the University of Lisbon, Campo Grande, 1000 Lisbon, Portugal James Daughton (205), NVE Corporation, 11409 Valley View Road, Eden Prairie, MN 55344-3617, USA Mark DeHerrera (231), Freescale Semiconductor, 1300 N Alma School Road, Chandler, AZ 85224, USA B. Dieny (67), SPINTEC, Unite´ de Recherche Associe´e CEA/DSM & CNRS/SPM-STIC, 38054 Grenoble Cedex, France Mark Durlam (231), Freescale Semiconductor, 1300 N Alma School Road, Chandler, AZ 85224, USA Brad Engel (231), Freescale Semiconductor, 1300 N Alma School Road, Chandler, AZ 85224, USA H.A. Ferreira (331), Physics Department, Instituto Superior Tecnico, R. Rovisco Pais, 1000 Lisbon, Portugal and INESC-Microsystems and Nanotechnologies, R. Alves Redol, 9, 1000 Lisbon, Portugal L. Fonseca (331), Bioengineering Research Group, Chemical Engineering Department, Instituto Superior Tecnico, R. Rovisco Pais, 1000 Lisbon, Portugal P.P. Freitas (331), INESC-Microsystems and Nanotechnologies, R. Alves Redol, 9, 1000 Lisbon, Portugal and Physics Department, Instituto Superior Tecnico, R. Rovisco Pais, 1000 Lisbon, Portugal D.L. Graham (331), INESC-Microsystems and Nanotechnologies, R. Alves Redol, 9, 1000 Lisbon, Portugal Jason Janesky (231), Freescale Semiconductor, 1300 N Alma School Road, Chandler, AZ 85224, USA Mark Johnson (1, 273), Naval Research Laboratory, Washington, DC 20375, USA Fred Mancoff (231), Freescale Semiconductor, 1300 N Alma School Road, Chandler, AZ 85224, USA V. Martins (331), Bioengineering Research Group, Chemical Engineering Department, Instituto Superior Tecnico, R. Rovisco Pais, 1000 Lisbon, Portugal Robert H. Meservey (151), Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

xii List of Contributors Jagadeesh S. Moodera (151), Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Jon Slaughter (231), Freescale Semiconductor, 1300 N Alma School Road, Chandler, AZ 85224, USA Saied Tehrani (231), Freescale Semiconductor, 1300 N Alma School Road, Chandler, AZ 85224, USA

Magnetoelectronics M. Johnson (Editor) Copyright q 2004 Elsevier Inc. All rights reserved.

Chapter 1 Introduction to magnetoelectronics Mark Johnson Naval Research Laboratory, Washington, DC 20375, USA

1.1

Introduction

The hallmark of a ferromagnetic material is that it displays spontaneous magnetization, developing a magnetic moment at temperatures below the characteristic ordering temperature Tc ; and this property can be used to create patterned thin film device components with bistable magnetic states. The magnetization state, with positive or negative orientation along some convenient axis, is stable at room temperature for common ferromagnetic materials. It has long been recognized that these bistable states can be correlated with binary ‘0’ and ‘1’ for digital applications. Early random access memories (RAMs) for computers were built from arrays of magnetic cells. Each cell was a torus of magnetic material, with bistable states described by clockwise or counterclockwise magnetization orientation. Arrays of cells were connected with rows and columns of wires, which were threaded through and around an arm of each torus. Since a magnetic field surrounds a wire that is carrying an electric current, and magnetic flux flows through the center of a wire coil, current pulses applied to the wires of a given row and column would locally apply sufficient magnetic field to the torus at the row/column intersection to set the magnetization state. Equivalently stated, the current pulses could write the bit state of the cell. Similarly, an inductively coupled voltage could be sensed by a wire, when an interrogating current was applied via another wire, for reading out the value of a bit. These toroidal cells were called cores (Campbell-Kelly, 1997), and gave rise to the term core memory. The invention of write and read heads allowed the application of similar principles to magnetic media. Each track on a disk or tape is broken up into bits, and the bistable orientation of the magnetization of the bit determines the binary value, ‘0’ or ‘1’. There are numerous recording schemes, but in one typical scheme each bit is made up of a pair of magnetization domains (a domain is defined as a region with uniform magnetization orientation) with colinear magnetization axes, and the bits are laid out end to end along the tracks. The bit state is determined by parallel or antiparallel orientation of the two domains. The magnetization states are ‘written’ using locally strong fringe fields from the pole faces of a thin film ferromagnetic write head. They are read by sensing the presence (or absence) of magnetic fringe fields associated with antiparallel (or parallel) magnetization of the two domains in the bit. Similar to the readout of early core

2 M. Johnson memories, reading stored values from magnetic media originally involved inductively coupled voltages sensed by a scanning pickup coil that floated above the moving track. Around 1993, this technology was replaced by an approach which used the anisotropic magnetoresistance (AMR) of a thin film ferromagnetic element to detect the magnetic fringe field (refer to Chapter 2). An intrinsic property of ferromagnetic metals, AMR means that the resistance of the material differs slightly when the electrical current is parallel or perpendicular to the material’s axis of magnetization (refer to Chapter 2). This proved to be a much more sensitive technique and, since the change, the density of bit storage in magnetic media has increased faster than Moore’s law. The yearly increase in areal density of 60% was further increased to roughly 100% in 1998 when giant magnetoresistive (GMR) materials were introduced in the magnetoresistive heads. In parallel with the basic research developments in the field of magnetism that were responsible for new magnetic media storage technologies, it was natural to revisit the original idea of ‘core memory’ and ask: Can magnetic materials be used in an electronic device and an integrated architecture in order to create some new kind of device with novel characteristics, useful for digital electronics? This question frames the emerging field that has become known variously as magnetoelectronics, spin electronics or spintronics. One approach, which can be described as conventional, is to incorporate a ferromagnetic component into a device structure and to take advantage of the properties of the ferromagnet for novel functionality. An example is the creation of a nonvolatile memory cell. The bistability of the magnetization orientation, which has nearly infinite durability, provides nonvolatile storage of a binary state. The goal of conventional magnetoelectronics is to identify the performance advantages that a new approach offers, and then to invent and develop appropriate devices and architectures, along with viable manufacturing and materials processing technologies that are compatible with the dominant semiconductor industry, complementary metal oxide semiconductor (CMOS). This approach addresses conventional ideas of information processing and conventional parameters of operation. Nevertheless, binary information is represented by a magnetization orientation rather than a capacitance or voltage, and this category of devices and applications represents a paradigm shift for digital electronics. Another approach, which can be called unconventional, is to address the magnetic moment of an individual electron (equivalently, its quantum mechanical spin), and to manipulate the spin to achieve some novel scheme of information processing. The ‘device’ can be a single electron or a small population of electrons, and the electrons can be itinerant or localized. This approach addresses unconventional ideas of information processing such as ‘quantum computing’ or ‘quantum cryptography’. Here the goal of spintronics is to identify appropriate spin systems that may be viable and to study their relevant characteristics, such as the spin coherence time. The focus of this book is the first approach, conventional magnetoelectronics. However, basic issues and characteristics of spin-dependent transport are often relevant to both subfields, and occasionally reference to more esoteric, unconventional spintronics will be made. The remainder of this introduction gives a brief overview of the first approach.

Introduction to magnetoelectronics

3

Between 1995 and 2001, research and development expenditures in the US in the field of magnetoelectronics doubled roughly every 2 years, with the growth rate slowing a little after 2001. Research funding is a complicated, nonlinear phenomenon, and this tremendous rate of increase has, in turn, focussed attention on spintronics. This ‘positive feedback’ has helped to sustain the growth of the field. But there are also objective, intellectually defensible reasons for optimism. From a broad viewpoint, the basic research advances in spin transport and magnetic materials have been applied with great success to the magnetic recording industry, and the idea of extending this success to integrated applications is plausible. In a more focussed view, there are specific characteristics of prototype magnetoelectronic devices that offer significant performance advantages. An analysis of the competition is an appropriate beginning of the overview. The dominant semiconductor technology, based on CMOS field effect transistors (FETs), is successful for a number of reasons that are readily articulated (Keyes, 1989). (i) The output levels are standardized. The HIGH (binary ‘1’) and LOW (binary ‘0’) output levels are pinned to the supply voltage VDD and ground. These stabilized levels can be transmitted to subsequent devices where they are used as inputs. Equivalently and succinctly stated, CMOS FETs have sufficient gain to enable fanout. (ii) The inputs are tolerant of fluctuations. Voltages that fall in a reasonable range of values are accepted as appropriate input levels. Thus, the devices operate using relatively large input margins so that mass replication of devices and massive device integration are possible. (iii) The signal-tonoise ratio is high. Voltage levels are interpreted as ‘l’s’ and ‘0’s’ with a high level of accuracy. (iv) There is good electrical isolation between input and output. (v) The devices are scalable and inexpensive. For these reasons and others, CMOS technology dominates about 99% of the world semiconductor market. Despite all of its success, CMOS devices are far from ideal for memory applications. Storage of a binary value is based on capacitance: A capacitor is either uncharged (‘0’) or charged (‘1’). While Coulomb forces are useful for generating and transmitting the relatively large voltages characteristic of CMOS devices, these same forces are a disadvantage for creating and maintaining bistable storage states. In other words, capacitors tend to leak charge. The strong Coulomb attraction between opposite charges causes leakage current across the capacitor’s dielectric. For high density dynamic random access memory (DRAM), the capacitor at the heart of the memory cell discharges in roughly 10 ms. DRAM is the leading example of volatile memory: stored data must be refreshed every few milliseconds. For these volatile memories, power is dissipated at all times, not only during read and write operations. This high quiescent power can be a performance disadvantage and, furthermore, volatile memories are unreliable to the extent that a power interruption destroys memory. It is relatively simple to articulate the most desirable attributes of an integrated memory cell (Brown and Brewer, 1997). Nonvolatility is at the head of the list, and other attributes include fast write, read, erase, and access times; low operating power; and high durability. The CMOS

4 M. Johnson approach to nonvolatile memory, nonvolatile random access memory (NVRAM), is based on the capacitance of a ‘floating gate’. In a floating gate cell, a thick dielectric layer separates the channel of an FET from its gate, and a small metal island is fabricated inside the dielectric (Sharma, 1997). This island can be uncharged (‘0’), or it can be charged (‘1’) by tunnel injection of electrons from the gate at high voltage. The charge state of the island determines the capacitance between the gate and the channel, and therefore the bit state of the cell can be read out as a voltage level. The dielectric is thick in order to prevent leakage currents, and nonvolatile states are stable for years. A result of the thick dielectric, however, is that charging times (write times) and uncharging times (erase times) are quite long, the order of 10 ms or more and 1 ms or more, respectively. Write and erase processes require relatively high voltage for long times, and the energy associated with writing or erasing a bit is quite high, 1027 and 1025 J, respectively. Furthermore, charge carriers tunneling at high voltage eventually degrade the dielectric, and floating gate cells have limited durability. Inexpensive FLASH memory cells may degrade after 103 cycles, and more expensive electrically erasable programmable read only memory (EEPROM) has a durability of roughly 105 cycles. The performance advantages of the magnetoelectronic approach are now apparent. Because of the intrinsic bistability of ferromagnetic elements, magnetoelectronic devices are natural memory cells. Magnetic switching times (read, write and erase times) are a few nanoseconds, and the energy per bit associated with these processes is about 10210 J. Furthermore, although durability depends on details of the device, it has been shown to be essentially infinite for at least several device prototypes. Thus, the magnetoelectronic paradigm can offer improvements by several orders of magnitude over CMOS floating gate NVRAM in categories of speed, energy consumption and durability. The promise of realizing these advantages has been the true driving force for the field. As magnetoelectronics seeks to generalize its success in magnetic media recording technology by expanding into integrated electronics, research and development in a variety of fields will become important. Physicists, materials scientists and electrical engineers bring unique expertise, and unique backgrounds, to the technology. This volume is written to be a resource for this eclectic group of researchers and engineers. Some topics and issues may seem trivial to some readers, but will be entirely new ground for others. This chapter is written to provide a background for the volume. It anticipates the needs and interests of readers from a wide variety of fields, necessarily having a wide variety of backgrounds. Section 1.3 offers a review of very basic ideas of transport phenomena in semiconductors and metals, and can be skipped by those readers who have had the equivalent of an undergraduate course in solid-state physics. Finally, with the expectation that individual readers will skip selected sections, this chapter has been written with some small amount of redundancy. A few topics and issues are treated briefly at first, and receive deeper attention in a subsequent section.

Introduction to magnetoelectronics

1.2

5

What is magnetoelectronics?

To follow the conventional approach of magnetoelectronics, incorporating a ferromagnetic material into an integrated device structure involves four related topics. (i) Ferromagnetic materials are unique because they have the property of spontaneous magnetization. Using magnetic engineering, this property must be used to construct device elements with appropriate, stable magnetization states. (ii) Since the magnetic state is a local property of the material, the ferromagnetic device element must be capable of communicating its state to the outside world, preferably in a nondestructive way. At the core of spintronics is the realization that the ‘spin’ states of itinerant conduction electrons can be used for this function. (iii) For device output to be electronically integrated, the ‘spin’ state must be converted to something that can be manipulated with standard electronics, either a voltage or current. (iv) There is a similar constraint at the input end. The device state (the magnetization state of the ferromagnetic element) must be set by current or voltage levels. (i) Spontaneous magnetization is a gift from nature. This is unlike any other property of other materials classes. Indeed, the spontaneous magnetization of lodestone has been known since ancient times, but a clear and complete theory of ferromagnetism (with, for example, the ability to predict transition temperatures) is lacking today. Some of the details of ferromagnetism will be discussed in later sections, but we can begin by stating that every conduction electron has an associated magnetic dipole moment. In a ferromagnetic material, a fraction of the dipoles in a region called a magnetic domain spontaneously order at room temperature. This is a local property of the material, and this property scales down to small sizes. For digital magnetoelectronic devices, a ferromagnetic component, or device element, is fabricated with a uniaxial anisotropy axis. This means that the spontaneous magnetization will have positive or negative orientation along this axis. The result is the existence of bistable states that take the form of these two stable magnetization orientations. The bistable states are intrinsically nonvolatile. Thus, nonvolatility is an intrinsic property of the material. Figure 1.1(a) shows a patterned ferromagnetic element, which will often be denoted in this chapter as F, and which is typically composed of a transition metal ferromagnet such as Ni, Fe or Co, or alloys such as Ni0.8Fe0.2 (Permalloy). When fabricated with an appropriate anisotropy, the ~ lies along a uniaxial anisotropy axis [^x in Fig. 1.1(a)], and has two stable magnetization M ~ is denoted in orientations, along positive (right) and negative (left) x^ : The vector magnetization M the figure by an arrow. The magnetization is set by an external magnetic field H; and the magnetic characteristic is graphically represented by the hysteresis loop, M vs H; shown in Fig. 1.1(b). ~ is positive, pointing to the right. As the field H is decreased, Starting at the top right ðH q 0Þ; M ~ follows the dotted line, and the dotted arrow denotes H decreasing from positive to negative M ~ still points to the right and the value of M at H ¼ 0 is called the values. At H ¼ 0; M remanent magnetization, Mr : Continuing to follow the dotted line, the field decreases further until ~ reverses orientation and becomes H ¼ 2HC ; the field value defined as the coercive field, where M

6 M. Johnson

(a)

(b)

M

H

M

MR

F x

f M=0 HS

H

(c)

B

H=0

HC

L

Fig. 1.1 An appropriately fabricated, thin ferromagnetic film has bistable magnetization states, with the magnetization oriented to the right or left along an easy magnetization axis x^ : (a) Thin ferromagnetic element F, lithographically patterned with minimum feature size f : (b) The magnetization states are graphically described by a hysteresis loop: an external magnetic field H with magnitude larger than Hs is required to set the orientation to the right, and a magnitude more negative than 2Hs is required to set the orientation to the left. When H is removed, the magnetization remains in the set orientation. The magnetization M at H ¼ 0 is the remanent value, Mr : The coercive field HC is the value of field such that the magnetization is zero, M ¼ 0: Dotted (solid) arrow refers to H decreasing (increasing) from positive (negative) to negative (positive) field values. (c) Dipolar fringe magnetic field B surrounds F in the same way that fields go from North to South pole of a bar magnet. These fields can act to disrupt the magnetization state of F, and are called demagnetizing fields.

negative, pointing to the left, for values H , 2lHC l: The magnetization follows the solid line as field H is increased from negative to positive values. Whereas HC is defined by the value of field for which the magnetization passes through zero, the saturation (or switching) field Hs is the field required to orient the magnetization completely. When fully oriented, the magnetization is said to reach its saturation magnetization value, Ms : For the ideally square hysteresis loop of Fig. 1.1(b), the remanent magnetization is the same as the saturation magnetization, Mr ¼ Ms : The hysteresis loop of Fig. 1.1(b) graphically demonstrates the bistability of element F. Using wording more familiar in digital electronics, F can be described as a latching, two-state system. It is interesting to note that Fig. 1.1(b) describes a magnetic field transducer with a large magnetic field gain. The mean internal field (inside F) is 4pMs ; which is roughly 1 or 2 T. In other words, if one could bore a small hole inside F and install a gaussmeter to measure magnetic field, one would measure a field of value 4pMs : However, a very small external field H < HC can be ~ Because the coercivity of typical F elements is on the order of used to control the orientation of M: 10 Oe, the magnetic field gain is bM ¼ 1000: This is one remarkable property of ferromagnetic materials. While this has long been used as the basis of transformers, it remains a solution in search of broader problems. (ii)

The magnetization state of a ferromagnetic element, such as that depicted in

Fig. 1.1(a), is a local property of the material. For digital applications, each of the binary values ‘0’ and ‘1’ is associated with one of the bistable states, ‘left’ or ‘right’, negative or positive along x^ :

Introduction to magnetoelectronics

7

To be useful, however, the magnetization orientation must be communicated to the external world, preferably in a nondestructive way. An equivalent statement is that the bit value must be sensed by some ‘readout’ process. One plausible technique is to sense the dipolar magnetic fringe fields that the F element generates. Figure 1.1(c) depicts an image that is familiar to everyone, from their earliest introduction to magnetic materials. Just as a macroscopic bar magnet generates magnetic field lines which emanate from the north pole and return at the south pole, a microscopic F element ~ that emanate from one end and close at generates fringe magnetic fields, described by field lines B the other. Within a few nanometers of the end surface of F, the magnitude of B is the same as the mean internal field, B ¼ 4pMs : Within 10– 100 nm of the end, the magnitude has decayed by an order of magnitude, and it further decays to the order of 1–10 Oe at distances of order 1 mm or more. When the magnetization of the element in Fig. 1.1(c) is reversed, the fringe fields are the same but with opposite direction. Sensing these fringe fields is the basis for ‘reading’ information from magnetic media, such as disks. The process is described in Chapter 2 and many details can be found in a number of excellent reviews (Zhu, 2003). The ‘bits’ are laid out, edge to edge, in tracks, and travel underneath a floating read head as the disk spins around. The head is composed of a magnetoresistive element biased by a current. The sensed voltage changes value when the magnetic field detected at the edges of the bits is positive, zero, or negative. Sensing these fringe fields is also the basis of one of the earliest integrated magnetoelectronic devices used in magnetic random access memory (MRAM) prototypes, which will be described in Chapter 4. A second plausible technique utilizes the spin state of the conduction electrons. Related concepts will be described in detail in following sections, but the basic idea can be described in a simple way. It is important to note that the following is a heuristic picture, which merely approximates an accurate model, presented later in the chapter. Figure 1.2(a) shows a ferromagnetic metal F, with uniform magnetization oriented along þ^x; in electrical contact with a nonmagnetic metal N. The magnetic moments of the itinerant conduction electrons in F are aligned along the axis of magnetization, as depicted schematically on the left side of Fig. 1.2(b). For ease of discussion, carriers with spins oriented along the positive (negative) x^ -axis will be called spin-up (spin-down). They can be described as spin-polarized conduction electrons. These electrons move around diffusively and carry with them a marker, their spin orientation, that indicates the magnetization state of F. If the spin state of some of these electrons can be sensed, the bit state of F can be determined. The itinerant conduction electrons native to N are not spin polarized. Their spin orientations are random. For ease of notation, unpolarized electrons on the right side of Fig. 1.2(b) are depicted with no spin axes to indicate random orientation. A bias source causes an electric current to flow from F to N. The current that crosses the interface is composed of spin-polarized electrons, and the polarized electrons can diffuse into N for a relatively large distance before their spin orientation is randomized. Figure 1.2(b) represents a snapshot of the

8 M. Johnson

(a)

F

N

I

(b)

x

Fig. 1.2 Heuristic picture of spin and charge transport in a system with ferromagnetic and nonmagnetic components. (a) Bias current I flows through a ferromagnetic material F in interfacial contact with a nonmagnetic material N. (b) Each electron that contributes to the electric current has a spin. In F, the orientations of the electrons are aligned (signified by parallel arrows) and the current is spin polarized. In the nonmagnetic material, most of the spins have random orientation (signified by the absence of an arrow) but a small number of spin-polarized electrons diffuse into N.

steady-state distribution of conduction electrons in F and N, near the F –N interface, under the bias current conditions of Fig. 1.2(a). Thus, electrons carrying a marker that indicates the magnetization state of F can be driven into a contiguous material by a process that is known as spin injection (Johnson and Silsbee, 1985). (iii)

It is necessary to sense the spin state of these electrons in order to infer the

magnetization state of F and thereby complete the readout process. For integrated electronics, the spin state should be converted to a current or voltage or, equivalently, a characteristic impedance. If we use light polarization as an analogy, then the ferromagnetic element F can be called a spin polarizer, remembering the important distinction that conduction electrons, unlike photons, are particles that move diffusively. Following that analogy, a second ferromagnetic film F2 can be used as a spin analyzer. In Fig. 1.3(a), ferromagnetic polarizer F1, with positive magnetization ~ 1 ¼ þM1 x^ Þ; is in electrical contact with a nonmagnetic region, which in turn is in orientation ðM electrical contact with ferromagnetic analyzer F2. The magnetization orientation of F2 is also positive. A bias source drives a current I through the structure and a voltage V is sensed from

Fig. 1.3 Spin and charge transport in F1– N– F2 and F1–I – F2 systems. (a) In a generalized device, ~2 ~ 1 and M ferromagnetic films F1 and F2 have parallel magnetization axes and magnetization orientations M that can be independently controlled, and F1 and F2 are separated by a thin layer of nonmagnetic metal or a thin, low transmission tunnel barrier. A bias current I flows through the device and the voltage across the ~ 2 parallel. (b) The intermediate layer is a nonmagnetic metal, N. Spin~ 1 and M device, V; is relatively low for M polarized electrons are driven from F1 to N and enter F2 with relative ease (low resistance). (c) The intermediate layer is a tunnel barrier, IT. The wave functions of electrons in F1 and F2 penetrate into the barrier. The overlap of up-spin electron wave functions is relatively large (low resistance tunneling). ~ 1 and M ~ 2 antiparallel. The voltage V across the device is relatively large. (d) The generalized device for M

Introduction to magnetoelectronics

9

(e) The spin-polarized electrons driven from F1 to N enter F2 with relative difficulty (high resistance). (f) The overlap of up-spin electron wave functions in F1 with up-spin electron wave functions in F2 is relatively small (high resistance tunneling). (g) A schematic perspective view of a planar spin valve or MTJ device structure. Typical thickness tN is ,few nm p‘; and typical thickness tI is # 1 nm.

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end to end. Conceptually, the nonmagnetic region may be a nonmagnetic metal N, with thickness tN , or a thin, insulating tunnel barrier IT , with thickness tI . Spin and charge transport for the former case are depicted in Fig. 1.3(b). Spin-polarized current is injected from F1 into N. Using converse reasoning or, equivalently, the analogy of light polarizers, polarized spin-up carriers incident on the N –F2 interface are transmitted into F2 with relative ease, and with characteristically high conductance. This argument is easier to understand in a more rigorous way for the case of spin-dependent tunneling (SDT), depicted in Fig. 1.3(c) (Julliere, 1975). Here the quantum mechanical wave function of electrons in F1 and F2 penetrates into the insulating tunnel barrier, IT, and the probability of tunneling is proportional to the wave function overlap. Tunneling from F1 to F2 has a relatively high probability (is characterized by relatively high conductance) because there is a large density of states of carriers with up-spin orientation on both sides of the barrier. A rigorous calculation shows that the tunnel current is proportional to the density of states NðEÞ on both sides of the tunnel barrier. But the Pauli exclusion principle forbids transfer of an up-spin to a down-spin state, so the spin subband densities of states determine the tunnel current. The situation changes for an F1 – N – F2 or F1 – IT – F2 structure with antiparallel magnetization orientations [Fig. 1.3(e) and (f), respectively]. Once again, the tunneling case [Fig. 1.3(f)] is simpler to understand. The tunneling probability is relatively low because the density of states for spin-up carriers is high in F1 but low in F2, and tunneling between F1 and F2 is thereby characterized by a low conductance. The same argument is qualitatively true for transport in the F1–N –F2 structure with antiparallel magnetization orientation [Fig. 1.3(e)]. Up-spin carriers cross the N –F2 interface with relative difficulty, and transport is characterized by a low conductance. Thus, a second ferromagnetic film can be used as a ‘spin analyzer’. Figure 1.3(g) depicts a schematic of a generic magnetoelectronic device cell composed of two planar ferromagnetic ~ 1 is always pinned in one direction and the bit state is stored as the orientation of F2, elements. If M then an F1 –N–F2 or F1–I–F2 structure constitutes a cell in which readout is performed by sensing a relatively low or high resistance for cell states with magnetization orientations that are parallel or antiparallel, respectively. This simple model of a device cell captures the essence of conventional spin electronics. The spin state of an electron is ‘converted’ to a property associated with its charge, and spin becomes a new control parameter that can be manipulated and used to achieve new functionality in a device. In this example, the function is nonvolatile storage of binary information. More generally, any property of the ferromagnetic material, or of the spin state of the carriers, can be modulated with an associated effect on charge transport. Similarly, any useful property of the ferromagnetic material, such as magnetization-dependent strain (known as magnetostriction), becomes available as a control parameter. (iv) At the input end, the device state (the magnetization state of the ferromagnetic element) must be set by an integrated technique, one that uses current or voltage levels. Whereas conventional semiconductor electronics operates with capacitively coupled voltage pulses,

Introduction to magnetoelectronics

11

Word Line Write Wire F H

IW

Fig. 1.4 Binary information input for an integrated device. The external field H that sets the magnetization state of F is applied by inductively coupling a current pulse applied to an integrated, contiguous ‘write wire’.

magnetoelectronics uses inductively coupled current pulses. Figure 1.4 is a perspective view of a ferromagnetic element, such as a component of the spin valve or magnetic tunnel junction (MTJ) of Fig. 1.3(g), along with an integrated write wire. In real applications, cells might be addressed using bit and word lines that also function as write wires. A thin insulating layer separates F from the write wire, which is fabricated with a nonmagnetic metal such as aluminum or copper. When ~ circulates around the write wire with clockwise carrying a write current IW ; a magnetic field H orientation, following the ‘right hand rule’. When the write wire is sufficiently wide to cover the ~ is approximately constant near the surface of the write wire, and of length of F, the magnitude of H F, and H decays with a long length scale in the direction normal to the interface. Thus, current IW provides a nearly homogeneous, local magnetic field that can be used to control the magnetization state of F. Since magnetization reversal in ferromagnetic films is rapid, occurring on a time scale of order 1 ns (Zelakiewicz et al., 2002), short current pulses can be applied through the write wire to set the magnetization state. A bipolar power supply is used to drive the write current. In the example of Fig. 1.4, a current pulse of positive polarity, þ2IW ; corresponds to a ‘0’ and sets the magnetization state negative along x^ and a current pulse of negative polarity, 22IW ; corresponds to a ‘1’ and sets the magnetization state positive. A subtle but important point is that the amplitude of the write pulse is set at þ2IW : This permits unique addressability of individual cells when memory cells are arranged in a two-dimensional array, incorporating an array of rows and columns of write wires. Details of write operations will be discussed in later chapters, but an introductory discussion is fairly simple. The amplitude of the write pulse applied to any row i or column j is set to provide half the required switching field value, aIW ¼ Hs =2; where a is a constant of proportionality for the inductive coupling. The field provided at cell ði; jÞ is then 2aIW ¼ Hs ; which is sufficiently large to orient the magnetization. Meanwhile, the field at any other cell on row i or column j is not adequate to change the existing magnetization state. This is called a ‘half-select’ write process. Having an acquaintance with the four topics discussed above provides a preliminary understanding of the technological underpinnings of ‘magnetoelectronics’. Next, issues related to real device applications can be analyzed.

12 1.2.1

M. Johnson How can spin be used for novel functionality?

This subsection introduces several applications where magnetoelectronics may have an impact, but we begin with a brief discussion that uses a broader viewpoint. The lifeline of a successful technology can be described as follows. It begins with a breakthrough appearance, typically fulfilling some particular need or offering unique advantages over an existing approach. After achieving this foothold, incremental improvements in design, engineering and manufacturing gradually increase the relative share of a market and expand the technology to new applications. The cycle of iterative improvements continues for generations, until the next new approach makes a breakthrough appearance and displaces the established technology from some area of applications. New approaches that seek a foothold are considered disruptive technologies, in contrast with a mature approach that enjoys incremental change. If the new technology succeeds at displacing the established technology from a majority of its applications, then it represents a paradigm shift – a completely new way of achieving a function (Kuhn, 1996). For any disruptive technology to gain a foothold in an established market, it must offer significant performance improvement. Generally speaking, one or more performance metric must improve by an order of magnitude, while all other metrics are competitively equal. The basic characteristics of magnetoelectronic devices can be listed simply. On the positive side, they (1) have intrinsic nonvolatility (equivalently, they are latching), (2) have fast switching speeds, (3) require low energy to switch, (4) can switch repeatedly with high durability, (5) retain their state with long endurance, (6) are scalable to small dimensions, (7) are fabricated from common metallic materials, (8) are not vulnerable to radiation damage, and (9) are lithographically processed with fairly standard techniques. On the negative side, and at the present state of research, they (1) do not have power gain, (2) have limited tolerance to variation of input levels, and (3) require processing steps not typically found on a CMOS production line. Furthermore, (4) scaling has not been successfully demonstrated at size scales below 100 nm. The discussion in the above section has offered an introduction to the positive attributes. The negative characteristics are treated in Section 1.2.2, but are worthy of a few remarks. (1) As mentioned above, a ferromagnetic element can be described as a transducer of magnetic field with magnetic gain, bM : The coercivity HC may be quite small, and the mean internal field 4pMs ; which is also the magnitude of the fringe field near the end of the element, is quite large. Thus, the magnetic gain can be the order of bM ¼ 4pMs =HC , 1000: This gain is similar to that offered by a transformer, which can give a current or voltage gain. Some spintronic devices have been designed in a way to provide current gain (Clinton and Johnson, 1999), however, prototypes that demonstrate significant gain have not been reported. A transformer cannot offer power gain, and there are no prototype spintronic devices that have come close to achieving power gain.

Introduction to magnetoelectronics

13

(2) For a given ferromagnetic element, and the associated magnetoelectronic device, the input levels are set by the value of the saturation (or switching) field Hs : For an ensemble of elements, or for a large number of switching events for a single element, this value does not reproduce with arbitrarily good precision. The study of the static and dynamic magnetization states of patterned ferromagnetic elements is presently at the forefront of basic research and is discussed in Chapter 5. An understanding of the key parameters that determine domain formation is crucial to improving the reproducibility of Hs : (3) While the introduction of a ferromagnetic metal, such as Ni, Fe or Co, to a CMOS production line is anathema to most process engineers, the successful introduction of Cu as a metalization layer offers hope for a more generalized acceptance of nonstandard metals. A greater concern is that most ferromagnetic device components are fabricated by dry etch, using new and original recipes uniquely developed for a given ferromagnetic material. These etching processes are nonstandard, and pose a risk of damage to underlying CMOS levels. While the damage may be repaired by a subsequent anneal, care must be taken that the anneal does not damage the magnetic device structure. (4) In many prototype devices, the aspect ratio of the ferromagnetic element [the ratio L=f in Fig. 1.1(a)] has been diminished in an effort to reduce the area of the cell. The consequent removal of shape anisotropy as a source of uniaxial anisotropy has made the reproducibility problems (2) worse. While individual prototypes with critical feature sizes f smaller than 100 nm have demonstrated successful operation, large-scale prototype arrays with such small feature sizes have not yet been demonstrated. Given these attributes, both positive and negative, one must analyze the capabilities and deficiencies of existing semiconductor technology in order to see where magnetoelectronics can make a successful breakthrough. In the subsections below, three applications areas are presented.

1.2.1.1

Nonvolatile random access memory

Because nonvolatility is a characteristic of the bistable states of a ferromagnetic element, magnetoelectronic devices are, intrinsically, nonvolatile storage cells and a natural application for the technology to pursue is integrated memory. The existing CMOS approach is based on the floating gate FET cell, discussed in some detail in Section 1.2.3. Historically, these devices have been called programmable read only memory (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM) and other acronyms, but the technology is based on a floating gate. Floating gate technology is highly successful, and has enjoyed many generations of incremental improvement. Some architectures are bit addressable, using one or two FETs for cell isolation and selection, and these memory chips with relatively high performance and low density are used in embedded applications. In other architectures (FLASH), the cells cannot be individually erased, but chips are fabricated with high density and relatively low cost. Cell size can

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be as small as 10 – 12f 2 : Some cell designs store 2 bits per cell, allowing cell size to shrink as small as 8f 2 : These inexpensive memories have become popular in consumer electronics (Campardo and Micheloni, 2003). Despite its success, the floating gate approach is made vulnerable by several weaknesses mentioned earlier. To reiterate a few key points, the write times of roughly 10 ms are slow, and the erase times of order 0.1–1 ms are glacially slow. Since the devices are drawing power during write and erase processes, energy consumption for writing and erasing is large. Tunneling at high voltage to move charge on and off the island gradually wears down the dielectric, resulting in poor endurance. Some devices wear out after a few thousand write/erase cycles, and few device designs withstand more than 100 000 cycles. Finally, floating gate cells are susceptible to radiation damage. For nonvolatile memory, magnetoelectronics can offer order of magnitude improvement in all of these performance categories. The write process also accomplishes an erasure, and writing times are on the order of a few nanoseconds, about 103 (105) times faster than floating gate write (erase) times. The operating power is about the same, so energy consumption per write (erase) cycle is smaller by 1023 (1025). Magnetoelectronic cells have nearly infinite durability and endurance, with many prototype designs tested at .1015 cycles. Finally, most spintronic cells are not susceptible to radiation damage. If magnetoelectronic memories can be manufactured with packing densities that are comparable to CMOS, 10 – 12f 2 ; it is plausible that spintronics can make a breakthrough and gain a foothold in the growing nonvolatile memory market.

1.2.1.2

Reprogrammable logic

Application-specific integrated circuits (ASICs), an extension of CMOS into new microprocessor applications, were extremely successful in the 1990s. However, the cost of engineering and manufacturing an individual ASIC chip can be prohibitive. Programmable logic offers a relatively inexpensive and flexible alternative, and has become quite successful in recent years. The typical CMOS approach is known as the field programmable gate array (FPGA). A chip is composed of an array of roughly 100–1000 cells. Each cell has an arrangement of FETs, called a Boolean function unit (BFU). Like any logic gate, the BFU receives two inputs, processes a result and sends out one output. However, the BFU has several additional inputs and the particular Boolean function that the unit performs is defined by values applied to those inputs. The cell contains a look-up table (LUT) which stores the values that will be applied to these controlling inputs. Finally, the cells are connected together by a network of switches. The FPGAs are mass produced, and an engineer modifies the FPGA for a specific application by first determining the function of each cell, second choosing the values for the LUT of each cell, and third designing the connectivity of cells. In most FPGAs, the BFUs are CMOS FETs, the LUTs are SRAM, and the connecting switches are typically either fuses or antifuses. Once the connecting paths are set, for example, by blowing all fuses except those for the desired paths (or by forming ‘antifuses’ along

Introduction to magnetoelectronics

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a desired path), the chip has been programmed and its function cannot be changed. Furthermore, since SRAM is volatile and loses memory if power is interrupted, FPGAs that are programmed for a specific application must be packaged with a ROM chip having backup LUT data. In competition against ASICs, FPGAs have enjoyed great success, but the approach is vulnerable. FPGAs are programmable, but it would be a much more powerful technology to offer reprogrammable logic. The function of a reprogrammable chip could be changed, and could be changed numerous times. In other words, a hardware upgrade becomes possible by purely using software. Reprogrammability allows circuits to be self-healing. It also allows systems engineers to reprogram circuits to perform new functions, offering endurance and diminishing the size of the required system. The advantages are obvious for remote applications such as a space platform. The magnetoelectronic approach to reprogrammable logic will be discussed in detail in Chapter 6.

1.2.1.3

System on a chip

While CMOS technology has become highly developed, the functions of digital circuit components have become differentiated. Described in more detail in Section 1.2.3, information processing and Boolean logic operations use planar FET cells, whereas memory (DRAM) typically uses ‘vertical’ cells with trenched capacitors. Because the processing steps are quite different, planar and vertical cells are not fabricated on the same chip, and it follows that logic and high density memory cannot easily share the same chip. Static random access memory (SRAM) is a high performance memory that uses planar cells, but the cell size is relatively large, packing densities are small, and SRAM memories have relatively small bit count. One of the challenges of magnetoelectronics is to develop CMOS compatible processing, so that MRAMs can be fabricated on the same chips as planar cells, facilitating the combination of memory and logic on the same chip. Going one step further, proposed ideas for reprogrammable and dynamically programmable logic use the same cell that is used for memory (Johnson, 2000b). Thus, large-scale integration of memory and logic is automatically achieved, and this is important for high performance computing. More specifically, the capacity of high performance on-chip cache memory may be increased by an order of magnitude. Furthermore, sectors of cells can be dynamically apportioned to perform as logic or memory according to changing needs. Finally, many embedded applications involve the acquisition of data from a sensor, with subsequent signal processing and storage of results. Many of the relevant sensors are magnetic, and these can be fabricated on the same chip as the magnetoelectronic logic and memory array, using the same processes (or subsets of the same processes). The result is a true ‘system on a chip’, described in greater detail in Chapter 6, with potential advantages in performance and cost.

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1.2.2

What are the key engineering issues magnetoelectronics must solve?

Challenging and important problems exist in a number of subfields of magnetoelectronics. A variety of prototype device structures have demonstrated performance properties that are more than adequate to compete as nonvolatile storage cells: good readout voltage levels, good signal-tonoise ratio, low operating power, good endurance and good durability under a wide range of operating conditions. However, several issues must be overcome before the technology is successful in the market. Even low density memories for embedded applications require capacities of roughly 1 Mb. For a product to reach viability, operating margins must be tight so that manufacturing yields are viable. The fraction of faulty bits must be on the order of one in 105 or better.

1.2.2.1

Margins on input levels

A key margin that limits magnetoelectronic device development is reproducibility of the switching threshold. Successful operation of half-select processes requires that repeated application of single write pulses IW must fail to alter the magnetization state, i.e. fail to ‘disturb’ the bit, but that application of two simultaneous write pulses must create the desired orientation with extremely high probability of success. Referring to Fig. 1.1(b), the hysteresis loop of each element must be sufficiently square that local application of field Hs =2 will not alter the magnetization orientation. Furthermore, the shape and characteristic saturation value Hs of each loop must reproduce within a narrow margin (of order a few percent) for each switching event. A more stringent requirement is that the loops for all elements must be identical within similar margins. Designing appropriate ferromagnetic elements involves basic research on the properties of magnetic materials, and is further discussed in Chapters 4 and 5. Details of the hysteresis loops and of magnetization switching depend on the statics and dynamics of domain formation. These are topics of intense materials research, along with related studies that might lead to the development of single domain elements. One approach involves film growth with a preferred crystallographic direction, in order to use an associated crystallographic magnetization anisotropy. Another uses a bilayer that incorporates a thin antiferromagnetic film to magnetically bias the magnetization of F. Engineering novel write architectures, for example, using sequences of pulses or write pulses from more than two write wires, may also solve this problem.

1.2.2.2

Margins on output levels

Equally important constraints exist on the reproducibility of the output levels. The problem can be illustrated with a simple example. Consider a device with average impedance of 100 V, 10% difference between low and high output levels, and a simple architecture that performs readout by

Introduction to magnetoelectronics

17

comparing output voltage with a standard, threshold value. Even with an infinite signal-to-noise ratio, average device impedance must reproduce within ^5% among all devices. If not, the low level of some devices will be confused with the high level of others. Achieving adequate readout margins involves device engineering and materials research. Spin valves in memory cells have average impedances of about 50 V and magnetoresistive ratios MR ¼ DR=R of roughly 10% (refer to Chapters 2 and 4). These low resistance structures tend to require high bias currents. Resistance drifts related to heating, or long-term irreversible damage resulting from electromigration in the magnetic metal multilayers, can be problems that limit margins. MTJs in memory cells have average impedances of about 10 000 V and magnetoresistive ratios (at low bias) of roughly 40% (refer to Chapters 3, 4 and 5). While the larger MR is favorable for easy discrimination, the device impedance is determined by the thin tunnel barrier that separates the two ferromagnetic layers. The device impedance varies exponentially with tunnel barrier thickness, and thicknesses of only a few monolayers (0.7 –0.9 nm) are required to achieve the relatively low impedance of roughly 10 000 V. Because of the difficulty of controlling the barrier thickness, values of device impedance can vary by 50% or more across an 8 in. wafer for the earliest prototype arrays. Thus, reproducibility of output levels is a problem for both spin valves and MTJs. One approach for solving this problem involves research on materials that are characterized by higher values of polarized current. The transition metal ferromagnets (Fe, Ni, Co and their alloys) have polarizations of approximately 35 –50% (Soulen et al., 1998). Other magnetic materials, including half-metal ferromagnets such as chromium dioxide and Heusler alloys, may have polarizations approaching 100%. Since MR depends sensitively on spin polarization, substantially larger values of MR may be possible for spin valves and MTJs, greatly easing problems with output margins.

1.2.2.3

Scalability

For magnetoelectronic technology to succeed, patterned ferromagnetic elements are required to maintain their characteristics when fabricated with small minimum feature sizes, f : However, all of the factors that affect this scaling are not entirely understood, and this is an area of active research. Thermally stable spontaneous magnetization should persist at dimensions as small as f , 10 nm. The anisotropy energy of an element, which maintains the two stable magnetization states, is proportional to its volume. At small dimensions, this energy may be smaller than the thermal energy kB T; with kB Boltzmann’s constant. ‘Superparamagnetism’ refers to this thermally unstable regime. The high density applications of magnetoelectronics that are planned for the future require that elements must be patterned with feature sizes f comparable with, or smaller than, those that are promised for the CMOS roadmap. The limits of the superparamagnetic regime must be delineated so that the limits of spintronic scaling will be known. While thermal stability imposes a strict limitation on scaling, the dependence of switching field (saturation field) Hs on feature size f is also crucially important. For many materials,

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Hs increases as f decreases (Ruhrig et al., 1996; Kirk et al., 1997). This drives up the amplitude of write current and therefore of operating power, and becomes a performance obstacle. There are some materials that show weak dependence of Hs with f ; and continuing research is focussing on the design of elements and architectures that can achieve reliable switching with low power at very small feature sizes.

1.2.3

What is the existing technology where magnetoelectronics seeks to find market entry?

The entry and establishment of magnetoelectronics in integrated digital electronics markets depends on successfully challenging existing CMOS industry. This section provides a brief review of some features of CMOS technology. The CMOS FET is the device at the heart of the technology. The CMOS FET uses supply voltages of few volts, has power gain, and can be fabricated with feature sizes of order f ¼ 100 nm. The industry is divided between memory and digital information processing (logic) applications. The latter requires power gain for device fanout from one logic gate to a series of subsequent gate operations. Memory is typically based on a passive device, a capacitor, similar to the spintronic approach that uses passive magnetoresistive devices.

1.2.3.1

CMOS memory

Three standard CMOS approaches to memory, DRAM, floating gate, and SRAM, are depicted in Fig. 1.5(a)–(c). The architecture for a DRAM cell is shown in Fig. 1.5(a). The two charge states of a single capacitor C, charged or uncharged, store the binary data ‘1’ or ‘0’. A single select transistor, addressed with a word line, is used for both writing and reading the charge state of C. Since leakage currents deplete the charge below a detectable threshold in a time on the order of milliseconds, this memory cell is volatile and circuitry must be provided to read and rewrite (refresh) the charge state of each cell with a period of every few milliseconds. As discussed below, a DRAM cell can be fabricated with small dimensions, cell sizes are as small as 6f 2 ; and DRAMs have correspondingly large packing density. The architecture permits read, write and access times on the order of 10 ns. A floating gate cell is depicted in Fig. 1.5(b). The ‘floating gate’ is a small metal island embedded in the gate dielectric of an FET. The two charge states of the island, charged or uncharged, store the binary data ‘1’ or ‘0’. The states are written by tunneling charge onto the island at relatively high voltage, and are erased by tunneling charge off the island at a higher reverse bias. The gate dielectric is sufficiently thick that charge can be stored on the island for years, and the memory of this cell is nonvolatile. The value of the gate capacitance Cg is a function of the charge state of the gate. Thus, the datum stored in the cell is read by measuring the

Introduction to magnetoelectronics

(a)

19

(b) Word Line

Word Line Floating Gate

Storage Capacitor Bit Line

Drive Line

Bit Line

(c)

(d) TOP VIEW

L

Word Line VDD

f

D

S G

G Bit Line

gate oxide

D

S CROSS SECTION

(e)

select transistor storage capacitor CROSS SECTION

Fig. 1.5 CMOS device structures used in a variety of memory cells. Schematic cell for (a) DRAM, (b) floating gate NVRAM. (c) SRAM cell and logic diagram. (d) Top and cross-sectional views of simplified CMOS FET structure. (e) Cross-sectional view of DRAM cell, showing trenched capacitor.

capacitance Cg using the word and drive lines (Sharma, 1997). The floating gate storage cell is the basis of semiconductor NVRAM. Although writing and erasing are slow, read and access times are fast. Floating gate cells can be fabricated with dimensions as small as f ¼ 100 nm, but scaling is expected to be a problem below f ¼ 45 nm. However, density is often less critical for NVRAM applications and memories are produced using older production lines and larger feature sizes. Cell sizes are roughly 12f 2 ; but some designs fit 2 bits per cell and achieve cell sizes as small as 8f 2 : A static RAM cell is shown in Fig. 1.5(c), along with its associated logic diagram. Each cell has a combination of 4–6 FETs arranged as cross-coupled inverters so that the output is latched

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HIGH or LOW. After the bit state has been written, the latched state is maintained by the static supply voltage VDD : If power is interrupted, memory is lost and storage is volatile. On the other hand, the datum does not need to be refreshed as long as the supply voltage is maintained. The read, write and access times are all fast, and SRAM is the high performance, low power memory that is used, for example, as cache memory for your computer’s central processing unit (CPU). CMOS FETs are planar device structures. Figure 1.5(d) shows top and side views of source (S), drain (D) and gate (G) of a simplified device. The source and drain are typically fabricated by doping regions of the substrate with dimensions as small as f : A variety of lithographic techniques can be used to make the channel length L between source and drain smaller than f : Channel lengths have become so small that many FETs operate in a nearly ballistic, rather than purely diffusive, transport regime. The gate dielectric and gate metal G are then fabricated over the channel. As a general rule, current driven through the FET of Fig. 1.5(d) is proportional to f =L: FETs with substantial power gain, used for signal and logical processing, typically have larger dimensions than FETs used as select transistors in memories, which require little gain. By contrast, DRAM cells are not planar structures. Engineers have minimized their size by making vertical capacitors (Sze, 1998). As shown in the cross-sectional drawing of Fig. 1.5(e), a deep trench is etched in the surface of the substrate, the opposing faces are coated with a metal film, and the gap between the metal electrodes is filled with a dielectric. Using this remarkable ‘trenching’ technology involves hundreds of process steps that are uniquely different from the fabrication steps for planar FETs, and separate process lines are built and used for DRAM and for planar FET production. But this approach has resulted in a cell with area dominated by the area of the select transistor. Including pitch, the distance between adjacent cells, DRAM cells are as small as 6f 2 : This is a remarkable achievement when you consider that the smallest possible cell is determined by the area of crossing bit and word lines and has area of 4f 2 : Note that SRAM cells require 4– 6 planar FET devices, and high density cannot be achieved. The high performance of SRAM is achieved by sacrificing density and cost.

1.2.3.2

CMOS logic and signal processing

The CMOS approach to Boolean logic and digital signal processing relies on the power gain of the CMOS FET to swing voltage thresholds and then to pin output values to levels used as inputs at subsequent logic gates. Operations are typically performed with digital voltage pulses and a single logic gate cell is composed of an arrangement of FETs that are linked together in an appropriate way. As an example, one standard arrangement of FETs that operates as an AND gate cell is depicted in Fig. 1.6 (Horowitz and Hill, 1980). As described below, and depicted with the logic diagram in Fig. 1.6(b), this cell is a NAND gate followed by an inverter. Each element FETi is an enhancement mode FET. For a simple understanding of gate operation, consider the FETs to be switches that can be latched ‘on’ or ‘off’ for the duration of the input pulses, depending on the voltage applied to the gate. FET1, FET2 and FET5 are p-channel FETs. A p-channel FET is in

Introduction to magnetoelectronics

21

VDD

(a) FET1

FET2

FET5 y

OUT

A FET3

FET6

B FET4

(b) A OUT B

Fig. 1.6 (a) An arrangement of CMOS FETs that operates as a Boolean AND logic gate. (b) Logic diagram for circuit (a).

the ‘off’ state when the gate voltage is equal to or larger than the source voltage. The impedance switches to a low value, and is therefore in the ‘on’ state, when the gate voltage is lower than a threshold value below the source voltage. A typical threshold value is a few hundred millivolts. FET3, FET4 and FET6 are n-channel FETs. An n-channel FET is ‘off’ when the gate voltage is zero or below ground and ‘on’ when the gate voltage is larger than a threshold value above ground. Voltage pulses of positive or zero amplitude (HIGH or ‘1’; or LOW or ‘0’) are applied simultaneously to the inputs A and B; and the cell operates as an AND gate in the following way. When A and B are HIGH (‘1’ þ ‘1’), FET3 and FET4 are ‘on’, FET1 and FET2 are ‘off’, and consequently the voltage at node y is LOW, i.e. at ground. Since FET6 is ‘off’ and FET5 is ‘on’ the voltage output (OUT) is HIGH (‘1’). When A and B are LOW (‘0’ þ ‘0’), FET3 and FET4 are ‘off’, FET1 and FET2 are ‘on’, and consequently the voltage at node y is HIGH. Since FET5 is ‘off’ and FET6 is ‘on’ the voltage output (OUT) 28 is LOW, at ground (‘0’). When A (or B) is HIGH and B (or A) is LOW (‘1’ þ ‘0’), FET3 and FET2 are ‘on’, FET1 and FET4 are ‘off’, and consequently the voltage at node y is HIGH and the voltage output (OUT) 28 is LOW, at ground (‘0’). The truth table for the above operations therefore corresponds to that of an AND gate. Cells with similar arrangements of FETs form other basic logic gates such as NAND, OR, NOR and XOR. In the example of Fig. 1.6, notice that an arrangement of four FETs (FET1 –FET4) performs the logical operation of a NAND gate and delivers a low or high voltage to node y.

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The output is inverted by FET5 and FET6 so that the final output voltage is pinned (for the duration of a clock cycle) at HIGH or LOW voltages, V ¼ VDD or V ¼ 0: The gain of the first four FETs is used to ensure reproducibility of the logical operation, and the gain of the output stage is used to provide voltage levels that are then transmitted, by fanout, to subsequent devices. Although logic gates of this design are the backbone of digital electronic information processing, they suffer from a few disadvantages. Each FET is a planar device and takes up considerable space. Numerous FETs [six in the example of Fig. 1.6(a)] are required to form the logic gate cell, and therefore each cell occupies a large area of the chip. Furthermore, the result of the Boolean process is not stored and must be synchronized with a clock cycle to be used in the next processing step. A goal of high performance computing is the on-chip integration of memory and logic. When memory and logic occupy different chips, the parasitic time delay associated with moving signals between chips, known as latency, degrades speed and performance. High performance memory that is characterized by read, write and access speeds that are comparable with the processor speed is known as cache memory and is fabricated on-chip with the processor. Presently, cache memory uses SRAM, which has sufficiently high performance. Of equal importance, SRAM uses planar FETs and therefore can be fabricated on the same production line, using the same production steps, as the processing cells. The tradeoff, of course, is area: SRAM cells have relatively low density, using 4–6 FETs [Fig. 1.5(c)] and requiring correspondingly large area on the chip. As the performance of DRAM has improved, interest in the possibility of fabricating integrated DRAM cache has grown. Unfortunately, the trenched, vertical cells used by DRAM cannot be fabricated on the same production line used for the planar cells of the CPU. This problem for high performance CMOS computing is presently unresolved, and represents a weakness that may be exploited by an alternative technology. As a general rule, however, the success of CMOS digital electronics is truly remarkable. Within a few years, commercially available chips will be fabricated with minimum features of f ¼ 70 nm and information processing will operate at multi-GHz clock speeds. Those readers who have a background in magnetism must realize that CMOS architecture is so well established that there are large design libraries of CMOS devices, and relatively inexpensive device simulation software is readily available to engineers. Chips can be designed with relative ease. As an alternative technology, magnetoelectronics is not established and has none of these refinements. Since the beginning of the semiconductor industry, pessimists have speculated about the limits of scaling and the ultimate demise of the technology. It is an obvious truth that the industry has always found solutions to the supposed limits and has continued to flourish. Magnetoelectronics will do well if it can identify niche applications where its advantages propel it to dominance. It may then expand its sphere of applications. The crucial point is that magnetoelectronics will succeed if it can coexist with CMOS in a complementary way.

Introduction to magnetoelectronics

1.3

23

Spin vs charge

Scientists with a strong background in charge transport, for example, a knowledge of electrostatics, electricity and magnetism, and/or electrical engineering, will find that magnetism and the transport of spin-polarized electrons are quite different from charge transport. Intuition that has developed based on electrostatics will be misleading for spin transport. In this section, a framework for physical insight into spin-polarized transport is developed. Basic concepts of transport in nonmagnetic and ferromagnetic metals are reviewed for the benefit of those coming from a semiconductor background. Basic concepts of semiconductor physics are reviewed for the benefit of those coming from a magnetism background. By the end of the section, the differences between operational principles of semiconductor and spintronic devices should be clear. 1.3.1

Heuristic ideas

Spintronics is based on the ‘coupling’ of electron charge and spin (Johnson and Silsbee, 1985, 1988a). Two fundamental properties reside with each conduction electron, the unit charge e and the unit magnetic moment mB ; the Bohr magneton, which is related to the quantum mechanical spin S by mB ¼ 2ðe"=mcÞS; with m the electron mass and c the speed of light. Here S is dimensionless and has values þ1/2 or 2l/2 for conduction electrons. Note that alternative discussions define S with units, S ¼ þ"=2 or 2"=2: The underlying principle of spin electronics relies on charge–spin coupling: parameters of charge transport, such as voltage or current, are modulated in a device structure by manipulating the spin, using new control parameters such as magnetic field or new materials properties such as magnetization. The charge–spin coupling that resides with individual electrons leads to the false intuition that charge and spin are closely coupled for populations of carriers. In fact, for an ensemble of particles, the coupling is statistical and is generally weak (Johnson and Byers, 2003). There are many possible spin distributions for any single charge distribution. But because of the statistics of large populations, the coupling of charge and spin results in substantial effects that can be used successfully for device modulation. Consider the differences between charge and spin in a heuristic picture of a nonmagnetic metal. Charge comes with two polarities, positive and negative, the basic charge is a monopole, and the unit charge on any electron is neither created nor destroyed. Coulomb interactions are very strong, and charge perturbations are shielded on a very short length scale, the Thomas–Fermi ˚ . These strong interactions lead to conveniently large forces, and screening length, of order 1 A relatively large transport effects (changes of currents or voltages) that are readily observed and easily used to control integrated devices. By contrast, the basic ‘moment’ of a spin is a dipole, not a monopole. The dipolar fields may be strong at very short distances, but moments on two itinerant carriers interact only by mutual

24

M. Johnson

torques that affect their spin orientations. This heuristic description neglects an important effect called the exchange interaction, but it remains correct to say that spin –spin interactions are different from the purely inverse square law of Coulomb charge interactions. The energies involved in spin perturbations (nonequilibrium spin excitations) are small, and the shielding length is long. Thus, spin perturbations can exist in the form of spin accumulation (Johnson and Silsbee, 1987; Johnson, 1993a), a nonequilibrium population of spin-polarized electrons that is pumped by electrical spin injection. This occurs over a long length scale, a spin diffusion pffiffiffiffiffiffiffiffiffi length ds ¼ DT2 ; where D is the electron diffusion constant and T2 (or T1 ) the spin relaxation time, of order 1 mm in metal films (Johnson, 1993a). It is conceptually important to note that there is no charge accumulation in metals. Metals cannot sustain a static charge, and the strict boundary condition of current conservation is imposed on charge currents. Any static charge concentrates at the surface of a metal, such as a surface of a capacitor plate. Any dynamic charge dissipates with a characteristic time known as a Maxwell time, many orders of magnitude faster than T2 : A related condition is that electron charge is quantized and never changes: charge is conserved in any sample. By contrast, although electron spin is quantized, spin transport effects are based on spin orientation, and the orientation is a continuous variable (Johnson and Silsbee, 1987): spin orientation is not conserved in any sample. Thus, ordinary electrodes attached to a conducting sample act as sources and sinks for charge current. A ferromagnetic electrode acts as a source for spin current, but spin relaxation is random and the sink for spin orientation is isotropic in a nonmagnetic metal sample. While these are important conceptual differences, it is also important to recognize that all-metal magnetoelectronic devices, MTJs and spin valves, do not operate in a regime sensitive to nonequilibrium effects. These devices are fabricated with layers that have thicknesses less than an electron ballistic mean free path, ‘: Device operation relies on diffusive transport over a very short length, d p ds ; and effects related to spin relaxation are relatively small. For the MTJ, a thin insulating barrier, with thickness dI ; separates two ferromagnetic films having thicknesses of order a few nanometers. The tunnel currents are small and nonequilibrium effects in the F films are negligible. For a CIP spin valve [refer to Fig. 1.3(g)], the thickness, dN ; of the nonmagnetic layer N is a few nanometers, dN , ‘ p ds : Current-perpendicular-to-the-plane (CPP) spin valves are typically multilayered

structures and the current flow is perpendicular to the plane of the layers. This is usually achieved by reducing the lateral dimensions to the order of 100 nm and using high conductivity electrodes on the top and bottom of the multilayer stack. Nonequilibrium spin populations can exist in the N layers and in the F layers, over the short length ds;f < 5 nm (Dubois et al., 1999), in CPP spin valves (Johnson and Silsbee, 1987; Johnson, 1991). However, these spin accumulation effects are smaller than the effects of interfacial spin scattering.

Introduction to magnetoelectronics

25

Thus, spin transport devices are designed to operate on spatial scales smaller than relevant nonequilibrium lengths. This contrasts with semiconductor technology, where traditional devices were designed to operate on spatial scales larger than the relevant charge shielding length.

1.3.2

Transport in semiconductors

For readers with a background in magnetism and little knowledge of semiconductors, this subsection provides a simplified presentation of a few of the most basic ideas. Readers with a strong electronics background may wish to skip this subsection. Section 1.3.3 describes basic ideas of transport in metals and, in particular, in ferromagnetic metals. Since there are many important differences, a brief review of semiconductors may serve as a foundation for contrast for any reader. A semiconductor is not an insulator, nor is it a good conductor of electric charge. In a band picture of a solid, each atom in the lattice can donate one or more of its valence electrons to the crystal. Each atom may alternatively accept an electron and donate a hole. The energy states available to each conduction electron are calculated from the periodic electrostatic potential profile of the ionic crystal and form ‘bands’. These states are then filled according to the number of available conduction electrons and the laws of thermal population distribution. It is common to ~ equivalently of the velocity ~v; of the carrier. It plot energy bands as a function of the wavevector k; is also useful to plot the density of energy levels, equivalently called the density of energy states NðEÞ; as a function of carrier energy E: An example of such a plot is shown in Fig. 1.7. By definition, semiconductors and insulators have no partially filled bands. At zero temperature, all of the states in the valence band are full of electrons (fully occupied) and all of the states in the conduction band are empty of electrons (entirely unoccupied). In a semiconductor at nonzero

E

empty electron states in conduction band

states filled with electrons in conduction band

EC µ

empty states (holes) in valence band

Eg EV filled states (electrons) in valence band

N(E)

Fig. 1.7 Energy bands of a semiconductor, density of states NðEÞ as a function of energy E: The chemical potential is in the middle of the gap.

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M. Johnson

temperature, some carriers at the top of the valence band may be thermally excited into states at the bottom of the conduction band, as shown in Fig. 1.7. Some important terminology can now be introduced. The chemical potential m is the energy required to add one more particle to the system. The Fermi energy EF is defined as the energy of the highest occupied level. In metals, the chemical potential is approximately the same as the Fermi energy. The chemical potential of an insulator or a semiconductor lies between the highest energy of the highest occupied band (the valence energy EV of the valence band) and the lowest energy of the lowest unoccupied band (the conduction energy EC of the conduction band). The difference between the conduction and valence energies is the gap energy, Eg ¼ EC 2 EV : For an insulator, the energy gap Eg is so large that carriers are never excited from the valence band to the conduction band, and the material is electrically ‘insulating’ (nonconducting) precisely because of the complete lack of carriers in the conduction band. In a semiconductor such as silicon or gallium arsenide, the energy gap has value 1.1 and 1.4 eV, respectively. This is more than an order of magnitude larger than kB T even at room temperature, kB T < 25 meV: For pure semiconductors that have not been doped with any impurities (called intrinsic semiconductors), the number of carriers that can be thermally excited is miniscule, and intrinsic semiconductors behave as reasonably good insulators. Returning to the schematic of a semiconductor at finite temperature in Fig. 1.7, the next particle added to the system could go into the top of the valence band or the bottom of the conduction band, with the relevant probabilities determined by thermal statistics. On average, the energy of this next particle is in the gap between the bands, as shown by the location of the chemical potential m in Fig. 1.7. The Fermi energy, however, is the energy of the highest filled band and therefore lies in the valence band. When talking about metals, it is a widespread practice to use the terms chemical potential and Fermi energy synonymously, and this is acceptable. When talking about semiconductors, it is similarly a widespread practice to use these terms synonymously, but this practice is not correct (Ashcroft and Mermin, 1976). The chemical potential is the most relevant term, and it is not identically the same as the Fermi energy. A further complication should be mentioned, which will be relevant in the discussion below. ~ A semiconductor can sustain an internal electric field, for example EðxÞ; that is described by an electrostatic potential fðxÞ: Inside a semiconductor, the position-dependent electrochemical potential is defined as me ðxÞ ¼ m þ efðxÞ: Dilute doping of a semiconductor adds impurity sites that donate conduction electrons (n-type doping) or accept electrons and donate holes (p-type doping) as carriers in the lattice. Doped semiconductors are called extrinsic. The effect of doping is to create and fill a narrow band of states near the conduction (n-doped) or valence (p-doped) band edges, and the chemical potential moves towards this narrow band. For relatively light doping, the chemical potential remains in the gap and, roughly speaking, is not within an energy range kB T of the conduction or valence band energy. For electron doping, for example, EC 2 m . kB T describes a lightly doped system. When EC 2 m is a few times kB T; the thermal distribution of carriers is described by

Introduction to magnetoelectronics

27

Maxwell –Boltzmann statistics, and such a system is called nondegenerate. As the doping is increased, the chemical potential moves closer to the conduction (or valence) band edge. For sufficiently high doping, the chemical potential shifts into the bands, mimicking the situation of metals. When EC 2 m (or lEV 2 ml) is less than kB T; the thermal distribution of carriers is described by Fermi statistics, and such a system is called degenerate. It is relatively common, and approximately correct, to use the terms chemical potential and Fermi energy synonymously for degenerate semiconductors. The response of an insulator to an electric field is a change of the electrostatic polarization of the material, described by the dielectric constant. In a conductor, mobile carriers can move in a way that cancels the perturbation and ‘screens’ the electric field from the crystal. The screening length (Ashcroft and Mermin, 1976) is inversely proportional with the square root of carrier density. This is consistent with intuition: When a high density of carriers is available, an electric field perturbation can be screened within a short distance, but a low density of carriers requires a much larger volume to cancel the field. In metals, carrier densities are on the order of 1022 cm23 and the screening length (the Thomas–Fermi length) ˚ . Extrinsic semiconductors have carrier densities typically in the range is on the order of 1 A 14 18 23 10 –10 cm , and the screening length is much longer. Thus, electric fields can exist in semiconductors over relatively large distances, of order 10– 1000 nm. The ability to sustain an internal electric field is one basis for the operation of semiconductor electronic devices. Such fields can be created in a semiconductor that has a doping profile that changes with position, and these materials are called inhomogeneous semiconductors. In one basic and fundamental example, an n-doped region is brought into contact with a p-doped region. This might be achieved, for example, by a lithographic process in which the semiconductor surface is protected by photoresist, except for a small region which is exposed to an ion implantation process of acceptor ions. In a subsequent step, the surface is protected by photoresist, except for a small contiguous region which is exposed to ion implantation of donors. There may be a small amount of mass diffusion of the donors and acceptors after implantation, but a sharp interface between an n-doped and a p-doped region can be achieved. The doping is relatively light, and the nondegenerate system can be described by Maxwell –Boltzmann statistics. This structure, of course, is called a p –n junction. Far away from the interface, the density of carriers in the conduction (valence) band in the n (p) region is approximately the same as the density of dopants, Nd ðNa Þ. Near the interface, electrons and holes diffuse in order to electrically neutralize the donor and acceptor sites. Some of the sites are neutralized, with the loss of some of the mobile carriers. An equilibrium state is reached when the internal (built-in) electric field in the interface region prohibits further charge flow. The two regions, on either side of the interface, where the number of carriers is reduced is called a ‘space-charge’ region. Since the density of carriers is depleted relative to the value remote from the interface, the space-charge region of the p–n junction is also called a depletion region.

28

M. Johnson

The internal field can be on the order of 105 –107 V/m, sustained over depletion regions with lengths of 10 –100 nm. It is important to recognize that charge neutrality is not maintained in the depletion region; there is net positive charge on one side of the interface, and net negative charge on the other side. This deviation from charge neutrality forces the energy bands to bend, in order to meet at the interface, and also results in the internal electric field characterized by the electric potential fðxÞ: In thermal equilibrium, the chemical potential m is constant on both sides of the interface. The electrochemical potential me ðxÞ ¼ m þ efðxÞ; however, varies smoothly and continuously throughout the depletion region. The ‘built-in’ electric field and associated band-bending have dramatic effects on charge transport. Current rectification is a remarkable example for the case of the p–n junction diode. Detailed treatments of p–n junctions can be found in a variety of texts for equilibrium conditions and under voltage or current bias (Ashcroft and Mermin, 1976; Sze, 1981). In the context of the present discussion, the important observation is that transport characteristics such as net current density or net voltage measured across a device structure are highly nonlinear functions of carrier density and bias conditions. More complicated device structures, such as bipolar transistors, can utilize these nonlinearities so that a small modulation of one device parameter can result in a much larger modulation of another parameter. In this way, semiconductor devices can achieve power gain: the input power of a modulated signal is increased at the output stage, with the power increase provided by a control parameter at a third terminal (Sze, 1981). The ability of an external electric field to penetrate a semiconductor is the basis for another kind of semiconductor electronics technology. When a metal is fabricated on a semiconductor with a thin insulating layer between them (MIS structure), redistribution of charge near the interface can result in bending of the conduction and valence bands and a thin space-charge region, depletion or accumulation, is formed in the semiconductor (Silsbee and Drager, 1997). The conductivity of this layer can be much larger than that of the bulk, and transport between two electrodes, a source and a drain that are laterally defined on either side of the MIS structure, is then dominated by the properties of this layer. Applying a voltage between the metal gate (M) and the bulk semiconductor (S), far away from the interface, results in an electric field that penetrates into the semiconductor. By attracting (repelling) itinerant charge carriers from (to) the bulk to (from) the space-charge region, modulation of the gate voltage causes a modulation of the carrier density in the layer, and a modulation of the conductance between electrodes. Application of gate voltages of a few volts can, remarkably, modulate the source –drain conductance by many orders of magnitude. These FETs are extremely good switches of current or voltage, and the ratio of the conductivity in the ON state compared with that in the OFF state can be 105 or higher. These are active devices and are characterized by power gain. When the switch is set to the ON state, for example, the output voltage can be held to that of the supply voltage, VDD ; with an output impedance sufficiently large that the output voltage can be transmitted to numerous other devices on a line,

Introduction to magnetoelectronics

29

without degradation. As with the bipolar transistor, the power is supplied by the voltage applied to a third terminal, in this case the gate. Early discussions of FETs appeared in the 1950s and 1960s (Shockley, 1952; Dacy and Ross, 1955; Mead, 1966), and several texts provide an excellent discussion of detailed operation (Sze, 1998). The MIS structure that is inherent in the design of the FET is also, intrinsically, a capacitor. This fact is central to a parametric view of CMOS technology. Binary information is encoded in the form of voltages and voltage pulses, with amplitudes of order a few volts. The pulses are routed through transmission lines, and information is processed by triggering switching events in FETs. Inputs for these processes are applied capacitively, and the capacitive coupling leads to some limitations that are inherent in CMOS technology. Circuits are susceptible to parasitic capacitance, so that transmission lines and resistive contacts must be carefully designed to avoid RC degradation of high speed pulses. These problems become particularly important at high frequencies, and parasitic losses are most challenging in chips fabricated with small feature sizes. In other words, RC degradation is an important problem for CMOS scaling to higher densities and higher frequencies. On a related note, capacitors are intrinsically characterized by leakage currents. As discussed in Sections 1.2.1 and 1.2.3, this creates design problems for memory applications. Consider another aspect of an MIS structure with a space-charge region near the insulator– semiconductor interface. The thickness d of this layer can be as thin as a few tens of nanometers, which is roughly the same scale as the de Broglie wavelength of an electron, le : A question naturally arises: are there quantum effects when carriers are confined in an accumulation layer with thickness d < le ? It is well known that the answer is ‘yes’. Using a simple model of the carriers as ‘particles in a box’, the boundary condition d < le quantizes the momentum and energy levels along the dimension perpendicular to the plane of the layer, and the layer is known as a quantum well. The two-dimensional electron gas (2DEG), or two-dimensional electron system (2DES), was one of the great achievements of materials physics and condensed matter physics in the latter part of the twentieth century. 2DEGs were first discovered in MIS accumulation layers (Schrieffer, 1957; Fowler et al., 1966; Ando et al., 1982). Another fabrication technique, which resulted in higher electron mobilities, can be qualitatively described. If one fabricates a thin layer of an intrinsic semiconductor between two insulating layers, the resulting sheet of semiconductor will have few carriers and, therefore, an extremely large sheet resistance per square, Rsq ¼ r=d: A similar sample can be prepared by doping the semiconductor layer. While this increases the number of carriers, it also decreases the mobility because each donor provides a scattering site. The solution for achieving relatively high carrier density and high mobility is to move the dopants away from the semiconducting, quantum well layer. In a typical example, a quantum well layer of GaAs is grown between two insulating layers of AlGaAs. The band gap of AlGaAs is larger than that of GaAs. Dopants added to the AlGaAs layer occupy an energy higher than the conduction band energy of the GaAs. The carriers will diffuse to the GaAs and fill lower energy states in the

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M. Johnson

conduction band. Thus, the carrier density in the GaAs quantum well is increased, but the impurity scattering sites are in the AlGaAs, remote from the quantum well. Typically, a thin insulating layer of AlGaAs separates the doped AlGaAs from the GaAs quantum well, to ensure that the Coulomb potential of the impurity sites is weak at, and has little effect on scattering in, the quantum well. These 2DEGs are remarkable systems for research, but have not yet found widespread applications. 1.3.3

Transport in metals

In a discussion of transport in metals, the band picture of a solid is still valid. Each atom in the lattice donates one or more of its valence electrons to the crystal. The energy states available to each conduction electron are again calculated from the periodic electrostatic potential profile of the ionic crystal and form ‘bands’. These states are filled as before, using the number of available conduction electrons and the laws of thermal population distribution. Here the key difference between a metal and a semiconductor becomes obvious: By definition, metals have at least one partially filled band. Equivalently stated, the chemical potential m and the Fermi energy EF lie in the middle of a band. The consequences of this difference are dramatic. The density of states for a metal and the filling of those states up to EF are depicted in Fig. 1.8. For a nonmagnetic metal such as copper, silver or gold [Fig. 1.8(a)], the conduction is dominated by electrons in a parabolic, free-electron band. Separate spin subbands for up- and down-spins are shown, because this will be important later, and the Fermi energy is on the order of a few electron volts. In a metal, electrons deep beneath the Fermi surface are ‘locked’ in their eigenstates. There are no empty states available for translation, and these electrons do not contribute to conduction. But there is nothing to prevent the relatively large number of electrons near the Fermi surface from conducting current. In a semiconductor, by contrast, the band gap prevents most carriers from contributing to electronic conduction. Furthermore, in a metal these electrons near EF have a large velocity, the Fermi velocity vF , 108 cm/s, and they can respond easily to an electric field. Thus, the electrical conductivity s (sometimes written as s ; g) of a metal is orders of magnitude larger than that of a semiconductor. It is more common to talk about resistivity r; and room temperature values of r for most common metals are in the range of 1026 V cm, compared with values of order 1021 V cm for a semiconductor (e.g. Si or Ge) with a doping level of order 1016 cm23. Another brief digression may help clarify some common terminology. In a semiconductor, a charge current Jq is caused to flow by the presence of an electric field E or by the presence of a gradient of carrier density, ›n=›x: These partial currents are called drift and diffusion currents, respectively. The former is characterized by a conductivity s that is proportional to the number of carriers and their mobility, mq ¼ etq =mq ; where q refers to electrons or holes, tq is a scattering time, and mq is an effective mass. Note that mq has nothing to do with the chemical potential, m:

Introduction to magnetoelectronics

(a)

g

E

31

g

EF

N (b) E

g g EF

3d 4s

Uex F N (E)

N (E)

Fig. 1.8 Energy bands of metals, density of states NðEÞ as a function of energy E: (a) Nonmagnetic metals have a free-electron, parabolic density of states, which is partially filled. (b) In a transition metal ferromagnet, the 4s and 3d bands are intersected by EF : The 3d band is exchange shifted by energy Uex :

The drift current is characterized by the self-diffusion constant of the carrier, Dq : The relationship between mobilities and diffusion constants is called the Einstein relations. In nondegenerate semiconductors, the Einstein relations are

mq ¼

eDq ; kB T

and they take a slightly different form for degenerate semiconductors (Ashcroft and Mermin, 1976). In metals, recall that charge neutrality is strictly obeyed and there are no gradients of carrier density. The conductivity of a metal is proportional to the density of electrons at the Fermi level, and therefore to the density of states of electrons at the Fermi level, NðEF Þ; and is given by a

32

M. Johnson

different Einstein relation, g / NðEF Þ (Ziman, 1972). The Pauli exclusion principle requires that up- and down-spin electrons be counted separately, and separate spin subbands can be used [Fig. 1.8(a)]. Electrons near the Fermi surface are constantly colliding, scattering and changing their momentum states. However, if the spin orientation remains unchanged during these events, it follows that a unique conductance can be written for both the up- and down-spin electrons (Johnson and Silsbee, 1988a): g" / N" ðEF Þ;

g# / N# ðEF Þ;

ð1:1Þ

as marked in Fig. 1.8(a). Notice that filling of the spin subbands for a nonmagnetic metal is symmetric and g" ¼ g# : Transition metal ferromagnets are quite different from nonmagnetic metals. First, the Fermi level cuts across more than one band. As sketched in Fig. 1.8(b), the Fermi surface intersects a free-electron 4s band. However, it also intersects a 3d band which is not a simple parabola. In a ferromagnetic metal, the 3d up- and down-spin subbands are shifted out of symmetry. Figure 1.8(b) represents a band model of ferromagnetism, and the shift is called an exchange splitting, Uex : In a ferromagnetic material, the ion cores in the lattice have a net, nonzero spin. These magnetic ions can interact with each other when their charge distributions overlap, and this effect is called the exchange interaction. Details of a band model of ferro-magnetism (Stoner, 1948; Ziman, 1972), and of the splitting Uex , are beyond the scope of this discussion, but the model has important ramifications. First, the number of down-spin conduction electrons differs from the number of up-spins, and this difference defines the spontaneous magnetization of the material: M ¼ mB

ð1

½N# ðEÞ 2 N" ðEÞ f ðEÞdE:

ð1:2Þ

0

Here f ðEÞ is the Fermi function which mathematically describes the filling of states pictured in Fig. 1.8. The down-spin subband is called the majority spin subband because it has more electrons and it therefore determines the magnetization direction. The up-spin subband is called the minority spin subband. Note that the choice of up- (down-) spin for the minority (majority) spin subband is arbitrary, and that the direction typically refers to the orientation of the magnetic moment. Second, the density of states at the Fermi level is different for the up- and down-spin subbands, N" ðEF Þ – N# ðEF Þ; and therefore the spin subband conductances are different: g" ðEF Þ – g# ðEF Þ:

ð1:3Þ

It follows that electrical currents carried by the two spin subbands are inequivalent, which is the same as saying that an electrical current in a ferromagnetic material has nonzero spin polarization. For a ferromagnetic material, the differences of band structure for the two spin subbands maintain unique and different conductances g" and g# : It was stated above for a nonmagnetic

Introduction to magnetoelectronics

33

U(r) s r

Fig. 1.9 An electron with spin ~s moves in the periodic potential UðrÞ of a metal with Fermi velocity vF : A weakly relativistic spin&orbit interaction can tip the spin orientation.

material that unique conductances could be defined if the electrons maintained their spin orientation during scattering events. This turns out to be true: spin orientation is robust. The spin orientation of an electron rarely flips, for a subtle but fundamental reason. Changing the orientation of a spin from an initial direction, known as spin relaxation, requires a magnetic torque, and there are few interactions that can provide an appropriate torque. A simple description of the dominant mechanism is aided with the sketch in Fig. 1.9 (Johnson, 2000a). An electron with some given spin orientation (up in Fig. 1.9) travels in a periodic potential UðrÞ which describes the internal periodic electric field of the ion cores (solid dots). During constant motion the electron is in an eigenstate of the periodic potential, moving at weakly relativistic velocity vF : But when the electron scatters and changes its direction (solid arrow), it traverses an effective ‘orbit’ in the vicinity of the ion core during the short time of the scattering event before it enters a new eigenstate. The local electric field transforms, in the rest frame of the electron, as a magnetic field. Since the scattering occurs over a very short time interval, the electron experiences an effective magnetic field pulse. This pulse can act as a torque on the spin and there is a small probability of tipping the spin orientation. The Fermi velocity is only weakly relativistic, and the probability of spin-flip scattering is also weak, of order 1025 –1023 per scattering event. Since electron scattering times are on the order of 10214 s, spin relaxation times in metals (at room temperature) are on the order of 10211 s (Johnson, 1993a). This ‘spin –orbit’ scattering mechanism was independently described by Yafet (1952) and Elliott (1954) and is often known as a Yafet–Elliott mechanism. Spin-flip scattering may also occur in a bulk ferromagnet. In this case, the band structure constrains the number of up- and down-spin electrons at the Fermi surface. However, there are small, local fluctuations in the magnetization that are of thermal origin. These fluctuations are known as magnons, and ‘magnon scattering’ refers to spin-flip scattering as an electron travels through such a region (Kittel, 1971).

1.4

Review of phenomenology

Some of the basic ideas of spin-polarized transport that form the underlying operational principles of magnetoelectronic devices have already been introduced. This section presents an historical review of the research that developed these basic concepts. Some ideas are rigorously described,

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M. Johnson

however, the goal of the section is to describe basic ideas from a conceptual viewpoint rather than focussing on mathematical formalism. 1.4.1

Spin-polarized currents

The concept that an electric current in a metal could be composed of spin-polarized carriers had its origin about 65 years ago. By calculating scattering rates for spin-up and spin-down itinerant electrons in the exchange-split d-band of transition metal ferromagnets, Mott (1936) deduced that the carriers of an electrical current in a ferromagnetic metal had a net spin polarization P: P ¼ ðJ" 2 J# Þ=ðJ" þ J# Þ ¼ ðg" 2 g# Þ=ðg" þ g# Þ – 0;

ð1:4Þ

where Ji are the spin subband partial currents and gi are the spin subband conductances. Experimentally, the study of the transport of polarized carriers began with low temperature tunneling spectroscopy about 30 years ago. Tedrow and Meservey (Tedrow et al., 1970; Tedrow and Meservey, 1971) fabricated planar tunnel junctions using thin aluminum films, aluminum oxide tunnel barriers, and a ferromagnetic (F) or nonmagnetic (N) metal counterelectrode (refer also to Chapter 3). At a temperature T below the superconducting transition temperature Tc of the aluminum (S), the critical field for magnetic fields applied in the sample plane, HC;3 ; is large. Relatively large in-plane fields, H , HC;3 ; cause a sizable Zeeman splitting of the quasiparticle density of states, Nqp;";# ðEÞ ¼ Nqp ðE ^ mB HÞ; where mB is the Bohr magneton. The tunneling conductance measures single particle tunneling and has peak values at the singularities of the density of states near the gap edge, at energies EF ^ D in zero magnetic field. When the counterelectrode is a nonmagnetic metal such as silver (Tedrow and Meservey, 1971), the tunneling conductance in a field H , HC;3 is symmetric about V ¼ 0 with four peaks at the Zeeman split values eV ¼ ^lD ^ mB Hl: When the counterelectrode is a ferromagnetic metal F such as Fe, Ni or Co, the peaks have asymmetric heights (Tedrow and Meservey, 1973). The tunneling current I is proportional to the density of states at the Fermi level of the counterelectrode, J / NF ðEF Þ: The d-band densities of states at the Fermi level of ferromagnets, Nd;" ðEF Þ and Nd;# ðEF Þ; differ for spin-up and spin-down subbands because of exchange splitting. By deconvolving the measured tunneling conductance, Tedrow and Meservey could deduce the net polarization P of the tunnel current crossing the F –S interface, directly proportional to the asymmetry of the density of states at the Fermi level: P ¼ ½N" ðEF Þ 2 N# ðEF Þ=½N" ðEF Þ þ N# ðEF Þ:

ð1:5Þ

Their experimental results gave values of P < 10 – 45% for transition metal ferromagnets such as nickel, iron and cobalt (Tedrow and Meservey, 1973). These seminal experiments had a broad impact. First, using the reasonable assumption that the polarization of the interfacial tunnel current was comparable with the polarization of the current inside F, they provided both an experimental confirmation of Mott’s theoretical assertion

Introduction to magnetoelectronics

35

and a quantitative estimate of the polarization P. Second, they demonstrated that polarized current could tunnel across a barrier at a boundary of F and maintain its polarization. Third, whereas these initial experiments used a thin superconducting film S as a detector of polarized carriers, it was soon recognized that a second ferromagnetic film F2 could also perform this function. Julliere’s (1975) spin dependent tunneling (SDT) experiments laid the foundation for the MTJ, a magnetoresistive device structure that shows high potential for broad applications. 1.4.2

Spin-dependent tunneling in magnetic tunnel junctions

Of the three significant device families, MTJs, spin valves and fringe field devices, the MTJ is considered to have the highest potential for success in electronics applications. Chapter 3 is dedicated to MTJs, but the basic principles can be described within the context of this historical review. As sketched in Fig. 1.10(a), an MTJ is a sandwich of two thin ferromagnetic films F1 and F2 separated by a very thin dielectric tunnel barrier. Ideally, each ferromagnetic film is a single domain and F1 and F2 are chosen to have different coercivities so that they switch their magnetization orientation at different values of field. Under voltage bias, the current of a tunnel junction is proportional to the density of states at the Fermi level of both electrodes (Simmons, 1963; Duke, 1969): J / NF1 ðEF ÞNF2 ðEF Þ:

ð1:6Þ

As discussed in Section 1.3, the up-spin and down-spin conductances of ferromagnetic metals are independent, and the tunneling current is determined by their parallel contributions. When the magnetization orientations are parallel [Fig. 1.10(b)], the minority spin subband current ðJ" Þ is large because the density of states at EF is large for both F1 and F2. The partial current J" is so large that it dominates transport in the junction, J" q J# : In a simple model where the junction resistance is the parallel combination of an up-spin resistance and a down-spin resistance, the small up-spin resistance effectively ‘shorts out’ the down-spin resistance and carries a relatively high proportion of tunnel current, Jpar < J" : When the magnetization orientations are antiparallel [Fig. 1.10(c)], the up- and down-spin partial currents are the same: J" / NF1;min ðEF ÞNF2;maj ðEF Þ ¼ J# / NF1;maj ðEF ÞNF2;min ðEF Þ: The net current Janti ¼ J" þ J# is smaller than the current that flows between minority spin subbands in the parallel configuration, Janti , Jpar ; and the device configuration with the magnetizations of F1 and F2 antiparallel has a higher resistance than the configuration with magnetizations parallel. SDT between two ferromagnetic materials was first demonstrated by Julliere (1975). His results were confirmed by Maekawa and Gaefert (1982), and this early work

36

M. Johnson

(a) I+ F2 Insulating barrier

V F1 I− x

(b) g

E EF;F,down

g

E

EF;F,up

EF;F,up

F2

F1 N (E)

N (E)

(c) E

g maj,min

E

F2

F1 N (E)

gmin,maj

N (E)

Fig. 1.10 (a) Perspective view of a typical magnetic tunnel junction (MTJ) planar device structure. (b) and (c) Density of states picture describing spin-dependent tunneling (SDT) in the MTJ. A simple understanding requires two rules. (1) Tunnel current (equivalently, the tunnel conductance) is proportional to the density of states at the Fermi level, EF : (2) Spin-up (-down) electrons can only tunnel from and to states in the spin-up (down) subband. (b) When the magnetization orientations are parallel, the tunnel conductance for up-spin electrons is large and completely dominates transport. (c) When the magnetization orientations are antiparallel, the up-spin and down-spin conductances are equal and are smaller than the large up-spin conductance of (b).

was followed by studies of vacuum tunneling related to spin-polarized scanning tunnel microscopy (Weisendanger et al., 1990; Johnson and Clarke, 1990). SDT is typically studied by making magnetoresistance measurements schematically depicted in Fig. 1.11. An external field H applied in the plane of the films [along x^ in Fig. 1.10(a)] ~ 2 of F1 and F2 and to switch the structure ~ 1 and M is used to control the magnetization states M between parallel and antiparallel configurations. In a typical measurement [Fig. 1.11(a)], the field

Introduction to magnetoelectronics

(a)

37

R R0 + ∆R

R0 − HC1

HC2

H

HC2

H

R

(b) R0 + ∆R

R0 − HC1

Fig. 1.11 Quasistatic magnetoresistance characteristic of an MTJ, with field H applied along x^ [Fig. 1.10(a)]. ~ 2 are parallel, which ~ 1 and M (a) The relatively low tunnel resistance R0 is measured when the magnetizations M occurs at large values of lHl: The relatively high tunnel resistance R0 þ DR is measured when the ~ 2 are changing their orientation and become antiparallel. This occurs in the field ~ 1 and M magnetizations M range where the orientations are changing, HC;1 , H , HC;2 : Because of the hysteresis of each film [refer to Fig. 1.l(b)], peaks of magnetoresistance are seen for symmetrically positive and negative field ranges. (b) Memory effect, as described in the text.

H begins at a (negative) value sufficiently large that it saturates the magnetizations of both films so that they are aligned parallel, for example along 2^x; and the resistance R0 represents the relatively low tunnel resistance described by Fig. 1.10(b). As the field increases to zero there are no changes in resistance because both F1 and F2 are in remanent states and their magnetization orientations have not changed. As H is further increased, the MTJ resistance increases over the field range HC;1 , H , HC;2 where the magnetization orientations are changing, with the peak value R ¼ ~ 1 and M ~ 2 are antiparallel. In the example of Fig. 1.11(a), R0 þ DR occurring when magnetizations M ~ 1 has reversed its F1 has a lower coercivity and the high resistance state is reached when M

38

M. Johnson

~ 2 is unchanged. When H is increased to H . HC;2 ; the magnetizations M ~ 1 and magnetization and M ~ M2 are once again parallel, now along þ^z; and the resistance reduces to the low value R0 : When the field is decreased from H q HC;2 to H p 2lHC;2 l; the same magnetoresistive peak [dotted line in Fig. 1.11(a)] is observed in the negative field range, 2lHC;2 l , H , 2lHC;1 l; because of the symmetric hysteresis of the films. The hysteresis and remanent properties of the ferromagnetic films are also used to ~1 demonstrate a memory effect, shown in Fig. 1.11(b). The external field H is increased until M ~ ~ reverses orientation, magnetizations M1 and M2 are antiparallel, and the tunnel resistance is maximum, R ¼ R0 þ DR: In this configuration, the external field can be reduced to zero and the relative orientation will remain antiparallel because F1 and F2 are in their remanent states. In fact, the antiparallel configuration and the high resistance value are maintained until the field H is ~ 1 to its original configuration, parallel reversed and set to the coercive value required to reorient M ~ 2 : The bistability exhibited by the memory effect characterized in Fig. 1.11(b) is a with M fundamental property used in digital applications, as will be discussed in detail in several following chapters. The magnitude of SDT effects was first calculated by Julliere, a result that is still commonly used. Solving for changes of tunnel conductance G; Julliere predicted the magnetoresistive ratio MR ¼ DG=G of an MTJ to be DG 2P1 P2 ¼ ; G 1 þ P1 P2

ð1:7Þ

~ 1 and M ~ 2 parallel, and P1 and P2 are the where G is the interfacial tunnel conductance for M polarizations of current that are characteristic of F1 and F2 (Julliere, 1975). For transition metal ferromagnets, P1 ; P2 , 0:5 and DG=G < 40%; a value that is confirmed by experiment. In the limit of perfect polarization, P1 ; P2 ! 1; Eq. (1.7) predicts DG ¼ G: In other words, Gpar 2 Ganti ¼ Gpar and it follows that Ganti ¼ 0: This result is consistent with the simple model of Fig. 1.10. For a half-metal ferromagnet, there are no available states in the antiparallel configuration and tunneling is forbidden: J ¼ 0; Ganti ¼ 0: Equation (1.7) is often written as Ranti 2 Rpar DR 2P1 P2 ¼ ¼ R Ranti 1 2 P1 P2

ð1:8Þ

in order to emphasize the divergence predicted for P ! 1: Such a divergence has not been experimentally observed. 1.4.3

Spin injection and diffusion in nonmagnetic metals

Continuing with the historical review, the tunneling experiments of Meservey et al. and Julliere also led to a fundamental question: Could a spin-polarized current, equivalently denoted as a magnetization current of oriented dipoles, JM ¼ ðJ" 2 J# Þ=ðJ" þ J# Þ; penetrate a nonmagnetic

Introduction to magnetoelectronics

39

material and maintain its polarization over some nonzero penetration depth? The prevailing view in the 1970s was ‘No’. This belief was based on the observation that the RKKY interaction, a coupling between dilute magnetic impurities in a nonmagnetic metal host that is mediated by conduction electrons, has a length scale of order 1 nm. It was believed that a spin-polarized current injected into a nonmagnetic metal N would have a comparably small penetration depth. The contrary view was presented by Aronov, who argued that the penetration depth was relatively long and proposed that a current JM could be injected successfully into nonmagnetic metals (Aronov, 1976a), semiconductors (Aronov and Pikus, 1976) and superconductors (Aronov, 1976b). At about the same time, Silsbee was studying spin diffusion in nonmagnetic metals using transmission electron spin resonance (TESR) (Silsbee et al., 1979). Stimulated by Meservey’s observation of interfacial spin tunneling, thin ferromagnetic films F1 and F2 were deposited on either side of a high purity nonmagnetic metal foil N. The trilayer sample was mounted in a spectrometer where the foil separated the ‘transmit’ and ‘receive’ cavities. Using standard TESR techniques, resonantly tuned microwaves applied to the transmit cavity in the presence of a ~ within a skin depth saturating, dc external field H creates a nonequilibrium spin population M of N. These polarized spins diffuse across the sample and, when the sample thickness d is less than a spin depth, d , ds (known as the TESR ‘thin limit’), microwave photons can be detected in the receive cavity. Comparing the transmission amplitude for foil samples with and without ferromagnetic film coatings, the transmission of the coated samples was substantially enhanced (Silsbee et al., 1979).

1.4.3.1

Spin injection and accumulation

Silsbee explained these results as an enhanced transfer of spin-polarized electrons across the F1–N interface. This was followed by their diffusion across the metal foil, and then enhanced transmission at the second, N–F2 interface. He proposed that similar transport phenomena would occur in a dc, electrically biased experiment. Silsbee’s (1980) model can be explained with a simple pedagogical geometry [Fig. 1.12(a)] and a microscopic transport model [Fig. 1.12(b) and (c)]. A bias current I driven through a single domain ferromagnetic film F1 and into a nonmagnetic metal sample N carries magnetization across the interface (with area A) and into N at the rate JM ¼ P1 mB I=e; where I=e is the number current and P1 is the fractional polarization of carriers. This is the process of spin injection. The sample thickness d is typically larger than an electron mean free path but smaller than a spin depth, d , ds ; (the same TESR ‘thin limit’ mentioned above). In the steady state, JM is constantly adding magnetization to the sample region, and relaxation at the rate 1=T2 is steadily removing magnetization by randomization processes. The nonequilibrium magnetization ~ ¼ IM T2 =Ad that results is a balance between these source and sink rates and is called M ~ / spin accumulation. It represents a difference in spin subband chemical potential in N, M EF;n;" 2 EF;n;# [Fig. 1.12(b) and (c)], and is depicted as dark gray shading in Fig. 1.12(a).

40

M. Johnson

(a) N F1

F2

I Z d

(b)

F1

N

E E F;n + eV0

F2 (Z=0)

g

g

E

E

)

E

EF;n;

E F;n

F2 (Z=

E F;n + eVs

E F;n

EF;n;

~ M

N (E)

N (E)

(c)

F2, F1 parallel

F1 E F;n + eV0 E F;n

N (E)

g

E

EF;n; EF;n;

N (E)

F2 (Z=

F2 (Z=0)

N g

E

)

E

E E F;n

E F;n − eVs

~ M

F2, F1 antiparallel

Fig. 1.12 Microscopic transport model of spin injection, accumulation and detection. (a) Cross-sectional schematic view of trilayer, three-terminal device with ferromagnetic spin injecting film F1, nonmagnetic layer N with thickness d q ‘; and ferromagnetic spin detecting film F2. (b) Transport described by density of states ~ 2 parallel. When bias current I flows across the F1– N interface, the chemical potential of ~ 1 and M models, for M F1 is raised by a small amount, eV0 ; in order to overcome finite interfacial resistance. Bias current I is a spin~ in N. When polarized current and generates a nonequilibrium spin population (spin accumulation), M; ~ drives a clockwise current in the detection arm, and a positive current is impedance Z [Fig. 1.12(a)] is zero, M detected by ammeter Z: When impedance Z is infinite, the chemical potential of F2 rises to align with EF;n;" ~ 1 and M ~ 2 antiparallel. The spin and a positive voltage Vs is measured by voltmeter Z: (c) Transport for M ~ drives a counterclockwise current in the accumulation in N is the same as in (b). When impedance Z is zero, M detection arm, and a negative current is detected. When impedance Z is infinite, the chemical potential of F2 lowers to align with EF;n;# and a negative voltage 2Vs is measured.

Introduction to magnetoelectronics 1.4.3.2

41

Spin detection at an N –F interface

A second ferromagnetic film F2 can be added, fabricated to be in interfacial contact with the sample region and connected to ground through a low impedance current meter [Z ¼ 0 in Fig. 1.12(a)]. A positive (negative) current Is / EF;n;" 2 EF;n (where EF;n is the average chemical potential of the two spin subbands) is driven across the N –F2 interface when F1 and F2 are parallel (antiparallel). Conceptually, this induced electric current is the converse of the injection process and is an interface effect: A gradient of spin subband chemical potential across the N –F2 interface causes an interfacial electric field that drives an electrical current, either positive or negative depending on the sign of the gradient, across the interface. This is an emf source and current conservation demands that a clockwise, or counterclockwise, current results in the detecting loop. If F2 is connected to ground through a high impedance voltmeter [Z ¼ 1 in Fig. 1.12(a)], ~ x is developed at the N –F2 interface. Here P2 is then a positive (negative) voltage eVs ¼ P2 mB M= the fractional polarization efficiency of the N–F2 interface, x is the Paul susceptibility, and eVs is recognized as the effective Zeeman energy of a spin-polarized electron in the presence of the ~ x associated with the nonequilibrium magnetization. The voltage Vs is directly effective field M= related to the interfacial, spin subband electrochemical potential gradient described above. The high impedance Z ! 1 forces the interfacial current flow to vanish, and the rise (or fall) of electrochemical potential of F2 is the mechanism that stops the current flow. ~ could be destroyed by Following the phenomenology of TESR, Silsbee noted that M application of an external, perpendicular magnetic field, H’ : Discussed in detail below, the amplitude of a Lorentzian feature, DVðH’ Þ; would be proportional to the spin-coupled voltage of ~ / T2 : Furthermore, anticipating techniques that later the accumulated spins, DVðH’ Þ ¼ Vs / M would be used in giant magnetoresistance (GMR), Silsbee predicted that manipulating the ~ 1 and M ~ 2 between parallel and antiparallel would give a measurement magnetization orientations M ~ decays exponentially away of 2Vs : When the sample thickness is larger than ds ; the value of M from the F1 –N interface and Vs is smaller than its value in the thin limit, Vs ðdÞ ¼ Vs;0 e2d=ds :

1.4.3.3

Formal theory

Three related phenomena form the cornerstones of magnetoelectronics: SDT (Tedrow and Meservey, 1973; Julliere, 1975), GMR (Binasch et al., 1989; Baibich et al., 1988) and spin injection (Silsbee, 1980; Johnson and Silsbee, 1985). Each of the two former topics has had some device applications, and each is the focus of a later chapter. Spin injection has been an important research technique, and it may have relevance for future generations of spin-injected semiconductor devices, or spin-injected all metal devices. It is presented with some depth in the following subsections, and some issues related to spin injection in semiconductors will be included in Chapter 6.

42

M. Johnson

The spin injection experiment (Johnson and Silsbee, 1985, 1988b,c) was important for several reasons. First, it demonstrated that spin-polarized carriers can be driven into a nonmagnetic material N over the relatively long length scale of ds : The accompanying theory (Johnson and Silsbee, 1988a) introduced the idea of separate resistances in a nonmagnetic material for up- and down-spin carriers. Second, it showed that spin-polarized carriers in N can create a voltage at a second N –F interface. In other words, information about spin states can be transformed into electronic information (a voltage or current). Indeed, the spin injection experiment was the first demonstration that the resistance of an F1 –N–F2 structure is modulated by the relative ~ 1 and M ~ 2 : Third, it provided direct measurements of spin relaxation magnetization orientations M times and spin diffusion lengths in metals. All of these are concepts central to magnetoelectronics, and they underpinned the later experiments that developed GMR and spin valve effects. More recently, the spin injection technique has been generalized and applied to novel materials systems, such as superconductors and semiconductors. The theory of spin injection and spin diffusion in nonmagnetic metals (N) begins with the realization, discussed in Section 1.4.1, that spin scattering events in N are rare. Transport in metal ferromagnets had long been modeled by using independent conductances for the up-spin and down-spin subbands (Mott, 1936). Because populations of up- and down-spin carriers in N mix weakly, separate up- and down-spin conductances can be introduced to describe transport in a nonmagnetic metal, as well as in the ferromagnetic metal (Johnson and Silsbee, 1988a). Referring again to Fig. 1.12(b) and using the simplifying assumption that spin relaxation in the ferromagnet is rapid so that its magnetization remains in equilibrium, EF;f;" ¼ EF;f;# ¼ EF;n þ eV0 ; (the general case of arbitrary spin relaxation in F is treated as a special topic in Section 1.5) the electric current from F1 to N is Je ¼ ð1=eÞ½g" ðEF;f1;" 2 EF;n Þ þ g# ðEF;f1;# 2 EF;n Þ ¼ ðg" þ g# ÞV0 : In the schematic representation of Fig. 1.12(b), the up-spin conductance g" dominates, but both spin conductances contribute and the magnetization current is JM ¼ ðmB =eÞ½g" ðEF;f1;" 2 EF;n Þ 2 g# ðEF;f1;# 2 EF;n Þ ¼ ðmB =eÞðg" 2 g# ÞV0 : The ratio of JM to Je is JM g 2 g# mB m ¼ P1 B ¼ " Je g" þ g# e e

ð1:9Þ

and this defines the interfacial spin polarization coefficient P1 ; under the assumptions of no interfacial spin scattering.

Introduction to magnetoelectronics

43

A current is driven across the N–F2 interface, for the low impedance case ðZ ¼ 0Þ; because of a gradient of spin subband electrochemical potential associated with the spin accumulation: Je ¼ ð1=eÞ½g" ðEF;n;" 2 EF;f2 Þ þ g# ðEF;n;# 2 EF;f2 Þ    ~ 1 mB M ðEF;n 2 EF;f2 Þðg" þ g" Þ þ ðg" 2 g" Þ : ¼ e x

ð1:10Þ

For the high impedance case, the spin-coupled voltage Vs that is a measure of the spin accumulation is found by setting Je ¼ 0 in Eq. (1.10): Vs ¼

~ P2 mB M ; e x

ð1:11Þ

where P2 is defined in analogy with P1 as the ratio of the difference and sum of spin-up and spin-down conductances. A device schematic for the spin valve, developed a few years after spin injection, is similar to the pedagogical schematic of Fig. 1.12(a). However, a few key differences are worth describing. As shown in the schematic of Fig. 1.13(a), the typical current-in-the-plane (CIP) spin valve involves diffusive transport in the plane of a trilayer sandwich F1–N –F2. The electrons move between regions of all three layers, and the magnetoresistance is measured as a voltage, across the length of the sandwich, that differs when the magnetizations M1 and M2 are varied between parallel and antiparallel. The CPP geometry is essentially the same as that of spin injection. Spin valves and GMR multilayers are fabricated with F and N layers having a thickness on the order of (or less than) an electron mean free path, ‘: The spin-dependent voltage Vs in a spin injection sample is related to the nonequilibrium spin accumulation. While these effects can be seen in thin N films, dN # ‘ (Johnson, 1991), the three-terminal geometry of Fig. 1.12(a) is more easily realized with thicker N layers, dN . ‘: The magnetoresistance DR in GMR systems derives predominantly from spin-dependent scattering at or near the F –N interfaces. If the layer thicknesses of a CIP spin valve are much larger than ‘n and ‘F ; the interfacial spin-dependent scattering is only a small fraction of all scattering events and DR is negligibly small. To maintain interfacial scattering as a large component of all scattering, the layer thicknesses must be kept small and the F –N interfaces must be clean and devoid of oxides. The standard formalism used to describe GMR adopted the Johnson–Silsbee idea of using separate spin subband conductances for F and N (Johnson and Silsbee, 1988a). A heuristic picture of the ‘two-current’ model is shown in Fig. 1.13, and is conceptually similar to the model of SDT (refer to Figs 1.10 and 1.11). When the magnetizations of adjacent F layers are parallel [Fig. 1.13(b)], up-spin electrons have a high conductance and dominate transport. When the magnetizations of adjacent F layers are antiparallel [Fig. 1.13(c)], the up- and down-spin conductances are equal and their parallel sum is less than the high up-spin conductance of Fig. 1.13(b). GMR and spin valve effects are discussed in detail in Chapter 2.

44

M. Johnson

(a)

N F1

F2 V

I

t

F1

(b)

N

E

F2 E

g

g

E

EF;f = EF;n

N (E)

N (E)

F2, F1 parallel gmin,n,min > g maj,n,maj

(c)

F1

N

E

g

F2 E

E

g

EF;f = EF;n

N (E)

N (E)

F2, F1 antiparallel

g min,n,maj = g maj,n,min < g min,n,min

Fig. 1.13 Microscopic transport model of spin transport in a current-in-the-plane (CIP) spin valve. (a) Cross-sectional schematic view of trilayer, two-terminal device with ferromagnetic film F1, nonmagnetic ~ 1 and M ~ 2 are parallel. The up- and layer N ðtN , ‘Þ; and ferromagnetic F2. (b) Transport when M down-spin subband conductances, g" and g# ; are independent. The g" ‘channel’ is large and dominates ~ 2 are antiparallel. ~ 1 and M conductance, resulting in a relatively low resistance. (c) Transport when M The g" and g# ‘channels’ are the same, and each is relatively small. The result is a relatively high resistance.

Introduction to magnetoelectronics

45

Two experimental transport techniques can be used measure spin injection effects. A unique test for the direct observation of spin accumulation is a demonstration of the Hanle (1924) effect, the zero frequency analogue of TESR. A transverse, external magnetic field H’ causes the spins to precess and, for sufficient field, the polarization is dephased and destroyed. The field dependence of the spin-coupled voltage Vs detected at the second ferromagnetic electrode F2 is found by solving the Bloch equations with transverse field and a diffusion term (Johnson and Silsbee, 1985, 1988a). For the quasi-one-dimensional wire geometry discussed below, it has the form: Vs ¼

pffiffiffiffiffiffiffiffiffi P1 P2 "2 p 2 IT2 expð2Lx f ðH’ Þ= DT2 Þ½F1 ðH’ Þ; F2 ðH’ Þ; 2 p e m kF 2Ads

ð1:12Þ

where   1 gH’ T2 f ðH’ Þcos½gðH’ Þ 2 sin½gðH’ Þ ; F1 ðH’ Þ ¼ f ðH’ Þ f ðH’ Þ   1 gH’ T2 cos½gðH’ Þ þ f ðH’ Þsin½gðH’ Þ ; F2 ðH’ Þ ¼ f ðH’ Þ f ðH’ Þ pffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðd= DT2 ÞgH’ T2 ; f ðH’ Þ ¼ 1 þ ðgH’ T2 Þ2 ; gðH’ Þ ¼ f ðH’ Þ

ð1:13aÞ ð1:13bÞ

where g is the gyromagnetic ratio, mp the electron effective mass, kF the Fermi wavevector, D the electron diffusion constant, A the cross-sectional area of the sample, 2Ads the approximate volume the spins occupy when they diffuse equally along ^^x; and Lx the length between injector and detector. Functions F1 ðH’ Þ and F2 ðH’ Þ determine the shape of Vs ðH’ Þ; either ‘absorptive’ or ‘dispersive’ for parallel or crossed injector and detector polarizations, respectively. In the limit d , ds ; the amplitude Rs of ‘absorptive’ Hanle data can be expressed simply as (Johnson, 1994a) Vs rd2 ¼ Rs ¼ P1 P2 s ; Ie Vol

ð1:14Þ

where r is the sample resistivity. Relaxation time T2 is measured from the lineshape, and the polarizations P1 (and P2 ) of injected (and detected) current are the sole fitting parameters. ~ 1 and M ~ 2 between parallel In-plane magnetic fields that flip the magnetizations M and antiparallel can also be used to measure spin accumulation, and the resistance difference is DR ¼ 2Rs : For the ‘wire’ geometry treated below, Eq. (1.14) has a particularly simple interpretation when the probe separation is Lx ¼ ds : Apart from a factor of 2 that arises from self-diffusion of spins along the ^x-axis, the result is Rs < P1 P2 R:

ð1:15Þ

The ‘spin-coupled resistance’ related to spin accumulation is simply proportional to the ohmic resistance, and the constant of proportionality is the product of the fractional, interfacial spin polarizations of injector and detector.

46

M. Johnson

1.4.3.4

Spin injection experiments on bulk metal wires

The first experimental spin injection geometry consisted of a ‘wire’ of bulk, high purity aluminum about 100 mm wide and 50 mm thick (Johnson and Silsbee, 1985, 1988a), sketched in Fig. 1.14. An array of ferromagnetic pads, about 15 mm wide by 45 mm long, were fabricated, by photolithography and liftoff, as electrodes on the top surface, with interprobe spacings x in multiples of 50 mm. The F electrodes were e-beam deposited from a single source of Ni0.8Fe0.2 in a pressure of 1026 Torr after cleansing the Al surface with an Ar ion mill, and the films had a thickness of about 60 nm. The nonlocal geometry used in the experiment can be discussed with the aid of Fig. 1.14(b). The quasi-one-dimensional wire extends along the x^ -axis. A narrow ferromagnetic electrode F1 spans the width of the wire near its center, at x ¼ 0: When bias current I is injected at F1 and grounded at the left end of the wire, x ¼ 2b; there is a linear voltage drop from x ¼ 0 to 2b: This is depicted by the regularly spaced equipotential (dotted) lines in Fig. 1.14(b). However, there is no net current flow in the region x . 0 and the wire is at a constant potential from x ¼ 0 to x ¼ b: A voltage measurement between the end of the wire and a narrow electrode that spans the wire at x ¼ Lx is necessarily a null measurement, V ¼ 0: (a)

injector x=0

100 µ

50 µm

x=Lx

m

detector

Lx

W

(b) x = −b

y x

x=0

x=b

I F1 injector

F2 detector V

I+

Fig. 1.14 (a) Perspective sketch of nonlocal, quasi-one-dimensional geometry used in original spin injection experiment (Johnson and Silsbee, 1985, 1988b). High purity Al was cold rolled into a foil about 50 mm thick. Narrow ‘wires’ were cut, fixed to a substrate, and annealed. The injector and detector were lithographically patterned ferromagnetic films F1 and F2. (b) Top view. Dotted lines represent equipotentials characterizing electrical current flow. Gray shading represents diffusing population of nonequilibrium spin-polarized electrons injected at x ¼ 0; with darker shades corresponding to higher density of polarized electrons.

Introduction to magnetoelectronics

47

Spin-polarized electrons injected at F1 diffuse equally along ^^x; and this isotropic diffusion may not be obvious. Charge and spin are coupled at the F1 –N interface, IM / Ie ; because these two properties reside with the same carrier. However, after the first scattering event inside N the coupling is removed. Charge and spin transport in N are statistical events described by ensembles of particles. The coupling is weak: the probability that any particular electron that was injected at the F –N interface with a specified spin orientation will contribute to the electric current in N is negligible. Equivalently stated, the electric field associated with bias current I is weak and selfdiffusion of the nonequilibrium spin is symmetric, with each polarized electron performing a random walk along the x^ -axis (Johnson and Silsbee, 1985; Johnson and Byers, 2003). The density of diffusing spin-polarized electrons is depicted in Fig. 1.14(b) by the shaded region, with darker shades representing higher density. When the electrode at x ¼ Lx is also a ferromagnetic film, F2, a potentiometric measurement V records a spin-dependent voltage that is ~ 2 is parallel (antiparallel) with M ~ 1: relatively high (low) when the magnetization orientation M Since V ¼ 0 in the absence of nonequilibrium spin effects, this is truly a nonlocal measurement that uniquely discriminates against any background voltages. The ideal geometry of Fig. 1.14(b) is achieved when the electrodes have negligible width [they are drawn as lines in Fig. 1.14(b)] and have uniform contact across the width of the wire. Departures from ideality result in a small, spinindependent baseline voltage V – 0: For an effective measurement, it is necessary to choose F1 and F2 to have slightly different coercivities, HC;1 – HC;2 ; for example, by using different materials or by using the same material but slightly different shapes for the two electrodes. Thus, in any given measurement the detected voltage V as a function of externally applied field H should be positive whenever the magnetizations of F1 and F2 are aligned and negative over a field range HC;2 2 HC;1 ; when antialigned. For the geometry of Fig. 1.14, spin diffusion lengths can be determined by measuring VF2 as a function of injector –detector separation, Lx : Figure 1.15(a) shows magnetotransport data for a sample with Lx ¼ 300 mm at T ¼ 4 K, plotting R ¼ Vs =I vs magnetic field Hy : An in-plane field H ¼ Hy is used to control the relative ~ 1 and M ~ 2 of F1 and F2. The field Hy is swept along the easy axis of F1 magnetization orientations M and F2 [refer to Fig. 1.14(b)] from positive to negative values. The region 2 80 , H , 30 Oe ~ 1 and M ~ 2 are reorienting between parallel and represents the region where magnetizations M antiparallel and the detected voltage Vs drops from positive to negative. In the region ~ 1 and M ~ 2 return to parallel and the original, positive 2 200 , H , 2 80 Oe the orientations M voltage is regained. A field sweep from negative to positive values shows the same feature in the field range 2 30 , H , 200 Oe, as expected for the hysteresis of the ferromagnetic films. Figure 1.15(b) shows similar data for a sample with Lx ¼ 50 mm at T ¼ 27 K. The coercive fields HC;1 and HC;2 of F1 and F2 are marked, and the detected voltage Vs is again observed to be ~ 1 and M ~ 2 are antiparallel. The spin accumulation Rs is identified as half the negative when M difference of the dip. The spin accumulation at Lx ¼ 50 mm [Fig. 1.15(b)] is larger than that for Lx ¼ 300 mm [Fig. 1.15(a)], and measurements of Rs ðLx Þ; at constant temperature and adjusted for

48

M. Johnson

(a) 0.4 0.2

0.0

--0.2 --0.4 --200

0

200

400

600

Field (Oe) (b) 2

1

0

--1 --150 --100

--50

0

50 H C1H C2 150

Field (Oe)

Fig. 1.15 (a) Example of data from bulk Al wire sample, presented in units of resistance as R ¼ V=I: External field is applied along y^ -axis, in the plane of F1 and F2, starting at Hy ¼ 600 Oe, sweeping down and stopping ~ 1 and M ~ 2 change their relative orientation from parallel to at Hy ¼ 2220 Oe. The dip occurs when M antiparallel. A similar dip occurs for symmetric positive field when Hy is swept from negative to positive. Lx ¼ 300 mm, T ¼ 4:3 K. (b) Similar data for a sample with Lx ¼ 50 mm, T ¼ 27 K. The field is swept from Hy ¼ 2140 Oe up to Hy ¼ 125 Oe.

sample-to-sample variations of P1 and P2 ; resulted in a determination of a long spin diffusion length (at 4 K), ds < 0:3 mm. As described above, spin injection, detection, accumulation and relaxation are directly and quantitatively measured by the Hanle effect. In the geometry of Fig. 1.14, a field applied along the x^ - or z^-axis is perpendicular to the orientation of the injected spins and causes them to precess (Johnson and Silsbee, 1988a). Since the spins are moving diffusively, those that enter the detector

Introduction to magnetoelectronics

49

film at any given time have a distribution of arrival times and, because of spin precession, a distribution of accumulated phase angle. In the limit of zero external field, all spins have zero phase and the signal has maximum value. At a sufficiently large magnitude of field, the distribution of accumulated phase angle will span 2p radians, and the detected signal is reduced to zero. This process is equivalently described as a one-dimensional random walk (Johnson and Silsbee, 1985). This is the same physics as TESR, but performed at zero frequency, and the half width at half maximum (hwhm) of an observed Lorentzian signal is a measure of the transverse spin relaxation time, DH ¼ ðgT2 Þ21 : In the limit T2 ! 1; the polarized spins remain coherent as the field increases and coherent precession would be observed in the form of a periodic spin-coupled resistance. A direct analogue in TESR is the observation of periodic transmission maxima associated with ballistic electrons, and these are called Larmor waves (Janossy and Monod, 1976). In the limit T2 ! 0; the linewidth of an absorptive Hanle feature broadens in field, Hhwhm ! 1: An example of the Hanle effect from an Al wire sample is shown in Fig. 1.16, presented in units of resistance, R ¼ Vs =I: For this sample, the injector and detector have magnetization anisotropies such that their easy magnetization axes are oriented perpendicular to each other and the resulting lineshape, dispersive in appearance, is fit using Eqs (1.12) and (1.13b). For these data, Lx ¼ 300 mm, T ¼ 4:3 K, and the deduced fitting parameters are P ¼ 5:0% and T2 ¼ 10 ns (when the injector and detector are fabricated from the same material, P ¼ P1 ¼ P2 ). In Fig. 1.16, note that the voltage Vs is bipolar. At H ¼ 0; injected spins are oriented at 908 to the detector, and Vs ¼ 0: As H increases with positive values the injected spins precess in a direction that brings them into alignment with the detector and Vs is positive. When H decreases, with negative values, the precession brings the injected spin orientation into antialignment with the detectors and Vs is negative. In general, the Hanle data are fit to a mixture of absorptive and dispersive contributions, using a linear combination of Eqs (1.13a) and (1.13b) to represent the relative orientation between injector and detector. Figure 1.17 presents more typical data, from a sample with Lx ¼ 50 mm and T ¼ 21 K. The uniaxial magnetization anisotropy axes of F1 and F2 were not perfectly parallel

0.4 0.2 0.0 --0.2 --0.4 --30

--20

0 --10 Field (Oe)

10

20

30

Fig. 1.16 Example of Hanle data, with dispersive lineshape, from bulk Al wire sample, presented in units of resistance as R ¼ V=I: Lx ¼ 300 mm, T ¼ 4:3 K. Solid line is fit to Eqs (1.12) and (1.13b): T2 ¼ 10 ns, P ¼ 0:050:

50

M. Johnson

3

R (nΩ)

2

1

0

120

80

40

0

40

80

120

Field (Oe)

Fig. 1.17 Example of Hanle data having absorptive lineshape, with small admixture of dispersive character. Lx ¼ 50 mm, T ¼ 21 K. Solid line is fit to Eqs (1.12) and (1.13): T2 ¼ 7:0 ns, P ¼ 0:075:

causing the small symmetry deviation from a Lorentzian lineshape. The deduced fitting parameters are P ¼ 7:5%; T2 ¼ 7:0 ns, z ¼ 0:84 and j ¼ 20:39; where z and j are the fractional contributions of absorptive and dispersive components (Johnson and Silsbee, 1988a). In these early experiments on bulk Al wires, the deduced values of P ranged from 5 to 8%, much lower than typical polarization values of 40–50% generally associated with transition metal ferromagnet films. Because the ‘wire’ samples were bulk Al, the lithographic processing resulted in a highly faceted surface along with the presence of oxides and other contaminants. Although the Al surface was cleansed with an Ar ion mill before deposition of the Py films, it is likely that the interface quality was poor, and the value of P was therefore diminished from ideality. An important impact of this first spin injection experiment was the demonstration that the polarization state of an itinerant electron in a nonmagnetic metal could be converted into a voltage. For the sample with Lx ¼ 50 mm, for example, the resistance of the segment of the Al wire between F1 and F2 was 220 nV at 4 K. The data of Fig. 1.15, with amplitude Rs ¼ 2:8 nV, correspond to a resistance modulation DR=R ¼ 2Rs =R ¼ 2:5%; slightly larger than the early spin valve results that were reported a few years later (Binasch et al., 1989). At 4 K the value of 2Rs =R in this sample was about 4%. As a technique for the study of spin transport, spin injection is highly sensitive for the detection of polarized electrons. The noise floor of the data of Fig. 1.17 represents the threshold of detection, corresponding to about one nonequilibrium spin out of 1012 equilibrium spins. Given the sample volume, typical data (on the order of 1 nV in Fig. 1.17) represent a population of roughly 106 nonequilibrium spins, a detection sensitivity that is several orders of magnitude better than that of TESR.

Introduction to magnetoelectronics 1.4.3.5

51

Quantitative analysis of T2

The dominant spin relaxation mechanism in metals is the weakly relativistic spin –orbit interaction, derived independently by Yafet (1952) and Elliott (1954) and introduced earlier in Section 1.3. An electron with spin ~s moves in a periodic potential UðrÞ with a weakly relativistic Fermi velocity vF (refer to Fig. 1.9). In the rest frame of the electron, any scattering event that changes the electron trajectory is a perturbation of the periodic electric field, which transforms as a magnetic field (Johnson, 2000a). This effective magnetic field ‘pulse’ can exert a torque on the spin. Formally, the effect derives from a term in the Dirac equation (Yafet, 1952): h ð7U £ p~Þ·~s; 4m2 c2

ð1:16Þ

with m the electron mass and c the speed of light. From inspection of Eq. (1.16), any scattering event that changes the momentum p~ can couple weakly to the spin. While scattering events with impurities, phonons, grain boundaries and surfaces can affect ~s with different strength, the parameter c2Y / t=T1 is a property of a given material and is relatively large (small) for high Z (low Z) elements. Here t is a mean scattering time given by Matthiessen’s rule, 1=t ¼ ð1=tin þ 1=timp Þ; T1 is the longitudinal spin relaxation time, and we note that the transverse and longitudinal times T2 and T1 are the same in metals. The probability of flipping a carrier spin, per scattering event and averaged over all scattering events, is determined experimentally and given by the ratio a ¼ t=T1 ; t=T2 : From the spin injection experiment, values of T2 for a number of samples and a range of temperature were deduced from fits to Hanle data. These compared well with values of T2 ðTÞ measured on Al foils by TESR. At low temperature (4 K), scattering is dominated by impurities and surfaces, and the ratio aAl ¼ 0:001 was found (Johnson and Silsbee, 1988b). 1.4.3.6

Spin injection in thin metal films

Spin injection has become an important research technique because it offers the ability to study spin relaxation in novel systems. For example, relaxation times in thin metal films are very short. TESR requires the detection of a broad lineshape at high magnetic field and background effects related to cyclotron orbits interfere with the measurement. The thin film sandwich geometry of Fig. 1.18 was developed for spin injection studies in metal films and the structure became known as the ‘bipolar spin switch’ (Johnson, 1993a,b). Spinpolarized carriers are injected through two identical ‘window’ junctions F1 into the sample N of thickness d; and they diffuse across the sample thickness. The ferromagnetic electrode F2 measures the nonequilibrium electrochemical potential in N, EF;n;# and the voltmeter V compares this with the average electrochemical potential EF;n detected by electrode N0 . ~ 1 and M ~ 2 are set in a remanent state in the x – z plane, the Hanle When magnetizations M effect can be demonstrated by biasing the sample with current I and measuring VðHy Þ:

52

M. Johnson

N N’

V F1 F2

I d z

y x

Fig. 1.18 Perspective sketch of thin film geometry known as ‘bipolar spin switch’ (Johnson, 1993b). Spinpolarized electrons are injected from F1 through two parallel ‘windows’ and diffuse across the sample volume. Detecting film F2 measures the spin subband chemical potential of the ‘spin accumulation’ relative to the ~ 2 are fixed in the x – z ~ 1 and M chemical potential averaged over both spin subbands. For the Hanle effect, M plane and external field Hy is applied along the y^ -axis.

This is demonstrated in a gold film ‘bipolar spin switch’ sample with the data of Fig. 1.19 (Johnson, 2002a). Since injector and detector had shape anisotropies along orthogonal axes, Eq. (1.13b) is used to fit the dispersive lineshape and the result, with T2 ¼ 80 ps, is also plotted in Fig. 1.19 as a solid line. Using Eq. (1.14) with r ¼ 1:0 £ 1026 V cm, d ¼ 200 nm,

40

R S (µΩ)

35 30 25 20 15 –2000

–1000

0

1000

2000

Field (Oe)

~ 1 and Fig. 1.19 Example of Hanle data from thin film Au sample, showing dispersive line achieved when M ~ 2 have relative orientation of approximately 908. Solid line is the fit to Eqs (1.12) and (1.13): T2 ¼ 80 ps. M T ¼ 4:3 K.

Introduction to magnetoelectronics

53

pffiffiffiffiffiffiffiffiffi Vol ¼ 10210 cm3, ds ¼ DT2 ¼ 1:8 mm, and noting the amplitude is 2Rs for dispersive lineshapes [Eq. (1.13b)], the value P1 ¼ P2 ¼ 25% is derived for the polarization of injector and detector. This is in reasonable agreement with values cited in the literature (Soulen et al., 1998). Whereas the dispersive Hanle data from the bulk Al wire (Fig. 1.16) were characterized by a bipolar voltage, the data of Fig. 1.19 are offset by a baseline resistance of about 28 mV. The likely source is a slight lithographic misalignment of the two detecting electrodes, N0 and F2. Of greater interest is a comparison of the magnitudes of the spin accumulation effects observed in Figs 1.16 and 1.19, the order of 1 nV in the former and 10 mV in the latter. The dramatic difference of four orders of magnitude is a graphic demonstration of the inverse scaling of spin ~ / 1=Vol; and the volume of the thin film sample is orders of magnitude accumulation, Vs / M smaller that that of bulk wire. Also of interest is the observation that the data of Fig. 1.19 are not symmetric about H ¼ 0; as is seen (and predicted) with a purely dispersive Hanle effect in bulk Al. A similar shift was observed for an absorptive Hanle feature in data taken on a thin Nb film (Johnson, 1994a). According to one theory, this shift is caused by a transfer of spin magnetization between the nonequilibrium spin-polarized electrons and the nuclei (Johnson, 2000c). Sometimes known as Overhauser coupling, a hyperfine contact interaction between conduction electrons and nuclei allows the transfer of spin angular momentum from a population of conduction electrons, each of which has a large magnetic moment, to the population of nuclei, each of which has a much smaller moment. The induced nuclear magnetization would appear as an effective magnetic field, thereby adding a small bias field to the observed results. These effects would be expected in thin film samples, where the injected nonequilibrium spin-polarized electron population is relatively large. Overhauser coupling to the nuclear spin system has been demonstrated in semiconducting samples by optical pumping of spin-polarized electrons (Lampel, 1968). ~ 1 and M ~2 An in-plane external field Hz can be used to manipulate the magnetizations M between parallel and antiparallel. The electrochemical potential of electrode F2 (Fig. 1.18) then rises or falls to line up with the nonequilibrium electrochemical potential EF;n;" or EF;n;# and the detected resistance difference DR is identified as DR ¼ 2Rs e2d=ds ; as discussed above. Experiments of this kind were performed on Au and Nb thin film samples, and the thickness d was varied so that a measurement of DRðdÞ would determine the spin depth ds : For Au (Nb), values ds ¼ 1:5 ^ 0:4 mm ðds ¼ 0:75 ^ 0:2 mmÞ and aAu ¼ 0:002 ðaNb , 0:00002Þ were found at low temperature ðT < 10 KÞ: For Au films, the deduced value of T1 ¼ 46 ps differs from the value deduced from Hanle data, T2 ¼ 80 ps, by a factor of roughly 2. This is reasonable agreement, but the discrepancy is not yet understood. Thus, these transport measurements give a value aAu ¼ 0:0015 ^ 0:0005: Further measurements on Au films were performed by using a novel, optical technique to measure the longitudinal relaxation time (Elezzabi et al., 1996). The value T1 ¼ 45 ps was found at room temperature. However, the resistivity of the Au sample was larger than that of the sample in the transport study, and the value of aAu was therefore smaller, aAu ¼ 0:0005: The difference between values of aAu could be related to differences of technique. It also suggests that the

54

M. Johnson

probability of spin scattering varies for different kinds of scattering events, differing for phonons and impurity scattering. The magnitude of DR observed in the transport measurement using in-plane fields deserves comment. The Hanle data were fit using two free parameters, T2 to fit the lineshape and P to fit the magnitude. The reasonable values T2 ¼ 80 ps and P ¼ 0:25 were deduced. The amplitude of dispersive Hanle data (Fig. 1.19) should be the same as the magnitude DR of the dip observed when ~ 1 and M ~ 2 are switched from parallel to antiparallel by an in-plane field, 2Rs : However, the latter M magnitude was substantially larger, DR q 2Rs ; for both Au and Nb sample sets. Rigorous attempts have not succeeded in explaining this result (Hershfield and Zhao, 1997). One proposed explanation ~ is relevant for the case of in-plane fields, and is smaller than is that a dynamic susceptibility, xðMÞ; the static Pauli susceptibility that is relevant for the Hanle effect (Cullen and Chui, 1995). Recently, spin injection has been applied to thin film aluminum mesoscopic structures and the inverse scaling of spin accumulation has been confirmed in samples with lateral dimensions as small as 200 nm. Several experiments are reviewed in Zutic, 2004. One set of experiments used the original Johnson–Silsbee geometry with a 50 nm thick Al wire, about 200 nm wide, and ferromagnetic injectors and detectors fabricated from cobalt thin films. The deduced fractional efficiency of injected polarization of roughly 11%, for interfaces that included aluminum oxide tunnel barriers, is the same order as the value P ¼ 6.5 ^ 1.5% that was observed for Permalloy electrodes (and no tunnel barriers) in the original spin injection experiment. At low temperature, 4 K, a spin relaxation time of about T1 < 100 ps was deduced, slightly longer than the value of T1 for Au films deduced from Hanle data (Fig. 1.19). These recent experiments included application of a transverse magnetic field and the observation of the Hanle effect. The Hanle data has an absorptive lineshape, and can be fit to Johnson–Silsbee theory, Eqs (1.12) and (1.13). The observation and quantitative description of spin accumulation effects in mesoscopic samples confirms the validity of Johnson-Silsbee theory over a range of 8 decades. Theory predicts that spin injection in mesoscopic devices could achieve values of a spin accumulation transresistance as large as 10 ohms in structures with characteristic dimensions of order 100 nm. Although not sufficiently large to compete with MTJs, spin injection devices that are shrunk to these small dimensions would have values of DR that are larger than CPP spin valves, which are considered to be competitive for future generations of read heads.

1.4.3.7

Further analysis of T2

Shortly after the spin injection results on thin Au films, values of ds ¼ 0:5 mm and aAg ¼ 0:005 for thin Ag films were deduced from GMR measurements using F/N multilayers (Yang et al., 1994). In this CPP GMR geometry, interfacial spin relaxation at the Py/Ag interfaces may contribute to the relatively high spin flip probability. By contrast, interfacial spin scattering at Py/Au interfaces is negligible, which is why substantial GMR effects have not been observed in samples using

Introduction to magnetoelectronics

55

Au layers. Considering this difference and variations of technique, the values of aAg and aAu are comparable, and are marginally larger than the value aAl ¼ 0:001 for aluminum. Since Ag and Au have a large value of Z but Al has a low value, these results would seem to be in contradiction with the Yafet –Elliott theory. An understanding of the apparent discrepancy came with the realization that polyvalent metals, such as aluminum, have nonspherical Fermi surfaces. A careful study of the Fermi surface showed that spin hotspots exist near degeneracy points and Brillouin zone boundaries (Fabian and Das Sarma, 1998). High spin relaxation rates that dominate spin relaxation processes are associated with these hotspots. Thus, while t=T1 is indeed roughly 0.0001 over most of the aluminum Fermi surface, the experimental value a ¼ 0:001 is an average over all of the Fermi surface, including the rapid hot spot relaxation. 1.4.4

Spin valves and giant magnetoresistance

Returning to the historical review of spin transport phenomena, following the SDT work of the 1970s and the spin injection work of the early 1980s, GMR effects were empirically discovered in the late 1980s in trilayer sandwich structures (Binasch et al., 1989) and, independently, in multilayers (Baibich et al., 1988). Related to GMR, coupling of the magnetization orientations of thin ferromagnetic films was studied in F –N–F trilayers and (F–N) multilayers. The basic idea of the ‘exchange bias’ at a ferromagnet/antiferromagnet interface was known for decades (Meiklejohn and Bean, 1956; Malozemoff, 1987). Grunberg showed that exchange bias could be used to couple the magnetization orientations of two thin Fe films separated by a thin N layer (Grunberg et al., 1986). It was later discovered that the magnetoresistance of a trilayer Fe – Cr –Fe sample was slightly larger than the expected AMR of the F layers (Binasch et al., 1989). At about the same time, Baibich et al. (1988) fabricated Fe/Cr multilayers and discovered that the low temperature magnetoresistance was much larger than the intrinsic AMR of the Fe layers. These three experiments launched the subfield known as GMR, which is discussed in detail in Chapter 2. Parallel developments were made with tunneling devices. Research on Josephson junctions for applications of superconducting logic led to new techniques for the fabrication of high quality tunnel junctions. Traditional junction fabrication used the native oxide of a superconducting metal electrode, such as Nb, as the tunnel barrier between top and bottom electrodes. These barriers suffered from poor reproducibility, poor thermal cycling, and high probability of pinhole shorts. In a new technique (Gurvitch et al., 1983), a thin film of Al (roughly 1 nm thick) was deposited on the bottom Nb electrode. The Al film wetted the surface such that a continuous, pinhole-free film was reliably formed for thicknesses that corresponded to only a few atomic layers. The Al film was then oxidized, and the top electrode was fabricated on top of the Al2O3 barrier. The resulting tunnel junction had remarkably reproducible and robust characteristics. In the late 1980s, Julliere’s idea of SDT between two ferromagnetic materials was revived for an application to scanning tunneling microscopy (STM). Chromium dioxide (CrO2) is

56

M. Johnson

a half-metallic ferromagnet, having one spin subband that lies almost entirely below the Fermi level. The transport current comes almost entirely from one spin subband and, therefore, the spin polarization is close to 100%. Single crystal chromium is antiferromagnetic, and a vicinal surface of a Cr sample has atomic plateaus with local spin ordering that alternates between up and down. An STM tip was fashioned from a CrO2 crystal and was scanned over a vicinal Cr surface in UHV (Weisendanger et al., 1990). A variation of the tunneling current was periodic with alternating plateaus, and the amplitude of the variation could be fit to a model of SDT. In a conceptually similar experiment (Johnson and Clarke, 1990), a single crystal of Ni was polished and mounted on an STM tip assembly. A portion of a small Permalloy torus was wrapped with 170 turns of wire. Current applied to the wire at audio frequency f modulated the magnetization in the Permalloy torus. Low frequency feedback was applied to maintain the Ni tip at constant height over the Permalloy surface, and modulation of the tunnel current at f was detected. The modulation amplitude was analyzed using a model of SDT, and tunnel conductance modulations DG=G of 14 –35% were observed at room temperature. Spin-polarized scanning tunnel microscopy continues as an important research technique (Wulfhekel and Kirschner, 1999). The Josephson junction fabrication technique became important to the field of spindependent transport when it was applied to the fabrication of planar MTJs (Moodera et al., 1995). Thin, pinhole-free Al films could be prepared on surfaces of transition metal ferromagnet films. After oxidation of the Al to form the tunnel barrier, a top ferromagnetic electrode was added and the resulting MTJs had high ratios of magnetoresistance at room temperature, DR=R ¼ 12%: Of equal importance, the characteristics of these devices were very reproducible and the structures did not degrade in ambient conditions. MTJs are highly promising for a variety of applications, and they are discussed in detail in Chapter 3.

1.4.5

The beginnings of magnetoelectronics

Magnetoelectronics is devoted to the invention and development of electronic device structures that incorporate a magnetic element. Applications in integrated digital electronics are the focus of this volume, but magnetoelectronics includes applications as magnetic field sensors. Magnetoelectronics as a field of applications developed from a number of important experiments. Numerous ideas for MRAM were proposed in the 1960s, and Chapter 4 reviews several of these concepts. Daughton and Pohm (Pohm et al., 1988) pioneered early ideas of block addressable, nonvolatile, magnetoresistive random access memories (MRAMs) in the 1980s. In the early 1990s, Prinz (1990) popularized the concept of magnetoelectronics by studying hybrid ferromagnetic –semiconductor structures, and Johnson proposed a bit addressable nonvolatile magnetic RAM (Johnson, 1993b) along with magnetoelectronic logic applications (Johnson, 1994b). By the late 1990s there were major MRAM research efforts in a variety of industrial and academic laboratories.

Introduction to magnetoelectronics

57

The technology for magnetic field sensors used as read heads for data stored on magnetic media involved inductive pickup until the 1990s. The invention and development of magnetoresistive read heads using the AMR of a thin ferromagnetic film was a paradigm shift for the recording industry (refer to Chapter 3). After their introduction in 1993, the density of data stored on magnetic disks (areal bit density) began to increase at a yearly rate of about 60%. Of equal importance, this shift to a magnetoresistive technology enabled the industry to take advantage of GMR materials, whose MR ratios of roughly 10% are four or five times larger than AMR ratios of 2–2.5%. When GMR read heads replaced AMR heads in 1998, the bit density began to increase at a yearly rate of 100%. A disk drive bought in 2003 has a GMR head with MR of 15% or more. It is likely that future generations of read heads will use MTJs, starting around 2005. Areal bit densities of several hundred Gb/in.2 can be expected by 2007.

1.5

Special topic

There is presently a high degree of interest in studies of spin injection from ferromagnetic metals to nonmagnetic metals, and from ferromagnetic semiconductors to nonmagnetic semiconductors. An issue of focussed interest is the relevance of the relative resistance of the magnetic and nonmagnetic materials, and the efficiency of spin injection across the magnetic/nonmagnetic interface. The goal of this book is to clearly present basic concepts of the physics that underlies magnetoelectronics, and narrowly defined issues have been avoided. However, the question of ‘conductance mismatch’ at a ferromagnet/nonmagnet (F/N) interface continues to cause confusion. A theoretical treatment of this topic is given in this section, with some depth, in order to clarify the issue (Johnson, 2002b,c; Johnson and Byers, 2003). The tensor formalism of Johnson and Silsbee (1987) was developed for diffusive charge and spin transport in three dimensions. In this section, vector quantities will be denoted with bold face in order to avoid confusion with tensor notation. Following an entropy production argument, currents of charge ðJq Þ; heat ðJQ Þ; and magnetization ðJM Þ in a bulk ferromagnetic (F) or nonmagnetic (N) metal are related to gradients of voltage ð7VÞ; temperature ð7TÞ; and magnetization potential ð7 2 H p Þ by the general equations of motion (Johnson and Silsbee, 1987): 0 1 B B B B a00 k2 T 2 B C B B JQ C ¼ 2gB B @ A B eEF B JM B @ pmB e 0

Jq

1

a00 kB2 T eEF a0 kB2 T e2   m T kB 2 p0 B EF e

1 pmB C0 1 e C 7V  2 C C m k T C CB 7T C p0 B B CB @ A; C e EF C C 7 2 Hp A m2B z 2 e

ð1:17Þ

with g ¼ 1=r the bulk conductivity. The magnetization potential H p is defined as ~ x 2 H ¼ M= ~ x (with x the susceptibility) for the relevant case of zero 2H p ; M=

58

M. Johnson

~ ¼ M 2 M0 ; with M0 the thermal external field H: The nonequilibrium magnetization, M equilibrium value (M0 ¼ 0 in N), arises from transport effects such as spin injection. For the simple case 7T ¼ 0; 7ð2H p Þ ¼ 0; Eq. (1.17) gives JM ¼ ðpmB =eÞJq : Here p ¼ ðJ" 2 J# Þ=ðJ" þ J# Þ ¼ ðg" 2 g# Þ=ðg" þ g# Þ is the fractional spin polarization of carriers defined earlier in this chapter, J" and J# are the spin subband partial currents, and g" and g# are the spin subband conductivities (note that g and s are synonymous). Recalling earlier remarks about the Einstein relations, the conductivity and current density are proportional to the density of states at EF ; Ji / Ni ðEF Þ: In a nonmagnetic material N, the spin subband densities of states at the Fermi level are equal, N" ðEF Þ ¼ N# ðEF Þ; the spin subband conductivities are equal, g" ¼ g# ; and pn ¼ 0:

ð1:18Þ

In a ferromagnetic metal, N" ðEF Þ – N# ðEF Þ and pf – 0; so that values of pf for transition metal ferromagnets vary from 0.1 to 0.45 (Soulen et al., 1998). The other kinetic coefficients Lij in Eq. (1.17) have been estimated from a free electron model. The fractional polarization constant p0 would be associated with spin flow driven by thermal gradients, and constants a0 and a00 can be related to the thermal conductivity k and thermopower e (Johnson and Silsbee, 1987). Finally, L33 ¼ zðmB =eÞ2 describes self-diffusion of nonequilibrium spins and z < 1 (z ¼ 1 for noninteracting electrons). Thus, a current of spin-polarized electrons in a nonmagnetic material is given by JM;n ¼ g

m2B 7ðH p Þ: e2

ð1:19Þ

The same approach can be applied to a discrete system, and interfacial currents of charge ðIq Þ; heat ðIQ Þ; and magnetization ðIM Þ are related to differences, across an interface, of voltage ðDVÞ; temperature ðDTÞ; and magnetization potential ðDð2H p ÞÞ: 0 B 1 B B B k2 T 2 B C B B IQ C ¼ 2GB B @ A B ee B IM B @ hmB e 0

Iq

1

kB2 T ee akB2 T e2   m T kB 2 h0 B e e

1 hmB C0 1 e C DV  2 C C m k T C CB h0 B B DT C CB @ A; e e C C C D 2 Hp A m2B j 2 e

ð1:20Þ

with G ¼ l=Ri the intrinsic conductance of the interface. The kinetic coefficients L013 ¼ L031 are identified in a manner similar to those of Eq. (1.17). Polarization parameter h describes the fractional polarization of current crossing the interface, h ¼ ðI" 2 I# Þ=ðI" þ I# Þ ¼ ðG" 2 G# Þ= ðG" þ G# Þ: The interface may be characterized by spin asymmetry and, in general, h # pf : Note that elsewhere in the chapter the parameter P is commonly used, even though h may be strictly correct.

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Using these equations of motion, Eqs (1.17) and (1.20), charge–spin coupling effects at the interface between a ferromagnetic and nonmagnetic material can be studied. The consequences of ‘resistance mismatch’ at an F –N interface were first derived by Johnson and Silsbee (1987), and the physical principles are described with the aid of Fig. 1.20. Equation (1.17) is written for transport in F and N, and Eq. (1.20) is written for the interface region, defined as a volume with a thickness of an electron mean free path ‘ on either side of the physical interface, x ¼ 0 ^ ‘ [Fig. 1.20(a)]. Far away from the interface, the current in F is polarized with the value in bulk, JM;f ¼ pf ðmB =eÞJq : The current in N, far from the interface, is unpolarized, JM;n ¼ 0: At the interface (x ¼ 0 in Fig. 1.20), polarized current JM is injected into N and creates spin ~ The density M ~ n in N decays exponentially away from the interface with accumulation M: characteristic length ds;n ; driven by self-diffusion and the L33 term of Eq. (1.20). This term also

(a) F

N

Jq µ JM = pf B Jq e

Jq

JM=?

JM= 0 H*

(b) Hf*(x=0)

Hn*(x=0) δs,n

δs,f

x

x=0 (c) slope

V(x) ρf

JqReff

slope ρ

n

JqRi

x (d)

JM pf

x

Fig. 1.20 Flow of charge and spin currents, Jq and JM ; near the interface between a ferromagnetic metal and ~ nonmagnetic material. (a) Model system. x ¼ 0 at the F –N interface. (b) Magnetization potential, H p / M: (c) Voltage. The self-diffusion of nonequilibrium spins, back across the interface, creates an effective interface resistance, Reff : (d) Spin-polarized current. JM is reduced from value in bulk of F by the backflow of polarized spins, an effect determined by ‘resistance mismatch’.

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~ back across the interface into F, where the nonequilibrium spin density drives the diffusion of M ~ xÞn ~ Mf decays with characteristic length ds;f : The associated magnetization potentials, Hnp ¼ ðM= p ~ xÞf ; are shown in Fig. 1.20(b). Since xf differs from xn ; it follows that and Hf ¼ ðM= p Hn ðx ¼ 0Þ – Hfp ðx ¼ 0Þ: The back diffusion of nonequilibrium spins has several consequences. Away from the interface, current flow is ohmic and a plot of VðxÞ shows slopes proportional to rf and rn in F and N, respectively [Fig. 1.20(c)]. Since both charge and spin reside on the same carrier, the backflow of polarized spins across the F –N interface is also a backwards flow of charge. This negative charge current must be overcome by the imposed current Jq ; causing the appearance of an effective interface resistance, Reff ¼ ½ pf ðmB =eÞHfp =Jq ; in addition to the intrinsic interface resistance Ri [Fig. 1.20(c)]. Furthermore, the backflow of polarized spins cancels a portion of the imposed polarized current JM;f : As JM approaches the interface, the fractional polarization is diminished from the bulk value, pf [Fig. 1.20(d)]. Rigorous expressions for JM are readily found. Assuming T is constant, and using the conditions that Jq and JM are continuous, a general form for the interfacial magnetization current is (Johnson and Silsbee, 1987, 1988d)   hmB 1 þ Gðpf =hÞrf ðj 2 h2 Þ=ðzf 2 p2f Þ ; J JM ¼ e q 1 þ Gðj 2 h2 Þ½ðrn =zn Þ þ rf =ðzf 2 p2f Þ

ð1:21Þ

where rf ¼ df rf ; rn ¼ dn rn and recall j; zf ; zn < 1: Interfacial spin transport is governed by the relative values of the intrinsic interface resistance Ri ¼ 1=G; and the resistances of a length of normal and of ferromagnetic material equal to a spin depth, rn and rf : Typical values for metal films are rf < 20 mV cm £ 5 nm , 10211V cm2 (Dubois et al., 1999) (nearly temperature independent), and rn < 2 mV cm £ 1 mm , 2 £ 10210 V cm2 at cryogenic temperature (Johnson, 1993a) (somewhat smaller at room temperature). The interface resistance Ri may be determined by a tunnel barrier, by a pinhole in a poorly conducting interface layer, or by a contact resistance Rc : The latter represents the low resistance limit, and a typical value for Rc can be found from the contact resistance measured between two copper layers making contact in a patterned structure, Rc < 1029 V cm2 (Bussman et al., 1998). Since all of these values fall within a range of two decades, all terms in Eq. (1.21) are expected to be important for the general case. For the limiting case G ! 1; Eq. (1.12) takes the simplified form (Johnson and Silsbee, 1987): JM ¼ p f

  mB 1 ; Jq e 1 þ ðrn =rf Þð1 2 p2f Þ

ð1:22Þ

and the injected polarization is reduced from that in the bulk of F by the factor: ½1 þ ðrn =rf Þð1 2 p2f Þ21 ¼ ð1 þ M 0 Þ21 :

ð1:23Þ

Introduction to magnetoelectronics

61

Using the above estimates for rf and rn ; M 0 can be as large as M 0 , 20 and consequently JM may be reduced to a small fraction of pf : But this is valid only for the condition Ri p rn ; rf (Johnson and Silsbee, 1988d). In the opposite regime, Ri q rf ; rn ; transport is dominated by Ri ; Eq. (1.21) reduces to JM ¼ hðmB =eÞJq

ð1:24Þ

and the polarization is given by the interfacial parameter h: Issues related to the effects of ‘resistance mismatch’ on the efficient injection of polarized electrons at an F –N interface have caused some confusion that can be clarified by discussing Eqs (1.21)–(1.24). The case where N is a semiconductor (Rashba, 2000) has been a focus of debate, but questions also arise when N is a nonmagnetic metal (Johnson, 2002d). The result for infinite interface conductance, Eqs (1.22) and (1.23), has been used to argue that the polarization of current driven across the interface between a ferromagnetic metal and a nonmagnetic semiconductor will be negligibly small because the mismatch factor M 0 is so large. However, the intrinsic interface resistance at such an interface is never zero and application of the infinite interface conductance form is not valid. The general result described by Eq. (1.21) must be used for this system. The simple expression that represents the opposite limit, Eq. (1.24), may be used in the typical case where the interface resistance Ri (determined, for example, by a Schottky barrier or a thin tunnel barrier) is larger than rf and rn : A variety of calculations have been used to show that a tunnel barrier employed at the ferromagnetic metal/semiconductor interface will promote efficient spin injection (Rashba, 2000; Hu and Matsuyama, 2001), and recent experiments have demonstrated that a Schottky barrier also permits efficient spin injection (Zhu et al., 2001). However, the conditions imposed by Eq. (1.21) merely require that Ri be sufficiently large to block diffusion back across the F –N interface. It must be emphasized that the presence of a high quality tunnel junction or Schottky barrier is not required for efficient spin injection. Effects of ‘resistance mismatch’ are negligible whenever the intrinsic interface resistance Ri is the dominant resistance, regardless of the detailed origin of Ri : This is almost always the case in real systems. The fully general expression for the interfacial magnetization current, Eq. (1.21), must also be used for spin injection across a ferromagnetic metal/nonmagnetic metal interface. The intrinsic interface resistance Ri cannot be approximated as zero because the unit resistances rn and rf are typically so small that the contact resistance Rc of the interface cannot be neglected, rf , 10211 V cm2, rn , 2 £ 10210 V cm2 p Rc < 1029 V cm2. In summary, the effects of resistance mismatch are almost always negligible. If spin injection experiments show weak effects, effects of resistance mismatch can almost certainly be eliminated as a cause. A variety of other issues may be relevant, and other causes must be considered.

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References Ando, T., Fowler, A.B., and Stern, S. (1982). Electronic properties of two-dimensional systems. Rev. Mod. Phys. 54, 437. Aronov, A.G. (1976a). Spin injection in metals and polarization of nuclei. Pis’ma Zh. Eksp. Teor. Fiz. 24, 37 [Sov. Phys. JETP Lett. 24, 32]. Aronov, A.G. (1976b). Spin injection in a superconductor. Sov. Phys. JETP 44, 193. Aronov, A.G. and Pikus, G.E. (1976). Spin injection into semiconductors. Sov. Phys. Semicond. 10, 698. Ashcroft, N.W. and Mermin, N.D. (1976). Solid State Physics, Holt, Rinehart and Winston, Philadelphia, PA. In particular, see Chapters 17 and 29. Baibich, M.N., Broto, J.M., Fert, A.F., Nguyen Van Dau, F., Petroff, F., Eitenne, P., Creuzet, G., Friederich, A., and Chazelas, J. (1988). Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices. Phys. Rev. Lett. 61, 2472. Binasch, G., Grnberg, P., Saurenbach, F., and Zinn, W. (1989). Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange. Phys. Rev. B 39, 4828. Brown, W.D. and Brewer, J.E. (1997). Nonvolatile Semiconductor Memory Technology: A Comprehensive Guide to Understanding and Using NVSM Devices, Wiley/IEEE Press, New York. Bussman, K., Cheng, S.F., Prinz, G.A., Hu, Y., Gutmann, R., Wang, D., Beech, R., and Zhu, J. (1998). CPP giant magnetoresistance of NiFeCo/Cu/CoFe/Cu multilayers. IEEE Trans. Magn. 34, 924. Campardo, G. and Micheloni, R. (2003). Special issue on Flash memory technology. Proc. IEEE 91(4), 483. Campbell-Kelly, M. (1997). Computer: A History of the Information Machine (The Sloan Technology Series), Basic Books, New York. In particular, see Chapter 7. Clinton, T.C. and Johnson, M. (1999). Nonvolatile switchable Josephson junctions. J. Appl. Phys. 85, 1637. Cullen, J. and Chui, S.T. (1995). Spin transmission in metallic trilayers. Phys. Rev. Lett. 74, 2118. Dacy, G.C. and Ross, I.M. (1955). The field-effect transistor. Bell Syst. Tech. J. 34, 1149. Duke, C.B. (1969). Tunneling in Solids. Solid State Physics, Supplement 10, Academic Press, New York. Dubois, S., Piraux, L., George, J.M., Ounadjela, K., Duvail, J.L., and Fert, A. (1999). Evidence for a short spin diffusion length in permalloy from the giant magnetoresistance of multilayered nanowires. Phys. Rev. B 60, 477. Elezzabi, A., Freeman, M.R., and Johnson, M.B. (1996). Direct measurement of the conduction electron spinlattice relaxation time T1 in gold. Phys. Rev. Lett. 77, 3220. Elliott, R.J. (1954). Theory of the effect of spin – orbit coupling on magnetic resonance in some semiconductors. Phys. Rev. 96, 266. Fabian, J. and Das Sarma, S. (1998). Spin relaxation of conduction electrons in polyvalent metals: theory and a realistic calculation. Phys. Rev. Lett. 81, 5624. Fowler, A.B., Fang, F.F., Howard, W.E., and Stiles, J.P. (1966). Magneto-oscillatory conductance in silicon surfaces. Phys. Rev. Lett. 16, 901. Grunberg, P., Schreiber, R., Pang, Y., Brodsky, M.B., and Sowers, H. (1986). Layered magnetic structures: evidence for antiferromagnetic coupling of Fe layers across Cr interlayers. Phys. Rev. Lett. 57, 2442. Gurvitch, M., Washington, M.A., and Huggins, H.A. (1983). High-quality refractory Josephson tunneljunctions utilizing thin aluminum layers. Appl. Phys. Lett. 42, 472. Hanle, W. (1924). Z. Phys. 30, 93.

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Hershfield, S. and Zhao, L.H. (1997). Charge and spin transport through a metallic ferromagneticparamagnetic –ferromagnetic junction. Phys. Rev. B 56, 3296. Horowitz, P. and Hill, W. (1980). The Art of Electronics, Cambridge University Press, Cambridge, UK. In particular, see Chapter 8. Hu, C.-M. and Matsuyama, T. (2001). Spin injection across a heterojunction: a ballistic picture. Phys. Rev. Lett. 87, 066803. Janossy, A. and Monod, P. (1976). Investigation of magnetic coupling at interface of a ferromagnetic and paramagnetic metal by conduction electron-spin resonance. Solid State Commun. 18, 203. Johnson, M. (1991). Analysis of anomalous multilayer magnetoresistance within the thermomagnetoelectric system. Phys. Rev. Lett. 67, 3594. Johnson, M. (1993a). Spin accumulation in gold films. Phys. Rev. Lett. 67, 3594. Johnson, M. (1993b). Bipolar spin switch. Science 260, 324. Johnson, M. (1994a). Spin polarization of gold films via transport. J. Appl. Phys. 75, 6714. Johnson, M. (1994b). The all-metal spin transistor. IEEE Spectrum 31(5), 47. Johnson, M. (2000a). Spin injection: a survey and review. J. Supercond. Incorp. Novel Magn. 14, 273. Johnson, M. (2000b). Magnetoelectronic memories last and last…. IEEE Spectrum 37(2), 33. Johnson, M. (2000c). Dynamic nuclear spin polarization by spin injection. Appl. Phys. Lett. 77, 1680. Johnson, M. (2002a). Spin injection in metals and semiconductors. Semicond. Sci. Technol. 17, 298. Johnson, M. (2002b). Overview of spin transport electronics in metals. Proc. IEEE 91, 652. Johnson, M. (2002c). Charge – spin coupling at a ferromagnet– nonmagnet interface. J. Supercond. Incorp. Novel Magn. 16, 679. Johnson, M. (2002d). Spin accumulation in mesoscopic systems. Nature 416, 809. Johnson, M. and Byers, J. (2003). Charge and spin diffusion in mesoscopic metal wires and at ferromagnet / nonmagnet interfaces. Phys. Rev. B 67, 125112. Johnson, M. and Clarke, J. (1990). Spin-polarized scanning tunneling microscope: concept, design, and preliminary results from a prototype operated in air. J. Appl. Phys. 67, 6141. Johnson, M. and Silsbee, R.H. (1985). Interfacial charge –spin coupling; injection and detection of spin magnetization in metals. Phys. Rev. Lett. 55, 1790. Johnson, M. and Silsbee, R.H. (1987). A thermodynamic analysis of interfacial transport and of the thermomagnetoelectric system. Phys. Rev. B 35, 4959. Johnson, M. and Silsbee, R.H. (1988a). Coupling of electronic charge and spin at a ferromagnetic – paramagnetic interface. Phys. Rev. B 37, 5312. Johnson, M. and Silsbee, R.H. (1988b). The spin injection experiment. Phys. Rev. B 37, 5326. Johnson, M. and Silsbee, R.H. (1988c). Electron spin injection and detection at a ferromagnetic – paramagnetic interface. J. Appl. Phys. 63, 3934. Johnson, M. and Silsbee, R.H. (1988d). Ferromagnet –nonferromagnet interface resistance. Phys. Rev. Lett. 60, 377. Julliere, M. (1975). Tunneling between ferromagnetic films. Phys. Lett. 54A, 225. Keyes, R.W. (1989). Physics of digital devices. Rev. Mod. Phys. 61, 279. Kirk, K.J., Chapman, J.N., and Wilkinson, C.D.W. (1997). Switching fields and magnetostatic interactions of thin film magnetic nanoelements. Appl. Phys. Lett. 71, 539. Kittel, C. (1971). Introduction to Solid State Physics, John Wiley and Sons, New York, NY. Kuhn, T.S. (1996). The Structure of Scientific Revolutions, 3rd edn. The University of Chicago Press, Chicago, IL.

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Lampel, G. (1968). Nuclear dynamic polarization by optical electronic saturation and optical pumping in semiconductors. Phys. Rev. Lett. 20, 491. Maekawa, S. and Gaefert, U. (1982). Electron-tunneling between ferromagnetic-films. IEEE Trans. Magn. 18, 707. Malozemoff, A.P. (1987). Random-field model of exchange anisotropy at rough ferromagnetic – antiferromagnetic interfaces. Phys. Rev. B 35, 3679. Mead, C.A. (1966). Schottky barrier gate field-effect transistor. Proc. IEEE 54, 307. Meiklejohn, W.H. and Bean, C.P. (1956). New magnetic anisotropy. Phys. Rev. 102, 1413. Moodera, J.S., Kinder, L.R., Wong, T.M., and Meservey, R. (1995). Large magnetoresistance at room temperature in ferromagnetic thin film tunnel junctions. Phys. Rev. Lett. 74, 3273. Mott, N.F. (1936). Prot. R. Soc. A 153, 699. Pohm, A.V., Huang, J.S.T., Daughton, J.M., Krahn, D.R., and Mehra, V. (1988). The design of a one megabit non-volatile MR memory chip using 1.5 £ 5 micron cells. IEEE Trans. Magn. 24, 3117. Prinz, G.A. (1990). Hybrid ferromagnet semiconductor devices. Science 250, 1092. Rashba, E.I. (2000). Theory of electrical spin injection: tunnel contacts as a solution of the conductivity mismatch problem. Phys. Rev. B 62, 16267. Ruhrig, M., Khamsehpour, B., Kirk, K.J., Chapman, J.N., Aitchison, P., McVitie, S., and Wilkinson, C.D.W. (1996). The fabrication and magnetic properties of acicular magnetic nano-elements. IEEE Trans. Magn. 32, 4452. Schrieffer, J.R. (1957). Mobility in inversion layers: theory and experiment. In Semiconductor Surface Physics, (Ed. R.H. Kingston). University of Pennsylvania Press, Philadelphia, PA, p. 55. Sharma, A.K. (1997). Semiconducting Memories; Technology Testing and Reliability, IEEE Press, New York. Shockley, W. (1952). A unipolar field effect transistor. Proc. IRE 40, 1365. Silsbee, R.H. (1980). Bull. Magn. Res. 2, 284. Silsbee, R.H. and Drager, J. (1997). Simulations for Solid State Physics, Cambridge University Press, Cambridge, UK. Silsbee, R.H., Janossy, A., and Monod, P. (1979). Coupling between ferromagnetic and conduction-spinresonance modes at a ferromagnetic – normal-metal interface. Phys. Rev. B 19, 4382. Simmons, J. (1963). J. Appl. Phys. 34, 1793. Soulen, R.J., Byers, J.M., Osofsky, M.S., Nadgorny, B., Ambrose, T., Cheng, S.F., Broussard, P.R., Tanaka, C.T., Nowak, J., Moodera, J.S., Barry, A., and Coey, J.M.D. (1998). Measuring the spin polarization of a metal with a superconducting point contact. Science 282, 5386. Stoner, E.C. (1948). Repts. Prog. Phys. 11, 43. Sze, S.M. (1981). Physics of Semiconductor Devices, 2nd edn. Wiley, New York. In particular, see Chapter 2. Sze, S.M. (1998). Modern Semiconductor Device Physics, Wiley, New York. In particular, see Chapter 3. Tedrow, P.M., Meservey, R., and Fulde, P. (1970). Magnetic field splitting of the quasiparticle states in superconducting aluminum films. Phys. Rev. Lett. 25, 1270. Tedrow, P.M. and Meservey, R. (1971). Spin-dependent tunneling into ferromagnetic nickel. Phys. Rev. Lett. 26, 192. Tedrow, P.M. and Meservey, R. (1973). Spin polarization of electrons tunneling from films of Fe, Co, Ni, and Gd. Phys. Rev. B 7, 318. Weisendanger, R., Guntherodt, H.J., Guntherodt, G., Gambino, R.J., and Ruf, R. (1990). Observation of vacuum tunneling of spin-polarized electrons with the scanning tunneling microscope. Phys. Rev. Lett. 65, 247.

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Wulfhekel, W. and Kirschner, J. (1999). Spin-polarized scanning tunneling microscopy on ferromagnets. Appl. Phys. Lett. 75, 1944. Yafet, Y. (1952). Calculation of the g factor of metallic sodium. Phys. Rev. 85, 478. Yang, Q., Holody, P., Lee, S.-F., Henry, L.L., Lolee, R., Schroeder, P.A., Pratt, W.P. Jr., and Bass, J. (1994). Spin flip diffusion length and giant magnetoresistance at low temperatures. Phys. Rev. Lett. 72, 3274. Zelakiewicz, S., Krichevsky, A., Johnson, M., and Freeman, M.R. (2002). Time-resolved Kerr measurements of magnetization switching in a crossed-wire ferromagnetic memory element. J. Appl. Phys. 91, 7331. Ziman, J.M. (1972). Principles of the Theory of Solids, 2nd edn. Cambridge University Press, Cambridge, UK. In particular, see Chapters 7 and 10. Zhu, H.J., Ramsteiner, M., Kostial, H., Wassermeier, M., Schonherr, H.P., and Ploog, K.H. (2001). Roomtemperature spin injection from Fe into GaAs. Phys. Rev. Lett. 87, 016601. Zhu, J.-G. (2003). New heights for hard disk drives. Mater. Today 6(7/8), 22. Zutic, I., Fabian, J., and Das Sarma, S. (2004). Spintronics: fundamentals and applications. Rev. Mod. Phys. 76, 323.

Magnetoelectronics M. Johnson (Editor) Copyright q 2004 Elsevier Inc. All rights reserved.

Chapter 2 Spin valves B. Dieny SPINTEC, Unite´ de Recherche Associe´e CEA/DSM & CNRS/SPM-STIC, 38054 Grenoble Cedex, France

2.1

Introduction

In the past 30 years, tremendous technological progress has been achieved in the development of ultrahigh vacuum equipment for the preparation of thin films and multilayers, in tools for their structural characterization, and for the measurement of their physical properties. Although interest in the properties of magnetic thin films and multilayers is not new (Ne´el, 1954, 1955, 1962, 1965, 1967, 1968), these advances have launched an intense activity in the field, stimulated by interests in both basic science as well as applications, particularly in magnetic storage (Thompson and Best, 2000), magneto-optic recording (Tsunashima, 2001) and more recently in non-volatile memories or reprogrammable logic (Johnson, 2000). A wealth of new phenomena has been discovered in these artificially made material systems. They include anomalous elastic properties, magnetic anisotropy perpendicular to the plane of the layers (den Broeder et al., 1991), enhanced magnetooptical Kerr rotation (Carcia et al., 1985; den Broeder et al., 1987), existence of an oscillatory exchange-like coupling between ferromagnetic layers separated by a non-magnetic layer (Parkin et al., 1990) and, among the most attractive for applications: giant magnetoresistance, GMR (Baibich et al., 1988; Binasch et al., 1989) and tunnel magnetoresistance, TMR (Moodera et al., 1995). The main applications of magnetic thin films and multilayers concern media for magnetic or magneto-optical recording, soft and hard magnetic thin films, magnetostrictive materials for actuators, magnetoresistive materials for magnetic field sensors and magnetic tunnel junctions (MTJs) for non-volatile memories or logic gates. The present chapter is devoted to spin valves (Dieny et al., 1991a–d) which represent a particular class of systems exhibiting GMR at low fields. These systems were discovered in 1990 and have been the object of an exponentially growing interest since 1994 when they became identified as the most promising candidates for magnetoresistive read-back heads used in magnetic hard disk drives. This application is clearly the most demanding in terms of performance. Spin valves reached market in 1998 when they were introduced for the first time in disk drives by IBM. Since then, this technology became the standard for read-back heads. Spin valves can be viewed as sensitive magnetic field sensors. As such, they may also be used in other applications: measurements of

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B. Dieny

electrical current, position or rotation encoders, magnetoresistive compass and magnetoresistive heads for videotapes or other storage media of lower density than hard disk drives. Prior to the discovery of GMR, the main magnetoresistive effect known in magnetic transition metals (Fe, Ni, Co and many of their alloys) at room temperature was the ‘anisotropic magnetoresistance’ (AMR) (Mc Guire and Potter, 1975). This effect is a consequence of an anisotropic mixing of spin-up and spin-down conduction subbands induced by the spin –orbit interaction (Campbell, 1970). Its manifestation is a dependence of the electrical resistivity on the relative angle between the direction of the sense current and the local magnetization. In the vast majority of cases, the resistivity is lower when the current flows perpendicular to the magnetization than when it flows parallel to it. The effect can be of the order of 3–5% in bulk NiFe or NiCo alloys at room temperature. In thin films, it tends to drop significantly when the thickness of the layer becomes lower than a few tens of nanometer because of the increasing role of the electron scattering at the outer surfaces of the film. This AMR reduction in very thin films, however, has been drastically limited by improving the structural quality of the film thus favoring specular reflection rather than diffuse scattering at outer boundaries (Dieny et al., 2000a,b). AMR thin films were used in magnetoresistive heads from 1992 to 1998. The introduction of AMR films in magnetic recording technology in 1992 has constituted a major breakthrough which actually led to a doubling in the rate of increase of storage areal density per year (from 30 to 60%/year). The first evidence of enhanced magnetoresistance in multilayers consisting of magnetic layers separated by non-magnetic spacer layers was obtained by Binasch et al. (1989) in antiferromagnetically coupled Fe/Cr/Fe sandwiches grown by molecular beam epitaxy (MBE). However, the first observation of really GMR in such multilayers is due to Baibich et al. (1988) who reported a decrease of resistivity in MBE-grown (Fe/Cr) multilayers by a factor 2 at 4.2 K in a field of 20 kOe. A model for the physical origin of the GMR in terms of spin-dependent scattering of the conduction electrons at the interfaces between Fe and Cr associated with a change in the relative orientation of the magnetization in the successive ferromagnetic layers under application of a magnetic field has also been proposed by the same authors (Baibich et al., 1988). This interpretation is widely accepted by the scientific community as the dominant contribution to GMR in these systems. A significant step towards applications of GMR in devices was achieved by Parkin et al. (1990). They demonstrated that GMR could be observed in sputtered multilayers and that the GMR amplitude could be even larger in sputtered samples than in their MBE-grown counterparts. Spin valves were discovered in 1990 (Dieny et al., 1991a– d). They offered the best field sensitivity at low fields since in contrast to the previously studied GMR multilayers, in which the ferromagnetic layers are coupled antiferromagnetically through the spacer layer, spin valves essentially consist of two uncoupled ferromagnetic layers separated by a noble metal spacer layer. The magnetization of one layer is free to rotate under application of a weak magnetic field while the other is pinned in a fixed direction.

Spin valves 69 Since 1989, GMR has stimulated numerous studies oriented either towards a basic understanding of the phenomenon or towards the optimization of the magnitude and sensitivity of the magnetoresistive response for magnetic field sensors. For read-head applications, other requirements for GMR materials are very low magnetostriction, good resistance to corrosion and good thermal stability up to 2508C. In the last 10 years, very significant progress was achieved in the preparation and optimization of spin valves in terms of magnetic and transport properties. These advances will be explained in detail in this chapter. They have dealt with (i) improving the overall structural quality of the stacks by appropriate choice of buffer layers, (ii) improving the biasing of the pinned layer on one hand, by using antiferromagnetic material with higher Neel temperature, and offering higher exchange bias energy, on the other hand, by using synthetic pinned layers, (iii) optimizing the thickness of each individual layer, most importantly those which are in the active part of the spin valve: the free layer, the non-magnetic spacer layer, the inner pinned layer, (iv) introducing nano-oxide layers (NOLs) at appropriate locations in the stack to favor specular reflection of the electrons in the active part of the spin valve, (v) reducing the shunting of the current in the parts of the stack which do not contribute to the GMR, and (vi) designing new spin valve stacks (e.g. dual spin valves, spin-filter spin valves) with more active interfaces or thinner free layer to increase the GMR sensitivity. At the present time, a GMR amplitude of 20% is achieved in spin valves. However, unless a new breakthrough occurs, such as the discovery of an antiferromagnetic insulator which would provide good exchange bias and specular reflection, the present performance is close to the ultimate limit. This is not in terms of amplitude but in terms of a compromise between amplitude and magnetic properties that are suitable for read-head applications. As a result, there is currently a significant evolution in research and development in the field of magnetoresistive materials. In the past, the vast majority of the studies on the transport properties in magnetic multilayers have dealt with the ‘current-in-plane’ (CIP) geometry. This means that the transport measurements are performed in a standard four-point probe geometry, the four contacts being made at the surface of the film so that the current essentially flows parallel to the plane of the layers. More recently, a growing interest is focused on the ‘current-perpendicularto-plane’ (CPP) geometry in which the current flows perpendicular to the interfaces (Pratt et al., 1991; Gijs et al., 1993). From a practical point of view, measuring the CPP GMR in metallic multilayers at room temperature requires one to pattern the multilayer in the form of a submicron pillar sandwiched between a bottom electrode and a top electrode. Reducing the lateral dimension of the pillar is important in order to have a measurable and usable resistance of the stack (typically 10 –30 V). Furthermore, in the perspective of application as read heads, this will allow higher spatial resolution of the reading process. There are several advantages of the CPP geometry over the CIP geometry for read heads, as will be explained later in more detail: The width of the read gap can be decreased, allowing an increase in the spatial resolution along the track; the amplitude of CPP GMR can be larger than in CIP; the heat evacuation from the sensor is better in CPP than in CIP, allowing more current to flow through the sensor during the reading process and resulting in

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an increase in the signal-to-noise ratio (SNR); and the design and technology required for CPP heads at very small dimensions (150 nm and below) are simpler than in CIP. Research efforts in this field are currently focusing on increasing the CPP resistance and magnetoresistance of metallic stacks by using laminated layers which allow an increase in the number of interfaces, or inserting discontinuous NOLs at appropriate locations to locally confine the current paths throughout the structure. Concerning CPP transport studies, MTJs also represent a large field of activity. The discovery of large magnetoresistance at room temperature in MTJs (Moodera et al., 1995; Miyazaki and Tezuka, 1995) has stimulated tremendous interest in these systems. Three main applications of MTJ are investigated. One is a storage unit in magnetic random access memories (MRAMs) (Tehrani et al., 1999; see also Chapters 4 and 5), another is a basic element of reprogrammable logic gates (Johnson, 2000; see also Chapter 6), and a third one is a magnetoresistive sensor for CPP read heads (Nakashio et al., 2001). The requirements of the properties, especially the product of resistance and area ðRAÞ are different for these various applications. Among these three areas of research and development, the most advanced is the field of MRAM which should reach market by the end of 2004. For sensor applications, the main source of noise in tunnel junctions is the shot noise. This can be reduced only by decreasing the RA product of the junctions, which implies making thinner tunnel barriers. Many attempts have been made towards the goal of achieving an RA product below 1 V mm2 with large TMR amplitude. These attempts have not been successful so far. Considering the intense activity in the field, however, new insulating or semiconductor materials may be discovered in the near future, having a narrower band gap which would allow the fabrication of low resistance tunnel barriers. Tunnel junctions would then offer a superior SNR than metal-based CIP or CPP sensors. This chapter has the following organization: After this introduction, the physical origin of GMR will be briefly explained in Section 2.2 and the differences between the magnetotransport properties in CIP and CPP geometry will be outlined. Section 2.3 presents the basic properties of spin valves. The dependence of the GMR on the thickness of the various layers will be discussed and the quantitative interpretation of the GMR based on the semiclassical theory initiated by Camley and Barnas (1989) and Barnas et al. (1990) for CIP and Valet and Fert (1993) for CPP will be explained. Section 2.4 will address the various spin-valve improvements which have allowed an increase of a factor of 4 in the GMR amplitude and an optimization of the magnetic properties of both the soft and the pinned layers. In Section 2.5, based on the semiclassical modeling of GMR, we will discuss things that could be done to further increase the GMR amplitude along with the consequences on the magnetic properties. Section 2.6 deals with a currently very active field of investigation: spin valves in CPP heads. Section 2.7 addresses the implementation of spin valves in CIP and CPP heads and the present trends in magnetoresistive heads.

Spin valves 71

2.2 2.2.1

Giant magnetoresistance Giant magnetoresistance effect

GMR has been observed in many multilayered structures of the form BtB =ðFtF =NMtNM Þn =CtC ; where B and C, respectively, designate a buffer and capping layer, F is a transition metal magnetic layer (Fe, Co, Ni or their alloys), NM is a non-ferromagnetic transition metal or a noble metal (V, Cr, Nb, Mo, Ru, Re, Os, Ir, Cu, Ag, Au), and tB ; tC ; tF represent the thickness of the corresponding elements. In magnetic multilayers, the thickness of each individual layer is typically in the nanometer range. The amplitude of the GMR depends considerably on the pair of (F, NM) materials and on the thicknesses of the various layers. It ranges from a tenth of a percent in V- or Mo-based multilayers to more than 100% in (Fe/Cr) (Fullerton et al., 1993) or Co/Cu multilayers (Mosca et al., 1991; Parkin et al., 1991). It has been shown in all of these structures that the GMR is associated with a change in the relative orientation of the magnetizations of the successive ferromagnetic layers. The GMR multilayers can be classified in three categories according to how the magnetic configuration between the various layers is controlled: (i)

Antiferromagnetically coupled multilayers: Typical examples are the Fe/Cr and Co/Cu multilayers previously mentioned, and (NiFe/Ag) (Rodmacq et al., 1993). In these multilayers, the interlayer coupling oscillates from antiferromagnetic to ferromagnetic as a function of the spacer layer thickness. Therefore, the GMR can only be observed in the range of thickness for which the coupling is antiferromagnetic. These multilayers offer large GMR amplitude. However, except for (NiFe/Ag) multilayers in which a saturation field of 100 Oe can be achieved, the fields required to overcome the antiferromagnetic coupling is generally too large (several kOe) to make these systems usable in magnetoresistive heads. Another drawback is that the magnetoresistance response is a symmetric function of the applied field in these systems, which requires that the magnetoresistive element be biased with a relatively

large field in order to obtain a linear response. This adds a complication to the realization of the sensor. (ii) Multilayers with double coercivity: A typical example is the (Ni80Fe20/Cu/Co/Cu) multilayer (Shinjo and Yamamoto, 1990). Since the Permalloy layers are softer than the Co ones, their magnetizations switch at different fields and therefore there are ranges of field in which the magnetizations in the successive magnetic layers are in parallel alignment (above the coercive fields of the two types of layers), and other ranges where they are in antiparallel alignment (between the coercive fields). These systems can also exhibit large GMR [16% variation in resistance between 0 and 50 Oe at 300 K in NiFe/Cu/Co/Cu multilayers (Sato, 1993)]. However, they have not been implemented in GMR heads because at low fields, when a minor loop is performed on the soft layers, the MR response depends on the magnetic history of the pinned layer. In particular, when the free layer switches,

72

B. Dieny

the resistance can increase or decrease depending on the direction of the magnetization of the pinned layer. Furthermore, the domain state of the pinned layer is poorly controlled in this type of system, and the hardness of the pinned layer often reduces the softness of the soft layer because of magnetostatic interactions between the two types of layers. (iii) Spin valves: These systems will be presented in more detail in the following section. They essentially consist of two magnetic layers separated by a non-magnetic spacer layer. The magnetization of one layer is pinned by exchange interaction with an adjacent antiferromagnetic layer whereas the magnetization of the other layer is free to rotate in an applied field (Dieny et al., 1991a–d). Since the two layers are very weakly coupled, the change from parallel to antiparallel magnetic configuration can occur in small fields giving these systems a large sensitivity. Several reviews on the physics of GMR have already been published (Fert and Bruno, 1992; Vouille et al., 1999; Tsymbal and Pettifor, 2001). The reader is therefore encouraged to consult these reviews for a deeper understanding of the physics of this effect. Only the main ideas will be surveyed here. The basic origin of the GMR is described as follows. In transition metals and in particular in ferromagnetic transition metals, the electrons which participate to the conduction of the electrical current are s, d and hybridized sd electrons. Two families of these electrons can be distinguished according to the projection of their spin along the local magnetization: the spin " electrons (respectively, the spin # electrons) conventionally have the z-component of their spin parallel (respectively, antiparallel) to the local magnetization. In this description, the z-axis is chosen as the quantization axis and is parallel to the local magnetization. The spin " electrons (respectively, the spin # electrons) are also named majority (respectively, minority) electrons. At a temperature sufficiently low compared to the Curie temperature, these two species of electrons can be considered as carrying electrical current in parallel. This ‘twocurrent model’ (Mott and Wills, 1936) is justified because the spin –orbit coupling is weak in these relatively light elements and because magnon scattering is negligible at low temperature. All other scattering events are unable to perturb the spin state of the electrons. Furthermore, in ferromagnetic transition metals, the spin " and spin # electrons have very different scattering rates (Fert and Campbell, 1976; Dorleijn and Miedema, 1975, 1977; Gurney et al., 1993), regardless of the nature of the scattering centers (for example, magnetic impurities; structural defects such as dislocations, stacking faults or grain boundaries; or even phonons). The spin dependence of the scattering rates results from the difference of the density of available states at the Fermi energy into which the electrons can be scattered. The difference in the spin " and spin # density of states is itself a consequence of the d-band exchange splitting, characteristic of the magnetism of transition metals, as described by the well-known Stoner model (Stoner, 1938). As an example, in Permalloy (Ni80Fe20), the mean free path of spin " electrons has been estimated to be at least five times longer than that of spin # electrons (Fert and Campbell, 1976).

Spin valves 73 Let us then consider a magnetic multilayer consisting, for example, of Co layers alternating with Cu layers. We assume that the relative orientation of the magnetization in the successive Co layers can somehow be changed from parallel to antiparallel. Figure 2.1 depicts the potential presented to conduction electrons as they move through the multilayered structure.

Co/Cu majority electrons : parallel magnetic configuration Co

Cu

Co

Cu

(a)

Co/Cu minority electrons : parallel magnetic configuration

(b)

Co/Cu majority electrons : antiparallel magnetic configuration

(c)

Co/Cu minority electrons : antiparallel magnetic configuration U(x,z) (d) x

z

Fig. 2.1 Schematic representation of the potential Uðx; zÞ presented to majority (spin " ) and minority (spin # ) conduction electrons in (Co/Cu) multilayers. The z-direction is perpendicular to the interface, the x-direction is in the plane of the layers. The electrons experience a spin-dependent lattice potential modulation due to the matching between electron bands in adjacent layers, which leads to reflection and refraction effects. They are also scattered by random interfacial and bulk localized scattering centers (represented by localized potential peaks). (a) and (b) correspond to the case where the magnetizations in the Co layers are parallel, (c) and (d) are for the antiparallel magnetic configuration. Adapted from Vouille et al. (1999).

74

B. Dieny

In addition to the spin-dependent density of scattering centers (narrow, pointed peaks in Fig. 2.1) located at the interfaces and in the bulk of the layers, the conduction electrons also experience a spin-dependent modulation of the lattice potential. This results from the difference in the positions of the bottoms of the conduction bands with respect to the Fermi energy in the successive layers. In the case of (Co/Cu) multilayers, for instance, the matching of the conduction bands is very good for spin " electrons and these carriers are presented with a nearly flat potential throughout the structure. In contrast, a strong mismatch exists for spin # electrons, resulting in large potential steps at the Co/Cu interfaces for these electrons. These lattice potential modulations cause reflection and refraction of the electrons. Furthermore, it will be important to understand that they play a very different role in the CIP and CPP geometry. In the CIP geometry, the presence of potential wells, for example, for minority electrons in Cu in parallel magnetic configuration [Fig. 2.1(b)], leads to channeling effects: The electrons which propagate within the Cu layers bounce back and forth between the two (Cu/Co) interfaces and remain confined in these layers while drifting along the electrical field. In contrast, the electrical field is perpendicular to the interface in the CPP geometry. Therefore, the electrons are forced to pass these potential steps. This effectively results in additional spin-dependent interfacial resistance related to the height of the potential steps (Vedyaev et al., 1995; Barnas and Fert, 1995). In the case of periodic multilayered structures with extremely good structural quality, quantum interference may take place between the successive quantum wells leading to oscillations of conductance as a function of the thickness of the layers. However, these effects, which frequently occur in semiconductor multilayers, are much more difficult to observe in metallic multilayers due to the short Fermi ˚ ) compared to that in semiconductors (tens to hundreds of A ˚ ). wavelength in metals (a few A We therefore will not address them further here. The origin of the GMR can now be simply understood, as a first step, by only considering the spin-dependent scattering effects. These have been shown to represent the main contribution to the GMR in spin valves. At saturation, the magnetization orientations of the magnetic layers are parallel. The spin " electrons are then weakly scattered in all layers [Fig. 2.1(a)] and can therefore carry a lot of current with relatively low resistance. In contrast, the spin # electrons are strongly scattered in the magnetic layers so that they weakly participate to the conduction of the current [Fig. 2.1(b)]. Within the assumption that the mean free paths of the electrons are much longer than the thickness of the various layers, and if r " and r# designate the resistivity of the spin " and spin # electrons, respectively, the resistivity of the multilayer in this parallel configuration ðrP Þ can be estimated in a simple resistor model as rP ¼ r " r# =ðr " þ r# Þ (Baibich et al., 1988; Edwards et al., 1991; Mathon, 1991). In contrast, in the antiparallel magnetic configuration, electrons of both species are alternately strongly and weakly scattered as they cross the successive ferromagnetic layers [Fig. 2.1(c) and (d)]. The resistivity of the multilayer in this antiparallel configuration ðrAP Þ becomes rAP ¼ ðr " þ r# Þ=4: The GMR amplitude is then given by Dr=rP ¼ ð1 2 aÞ2 =4a; where a ¼ r " =r# : This expression is valid for CIP as well as for CPP transport in the limit that the layers

Spin valves 75 are thin compared to the spin " and # electron mean free paths, and neglecting the effects of the modulation of the lattice potential. This expression shows the key role played by the spin scattering asymmetry in the origin of the GMR. While the above model gives a good description of the basic GMR mechanism, various theories have addressed a detailed and complete interpretation of GMR in magnetic multilayers. A very comprehensive review of these theories has been written by Tsymbal and Pettifor (2001). They can be distinguished in two classes. The simplest theories, ‘semiclassical’, use the spindependent resistivities of the various materials and the spin-dependent interfacial resistances as input parameters (Camley and Barnas, 1989; Dieny, 1992; Dieny et al., 1992; Barthelemy and Fert, 1991; Hood and Falicov, 1992; Hood et al., 1994). The former parameters have been determined through extensive studies carried out more than 20 years ago to explain the anisotropic MR of ferromagnetic transition metals (Dorleijn, 1976; Campbell and Fert, 1982). The spindependent interfacial resistances have been determined from CPP measurements, most often at low temperature, and can be adjusted from their fit to the experimental data. Values of these parameters can be found in several reviews of CPP GMR (Gijs and Bauer, 1997; Bass and Pratt, 1999; Barthelemy et al., 1999). These theories then calculate the CIP transport properties (resistance and magnetoresistance amplitude) by using an adaptation of the Boltzmann theory of transport to the present case of magnetic multilayers. Theories in the second class start from a more basic point of view. Through tight binding or first principle models, they recalculate the electronic structure of the multilayered stack and, from this electronic structure, derive the transport properties. These theories are clearly more rigorous than the first ones but are unfortunately more difficult to handle and require long computation times, especially for the ab initio theories. In that respect, mainly the semiclassical theories have been used and have proven to be quite successful in explaining most of the general trends of the transport properties in spin valves. These include, for example, the dependence on the thickness of the various layers, the effect of inserting NOLs at particular locations to enhance the specular reflection, or the effect of inserting a conductive layer behind the free layer in spin-filter spin valves. In the following section, we will therefore present the basis of the semiclassical theory of CIP GMR. This theory has been extensively used to interpret the CIP GMR properties of magnetic multilayers and spin valves in particular. 2.2.2

Semiclassical theory of CIP giant magnetoresistance

The aim of this approach is to relate the microscopic transport parameters, the spin-dependent electron mean free paths and coefficients of interfacial transmission/reflection, to the macroscopic measurable quantities R and DR=R: The microscopic parameters are presumed to be weakly dependent on the thickness of the layers, so that once they have been determined by adjusting the calculated resistance and magnetoresistance to the experimental data on a few series of samples, the theory can then be used in a predictive way, or at least as a guideline for the optimization of

76

B. Dieny

the properties of spin valves. In this approach, the conduction electrons are described as a free electron gas submitted to scattering potentials randomly distributed in the interior of the layers and at the interfaces. Furthermore, the modulation of the lattice potential can lead to interfacial spindependent specular reflections, and these are taken into account. The theory is an extension of the Fuchs –Sondheimer theory which assumes parallel conductivity of the two species of conduction electrons. It is based on a semiclassical description of the electrons in metals in the presence of an external electrical field using a statistical distribution function. This distribution is written as the sum of two components: f s ð~r; ~vÞ ¼ f0s ð~r; ~vÞ þ gs ð~r; ~vÞ; in which f0s ð~r; ~vÞ represents the equilibrium Fermi –Dirac distribution and gs ð~r; ~vÞ is the perturbation to the equilibrium distribution induced by the applied electrical field. Superscript s refers to the electron spin, and ~r and ~v are, respectively, the position and velocity of the electrons. We then consider a multilayered stack consisting of layers in the x – y plane having a thickness ti : N is the total number of layers. The electric field is assumed to be applied along the x-axis parallel to the plane of the layers. The z-axis is perpendicular to plane. In this CIP geometry, the electric field is uniform in the structure. Furthermore, all scattering events in the metal layers occur at the Fermi energy so that the perturbation gs ð~r; ~vÞ only depends on the z-coordinate and on the direction of the velocity v: In steady state and in the relaxation time approximation, the perturbation gs ðz; vÞ is a solution of the Boltzmann equation:

›gs ðz; vÞ gs ðz; vÞ eE ›f 0 ðvÞ ¼ ; þ s mvz ›vx ›z t vz where e and m denote the charge and effective mass of the electrons. ts are the spin-dependent relaxation times related to the mean free paths ls by ts ¼ ls =vF ; where vF is the Fermi velocity. Within each layer, the solution gs ðz; vÞ of the Boltzmann equation takes a simple form: gs^ ðz; vÞ ¼ eEts vx


 ›f ð Þ z : 1 2 Asð^Þ exp 7 s ›1 t lvz l

ð2:1Þ

In this expression, the signs ^ refer to whether the z-component of the electron velocity is positive or negative. The Asð^Þ ’s are integration constants which need to be determined by using boundary conditions at each interface and at the outer surfaces. These boundary conditions relate the distribution of velocity of the electrons on both sides of the interface via spin-dependent coefficients of transmission T s and reflection Rs : These coefficients are defined to mean that an electron impinging on an interface has a probability T s of being coherently transmitted, Rs of being specularly reflected and consequently ð1 2 T s 2 Rs Þ of being diffusely scattered. The boundary conditions between layers i and i þ 1 are then given by gsiþ1;þ ¼ Tis gsi;þ þ Rsi gsiþ1;2 ;

ð2:2Þ

gsi;2 ¼ Tis gsiþ1;2 þ Rsi gsi;þ :

ð2:3Þ

Spin valves 77 At the outer surfaces, the same relations are used except that only the reflection terms must be kept since the conduction electrons cannot be transmitted outside the metal. By using relations (2.1), (2.2), and (2.3), the perturbation gs ðz; vÞ can be calculated in a self-consistent way throughout the multilayered stack. The local density of current at a given point z induced by the electrical field is then obtained by integrating, over all directions of velocity, the following Ð P expression, jðzÞ ¼ e s¼";# vx gs ðvz ; zÞd2 V; which yields jðzÞ /



 2ti ti s s 2 Ai;2 exp s dm: ð1 2 m Þ 2 2 Ai;þ exp lsi m li m 0

X ð1 "#;i

2

ð2:4Þ

In this expression, m represents the cosine of the angle between the electron velocity and the normal to the film. From the expression of the current density, the local magnetic field generated by the sense current can be calculated. Let
j be the average current density through the structure (
j in A/m2) and D the total thickness of the stack (in meters). The magnetic field due to the sense current at point z is then given by BðzÞ ðteslaÞ ¼ 2

ðD m0
jD þ m0 jðzÞdz with m0 ¼ 4p £ 1027 : 2 0

ð2:5Þ

As will be shown further, in magnetoresistive heads used in computer disk drives, current density of the order of 2 £ 107 A/cm2 can flow through the sensor. The magnetic field due to the sense current can then reach several millitesla. This has a quite significant impact on the magnetic properties of the sensor and in particular on its bias point. It is therefore quite important to take into account the field generated by the sense current. Furthermore, the total conductance is given by integrating the local current density over the entire thickness of the stack. The integration leads to two terms: G ¼ G0 2 G1

ð2:6Þ

with G0 ¼ e 2

N N X X lsi nsi ti ¼ rsi ti ; v m F i i¼1;"# i¼1;"#

ð2:7Þ

where rsi are the resistivity of each spin channel and G1 ¼


 


ð 3lsi X 1 2ti ti 2 s s d m ð1 2 m Þ m A 1 2 exp 1 2 exp þ A : i;þ i;2 4rsi "#;i 0 lsi m lsi m

ð2:8Þ

The first term ðG0 Þ gives the same conductance as if the various layers were simply carrying the current in parallel. The second term ðG1 Þ contains all finite size effects and in particular the change of conductance responsible for the GMR. This term must be calculated in the parallel and

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B. Dieny

antiparallel magnetic configurations. The magnetoresistance is then given by DG ¼ Gparallel 2Gantiparallel ¼ Gantiparallel 2 Gparallel : 1 1 Since all layer thickness appear in t=l ratios in Eq. (2.8), it is clear that the characteristic scaling lengths in CIP transport are the mean free paths. This represents a significant difference with CPP transport, as will be further discussed below. At this stage, we point out that the current and therefore the CIP conductance are linearly related to the perturbation induced by the electrical field gs ð~r; ~vÞ: Therefore, from a basic point of view, DG is the macroscopic quantity most directly related to the MR of spin-valve structures (Dieny, 1992; Dieny et al., 1992). Other quantities such as DG=G; DR=R or DR are influenced not only by the intrinsic magnetoresistance of the structure but also by extrinsic effects, such as shunting of the current by outer layers, which affect the overall conductance of the structure. The point of view is different if one thinks in terms of the specific application of GMR to magnetoresistive sensors. As will be explained in more detail in Section 2.6, it is then DR which determines the amplitude of the readout signal and DR=R which gives the SNR. We point out that since R ¼ G21 ; the various quantities DG=G and DR=R are related to each other by DR=Rparallel ¼ DG=Gantiparallel : Several refinements have been brought to the semiclassical theory presented above. The dependence of the coefficients of interfacial transmission and reflection on the angle of incidence of the conduction electrons has been introduced. These coefficients are assumed to vary according to TðmÞ ¼ ðT0 Þ1=m with m ¼ cos u; where u is the angle between the electron velocity and the 2 normal to the interface, and RðmÞ ¼ ðR0 Þm : The improvement has been shown to bring the results of the semiclassical theory very close to those of the more elaborate quantum mechanical theories (Camblong and Levy, 1992). Furthermore, in order to take the columnar structure of the samples into account, an anisotropy in the mean free path was introduced. The electrons propagating with in-plane velocity undergo scattering at grain boundaries, whereas those propagating perpendicular to the interfaces do not experience this scattering. This leads to a slightly longer mean free path perpendicular to the plane than in the plane. Introducing a mean free path lgr associated with the scattering at grain boundaries, the mean free path for an incidence u is given by (Rijks, 1996) 1 1 sin u : ¼ s þ lgr ls ðuÞ l ð0Þ Another source of anisotropy in the mean free path is the AMR in the magnetic layers which leads to longer (respectively, shorter) mean free paths when the electrons propagate perpendicular (respectively, parallel) to the magnetization. This has been taken into account by some authors (Rijks et al., 1995) and it leads to a slight anisotropy in the GMR, i.e. a difference in the relative variation of resistance between the parallel and antiparallel magnetic configurations depending on the direction of the current (parallel or perpendicular) relatively to the magnetization direction. Shown below are a few general trends of CIP GMR which can be simply understood in model systems using the semiclassical theory. We first consider a simple sandwich consisting of

Spin valves 79 two ferromagnetic layers separated by a non-magnetic spacer layer, F tF =NM tNM =F tF ; in which the relative orientation of the magnetization in the two ferromagnetic layers can be changed from parallel to antiparallel. The parameters chosen in the calculation are representative of the case of NiFe/Cu/NiFe sandwiches. We investigate the dependence of the magnetoresistance on the thickness of the magnetic layers and non-magnetic spacer layer. We, furthermore, make several assumptions on the degree of specular reflection at the outer boundaries of the sandwich in order to discuss the influence of this reflection or diffuse scattering on the magnetotransport properties. The results are shown in Figs 2.2 and 2.3.

(a)

0.3 0.25

G (Ω 1)

0.2 p=1

0.15 0.1

p=0

0.05 (b)

0 p=1

∆G (Ω 1)

0.003 0.002 p=0 0.001

(c)

0 p=1

∆R/Rp (%)

10

5 p=0 0 0

50

100 150 200 250 300 tF (nm)

Fig. 2.2 Calculated transport properties: (a) conductance, (b) absolute change of sheet conductance and (c) relative magnetoresistance ratio normalized by the resistance in parallel magnetic configuration Rp for a sandwich of composition F tF /NM 2 nm/F tF as a function of the thickness of the ferromagnetic layers. ¼ 7 nm; lNiFe ¼ The chosen parameters are representative of the case of NiFe/Cu/NiFe sandwiches: lNiFe " # NiFe=Cu NiFe=Cu ¼ T# ¼ 0:9: The coefficient of specular reflection p at outer boundaries 0:8 nm; lCu ¼ 12 nm; T" varies from 0 to 1 by step of 0.25.

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B. Dieny

20 p=1 ∆R/Rp (%)

15

10

5

0

p=0 0

50 tNM (nm)

100

150

Fig. 2.3 Magnetoresistance versus thickness of the non-magnetic spacer layer for the trilayer structure of composition F 3 nm/NM tNM /F 3 nm. The parameters in the calculation are the same as in Fig. 2.2.

The conductance in Fig. 2.2(a) increases approximately linearly with the thickness of the layers. This reflects the fact that in CIP, at the lowest order of approximation, the layer can be considered as carrying the current in parallel so that the dominant term in the conductivity is the expression given in Eq. (2.7). However, even though this lowest level of approximation is sufficient to approximate the variation of the conductance, it cannot explain the magnetoresistance. Indeed, if the layers and the two spin channels are simply assumed to carry the current in parallel in a resistor model, no change in resistance would occur between the parallel and antiparallel magnetic configurations. To explain CIP GMR, the finite size effects must be taken into account. As will be shown later, this constitutes a major difference with CPP transport. Figure 2.2(a) also demonstrates sensitivity to the specular reflection coefficient. It shows that the conductance is slightly lower when the scattering is diffusive on the outer boundary, due to a locally reduced conductivity caused by the scattering at these outer boundaries. Figure 2.2(b) and (c) shows the magnetoresistance in two different forms. The absolute change of conductance DG [Fig. 2.2(b)] increases qualitatively as ð1 2 expð2tF =l"F ÞÞ versus tF for p ¼ 0 and as ð1 2 expð2tF =l#F ÞÞ for p ¼ 1: It is interesting to note that all curves reach the same asymptotic value independent of the degree of specular reflection at outer surfaces. Similarly, if a buffer or a capping layer were added to the sandwich structure, the same asymptotic DG would be obtained, therefore, reiterating that DG is the quantity that intrinsically characterizes the magnetoresistance of the sandwich. In contrast, the relative magnetoresistance exhibits a maximum which shifts towards lower thickness as the specular reflection at the outer surfaces increases. In correlation, the MR ratio increases and is maximum for perfect specular reflection.

Spin valves 81 Here, too, the variation of MR can be qualitatively described by

DR ¼ R

DR ¼ R







DR R

DR R

1 2 exp

 0

0

!!

l"F
 t 1þ F trest

1 2 exp



2tF

2tF

l#F
 t 1þ F trest

for p ¼ 0;

ð2:9Þ

for p ¼ 1:

ð2:10Þ

!!

These expressions simply result from the equality DR=Rparallel ¼ DG=Gantiparallel and the observation that the conductance increases linearly with the thickness of the tF layer. trest represents an effective thickness related to the equivalent conductance of the sandwich without the considered F layers. The decay lengths l"F and l#F are related to the corresponding mean free paths l"F and l#F (Dieny, 1992; Dieny et al., 1992). They are usually shorter than the corresponding mean free paths by a factor of the order of 2 because of the averaging over all incidence of conduction electrons. In these curves, increasing the specular reflection has the same effect on the MR ratio as increasing the number of repeats has in ðF=NMÞn multilayers. This is because the specular reflection introduces a mirror symmetry in the structure. As a result, a sandwich of composition F tF =NM tNM =F tF with purely specular reflection at outer boundaries ðp ¼ 1Þ would have the same magnetoresistance ratio as a multilayer consisting of an infinite number of repeats of ðF 2tF =NM tNM Þ: The shift in the position of the maximum in DR=R as p varies from 0 to 1 [Fig. 2.1(c)] and the correlated change in the characteristic lengths of the exponential variation in the phenomenological formula given above for DR=RðtF Þ can be qualitatively understood as follows. The GMR amplitude is related to the differences of overall scattering which occur for spin " and spin # electrons in the structure. For the following discussion, let us assume that the spin " electrons have the longer mean free path and consider an F tF =NM 2 nm=F tF sandwich with diffuse scattering at outer boundaries ð p ¼ 0Þ: If tF , l"F ; the incoming electrons entering the F layer from the spacer are very rapidly scattered at the outer surface. This reduces their ‘scattering contrast’ with spin # electrons. When the thickness of the ferromagnetic layer becomes of the order of the mean free path, the GMR amplitude reaches maximum. For larger thickness, a portion of the current is shunted in a part of the sandwich which is inactive from the point of view of the GMR leading to an hyperbolic decrease of the MR ratio for further increases in thickness. If we now assume specular reflection at the outer boundaries, the situation is very different. Since the incoming spin " electrons are reflected without losing momentum at the outer boundaries, the constraint is now on spin # electrons. The magnetic layer must be thick enough to scatter them efficiently. If not, they

82

B. Dieny

can conduct more current and the ‘scattering contrast’ with the spin " electrons is again diminished. Figure 2.3 shows the calculated variation of the GMR in a series of F 3 nm=NM tNM =F 3 nm sandwiches in which the thickness tNM of the non-magnetic spacer layer is varied. The GMR decreases monotonically with increasing non-magnetic spacer layer thickness. Qualitatively, this decrease can be described by

DR ¼ R





 2tNM  exp DR lNM
 : t R 0 1 þ NM trest

ð2:11Þ

The numerator shows that the number of electrons traversing from one ferromagnetic layer to the other through the spacer decreases exponentially with increasing thickness of this layer, with a characteristic length lNM related to the mean free path in this layer. The denominator is related to the increased shunting of the current in the spacer layer as its thickness increases. Other examples of the use of semiclassical theory of transport will be shown later in this chapter. We now discuss the main differences between CIP and CPP transport in these metallic multilayers. 2.2.3

Current perpendicular to plane giant magnetoresistance

In the CPP geometry, the current flows perpendicular to the plane of the layers as illustrated in Fig. 2.4. In the simplest approximation, the various layers can be considered as carrying the current in series. In the absence of a spin-flip mechanism during scattering, the transport properties can be described in a very simple two-channel resistor model. A resistor network for a sandwich "ð#Þ F tF =NM tNM =F tF is shown in Fig. 2.5, where rF are the spin-dependent resistivities in the "ð#Þ F layers, and ARF=NM are the spin-dependent interfacial resistances, per unit area, at the F/NM interfaces. In CPP, it is quite common to express the value of CPP resistance in terms of the product of area £ resistance. This comes from the fact that the resistance of a homogeneous pillar of section A varies as the product of the resistivity times the thickness of the pillar divided by the I I V I

I

V

I

CPP

CIP

Fig. 2.4 Schematic representation of the difference between CPP and CIP transport geometries. In the CPP geometry, the multilayered structure is sandwiched between bottom and top electrodes.

Spin valves 83

(a) Parallel magnetic configuration : rF↑tF

↑ ARF/NM

rNMtNM

↑ ARF/NM

rF↑tF

rF↓tF

↓ ARF/NM

rNMtNM

↓ ARF/NM

rF↓tF

(b) Antiparallel magnetic configuration : rF↑tF

↑ ARF/NM

rNMtNM

↓ ARF/NM

rF↓tF

rF↓tF

↓ ARF/NM

rNMtNM

↑ ARF/NM

rF↑tF

Fig. 2.5 Two-channel resistance network which can be used to model the CPP GMR in F tF /NM tNM /F tF sandwiches: (a) parallel magnetic configuration; (b) antiparallel magnetic configuration.

area. The best way to describe the intrinsic properties of the material independently of geometrical consideration is therefore to give the value of its resistance £ area product. It is interesting to note that this simplest approximation can already explain the CPP GMR, which was not the case for the CIP GMR. The CIP GMR requires consideration of finite size effects and, in particular, the influence of the electron mean free paths. This is not the case for CPP GMR. The mean free paths are no longer characteristic lengths in CPP transport. They play an indirect role through the spin-dependent resistivities but do not determine how the CPP GMR varies as a function of the thickness of the various layers. The serial resistance network has been successfully used to interpret a number of experimental results obtained primarily at low temperature (Pratt et al., 1991; Lee et al., 1992, 1993, 1995; List et al., 1995; Piraux et al., 1996; Doudin et al., 1996 and for reviews: Bass and Pratt, 1999; Fert and Piraux, 1999). A summary of the characteristic transport parameters determined at low temperature is given in Table 2.1. These parameters are defined by introducing the following notations: "ð#Þ

ð2:12Þ

"ð#Þ

ð2:13Þ

rF ¼ 2rpF ½1 2 ðþÞb; rN ¼ 2rpN ; "ð#Þ

ARF=NM ¼ 2ARpF=NM ½1 2 ðþÞg:

ð2:14Þ

Parameters b and g; with values between 2 1 and 1, characterize the scattering asymmetry in the bulk and at the interface between the successive layers, respectively. The measurable resistivities of the ferromagnetic metal rF and of the non-magnetic metal rN and the measurable F/NM interfacial resistance are related to these parameters by the following relations:

rF ¼ rpF ð1 2 b2 Þ;

rN ¼ rpN ;

ARF=NM ¼ ARpF=NM ð1 2 g2 Þ:

Table 2.1 summarizes the results obtained by different groups using various preparation techniques. A sizeable spread in the results is observed reflecting the variation in the density of

Table 2.1 Characteristic parameters of CPP transport deduced from low temperature measurements of the CPP GMR in (Co/Cu) and (NiFe/Cu) based multilayers prepared under various conditions Sputtered multilayers, 4.2 K (MSU) (Bass and Pratt, 1999)

MBE-grown multilayers, 4.2 K (List et al., 1995)

Grooved substrates, 4.2 K (Oepts et al., 1996)

Electrodeposited nanowires, 77 K (Piraux et al., 1996)

Electrodeposited nanowires, 20 K (Doudin et al., 1996)

3.1

1.3 – 3.3

rpCu (mV cm)

0.6 ^ 0.1

1.3 ^ 0.3

0.39 ^ 0.07

rpCo (mV cm) bCo ARpCo/Cu (mV mm2) gCo/Cu

6.6 ^ 0.5

3.0 ^ 0.6

4.2 ^ 0.7

18 ^ 2

0.38 ^ 0.6 0.38 ^ 0.03 0.71 ^ 0.05 15.9

0.48 ^ 0.04 0.43 ^ 0.04 0.71 ^ 0.02

0.27 ^ 0.03 0.25 ^ 0.04 0.50 ^ 0.09

0.36 ^ 0.04 0.30 ^ 0.05 0.85 ^ 0.10 26.3

rpNiFe (mV cm) bNiFe ARpNiFe/Cu (mV mm2) gNiFe/Cu

0.73 0.54 0.70

lsf Cu (nm)

0.8 ^ 0.1 140 ^ 20 59 ^ 18

lsf Co (nm) lsf NiFe (nm)

0.8 ^ 0.1

5.5

Adapted from Fert and Piraux (1999) and Tsymbal and Pettifor (2001).

4.3 ^ 1

51 –57 0.46 ^ 0.05 0.3 – 1.1 0.55 ^ 0.07

Spin valves 85 defects in these different structures. However, some general trends clearly arise. For example, scattering asymmetry at the Co/Cu interface ðgCo=Cu Þ is larger than in bulk Co ðbCo Þ: By contrast, NiFe seems to have comparable scattering asymmetry in the bulk and at NiFe/Cu interfaces. From these parameters, it is possible to point out the important role played by interfaces, particularly in the CPP GMR. In the resistor network model, the contribution from the bulk scattering balances the contribution from the interfacial scattering for a characteristic thickness tFp given by brpF tFp ¼ 2ARpF=NM (assuming that the layer is delimited by two interfaces). This leads to values for Co and p p NiFe of tCo < 20 nm and tNiFe < 6:5 nm; respectively. The resistor model has been able to explain a large number of results, especially at low temperature, in Co-based multilayers having relatively thin layers. However, strong deviations from this model were observed in NiFe-based systems. Similarly, the resistor model cannot explain the different magnetoresistive properties obtained in multilayers in which the ordering of the layers is changed, for example, interleaved (Co 1 nm/Cu 2 nm/Co 6 nm/Cu 2 nm)4 multilayers compared to separated (Co 1 nm/Co 20 nm)4/(Co 6 nm/Cu 20 nm)4 multilayers (Bozec et al., 2000). The main difference between these two situations is described as follows. In the antiparallel magnetic configuration of the interleaved multilayers, every other Co layer has a down magnetization. In the separated multilayers, by contrast, one half of the stack has magnetization up and the other half has the magnetization down. These deviations from the simple resistor network are mainly caused by spin relaxation and spin accumulation effects, which play a very important role in CPP transport (Valet and Fert, 1993). Interfacial spin accumulation can be understood in a simple way by looking at Fig. 2.6. In bulk magnetic materials, as already discussed, the two spin channels do not carry the same amount of current because the two species of electrons have different scattering rates. Consider an interface separating two magnetic semi-infinite layers (Fig. 2.6) having antiparallel magnetic configuration, and suppose a current is flowing from right to left, i.e. electrons are drifting from left to right. We further assume that the spin " (majority electrons) are less scattered than the spin # electrons ðb . 0Þ: For simplicity, we adopt the convention that the magnetization is parallel to the spin of the majority electrons. In the left ferromagnetic layer, far from the interface, the current is mainly carried by spin " electrons. The spin " current is given by j" ¼ ðJ=2Þð1 þ bÞ; where J is the total current density. The spin # electrons carry a smaller current j# ¼ ðJ=2Þð1 2 bÞ: Figure 2.6 has been drawn assuming b ¼ 0:7; a value close to that determined for Permalloy (Table 2.1). On the right-hand side, the magnetization is down and the roles of spin " and spin # electrons are inverted. More spin # electrons flow away from the interface than spin " electrons. Within each spin channel, there is therefore a clear unbalance between the number of electrons moving towards (on the left) and away from (on the right) the interface per unit time. This results in a spin accumulation which consists (Fig. 2.6) of a local excess of spin " electrons around the interface and a correlated local deficit in spin # electrons. In steady state, this spin accumulation does not increase with time because it is counterbalanced by spin-flip processes. Due to spin –orbit interaction and magnons, the electrons can undergo scattering events which modify their spin.

86

B. Dieny

(a)

∆µ

Direction of electron drift

lFsf lFsf z J(1 + β)

j↑

jσ

(b)

J/2

J(1

β)

j↓

lFsf lFsf z

Fig. 2.6 Illustration of the phenomenon of spin accumulation at a single interface separating two ferromagnetic layers of opposite magnetization. The electrons drift from left to right (the current flows from the right). The plot is drawn assuming that the spin " (majority electrons) are less scattered than the spin # electrons ðb . 0Þ: The large arrows represent magnetization orientation. (a) The spatial variation of the difference in chemical potential Dm ¼ m" 2 m# between the two species of electrons. Dm . 0 means an accumulation of spin " electrons at the interface. (b) The spatial variation in current density for each spin channel. The gradient of current reflects the spin relaxation which takes place within the characteristic spindiffusion length scale lsf F : Adapted from Valet and Fert (1993).

We recall that magnons are also named spin waves and represent elementary excitations of the magnetization. The characteristic length scale over which the electrons maintain their spin orientation in a given material is the spin-diffusion length lsf : In a ferromagnetic material, the latter is related to the spin-flip relaxation time tsf via 1 ðlsf Þ2

¼

1 1 þ # 2; 2 " ðl Þ ðl Þ

where the ls are given by ls ¼ ½ 13 ðvF ls Þtsf 1=2 :

ð2:15Þ

vF is the Fermi velocity and ls are the elastic mean free paths. Values of the spin-diffusion lengths in various commonly used materials at low temperature are given in Table 2.1. The balance between the spin accumulation and spin relaxation leads to local variations in the difference Dm of electrochemical potential of spin " and spin # electrons as illustrated in Fig. 2.6(a). The result is a small non-equilibrium local magnetization near the interface,

Spin valves 87 proportional to the current (Valet and Fert, 1993). The Valet and Fert theory addresses the effect of spin accumulation in detail, using a relatively simple macroscopic model based on two basic equations: 2erp

›js ðms 2 m2s Þ ¼2 ; ›z ðlsf Þ2

ð2:16Þ

js ¼

1 ›ms : ers ›z

ð2:17Þ

Here, e represents the absolute value of the electron charge, and the resistivities rp and rs are given by relations (2.12) and (2.13). The first equation describes spin relaxation effects, whereas the second is a generalized form of Ohm’s law. A result of these equations is that Dm obeys a simple diffusion equation within each layer, having the general solution:
Dm ¼ A exp

z lsf




 z þ B exp 2 : lsf

The constants A and B must be determined by interfacial boundary conditions as in the semiclassical model of CIP GMR. These boundary conditions express the continuity of the current for each spin channel through the interfaces and in the presence of spin-dependent interfacial resistance ARs ; the electrochemical potential must fulfill the equation: s 2 ms ðz ¼ zþ 0 Þ 2 m ðz ¼ z0 Þ ¼

ARs s j ðz ¼ z0 Þ: e

Using these equations, it is possible to calculate the CPP resistance and CPP magnetoresistance of any magnetic multilayered stack, taking into account spin-flip processes (Strelkov et al., 2003). The failure of the simple resistor network to explain the CPP GMR of NiFe-based multilayers and multilayers in which the ordering of the layer is changed can be understood in terms of spin relaxation effects. In both types of systems, the length scale over which electrons propagating perpendicular to the plane experience a change from up magnetization to down magnetization is longer than the spin-diffusion length. This is true in NiFe-based systems because of the relatively short spin-diffusion length in NiFe (5.5 nm at 4.2 K) (Steenwyk et al., 1997). It is also true in the separated (Co 1 nm/Cu 20 nm)4/(Co 6 nm/Cu 20 nm)4 multilayers because the spin-diffusion length in Co and Cu is not long compared to the total thickness of the stack. Furthermore, some additional spin-flip scattering may take place at Co/Cu interfaces (Eid et al., 2002). A dependence of the interface resistance on the proximity of the other interfaces has also been proposed as an alternative explanation to the observed difference between interleaved and separated multilayers (Bozec et al., 2000). Based on the Valet and Fert theory, we now discuss the influence of parameters such as layer thickness on the CPP properties of magnetic sandwiches inserted between thick Cu electrodes.

88

B. Dieny

Consider the model system Cu=F tF =NM 3 nm=F 5 nm=Cu; where F represents Ni80Fe20 or Co. In the following calculations, the values listed in the fifth column of Table 2.1 (Piraux et al., 1996) were used for NiFe and Co. Figure 2.7 shows the variation of MR versus the thickness of the ferromagnetic layer in terms of the absolute MR [Fig. 2.7(a)] and relative MR ratio [Fig. 2.7(b)]. With NiFe, a clear maximum in DR=R is observed versus tNiFe at a thickness slightly larger than the spin-diffusion length lsf NiFe ¼ 4:3 nm; while ADR increases and reaches an asymptotic value for tNiFe q lsf NiFe : The absolute MR magnitude is quite large, much larger than in Co/Cu/Co sandwiches of the same thickness. This comes from the large contribution of the bulk spindependent scattering in NiFe, which is much larger than the bulk contribution in Co. The decrease in DR=R at thicknesses larger than lsf NiFe is caused by the serial contribution of the resistance of a part of the NiFe layer which is further from the other NiFe layer than lsf NiFe : This portion contributes little to the MR and a dilution of the DR=R results for large tF :

(a)

0.008 NiFe tF/Cu 3nm/NiFe 5nm A.∆R (Ω.µm2)

0.006

(b)

0.004

Co tF/Cu 3nm/Co 5nm

0.002

=0.25

0

NiFe tF/Cu 3nm/NiFe 5nm ∆R/Rp (%)

100

50 Co tF/Cu 3 nm/Co 5nm γ = 0.25 0

0

10

20 30 tF (nm)

40

50

Fig. 2.7 Calculation of CPP magnetoresistance of NiFe tF /Cu 3 nm/NiFe 5 nm and Co tF /Cu 3 nm/Co 5 nm sandwiches inserted between Cu electrodes versus thickness of one of the ferromagnetic layers. (a) Absolute magnetoresistance £ area product. (b) Relative MR ratio, DR=R; at 77 K. The calculated resistances and MR are those of the sandwich itself, i.e. without considering the additional resistance of the electrodes. The dotted curve is calculated using the same parameters as for Co/Cu/Co except that the interfacial scattering asymmetry has been reduced from 0.85 to 0.25 to show the role of the relative influence of bulk and interfacial scattering on the shape of these curves.

Spin valves 89 In a Co/Cu/Co sandwich, DR=R decreases monotonically versus tCo [Fig. 2.7(b)]. This is caused by the dominant role of interfacial spin-dependent scattering in this system. The dotted curves in Fig. 2.7 were calculated using the same parameters for the Co/Cu/Co particular sandwich with the sole difference that the parameter g has been reduced from 0.85 to 0.25. A maximum in DR=R versus tF is then seen [Fig. 2.7(b)]. ADR also reaches an asymptotic value but more slowly than with NiFe because of the longer spin-diffusion length in Co. It is interesting to note that ADR in CPP transport as the same functional form ð1 2 expð2t=lÞÞ; as DG in CIP transport. However, the characteristic length in CPP transport is the spin-diffusion length compared to the elastic mean free path in CIP transport. Figure 2.8 shows the dependence of CPP MR on the thickness of the non-magnetic spacer layer, which is Cu in our own model system.

(a)

0.006

A.∆R (Ω.µm2)

NiFe tF/Cu 3nm/NiFe 5nm 0.004

0.002 Co tF/Cu 3nm/Co 5nm γ=0.25

(b)

0

∆R/Rp (%)

NiFe tF/Cu 3nm/NiFe 5nm 100

50 Co tF/Cu 3nm/Co 5nm γ=0.25 0

0

10

20 30 tNM (nm)

40

50

Fig. 2.8 Calculation of CPP magnetoresistance of NiFe 5 nm/Cu tNM /NiFe 5 nm and Co 5 nm/Cu tNM /Co 5 nm sandwiches inserted between Cu electrodes versus thickness of the non-magnetic spacer layer. (a) Absolute MR. (b) Relative MR ratio, DR=R; T ¼ 77 K. The dotted curve is calculated using the same parameters as for Co/Cu/Co except that the interfacial scattering asymmetry has been reduced from 0.85 to 0.25.

90

B. Dieny

The CPP magnetoresistance ADR decreases monotonically versus the thickness of the non-magnetic spacer layer, having the approximate form expð2t=lÞ with the characteristic decay length represented by the spin-flip diffusion length in Cu, lsf Cu : In order to get a large CPP GMR amplitude, the spin-diffusion length in the spacer must be much larger than the thickness of this layer. In that respect, pure Cu is a good spacer layer. The spin-diffusion length of Au is shorter because Au has a higher atomic number, larger spin orbit interactions and shorter spin relaxation time (see Chapter 1). Certain types of impurities such as Mn and Pt have been shown to dramatically shorten the spin-diffusion length in Cu or Ag (Yang, 1994). While these experiments confirmed details of CPP theory, the presence of such impurities must be avoided between the free and pinned layers. The exponential decrease of ADR versus tNM can be compared to a corresponding exponential decrease of DG in CIP GMR where the characteristic length is related to the elastic mean free path in Cu. Concerning the MR ratio [Fig. 2.8(b)], DR=R exhibits a steeper decrease versus tNM than ADR due to the combined effect of spin relaxation, which leads to the exponential decrease of ADR; and to the series addition of an increasing amount of spacer layer resistance. This causes a dilution effect and leads to a further hyperbolic decrease of the magnetoresistance. Again this can be compared to the variation of DG=G given by relation (2.11) (we remind that DG=Gparallel ¼ DR=Rantiparallel ). In this latter case, the variation was also a combination of an exponential and a hyperbolic decrease in GMR, the hyperbolic decrease arising from the increasing parallel shunting of the current in the spacer layer. In concluding this section, the above discussions have shown the intrinsic differences between CIP and CPP transport. The CIP GMR cannot be modeled by a simple parallel resistor network. The lowest order of approximation requires inclusion of finite size effects for which the characteristic lengths are the spin-dependent elastic mean free paths. In contrast, CPP transport can be described in the lowest order of approximation by a two-channel serial resistance network. Finite size effects can play an important role when the thickness of the layers becomes larger than the spin-diffusion lengths.

2.3 2.3.1

Basic properties of spin valves Spin valves

The simplest spin valves comprise two ferromagnetic layers (F1 and F2) separated by a nonmagnetic spacer layer (NM). The magnetization of F2 is pinned by coupling with an adjacent antiferromagnetic layer using the so-called exchange anisotropy phenomenon. Figure 2.9(a) and (b) shows the room temperature hysteresis loop and magnetoresistance of a sample of structure Ta 5 nm/NiFe 6 nm/Cu 2.2 nm/NiFe 4 nm/FeMn 7 nm/Ta 5 nm (Dieny et al., 1991a).

Spin valves 91

1

M (10

3

emu)

(a)

(b)

0 1

4

∆R/R (%)

3 2 1 0 (c)

200

0

200 400 H(Oe)

600

800

4

∆R/R (%)

3 2 1 0

40

20

0 20 H(Oe)

40

Fig. 2.9 (a) Hysteresis loop; (b) magnetoresistance of a spin-valve sample of composition Ta 5 nm/NiFe 6 nm/Cu 2.2 nm/NiFe 4 nm/FeMn 7 nm/Ta 5 nm; (c) magnetoresistance observed when a minor loop is performed on the nominally free layer (T ¼ 300 K).

The hysteresis loop of this structure consists of two loops. The first one is centered at 6 Oe, has a coercivity of less than 1 Oe, and corresponds to the reversal of the free NiFe layer. The second has a coercivity of 100 Oe and a loop shift of 420 Oe which is associated with the reversal of the magnetization of the NiFe layer that is exchange coupled to FeMn (pinned layer). When the field is swept between ^ 1 kOe, the magnetizations of the NiFe layers change from parallel (below 4 Oe and above , 600 Oe) to antiparallel (between 8 and ,250 Oe). The 6 Oe loop shift of the nominally free NiFe layers [Fig. 2.9(c)] indicates the presence of a slight ferromagnetic coupling through the Cu spacer layer. The magnetoresistance curve of Fig. 2.9(b) exhibits a very sharp rise corresponding to the switching of the free layer, followed by a gradual decrease to zero as the magnetization of the pinned layer reverses. The interesting feature of spin valves is that the change in the relative orientation between the magnetization in the magnetic layers does not rely

92

B. Dieny

on the existence of an antiferromagnetic coupling through the spacer, but on the existence of asymmetric pinning forces acting on the magnetization of the two ferromagnetic layers. This allows the realization of very high magnetoresistance sensitivity at low fields. The denomination ‘bottom’ and ‘top’ spin valves has been introduced to specify whether the antiferromagnetic pinning layer and its adjacent ferromagnetic pinned layer are deposited before the free layer (at the bottom of the stack) or after the free layer (at the top of the stack). 2.3.2 2.3.2.1

Magnetic properties Exchange anisotropy

The phenomenon of exchange anisotropy was discovered by Meiklejohn (1962) but a quantitative understanding has not yet been achieved. Reviews of the topic have been published by Kools (1996), Nogues and Schuller (1999), and Berkowitz and Takano (1999). The ferromagnetic/ antiferromagnetic coupling causes both enhanced coercivity and a loop shift. The intrinsic anisotropy of the antiferromagnetic material and the thickness of the antiferromagnetic layer (AF) are dominant factors, but in polycrystalline samples, the grain size, the homogeneity in the distribution of grain size and the coupling between grains, all play significant roles. Indeed, in order to observe a large pinning of the magnetization in the ferromagnetic layer, it is important that the magnetization of the antiferromagnetic layer is not dragged by the torque exerted by the magnetization of the ferromagnetic layer, across the interface, as the latter switches. The energy barrier due to the magnetocrystalline anisotropy in each antiferromagnetic grain is defined as Ea ¼ KV ¼ KAtAF ; where K is the anisotropy per unit volume, A is the area of the grain, and tAF is the thickness of the antiferromagnetic layer. The coupling energy between the ferromagnetic layer and the antiferromagnetic layer is given by Eexb ¼ JA; where J is the coupling per unit area. Taking into account the thermal activation of the antiferromagnetic grains, the condition of stability of the spin lattice in the antiferromagnetic layer for a certain duration tstability is written as
KAtAF . JA þ Ln

 tstability kB T; t0

where t0 is the attempt time of the order of 1029 s. For a typical device lifespan of 10 years, the factor Lnðtstability =t0 Þ is of the order of 40. This qualitative argument shows that increasing the stability of the antiferromagnetic layer can be achieved by increasing its anisotropy, its thickness or the grain size. Alternatively, improving the coupling between grains would lead to an effect comparable with increasing the grain size. In spin valves for read-head applications, the qualities that are required of antiferromagnetic layer are that it must provide a sufficiently large exchange field ðHexb . 500 OeÞ at the operating temperature (typically 1008C), it must be highly resistive in order to reduce parasitic shunting of

Spin valves 93

Fig. 2.10 Temperature dependence of the exchange energy in spin-valve structures with different biasing layers (Nozieres et al., 2000).

the current in CIP geometry, it must have sufficiently low processing temperature in order not to perturb the structural integrity of the stack, and it must be corrosion resistant and thermally stable. Furthermore, as will be explained in Section 2.6, if the antiferromagnetic layer is metallic, it must be thin enough to maintain a read gap width as small as possible. Oxide antiferromagnetic materials such as NiO, a-Fe3O4, Fe2O3 have been implemented in spin valves, but they have not provided good pinning properties despite large GMR amplitude (Sakakima, 1999). The most widely used antiferromagnetic layers are Mn-based alloys, in particular ordered alloys such as Pt50Mn50, which provide a large bias field with a high blocking temperature. Figure 2.10 shows the exchange bias energy of a variety of antiferromagnetic materials as a function of temperature (Nozieres et al., 2000). NiMn is seen to be a good candidate but it usually leads to lower MR amplitude than PtMn-based spin valves. The exchange bias field ðHexb Þ is a parameter that results from a balance between the volume Zeeman energy supplied by the applied field to the free layer magnetization and the surface energy of coupling with the adjacent antiferromagnetic layer. It scales as the inverse of the pinned layer thickness. For optimizing the magnetic properties, it is therefore better to reduce the thickness of the pinned layer. However, for maximizing the GMR amplitude, there is an optimum thickness below which the GMR drops, as explained in the discussion of Fig. 2.2. In this respect, increasing the specular reflection at the interface between the pinned layer and the AF layer is beneficial since this reduces the optimum thickness of the pinned layer and therefore leads to a larger Hexb of the pinned layer. 2.3.2.2

Interlayer coupling

In spin valves, the interlayer coupling between the free and the pinned layers causes a shift in the hysteresis loop of the free layer. There are three main contributions to this interlayer coupling:

94

B. Dieny

Fig. 2.11 Structure of the ferromagnetic/non-magnetic spacer/ferromagnetic sandwich which leads to the onset of the orange peel coupling. When the magnetizations of the two ferromagnetic layers are parallel, magnetostatic charges of opposite sign appear symmetrically on opposing interfaces (see, for example, the encircled area). In contrast, if the magnetizations are antiparallel, charges of the same sign are facing each other leading to an increase in energy. This results in an effective ferromagnetic coupling between the two magnetic layers.

(1) At very low thickness, direct coupling through pinholes in the non-magnetic spacer layer may occur. The thickness below which this coupling becomes dominant clearly depends on the roughness of the layers and on the degree of interdiffusion between the magnetic and nonmagnetic spacer material. Use of an optimized buffer, such as a NiFeCr-based alloy instead of Ta, has allowed a reduction of the critical thickness from about 1.8 nm down to 0.8 nm. (2) Another source of ferromagnetic coupling which is often encountered in multilayers, and particularly spin valves of average crystallographic quality, is caused by the orange peel mechanism initially described by Ne´el (1962). In multilayers, the roughness of the interfaces is often correlated from one interface to another by the very fact that the thickness of the layers is uniform (cf. Fig. 2.11). Dipolar interactions between the magnetostatic charges which then appear on the interfaces give rise to a ferromagnetic coupling between the magnetic layers. Quantitatively, describing the interfacial roughness as a sinusoidal function of amplitude h (2h being the peak to peak roughness), and wavelength L (typically of the order of the grain size), one can show, using Ne´el’s model, that the resultant dipolar coupling between the magnetic layers across a non-magnetic layer of thickness tNM is given in CGS units by (Schulthess and Butler, 2000) pffiffiffi
 pffiffiffi 2 h2 2 22 2ptNM Ms exp : J ¼ 2p L L

ð2:18Þ

In general, this coupling is weaker than the direct coupling due to pinholes and usually manifests itself at greater thicknesses, i.e. at tNM of the order of 2–10 nm. (3) A third contribution to the interlayer coupling observable in spin valves of high structural quality is the oscillatory RKKY (Ruderman–Kittel –Kasuya– Yosida) coupling (Ruderman and Kittel, 1954; Kasuya, 1956; Yosida, 1957). This results from a spin polarization of the electrons of the non-magnetic layer induced by a contact interaction with the magnetic layers. In bulk non-magnetic metals, a ferromagnetic impurity (e.g. a Mn impurity) placed in a Cu matrix polarizes the sea of conduction electrons in the Cu in the vicinity of the Mn ion.

Spin valves 95 The densities of all the spin " and spin # electrons, not just the electrons near the Fermi energy, instead of being equal, are slightly different in the vicinity of the impurity. The resulting spin polarization oscillates with a wave vector 2kF (where kF is the Fermi wave vector) and attenuates as 1=r3 ; where r is the distance from the impurity. If a second magnetic impurity is found at a certain distance from the first, the reciprocal coupling effect between the conduction electrons of the matrix and this second impurity give rise to an indirect coupling between the spins of the two impurities. The coupling may be ferromagnetic or antiferromagnetic, depending on the distance between them. The same coupling mechanism occurs in multilayers. In this case, the oscillatory polarization of the electrons of the nonmagnetic interlayer is induced by magnetic atoms situated at the F/NM interface. The resultant coupling may be ferromagnetic or antiferromagnetic, depending on the thickness of the spacer layer. Theoretical models relate the period of the oscillations with certain details of the Fermi surface (Bruno and Chappert, 1991, 1992; Deaven et al., 1991). In samples of very good structural quality, the superposition of a number of periods of oscillation may be observed. Figure 2.12 shows the variation of the loop shift of the free layer in sputtered spin valves of the composition NiFeCr 6 nm/NiFe 4 nm/CoFe 1 nm/Cu tCu /CoFe 2 nm/Ru 0.9 nm/CoFe 2.5 nm/ PtMn 10 nm. By optimizing the growth conditions, the RMS roughness of these samples has been reduced to less than 0.2 nm. This permits the observation of the oscillatory RKKY coupling, even though it is not obtained with non-optimized conditions such as, for instance, when Ta buffer layers are used. Good control of the Cu thickness then allows an adjustment of the bias point of the spin valve, as will be explained in Section 2.6.

100 80 60 Ferro

He (Oe)

40 20 0 20

Antiferro

40 60 0

0.5

1 1.5 2 Cu thickness (nm)

2.5

3

Fig. 2.12 Loop shift of the free layer versus thickness of the non-magnetic spacer layer in spin valve of the composition NiFeCr 6 nm/NiFe 4 nm/CoFe 1 nm/Cu tCu /CoFe 2 nm/Ru 0.9nn/CoFe 2.5 nm/PtMn 10 nm. From M. Li, S. Liao, C. Horng, K. Ju, Headway Technologies.

96

B. Dieny

2.3.3

CIP transport properties

2.3.3.1

Influence of the thickness of the ferromagnetic layer

Figure 2.13 shows the magnetoresistance variation as a function of thickness of the free layer, for a series of three spin valves of the composition Si/SiO2/F tF /Cu 2.5 nm/NiFe 5 nm/FeMn 10 nm, and having different free layer material F ¼ Ni80Fe20, Co and Fe (Dieny et al., 1991a–d). The general shape of these curves is consistent with the prediction of the semiclassical theory for the case of weak specular reflection at the buffer/free layer and pinned layer/AF interfaces (see Fig. 2.2). The increase in GMR at low ferromagnetic thickness is due to decreased scattering of the spin " electrons at the substrate/free layer interface, therefore increasing the scattering contrast between spin " and spin # electrons. The decrease in GMR at larger thickness is associated with increased shunting of the current in the portion of the free layer which does not contribute to the magnetoresistance because it is further from the pinned magnetic layer than the spin " mean free path. It is interesting to note in Fig. 2.13 that the maximum in MR occurs at lower thicknesses for Fe than for Co or NiFe. This can be explained as a change in the fractional contributions between bulk and interfacial scattering for these various materials. NiFe and Co have been shown to have a significant contribution to the GMR from the bulk of the layer in addition to the contribution arising from the interfacial spin-dependent scattering. This was confirmed by measurements performed in CPP transport (see Table 2.1). The case of Fe provides a contrast. Although less data are available concerning the determination of the bulk and interfacial scattering parameter in this material, bulk scattering seems to have less spin asymmetry than is the case for NiFe or Co (Gijs et al., 1993). This can be understood by considering the band structures of these various materials. In the simple sd model, Ni and Co are strong ferromagnets which means that their majority d-band

Fig. 2.13 Magnetoresistance at room temperature as a function of the thickness of the nominally free layer for spin valves of the composition F tF /Cu 2.5 nm/NiFe 5 nm/FeMn 10 nm, with F ¼ Ni80Fe20, Co and Fe (Dieny et al., 1991a – d). The solid lines are fits of the experimental data according to the phenomenological expression [Eq. (2.9)] given in the text. Open diamonds: Fe, open circles: Co, closed squares: NiFe.

Spin valves 97 is considered as completely filled. Therefore, there is a large difference in the density of spin " and spin # empty states at the Fermi energy into which the electrons can be scattered. The result is a large bulk scattering asymmetry in these materials. By contrast, Fe is a weak ferromagnet which means that both spin " and spin # d-subbands are only partially filled, there is less difference between the corresponding density of empty states at Fermi energy, and it follows there is a weaker bulk scattering asymmetry. The relatively larger role of interfacial scattering in Fe-based spin valves may explain the occurrence of the maximum at lower thickness. An alternative explanation may be based on larger specular reflection at the substrate Fe interface. However, the structural quality of these samples was not optimized, and therefore it is not likely that specular reflection occurred here. The variations of GMR versus the thickness of the magnetic layer can be very well accounted for by the semiclassical theory of GMR presented in Section 2.2 and such a calculation is shown in Fig. 2.14. In particular, the shift in the position of the maximum of DR=RðtF Þ for Fe, for which the spin asymmetry of the interfacial scattering is dominant, is well reproduced. We point out that the CIP GMR in these samples is extremely sensitive to the transmission of the majority electrons through the ferromagnetic/spacer layer interfaces. The main difference in the calculated GMR between NiFe and Co samples comes from a change in transmission coefficient from 95% for Co to 85% for NiFe. Indeed, any reduction in the transmission of spin " electrons leads to a reduction in the spin-dependent scattering contrast, which results in a lower GMR. The large spin " transmission at Co/Cu interface can be attributed to the very good electronic band matching

5 4

∆R/Rp (%)

Co 3

NiFe

2 Fe 1 0

0

10

20

30 tF (nm)

40

50

Fig. 2.14 Semiclassical calculation of GMR for the same spin valves shown in Fig. 2.13, with composition F tF /Cu 2.5 nm/NiFe 5 nm/FeMn 10 nm. In contrast to Fig. 2.12, the full lines are here the results of the semiclassical theory [Eqs (2.7) and (2.8)] whereas the full lines of Fig. 2.13 are phenomenological fits using " ¼ 0:85; Eq. (2.9). The parameters used in the calculation are: l"NiFe ¼ 7 nm; l#NiFe ¼ 0:7 nm; TNiFe=Cu # " # " # " TNiFe=Cu ¼ 0:30; lCo ¼ 9 nm; lCo ¼ 0:9 nm; TCo=Cu ¼ 0:95; TCo=Cu ¼ 0:30; lFe ¼ 4:5 nm; l#Fe ¼ 4:5 nm; " # ¼ 0:70; TFe=Cu ¼ 0:30: NiFe and Co have both bulk and interfacial spin-dependent scattering whereas TFe=Cu the GMR of Fe arises only from the interfacial contribution.

98

B. Dieny

between Co and Cu majority electrons. The relatively poor transmission at NiFe/Cu interface may be attributed to the interdiffusion of Ni and Cu at the interface, which tends to form solid solution. Furthermore, the formation of an interfacial NiFeCu alloy leads to the development of a significant density of interfacial spin waves since the Curie temperature of NiCu alloys decreases rapidly with increasing Cu content. These spin waves contribute to the interfacial electron scattering. In the case of Fe, the lower transmission of spin " electrons can be attributed to the poor structural quality of the interface due to the mismatch between bcc Fe and fcc Cu.

2.3.3.2

Influence of the thickness of the non-magnetic spacer layer

Figure 2.15 shows the variation of the GMR amplitude in a series of spin valves in which the spacer layer thickness was varied. Both Cu and Au spacer layers were used. The lines are fits of the experimental data according to Eq. (2.11) and they combine an exponential decay with a hyperbolic decay. The former is associated with the decreasing fraction of electrons that traverse the spacer layer as its thickness increases, whereas the latter is due to the increased shunting of the current in the spacer layer. The decay lengths found for Cu and Au are lCu ¼ 6 nm and lAu ¼ 5 nm, respectively. These decay lengths are related to the electron mean free path in the spacer layer. The larger decay length found for Cu compared with that for Au is consistent with the lower resistivity of Cu compared to Au: rCu < 5 mV cm, rAu < 7 mV cm, at 300 K. Besides the shorter decay length, the GMR amplitude is lower for the Au than for the Cu spacer layer. This can be explained as a lower transmission of spin-up electrons at Co/Au and NiFe/Au interfaces due to a larger lattice mismatch between the magnetic elements and Au than is the mismatch with Cu. It may also reflect that larger spin– orbit scattering rates are expected from the heavier element, which leads to more spin-flip scattering in the spacer layer.

Fig. 2.15 Magnetoresistance at room temperature as a function of thickness of the noble metal spacer in spin valves of the composition: Si/SiO2/Co 7 nm/NM tNM /NiFe 5 nm/FeMn 8 nm/NM 1.5 nm with NM ¼ Cu and Au. The solid lines represent fits according to Eq. (2.11) (Dieny et al., 1991a– d).

Spin valves 99 Ag has also been used as spacer layer (Dieny et al., 1991a–d). The corresponding GMR amplitudes are intermediate between those of Cu and Au for Ag thickness larger than 5 nm. However, it has been shown that, at room temperature, Ag does not wet at all on Co or NiFe surfaces. Ag grows as three-dimensional islands leading to a very strong ferromagnetic coupling between the free and pinned magnetic layers, up to Ag thickness of the order of 5 nm. Ag is therefore not a suitable spacer for spin valves grown at room temperature. However, antiferromagnetically coupled (NiFe 2 nm/Ag 1 nm) multilayers exhibiting large GMR amplitude and relatively low saturation field (100 Oe) can be obtained by cooling the substrate to liquid nitrogen temperature during growth (Rodmacq et al., 1993). Once the growth is completed, these multilayers can withstand annealing temperatures up to 2508C. In conclusion, in order to increase the GMR amplitude in spin valves, the spacer layer thickness must be reduced as much as possible. However, due to the increasing parallel coupling between the free and pinned layers at low spacer layer thickness, a compromise must be found between a large GMR amplitude and a coupling that is too large. This compromise is usually obtained for Cu spacer layer thickness between 1.8 and 2.2 nm.

2.3.3.3

Influence of temperature on the CIP GMR

The GMR in magnetic multilayers and spin valves, in particular, decreases with increasing temperature. It drops typically by a factor of 2 or 3 as the temperature is raised from 4 to 300 K. As an example, Fig. 2.16 shows the thermal variation of the GMR in two series of spin valves having Cu and Au as the non-magnetic spacer material (Dieny et al., 1991a–d). The GMR decreases almost linearly with temperature and extrapolates to zero amplitude for the same temperature, T0SV ; independent of the thickness of the spacer layer and composition. On the other hand, the characteristic temperature T0SV strongly depends on the nature of the magnetic materials comprising the free and pinned layers. There is a positive correlation between the value of T0SV and the Curie temperature Tc of these magnetic materials (higher Tc correlates with higher T0SV ). Two main contributions to the thermal decrease of GMR have been identified: (1) Inelastic scattering by phonons. Phonon scattering does not affect the spin of the electrons. However, it is spin dependent because of the spin dependence of the density of states at the Fermi energy. If the spin asymmetry associated with this scattering is different from the scattering asymmetry due to structural defects, then phonon scattering may influence the thermal variation of GMR. Furthermore, the phonon scattering shortens the mean free paths, in particular in the spacer layer. This reduces the flow of electrons between the free and pinned layer and further reduces the GMR. Phonon scattering alone, however, cannot explain the decrease by a factor of 2 of the GMR between 4 and 300 K, even if the phonon scattering is considered to be spin dependent. Indeed, for sputtered samples,

100 B. Dieny

Fig. 2.16 Temperature dependence of the GMR amplitude for two series of spin valves of the composition: glass/Co 7 nm/NM tNM /NiFe 5 nm/FeMn 8 nm/NM 1.5 nm, where NM is either (a) Cu or (b) Au (Dieny et al., 1991a –d).

the resistivities of the various materials comprising the spin valve typically vary by 50% in this temperature range. Shortening the mean free path in a 2.5 nm thick Cu spacer layer from 30 to 20 nm only leads to a small change in the GMR amplitude, of the order 10%, according to the semiclassical theory. Similarly, taking into account the thermal variation of mean free paths in the other layers explains variations of the order of 10 –20% but not a factor of 2 or 3. Therefore, another contribution to the thermal decrease of GMR must be put forward. (2) Magnon scattering, either in the bulk of the ferromagnetic layer or at the interfaces. The importance of this contribution at room temperature depends on how high the Curie temperature of the magnetic element is. For Co or Co12x Fex ð0 , x , 0:3Þ alloys (Tc Co ¼ 1394 K, Tc Fe ¼ 1043 K), the density of magnons at room temperature remains relatively low. In contrast, room temperature for Permalloy Ni80Fe20 (Tc Permalloy ¼ 595 K) corresponds to Tc =2: Magnon scattering then plays a significant role. Contrary to phonons, scattering by magnons causes spin flip of conduction electrons, leading to a mixing between the two spin current channels. In the framework of the semiclassical theory of transport, this spin mixing can be described by adding an interband mixing term in the

Spin valves

101

Boltzmann equation:

›gs ðz; vÞ gs ðz; vÞ gs ðz; vÞ 2 g2s ðz; vÞ eE ›f 0 ðvÞ þ þ ¼ ; mvz ›vx ›z ts vz t"# vz

ð2:19Þ

in which t"# represents the spin-flip relaxation time. Magnon scattering naturally explains the correlation observed between T0SV (the rate of decrease of the GMR with temperature) and the Curie temperature of the magnetic element. Magnon scattering can also play a very important role at interfaces. In the presence of interfacial roughness and interdiffusion, a significant weakening of the exchange stiffness may occur in the interfacial region. These effects lead to reduced interfacial magnetic moment. They are more pronounced with Ni80Fe20/Cu interfaces but are present, although weaker, at Co/Cu interfaces (Nozieres et al., 1993). At room temperature, a large density of interfacial magnetic fluctuations is present in these magnetically weakened regions. They can cause spin-flip scattering and thus reduce the GMR amplitude. A quantitative analysis of the thermal variation of GMR based on the semiclassical theory of GMR including spin flip, in several series of spin valves comprising Ni80Fe20 and Co ferromagnetic layers and Cu and Au spacer layers can be found in Dieny et al. (1995). 2.3.3.4

Angular variation of GMR

In the vast majority of magnetic multilayers, the CIP resistance is maximum in the antiparallel magnetic configuration and decreases in the parallel magnetic configuration. The opposite behavior has been observed in a few cases prepared to purposely validate the basic understanding of GMR. In these structures, layers having opposite scattering rates (for instance, l" . l# in the free layer and l" , l# in the pinned layer) were prepared (Renard et al., 1996; Vouille et al., 1997) so that the ‘short circuit effect’ by one species of electrons leads to the low resistance state in the antiparallel magnetic configuration. The question to be addressed by the angular variation of GMR is the following: how does the resistance vary as a function of the angle between the magnetization orientation in the free and pinned layers, between these extremum values corresponding to parallel and antiparallel magnetic configurations. This angular variation was investigated by various authors, both experimentally (Chaiken et al., 1990; Dieny et al., 1991a– d; Steren et al., 1995) and theoretically (Vedyaev et al., 1994; Wang et al., 1996; Vedyaev et al., 1997; Blaas et al., 1999; Coehoorn, 2000). When a rotating field of the order of a few tens of oersteds is applied to a spin valve, the magnetization of the free layer rotates with the field whereas the magnetization of the pinned layer remains pinned in a fixed direction. At most, it may oscillate slightly around the exchange bias field Heb : If Heb is sufficiently large compared to the amplitude of the rotating field, these oscillations are negligible. There are then two contributions to the variation in resistance as a function of the direction of the field. One is the AMR which varies as the cosine squared of the angle between the magnetization

102 B. Dieny

Fig. 2.17 Relative change of resistance versus cosine of the relative angle between the magnetizations of the two NiFe layers in Si/NiFe 6 nm/Cu 2.6 nm/NiFe 3 nm/FeMn 6 nm/Ag 2 nm. The inset shows the orientation of the current J; exchange anisotropy field Hex ; applied field H and magnetizations M1 (free layer) and M2 (pinned layer) of the two ferromagnetic layers (Dieny et al., 1991a– d).

of the free layer and the current, and the other is the GMR. As shown in Fig. 2.17, by subtracting the AMR contribution from the total magnetoresistance, it was found that the GMR varies according to RðuÞ ¼ RP þ ðRAP 2 RP Þ

ð1 2 cos uÞ ; 2

ð2:20Þ

where RP and RAP are the resistances of the spin valve in parallel and antiparallel magnetic configuration, respectively (Dieny et al., 1991a– d), and u ¼ u1 2 u2 is the relative angle between magnetization orientations. From a theoretical point of view, it was shown that the conductance, rather than the resistance, is expected to vary as cos u (Vedyaev et al., 1994, 1997; Coehoorn, 2000). This was experimentally observed in the angular variation of GMR in NiFe/Ag/Co/Ag multilayers (Steren et al., 1995). The difference between the two descriptions, one with a cos u resistance variation, the other with a cos u conductance variation, only involves a second-order term in the GMR ratio. Therefore, the difference is negligible if the GMR amplitude is small, but may become sizeable if the value of GMR is relatively large, as is the case for the NiFe/Ag/Co/Ag multilayers (Steren et al., 1995). The free electron theory also predicts a strong deviation from linearity in the presence of interfacial potential steps due to lattice potential modulation (Vedyaev et al., 1994). So far, these deviations have not been observed experimentally, reinforcing the picture that spin-dependent scattering effects play the primary role in the origin of GMR, rather than lattice potential modulation effects. The angular variation of GMR has also been investigated in the CPP geometry. Stronger deviations from linearity were observed in this case (Dauguet et al., 1996). Finally, an additional, small anisotropy in the GMR amplitude was observed by several groups (Dieny et al., 1995; Miller et al., 1999). This phenomenon consists of a difference in the change of resistance between parallel and antiparallel magnetic configurations depending on

Spin valves

103

whether these configurations correspond to the two magnetizations being parallel or perpendicular to the sense current. Measuring this effect requires that the direction of the pinned layer is reoriented between the measurements, to be parallel or perpendicular to the sense current. This can be done by annealing the spin valve above the blocking temperature of antiferromagnetic pinning layer and then cooling down in a magnetic field applied in the desired direction. The GMR ratio was found slightly larger (by about 5% in relative value) when the magnetizations are perpendicular to the current than when they are parallel to it (Dieny et al., 1995). This effect is another manifestation of the dependence of the mean free path on the angle between electron velocity and magnetization which gives rise to the AMR. Because of this anisotropy in mean free path, the scattering asymmetry also depends on the angle between electron velocity and magnetization, thus leading to the observed anisotropy in the GMR. These effects have been interpreted within the semiclassical theory of GMR (Rijks et al., 1995).

2.4

Spin-valves optimization

Since their discovery in 1990, the magnetic and transport properties of spin valves have been considerably improved especially in terms of magnetic stability of the pinned layer and MR amplitude. The overall structural quality of the stack has been highly improved by using appropriate buffer layer such as NiFeCr alloys. The pinning strength has been enhanced because of the use of antiferromagnetic layers having higher Neel temperature and by the introduction of the so-called synthetic pinned layer. The GMR amplitude has been raised up to 20% by introducing interfacial CoFe layers, by improving the overall structural quality of the stack thus reducing the scattering of the majority electrons (supposed to be more weakly scattered than the minority electrons), and by enhancing the specular reflection of electrons around the active part of the spin valve so as to favor the mobility of the weakly scattered electrons in the parallel magnetic configuration as much as possible. In the following of this section, these various improvements are reviewed in more detail. 2.4.1

Structural improvements achieved with NiFeCr buffer layers

In the first spin valves, Ta was most often used as buffer layer because it provides a (111) texture to Permalloy and to the other fcc layers deposited in the stack. When FeMn is used as the antiferromagnetic pinning layer, the (111) texture allows one to get a larger pinning energy. Furthermore, Ta has relatively good wetting properties on SiO2. The roughness of the layers is relatively low (RMS , 0.3 nm). The grain size is of the order of 10 nm for typical spin valves. Spin valves grown on Ta have provided GMR amplitude in the range 4 –10%. In later work, NiFeCr buffer layers were introduced as buffer layers. These alloys were already used as buffers in magnetoresistive heads based on the AMR of thin NiFe films. They have been shown to favor the specular reflection of conduction electrons at the interfaces of the NiFe

104 B. Dieny layer thus limiting the drop of AMR amplitude when the thickness of the layer was reduced below 10 nm (Dieny et al., 2000a,b). Because of the use of these buffer layers, AMR amplitudes of the order of 4% at room temperature were achieved using Permalloy films 6 nm thick. The most suitable compositions of these alloys are in the range (Ni80Fe20)60Cr40 –Ni60Cr40. These alloys have very good lattice matching with Permalloy. As shown in Fig. 2.18 (Bozorth, 1951), they remain in the fcc phase up to 40 at% Cr content. Furthermore, Fe and Cr are known to have low surface tension and therefore to offer very good wetting properties on most substrates, in particular Al2O3 or SiO2. As a result of the good lattice matching and wetting, the roughness of the layers is very low (RMS , 0.2 nm) and the grain size can be very large. As an example, Fig. 2.19 presents a transmission electron microscope cross-sectional view of a spin valve grown on NiFeCr buffer inserted between Permalloy shields in a magnetoresistive heads. The spin valve is isolated from the shields by alumina layers. Figure 2.19 shows that the grain size is very large in these structures, of the order of 50 nm, which is about five times larger than with Ta buffer. This grain size is much larger even than the thickness of the spin valve. The active part of the spin valve, which is comprised of the free layer/ non-magnetic spacer/inner pinned layer (NiFe 4 nm/CoFe 1 nm/Cu 2 nm/CoFe 2 nm in the example of Fig. 2.19), almost appears as an epitaxial single crystal. As a result of this structural improvement, the overall resistivity of the stack in parallel magnetic configuration is reduced. The transmission of the weakly scattered electrons through the interfaces between the ferromagnetic layers and the non-magnetic spacer is increased, thus enhancing the flow of electrons between the free and pinned layers. Furthermore, as will be explained further in more detail, the lower roughness of the interfaces also enhances the specular reflection of conduction electrons on both sides of the active part of the spin valves, i.e. at the buffer/free layer interface and inner pinned layer/Ru interface when a synthetic pinned layer is used (see Section 2.4.2), or pinned layer/antiferromagnetic layer when a simple pinned layer is used. Besides the direct impact of the structural improvements on the transport properties, the larger grain size has also allowed a decrease in the thickness of the antiferromagnetic layer while maintaining sufficient pinning properties. For instance, with PtMn the increase in grain size has allowed a decrease of the lower thickness limit down to 8 nm with NiFeCr buffer as compared to 14 nm with Ta buffer. Reducing the AF layer thickness reduces the shunting of the current in this inactive part of the spin valve, therefore increasing the MR ratio. As a result of these structural improvements, the GMR amplitude of spin valves has been increased from the range 4–10% to the range 12 –15% as illustrated in Fig. 2.20. 2.4.2

Improvement in the pinning related to the use of a synthetic pinned layer

Spin valves with a synthetic antiferromagnetic pinned layer (SyAP) (Heim et al., 1994) provide a stronger pinning of the pinned layer. They are of the form buffer/F/Cu/AP1 tAP1 /Ru tRu /AP2 tAP2 / AF where F is the soft ferromagnetic layer (typically NiFe with a CoFe interfacial layer), AP1 and

Spin valves

105

Fig. 2.18 Upper graph: Structural properties of NiFeCr alloys, showing that for Cr concentration up to 40%, the alloy remains in the same fcc phase than Ni80Fe20. Bottom graph: Resistivity versus Cr concentration in various series of NiFeCr alloys. Note the dramatic increase in resistivity when a few % Cr atoms are introduced in the alloy. Correlatively the Curie temperature drops very rapidly to become lower than room temperature for Cr content larger than 20%. From Bozorth (1951).

106 B. Dieny

Fig. 2.19 Transmission electron microscope view of a spin valve of the composition NiFeCr 6 nm/NiFe 4 nm/CoFe 1 nm/Cu 2 nm/CoFe 2 nm/Ru 0.9 nm/CoFe 2 nm/PtMn 14 nm grown on NiFeCr buffer layer. Note the very large grain size . 50 nm which is greater than the thickness of the stack. The layers located on the right side of the spin valves between the Al2O3 layers are the permanent magnet biasing layer (see Section 2.6), and the conducting leads. Image from Headway Technologies.

AP2 are two ferromagnetic layers (typically CoFe alloys) of respective thickness tAP1 and tAP2 (in the range 1.5–3 nm) antiferromagnetically coupled through a thin Ru layer (Parkin et al., 1990). The Ru spacer layer provides a very strong antiparallel coupling between Co or CoFe layers for tRu thickness in the range 0.5–1.0 nm. AP2 is exchange biased by an adjacent antiferromagnetic layer (AF, for instance, IrMn). The improvement in the pinning properties of the AP1/Ru/AP2/AF synthetic pinned layer as compared to a single AP/AF pinned layer is due to the reduced net moment of the AP1/Ru/AP2 sandwich which results from the antiparallel alignment of the magnetization of the two AP layers. Since the antiparallel coupling through Ru is much stronger than the interfacial coupling between AP2 and AF, the two AP layers are maintained antiparallel

16 14 12

GMR (%)

10 8 6 4 2 0

-1000

-500

0

500

1000

H(Oe)

Fig. 2.20 Magnetoresistance associated with the switching of the free layer in spin valves of the composition NiFeCr 6 nm/NiFe 4 nm/CoFe 1 nm/Cu 2 nm/CoFe 2 nm/Ru 0.9 nm/CoFe 2 nm/PtMn 10 nm. From M. Li, S. Liao, K. Ju, C. Horng, Headway Technologies.

Spin valves

107

up to very large fields, above which they undergo a spin-flop transition (see below, also Chapter 5). The torque exerted by the applied field on the AP1/Ru/AP2 sandwich is reduced compared to a single AP layer thus improving its magnetic stability. Another advantage of using synthetic antiferromagnetic pinned layers (SyAP) is that, in a microscopic device the antiparallel alignment of the magnetization in AP1 and AP2 reduces the magnetostatic stray field created by the pinned layer on the sensing layer (Heim et al., 1994). An analytical calculation of the magnetic response of such spin valves with synthetic AP layers is now presented (Dieny et al., 2000a,b; Dimitrov et al., 2000). Such a calculation for antiferromagnetically coupled sandwiches (for instance, Co t1 /Ru 0.8 nm/Co t2 ) without antiferromagnetic pinning but taking into account a uniaxial or cubic anisotropy in the ferromagnetic layers can be found in Dieny et al. (1990) and Dieny and Cavigan (1990). These calculations are carried out under the assumption that the reversal of the magnetization in the three magnetic layers occurs via a coherent rotation mechanism. This is a fairly reasonable assumption in spin valves with synthetic pinned layers. Indeed, because of the strong torque exerted by the antiferromagnetic coupling on the magnetization in the two AP layers, a coherent rotation of the magnetization is favored with respect to a mechanism based on nucleation/propagation of walls in the AP layers. An experimental indication of this effect is that spin valves with synthetic AP layers usually exhibit much less hysteresis associated with the reversal of the magnetization in the AP layers than simple spin valves. This is illustrated, for example, in Fig. 2.21 which compares the hysteresis loop of PtMn-based spin valves with single and synthetic pinned layers. Clearly, the hysteresis associated with the partial reversal of the pinned layer is much larger in the former case. The same is true in Ir20Mn80-based spin valves [see Fig. 2.2 in Mao et al. (1999)]. Concerning the free layer, the easy axis of magnetization is usually set perpendicular to the direction of the applied field and to the pinning direction in order to obtain a linear MR response. As a result, the magnetization of this layer also rotates coherently. In the calculation of the magnetic response of these spin valves with SyAP layers, the following notations are used (see Fig. 2.22). MF ; M1 and M2 are, respectively, the magnetic moment per unit area (in emu/cm2) of the free ferromagnetic layer and of the AP1 and AP2 layers. These moments lie in the plane of the film. uF ; u1 ; u2 are the respective angles of these magnetic moments with respect to the direction of the applied field. Aex is the exchange coupling energy per unit area (in erg/cm2) between the AP2 pinned layer and the antiferromagnetic layer. It is typically of the order of 0.2–0.3 erg/cm2. The pinning direction is the reference direction for the angles. A is the exchange coupling per unit area between AP1 and AP2 through the Ru spacer. The strength of this coupling strongly depends on the Ru thickness and can be of the order of 1 erg/cm2 for Ru thickness around 0.8 nm. H is the external field applied parallel to the pinning direction (z-axis). We first consider the sandwich formed by the two AP layers separated by the thin Ru interlayer. The energy of this sandwich is written as E ¼ 2M1 H cos u1 2 ðM2 H þ Aex Þcos u2 þ A cosðu1 2 u2 Þ:

ð2:21Þ

108 B. Dieny

(a)

14 12

MR [%]

10 8 6 4 2 0 -3000

-2000

-1000

0

1000

2000

3000

1000

2000

3000

H [Oe] (b)

16 14

MR [%]

12 10 8 6 4 2 0 -3000

-2000

-1000

0 H [Oe]

Fig. 2.21 Comparison of the magnetoresistive response of two spin valves differing only by their pinned layer. In the upper graph (a), a single pinned layer is used whereas in the bottom graph (b) a synthetic pinned layer is introduced. The compositions of these spin valves are (a) NiFeCr 5 nm/PtMn 13 nm/CoFe 3 nm/ Cu 2.4 nm/CoFe 3 nm/Cu 1 nm/Ta 5 nm. (b) NiFeCr 5 nm/PtMn 13 nm/CoFe 3 nm/Ru 0.8 nm/CoFe 3 nm/ Cu 2.4 nm/CoFe 3 nm/Cu 1 nm/Ta 5 nm. From Headway Technologies.

The energy is then minimized with respect to u1 and u2 by solving the following set of coupled equations:

›E ¼ M1 H sin u1 2 A sinðu1 2 u2 Þ ¼ 0; ›u1

›E ¼ ðM2 H þ Aex Þsin u2 þ A sinðu1 2 u2 Þ ¼ 0 ›u2

associated with the stability conditions:

›2 E ›2 E ›2 E ›2 E ›2 E . 0 and 2 . 0: ›u1 ›u2 ›u2 ›u1 ›u21ð2Þ ›u21 ›u22

Spin valves

z θ2

109

Pinning direction θ1 M1

M2

H Soft layer easy-axis

θF MF J

Fig. 2.22 Notation used for the calculation of the magnetic response of a spin valve with synthetic pinned layer.

Once u1 and u2 have been calculated, the magnetic moment of this subsystem is given by M ¼ M1 cos u1 þ M2 cos u2 : In order to define the characteristic fields of the magnetization curves, some examples of calculated MðHÞ curves for the AP1/Ru/AP2/AF subsystems are shown in Fig. 2.23. The calculations were carried out for various values of the M1 =M2 ratio. Qualitatively, five parts can be distinguished in these curves: þ (i) Positive saturation above a saturation field Hsat : þ (ii) Coherent rotation of M1 and M2 between Hsat and a critical positive field H0þ : Between these two fields, M2 rotates from its initial direction to an intermediate tilted direction and comes back parallel to the pinning direction at H0þ : In contrast M1 undergoes a 1808 rotation so that at H0þ ; M1 is antiparallel to M2 : (iii) A remanent plateau between H0þ and H02 where the two magnetic moments remain antiparallel. 2 (iv) Coherent rotation of M1 and M2 between H02 and the negative saturation field Hsat : M1 only makes a small oscillation from the direction opposite to the pinning direction whereas M2 undergoes a full 1808 rotation. 2 (v) Negative saturation above Hsat :

This magnetization process has strong similarities with the magnetic response of antiferromagnetically coupled sandwiches with uniaxial anisotropy when the field is parallel to the easy axis. The fields H0þ and H02 are analogous to the spin-flop fields of antiferromagnetic or ferrimagnetic materials. However, in an antiferromagnet, the magnetization undergoes a first-order hysteretic spin-flop transition whereas in the present case, the magnetization process is completely continuous and reversible.

110 B. Dieny


M CoFe/Ru9¯/CoFe/IrMn


M AP2

AP1

Exchange anisotropy

A MAP2 > MAP1 M/Msat 1

θAP1

MAP1=0.003emu/cm2 MAP2=0.005emu/cm2 Aex= 0.3erg/cm2 A=0.5erg/cm2 -10000

0

-5000

5000

10000

-10000

Aex π

-5000

0

5000

10000

H(Oe)

H(Oe) -1

MAP1 < MAP2 M/Msat 1

θAP2

π

θAP1

π

MAP2=0.002emu/cm2

-10000

-5000

0

5000

H(Oe) -1

H− sat

H− 0

H+ 0

10000

-10000

-5000

0

5000

10000

H(Oe) θAP2

π

H+ sat

Fig. 2.23 Magnetic response of a synthetic pinned layer for two different ratios MAP2 =MAP1 : The left curves are the magnetization curves. The right curves represent the variation of the angle between the magnetization of each layer and the exchange unidirectional anisotropy direction versus field.

The following analytical expressions are obtained for the four characteristic fields associated with this magnetization process: þ Hsat

2 Hsat

0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi1 s
 1@ A A Aex A A Aex 2 4AAex A ¼ þ 2 þ þ 2 þ ; 2 M1 M2 M1 M2 M2 M2 M1 M2 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi1 s
 1@ A A Aex A A Aex 2 4AAex A ¼2 þ þ þ þ þ 2 ; 2 M1 M2 M1 M2 M2 M2 M1 M2

ð2:22Þ

ð2:23Þ

and for the fields characterizing the edges of the remanent plateau in the MðHÞ curve: H0þ

0 1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s
 1@ A A Aex A A Aex 2 4AAex A ¼ 2 2 þ 2 þ þ þ ; 2 M1 M2 M1 M2 M2 M2 M1 M2

ð2:24Þ

Spin valves 0 1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s
2 1 A A A A A A 4AA ex A H02 ¼ 2 @2 þ þ ex þ 2 þ þ ex þ : 2 M1 M2 M1 M2 M2 M2 M1 M2

111

ð2:25Þ

In the various intervals of fields, the direction of the magnetic moment in each layer and the total magnetic moment of the subsystem along the field direction are given as follows. þ ; u1 ¼ 0; u2 ¼ 0; Mz ¼ M1 þ M2 : For H . Hsat þ For Hsat . H . H0þ ;  u1 ¼ arc cos

 A AðM2 H þ Aex Þ ðM2 H þ Aex Þ 2 þ ; 2ðM2 H þ Aex Þ 2A 2M12 H 2   A AM1 H M1 H ; 2 u2 ¼ 2arc cos þ 2M1 H 2A 2ðM2 H þ Aex Þ2 Mz ðHÞ ¼

AM2 AM1 AM1 M2 H þ 2 2M1 H 2ðM2 H þ Aex Þ 2ðM2 H þ Aex Þ2 AðM2 H þ Aex Þ M ð2M2 H þ Aex Þ : 2 þ 1 2 2A 2M1 H

ð2:26Þ

ð2:27Þ

ð2:28Þ

For H0þ . H . H02 ; u1 ¼ p; u2 ¼ 0; Mz ¼ 2M1 þ M2 : 2 For H02 . H . Hsat ; u1 ; u2 ; and M are given by the same analytical expressions (2.26), þ (2.27), and (2.28) as in the interval Hsat . H . H0þ : 2 For H0 . H; u1 ¼ p; u2 ¼ p; Mz ¼ 2M1 2 M2 : We next consider the entire spin valve with its soft ferromagnetic layer. A weak coupling Ac generally exists between this ferromagnetic layer F and the AP1 magnetic layer through the Cu spacer. The associated coupling energy is typically of the order of 2 £ 1023 erg/cm2 which is much weaker than the coupling energy A between AP1 and AP2 through the Ru layer or Aex between AP2 and the antiferromagnetic layer. Consequently, this coupling has a negligible effect on the magnetic behavior of the AP1 and AP2 layers so that the above calculation can be considered as valid even in the presence of the soft ferromagnetic layer. In contrast, it is important to take the coupling into account in the determination of the magnetic response of the soft layer at low field since the magnetic energies governing the rotation of the magnetization in this layer are much weaker than for the AP pinned layers. At the wafer level, i.e. without considering the magnetostatic interactions due to the edges of the device, this magnetic response is actually the same as in single spin valves. With the notation shown in Fig. 2.22, the energy of the soft layer is written as E ¼ KtF cos2 uF 2 MF H cos uF 2 Ac cosðuF 2 u1 Þ with u1 ¼ p during the rotation of the magnetization of the soft layer. K is the uniaxial anisotropy of the soft layer of thickness tF : Minimizing this energy with respect to uF yields þ Hsat;F


 Ac Ac 2 ; ¼ 2KtF þ and Hsat;F ¼ 2 2KtF 2 MF MF

112 B. Dieny þ 2 where Hsat;F and Hsat;F are, respectively, the positive and negative saturation fields of the soft layer. Between these two fields, the direction of the magnetization of the soft layer is given by
 MF H 2 Ac uF ¼ arc cos : ð2:29Þ 2KtF

The magnetic moment of this layer along the field direction varies linearly according to
 M F H 2 Ac : Mz;F ¼ MF 2KtF By using the above analytical expressions of uF ; u1 ; u2 ; it is then possible to calculate the magnetoresistance of the structure. It is given by     1 2 cosðuF 2 u1 Þ 1 2 cosðu1 2 u2 Þ R ¼ Rsat þ ðDRÞF;AP1 þ ðDRÞAP1;AP2 þ AMRF 2 2  sin2 uF þ AMR1 sin2 u1 þ AMR2 sin2 u2 ;

ð2:30Þ

where ðDRÞF;AP1 and ðDRÞAP1;AP2 are the GMR amplitudes associated with the change in the relative orientation of the magnetization in the corresponding pairs of layers. The AMR coefficients represent the anisotropic MR amplitudes in the various layers. Figure 2.24 shows an example of the calculation of MðHÞ and RðHÞ curves using the above expressions. The following parameters were used: A ¼ 1 erg/cm2, Aex ¼ 0:18 erg/cm2, Ac ¼ 1023 erg/cm2, MF ¼ 0:00045 emu/cm2, M1 ¼ 0:00018 emu/cm2, M2 ¼ 0:00018 emu/cm2. A situation of particular interest from a device point of view is when the two edges of the remanent plateau of the AP layers are symmetric with respect to zero field. This insures the maximum stability of these layers with respect to arbitrarily positive or negative perturbation fields. From expressions (2.24) and (2.25), it is straightforward to establish that this situation is realized when the pinned AP2 layer is slightly thicker than the unpinned AP1 layer, the ratio of magnetic moments in these two layers being given by M2 ðA þ Aex Þ ¼ : A M1

ð2:31Þ

When this equality (2.31) is fulfilled, the switching fields of the AP layers are given by H0þ ¼ 2H02 ¼

1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Aex ðA þ Aex Þ: M2

ð2:32Þ

This expression points out the interest in using synthetic AP layers to increase the pinning field. In a standard spin valve with a simple pinned layer, within the same coherent rotation model, the switching field of the pinned layer would be given by H0 ¼

Aex : M2

ð2:33Þ

Spin valves

M/Msat

MAP1=0.0018emu/cm2 MAP2=0.0018emu/cm2 Aex= 0.18erg/cm2

113

1

A=1erg/cm2

-10000

-5000

0

5000

10000

H(Oe) -1

R/Rmax 1

-10000

-5000

0

H(Oe)

5000

10000

Fig. 2.24 Calculated MðHÞ and RðHÞ response of a spin valve with synthetic pinned layer. The parameters are given in the text. The parameters have been chosen to fit the experimental curve obtained in NiFe/CoFe/Cu/CoFe/Ru/CoFe/IrMn spin valves [see Fig. 2.2(c) and (d) in Mao et al. (1999)].

In practice, the exchange coupling through the Ru layer is much larger than the exchange anisotropy coupling between AP2 and AF (typically A , 1:4 erg/cm2 through Ru whereas Aex , 0:2 erg/cm2 between AM2 and AF), and Eq. (2.32) shows that the pinning field can be 2 £ 3 times larger in spin valves with synthetic pinned layer than in standard spin valves. The above analytical expressions provide an easy way to extract the fundamental parameters of spin valves with synthetic AP layers such as the exchange coupling energy between AP2 and the AFM layer and the interlayer coupling energy through the Ru layer. It will be shown later in this chapter that some degree of specular reflection also occurs at Co/Ru or CoFe/Ru interfaces, which constitutes a further advantage of using synthetic pinned layer. In current practice, synthetic pinned layers are used in all spin valves for read heads in disk drives.

2.4.3

Improvement in the MR amplitude obtained by Co or CoFe interfacial doping

Starting from NiFe/Cu/NiFe/FeMn spin valves, it was observed that introducing very thin Co or Co-rich CoFe alloys at the interfaces between NiFe and Cu can lead to a doubling of the MR amplitude at room temperature, as illustrated in Fig. 2.25(a) and (b) (Parkin, 1993). Furthermore, if an ultrathin Co layer is introduced at the NiFe/Cu interfaces and then moved inside the NiFe layers, the GMR drops very rapidly with a characteristic length of the order of an atomic plane to its value without Co [Fig. 2.25(c)]. There are several factors contributing to these observations.

114 B. Dieny

Fig. 2.25 Effect of the insertion of a thin layer of Co or NiFe at the interface between the non-magnetic spacer and the ferromagnetic layers in spin valves. (a) Resistance at 300 K versus magnetic field for Si/NiFe 5.3 nm/Cu 3.2 nm/NiFe 2.2 nm/FeMn 9 nm/Cu 1 nm with (open circles) and without (filled circles) 0.25 nm of Co inserted at the NiFe/Cu interfaces. Dependence of the magnetoresistance amplitude on (b) thickness of the interfacial Co layer, tCo ; in Si/NiFe (5.3-tCo )/Co tCo /Cu 3.2 nm/Co tCo /NiFe (2.2-tCo )/FeMn 9 nm/Cu 1 nm spin valves, (c) distance d of a 0.5 nm thick Co layer from the NiFe/Cu interfaces in Si/NiFe (4.9-d)/Co 0.5 nm/NiFe d/Cu 3 nm/NiFe d/Co 0.5 nm/NiFe (1.8-d)/FeMn 9 nm/Cu 1 nm spin valves, and (d) NiFe interface layer thickness, tNiFe ; in Si/Co (5.7-tNiFe )/NiFe tNiFe /Cu 2.4 nm/NiFe tNiFe /Co (2.9-tNiFe )/FeMn 10 nm/Cu 1 nm spin valves (Parkin, 1993).

According to the CPP studies carried out on systems comprising NiFe/Cu and Co/Cu interfaces, the interfacial resistance and interfacial scattering asymmetry are close for these two types of interfaces (see CPP parameters in Table 2.1) at low temperature. Therefore, a more pronounced spin-dependent scattering at Co/Cu interfaces than at NiFe/Cu interfaces cannot be proposed as the main factor for this doubling of the GMR amplitude. Other reasons can be put forward to explain this very large MR increase due to Co insertion. NiFe and Cu are known to be miscible and to form a solid solution. Consequently, at a NiFe/Cu interface, some intermixing takes place leading to the existence of a gradient of NiFeCu concentration. It is known that the introduction of Cu in Ni reduces dramatically the Curie temperature of NiCu alloy (Bozorth, 1951). The same is true with NiFeCu alloys. This means that the exchange stiffness around the NiFe/Cu interface is reduced compared to bulk NiFe. As a result, at room temperature, many thermal magnetic excitations exist around the NiFe/Cu interfaces. These magnetic excitations lead to spin-flip scattering of the conduction electrons which traverse these interfaces. The spin flip is equivalent to a loss of spin memory for the electrons which traverse the spacer layer, and this has a detrimental impact on the MR amplitude. By contrast, when Co is introduced at the interface between NiFe and Cu, since Co is only very weakly miscible (, 3%) with Cu, it constitutes a good barrier against diffusion between NiFe and Cu. Furthermore, Co has a much higher Curie temperature than NiFe (Tc Co ¼ 1400 K, Tc NiFe ¼ 800 K). Therefore, the Co insertion leads to an interfacial magnetic stiffening, thereby reducing the magnitude of magnetic fluctuations along the interfaces. This effect is the main reason for the increase in MR amplitude at

Spin valves

R(H)/R(0) (%)

100

115

Measured at 4.2K Measured at 300K

95 90

Without Co

85

With Co

80 0

500

1000 H (Oe)

1500

2000

Fig. 2.26 Magnetoresistance curves measured at room temperature and 4.2 K in (NiFe 2.5 nm/Ag 1.2 nm)20 multilayers and in Co-doped (Co 0.2 nm/NiFe 2.1 nm/Co 0.2 nm/Ag 1.2 nm)20 multilayers.

room temperature with Co or CoFe interfacial doping. A further confirmation of this statement is obtained by measuring the thermal variation of GMR in systems comprising undoped and Co-doped interfaces. As an example, Fig. 2.26 shows the thermal variation of GMR in (NiFe/Ag) and (Co/ NiFe/Co/Ag) antiferromagnetically coupled multilayers. In the Co-doped multilayers, a monolayer of Co was introduced at each NiFe/Ag interfaces (Cowache et al., 1996). A very large change in GMR amplitude (75% increase in relative value) exists at room temperature between the Co-doped and the undoped multilayers (7.5 and 13% GMR amplitude without and with Co insertion, respectively). At low temperature, by contrast, the Co insertion only leads to a 10% increase in relative value of the MR amplitude (18.2 and 20% GMR amplitude without and with Co insertion, respectively). This result is consistent with the interpretation given above for the results of Fig. 2.25, since at low temperature the magnetic excitations are reduced by the lower thermal activation whether Co is present or not along the NiFe/Ag interface. In spin valves developed for magnetoresistive heads, a Co90Fe10 interfacial layer 0.4–1 nm thick is commonly introduced at the interfaces between the NiFe free layer and the non-magnetic spacer layer. The pinned layer (single or synthetic) is most often made of Co90Fe10. This particular CoFe composition has been selected because it offers a very low magnetostriction which helps the free layer to keep soft magnetic properties. Furthermore, this interfacial layer improves the thermal stability of the structure upon annealing up to 2508C. These anneals are necessary during the processing of heads to reorient the direction of pinning of the pinned layer at 908 of the quiescent direction of magnetization of the free layer in an MR head (see Section 2.6).

2.4.4

Effect of specular reflection on MR amplitude

In CIP transport, the current and therefore the electrical field are parallel to the interfaces. When an electron is specularly reflected at an interface, the component of its momentum parallel to the interface is conserved whereas the perpendicular component changes sign. As a result, from a

116 B. Dieny transport point of view, the electrons behave as if the structure was repeated in a mirror symmetry, the plane of symmetry being the reflective interface. As discussed in Section 2.2.2, increasing the specular reflection at the outer interface of the free or pinned layer is therefore equivalent to increasing the number of repeats in a multilayer. This generally leads to an increase in the GMR amplitude and to a change in the optimum thickness of the magnetic layers. In spin valves based on NiO antiferromagnetic pinning layers, enhanced GMR up to 15% at room temperature has been observed. This large GMR amplitude was attributed to specular reflection at the Co/NiO interface (Anthony et al., 1994; Swagten et al., 1996). Since the NiO layer is insulating, it acts as a high potential energy wall for the conduction electrons. This provokes reflection of the electrons. If the roughness of the interface is low enough, the reflection can be at least partly specular; otherwise, it is diffuse. In spin valves, specular reflection can be introduced on one side of the active part of the spin valve as in NiO/Co/Cu/Co single spin valves (Swagten et al., 1996) or on both sides as in NiO/ Co/Cu/Co/Cu/Co/NiO symmetric or dual spin valves (Egelhoff et al., 1995, 1996, 1997a,b). In the latter case, the electrons experience some degree of specular reflection at both NiO/Co interfaces which further enhances the GMR amplitude (DR=R ¼ 23% at RT). The same enhancement was observed with a-Fe2O3 pinning layer (Sujita et al., 1996). Another beneficial effect of using an oxide antiferromagnetic layer is to avoid shunting of the current in the pinning layer, thus further increasing the GMR amplitude. Unfortunately, the magnetic properties of the pinned layer provided by these known oxide antiferromagnetic layers show pinning energy and blocking temperature that are not adequate for read-head applications. Some overlayers can also be introduced on top of the free layer in bottom spin valves in order to increase the specular reflection at the free layer/overlayer interface. Overlayers of Au, Ag, Cu (Egelhoff et al., 1997a,b), or oxide overlayers such as Al2O3 or TaOx (Gillies and Kuiper, 2001; Hong et al., 2001), have been shown to induce specular reflection and hence to increase the GMR amplitude. The oxide overlayers are preferable since they do not induce additional shunting of the current in the structure. The semiclassical theory of GMR accounts for the increase in GMR induced by specular reflection. As an example, Fig. 2.27 shows the calculated variation of conductance and GMR in bottom spin valves with TaO reflective overlayer for various assumptions about the coefficient of specular reflection p at the CoFe/TaO interface. Several points must be noted on these curves. The overall conductance of the structure increases when the coefficient of specular reflection ðpÞ increases due to reduced diffuse scattering at the CoFe/TaO interface, leading to a local increase in conductivity around this interface. However, the asymptotic value of DG remains independent of the degree of specular reflection at this outer interface, further confirming the particular role played by this quantity to characterize the intrinsic amplitude of the GMR. The influence of the degree of specular reflection at the free layer/overlayer interface on the magnetoresistance is very pronounced when the thickness of the free layer is lower than the mean free path of the weakly scattered electrons. If the reflection at the free layer/overlayer interface is diffuse ðp ¼ 0Þ; DR=R shows a maximum as a function of the free layer thickness. As p increases, this maximum shifts

Spin valves

117

0.2

G (Ω -1)

0.15

0.1

p=1 p=0

0.05

0 p=1

G (Ω-1)

0.006

0.004 p=0 0.002

0 p=1

∆R/Rp (%)

15

10 p=0 5

0 0

5

10

15 tF(nm)

20

25

30

Fig. 2.27 Semiclassical modeling of the influence of specular reflection at capping layer (TaO)/free layer (CoFe) interface in spin valves of the form: NiFeCr 5 nm/PtMn 12 nm/CoFe 2.5 nm/Cu 2 nm/CoFe tF /TaO. The coefficient of specular reflection is varied from p ¼ 1 for the upper curves to p ¼ 0 for the lower curves by steps of 0.25. The parameters used in the calculation are listed in Table 2.2.

towards lower thickness, as discussed in Section 2.2.2, and eventually even occurs at tF ! 0 as observed in Fig. 2.27 for p . 0:25: This situation is encountered when the interfacial spindependent scattering is large enough compared to the bulk spin-dependent scattering contribution. Note that in real systems, the GMR always drops for very thin ferromagnetic layers because of the increased role played by magnetic fluctuations at room temperature when the thickness of a

118 B. Dieny magnetic layer approaches zero. These fluctuations are not taken into account in the semiclassical calculations of Fig. 2.27. The shift in the position of the maximum of DR=R towards lower tF thickness when the specular reflection at the outer interface of this layer is increased has been observed experimentally in various systems. For instance, spin valves of the form NiFe 6 nm/Cu 2 nm/NiFe tNiFe /FeMn 10 nm present an optimum magnetoresistance of the order of 4% for a thickness of the NiFe pinned layer of 4.5 nm. In comparison, similar spin valves using NiO or PtMn as pinning antiferromagnets instead of FeMn exhibit an optimum magnetoresistance of the order of 8% for an optimized thickness of the pinned ferromagnetic layer of the order of 2.5 nm. The larger MR obtained for thinner ferromagnetic layers in NiO or PtMn based spin valves can be attributed to a larger degree of specular reflection at the NiO/NiFe or PtMn/NiFe interfaces than at the FeMn/NiFe interface. Specular reflection has also been shown to occur at Co/Ru or CoFe/Ru interfaces (Dieny et al., 2000a,b) when synthetic pinned layers are used. This conclusion was based on the following observations. The MR in NiCr/NiFe/CoFe/Cu 2 nm/CoFe tAP1 /Ru 0.7 nm/CoFe tAP2 /PtMn spin valves was of almost the same amplitude (, 8%) as that obtained in simple spin valves (, 9%) of composition NiCr/NiFe/CoFe/Cu 2 nm/CoFe tAP /PtMn. This is surprising considering the additional shunting of the current in the Ru and AP2 layers and the fact that the specular reflection which occurs at the CoFe/PtMn interface is screened from the active part of the spin valve by the scattering in the Ru layer and at the CoFe/Ru interface. However, these observations can be consistently explained by assuming that the screening of the specular reflection at the CoFe/ PtMn interface is compensated by a slightly higher specular reflection occurring at the CoFe/Ru interface. Quantitatively, the coefficient of specular reflection was estimated by semiclassical modeling to be roughly 0.30 at CoFe/PtMn interfaces and 0.4 at CoFe/Ru interfaces. This specular reflection at CoFe/Ru interface can also explain the low MR contribution from the CoFe/Ru/CoFe sandwich when a sufficiently large field is applied to saturate the antiferromagnetic coupling through the Ru spacer. This MR contribution is typically of the order of 0.2%. Its low amplitude may be attributed to channeling of the electrons in the Ru layer due to specular reflection at both interfaces of this layer. Such channeling may prevent the flow of electrons between the two AP layers on both sides of the Ru layer. A large increase in spin-valve MR has been obtained by optimizing the specular reflection of conduction electrons on both sides of the active part of the spin valve. Some groups have instead tried to increase the specular reflection within the pinned layer by introducing an NOL in the AP1 inner layer of the synthetic pinned layer (Kamiguchi et al., 1999). The composition of the stack is then of the type: NiFeCr 5 nm/PtMn 12 nm/CoFe 2 nm/Ru 0.7 nm/CoFe 0.5 nm/NOL/CoFe 2 nm/ Cu 2 nm/CoFe 1 nm/NiFe 2 nm/TaO 2 nm. The introduction of this NOL is beneficial only if the specular reflection introduced by this additional NOL is larger than the specular reflection already existing at the Ru/CoFe interface. The NOL may be produced by natural or plasma oxidation of the CoFe layer or can be a different oxide such as Fe3O4, TaOx, HfO2 or Al2O3. The NOL must be discontinuous or magnetic so that a strong ferromagnetic coupling remains between the two parts

Spin valves

119

25

GMR (%)

20

15

10

5

0 -1000 -800 -600 -400 -200

0

200

400

600

800 1000

H (Oe)

Fig. 2.28 MR of a spin valve of the composition NiCr 5 nm/PtMn 8 nm/CoFe 2 nm/Ru 0.7 nm/CoFe 2.5 nm/Cu 2 nm/CoFe 1 nm/NiFe 2 nm/Cu 1 nm/TaO 2 nm having large specular reflection at the Ru/CoFe interface and Cu/TaOx interface. From M. Li, S. Liao, C. Horng, K. Ju, Headway Technologies.

of the AP1 layer on both sides of the NOL. This is important to insure a sufficient pinning of the inner part of the AP1 layer (Kools et al., 2001). A typical thickness of the NOL is 0.5 nm. By optimizing the specular reflection on both sides of the active part of the GMR element, MR amplitudes larger than 20% have been obtained, associated with suitable magnetic properties as illustrated in Fig. 2.28.

2.4.5 2.4.5.1

Improved spin-valve designs Dual spin valves

Dual spin valves basically consist of a central free layer (F) sandwiched between two pinned layers (AP and AP0 ). Their typical composition is of the form AF/AP/NM/F/NM/AP0 /AF. Each AP layers can be replaced by a synthetic pinned layer. These structures provide larger MR than standard simple spin valves because of the increase in the number of interfaces in the active part of the spin valves providing a larger scattering contrast between spin " and spin # electrons. Another advantage is that because the free layer is at the center of the structure, its thickness can be reduced as compared to standard spin valves. Indeed, the geometry of dual spin valves is equivalent to that of a simple spin valve in which a perfect reflective layer would have been introduced in the middle of the free layer (mirror symmetry). We have already shown that the introduction of such specular reflection reduces the optimum thickness of the free layer (see Fig. 2.27). Reducing the thickness of the free layer is a significant advantage in MR heads

120 B. Dieny since this increases the sensitivity of the device as will be explained in Section 2.6. In dual spin valves, as in standard spin valves, the specular reflection also can be improved by introducing NOLs in the pinned layers. However, the MR enhancement that may be gained by increasing the specular reflection in these systems is significantly weaker than in simple spin valves. Indeed, because of the larger thickness of the active part in dual spin valve, the relative role of the scattering at the outer boundaries of this active part on the overall transport properties of the system is reduced. Despite the various advantages of dual spin valves listed above, a major drawback of these structures is that their total thickness is almost double that of simple spin valves. In MR heads, the MR element is inserted between two thick magnetic shields and electrically isolated from the shields by insulators consisting typically of alumina layers 10 –20 nm thick. The shield-to-shield separation is the read gap width of the MR head. It determines the linear spatial resolution along the track (see Section 2.6). At areal density of the order of 65 Gbit/in.2, the bit dimension is of the order of 50 nm along the track and 200 nm across the track. This imposes the condition that the read gap width to be smaller than 50 nm to insure sufficient spatial resolution in the readout process. Dual spin valves have a typical thickness of 45 nm, compared to 28 nm for simple spin valves. Taking into account the additional thickness of the insulating layers, dual spin valves are therefore too large to fit in the gap of a read head for high density recording. Increasing the specular reflection at the outer boundary of simple spin valves is a better way to effectively increase the number of repeats in the stack without increasing its total thickness.

2.4.5.2

Spin-filter spin valves

As already mentioned, in MR spin-valve read heads, the thickness of the magnetic free layer must decrease as the bit size decreases. The reason is that for a given amount of magnetic flux coming out of a transition between two adjacent bits, the amplitude of the rotation of the magnetization of the free layer decreases as the magnetic moment of this layer increases due to the conservation of the magnetic flux through any section of a field tube. However, in standard spin valves without specular reflection, decreasing the thickness of the free layer below the optimum thickness (which is related to the mean free path of the weakly scattered electrons within the free layer) leads to a decrease in the MR amplitude caused by diffuse scattering of these electrons at the outer interface of the free layer. The idea of ‘spin-filter spin valves’ is to add a highly conductive non-magnetic layer (HCL, such as Cu) at the back of a very thin free layer (F) in order to give the weakly scattered electrons a long mean free path and thereby allow them to carry lot of current when they penetrate the F/HCL bilayer (Gurney et al., 1993). A typical composition of a spin-filter spin valve with synthetic pinned layer is NiFeCr 5 nm/PtMn 12 nm/CoFe 2 nm/Ru 0.7 nm/CoFe 2.5 nm/Cu 2 nm/CoFe 2 nm/Cu 2 nm/NiFeCr 5 nm.

Spin valves

2.5

121

Directions to further improve the CIP GMR of spin valves

Based on the semiclassical modeling of CIP GMR, it is straightforward to simulate new spin-valve structures and to calculate their transport properties. These calculations should not be considered as quantitatively predictive since the microscopic transport parameters used in the calculations are not accurately known in these new structures, or may change because the nanostructure of the stack may be altered by the addition or removal of layers. However, these calculations give reliable semiquantitative trends which turn out to be very useful in the optimization of spin-valve structures. In the following, starting from an experimental situation, we show how the semiclassical calculations can be used to predict what should be tried to further increase the GMR amplitude. Of course, the calculations only address the magnetoresistance, and not the magnetic properties themselves. As will be discussed, some modifications of the stack which aim to improve the GMR amplitude may in turn deteriorate the magnetic properties. The actual optimization of the spin valves for MR sensors, of course, requires a consideration of both aspects simultaneously. (1) We start from a spin valve with synthetic pinned layer optimized for read out of an areal density of the order of 80 Gbit/in.2: NiFeCr 5 nm/PtMn 10 nm/CoFe 2 nm/Ru 0.7 nm/CoFe 1.8 nm/Cu 2 nm/CoFe 1 nm/NiFe 2 nm/NiFeCr 2 nm. The parameters used in the calculation are the same as in Table 2.2 plus the following: " # l"NiFe ¼ 7 nm; l#NiFe ¼ 0:7 nm; TNiFe=CoFe ¼ 1; TNiFe=CoFe ¼ 1; R"NiFe=CoFe ¼ 0; R#NiFe=CoFe ¼ 0;

Table 2.2 Parameters used in the semiclassical modeling of Fig 2.27. l" and l# are the spin-dependent mean free paths in the bulk of the layers, T" ; T# ; R" ; and R# are the coefficients of spin-dependent transmission and reflection through the various interfaces

l≠ (nm) lØ (nm) Tao

0

0

CoFe

9

0.9

Cu

12

12

CoFe

9

0.9

PtMn

0.1

0.1

NiFeCr

0.2

0.2

T≠

TØ

RØ

RØ

0

0

p

p

1

0.5

0

0

1

0.5

0

0

0.2

0.2

0.2

0.2

0.2

0.2

0

0

122 B. Dieny " # l"Ru ¼ 3 nm; l#Ru ¼ 3 nm; TRu=CoFe ¼ 0:2; TRu=CoFe ¼ 0:2; R"Ru=CoFe ¼ 0:35; R#Ru=CoFe ¼ 0:35;

" # l"NiFeCr ¼ 0:4 nm; l#NiFeCr ¼ 0:4 nm; TNiFe=NiFeCr ¼ 0:1; TNiFe=NiFeCr ¼ 0:1; R"NiFe=NiFeCr ¼ 0:50;

R#NiFe=NiFeCr ¼ 0:50: Both the experiment and the calculation performed with the adjusted parameters listed above give: Rs ¼ 22:2 V

DR=R ¼ 12:5%

DR ¼ 2:78 V

Rs represents the sheet resistance of the spin valve. (2) We then introduce an NOL in the inner pinned layer of the structure. The spin-valve composition thus becomes: NiFeCr 5 nm/PtMn 10 nm/CoFe 2 nm/Ru 0.7 nm/CoFe 0.6 nm/NOL/ CoFe 1.2 nm/Cu 2 nm/CoFe 1 nm/NiFe 2 nm/NiFeCr 2 nm. Various assumptions are made about the degree of specular reflection ðRNOL Þ at the NOL/CoFe interface. All other parameters are supposed to be the same as those in case 1. The following results are obtained: RNOL RNOL RNOL RNOL

¼0 ¼ 0:3 ¼ 0:6 ¼ 0:9

Rs Rs Rs Rs

¼ 26:96 V ¼ 23:81 V ¼ 23:86 V ¼ 24:31 V

DR=R ¼ 4:45% DR=R ¼ 11:33% DR=R ¼ 13:42% DR=R ¼ 15:35%

DR ¼ 1:20 V DR ¼ 2:70 V DR ¼ 3:20 V DR ¼ 3:73 V

From these results, it is clear that introducing an NOL in the pinned layer is beneficial for the GMR only if the specular reflection occurring at the NOL/CoFe interface is larger than "ð#Þ

the specular reflection already existing at the CoFe/Ru interface ðRNOL . RCoFe=Ru Þ: If this condition is not fulfilled, the introduction of the NOL reduces the GMR amplitude because it prevents the electrons reflected from the CoFe/Ru interface to go back into the active part of the spin valve. A good quality NOL typically leads to specular reflection coefficients of the order of 0.6 –0.8. (3) We next assume that an NOL is also introduced at the free layer/capping interface to enhance the specular reflection ðRNOLb Þ at this interface. The specular reflection at the NOL/CoFe interface within the inner pinned layer is set to 0.6 whereas RNOLb is varied. The obtained results are: RNOLb RNOLb RNOLb RNOLb

¼0 ¼ 0:3 ¼ 0:6 ¼ 0:9

Rs ¼ 26:77 V Rs ¼ 24:8 V Rs ¼ 24:89 V Rs ¼ 25:23 V

DR=R ¼ 8:93% DR=R ¼ 12:88% DR=R ¼ 14:42% DR=R ¼ 15:89%

DR ¼ 2:39 V DR ¼ 3:19 V DR ¼ 3:59 V DR ¼ 4:01 V

As in case 2, an increase in the GMR amplitude can be expected only if the specular reflection obtained with this additional NOL is larger than that previously existing at the "ð#Þ

NiFe/NiFeCr interface ðRNOLb . RNiFe=NiFeCr Þ:

Spin valves

123

(4) It is then possible to estimate what would be the GMR in the case of optimal specular reflection at both NOL interfaces. By setting RNOL ¼ RNOLb ¼ 1; the GMR becomes: RNOLb ¼ RNOL ¼ 1

Rs ¼ 27:40 V

DR=R ¼ 21:0%

DR ¼ 5:74 V

Since the degree of specular reflection has been increased, the optimal thickness of the free layer which gives the maximum GMR has also changed. This maximum tends to occur at lower thickness because of the mirror symmetry effect. It is then possible to further increase the GMR by reducing the thickness of the free layer. Instead of CoFe 1 nm/NiFe 2 nm, we set the free layer to be CoFe 1 nm/NiFe 0.5 nm. The GMR then becomes: RNOLb ¼ RNOL ¼ 1

Rs ¼ 30:9 V

DR=R ¼ 24:0%

DR ¼ 7:43 V

(5) At this point, the specular reflection has been optimized. The only way to further increase the GMR is to reduce the shunting of the current in the inactive parts of the structure (outer pinned layer, buffer, AF, cap layer) as well as in the spacer layer. One approach is to use materials with high resistivity for these layers and to avoid specular reflection in the inactive part of the spin valve. For instance, when an NOL is introduced in the inner pinned layer, it is preferable to reduce the specular reflection at the Ru/CoFe interface. Indeed, this remaining specular reflection does not help to increase the GMR since its effect is screened from the active part of the spin valve by the NOL. Furthermore, it contributes to the shunting of the current in this inactive part of the spin valve by increasing the local conductivity around the CoFe/Ru interface. Along the same line, the material in the outer pinned layer (AP2) could advantageously be changed from CoFe to a more resistive magnetic material to reduce shunting. From a pure transport point of view, the best way to reduce shunting in the AP2/Ru layers is to use a single pinned layer instead of a synthetic pinned layer. Synthetic pinned layers have been introduced to improve the magnetic properties (better stability of the pinned layer) and not the GMR amplitude. As a matter of fact, if AP2/Ru/AP1 in the structure of case 4 is replaced by a single AP layer so that the structure becomes: NiFeCr 5 nm/PtMn 10 nm/CoFe 0.6 nm/NOL/CoFe 1.2 nm/Cu 2 nm/CoFe 1 nm/NiFe 0.5 nm/NOL/NiFeCr 2 nm, then the following properties are obtained: RNOLb ¼ RNOL ¼ 1

Rs ¼ 38:2 V

DR=R ¼ 31:0%

DR ¼ 12:0 V

(6) The next direction to further reduce the shunting is to find an oxide antiferromagnetic material which would be electrically insulating and would provide good pinning of the magnetization of the adjacent ferromagnetic layer. Antiferromagnetic materials such as NiO and Fe2O3 have been investigated but did not have sufficiently good magnetic properties. These materials have, however, been shown to provide very good specular reflection. If we assume that an appropriate oxide antiferromagnetic (OAF) exists and provides ideal specular reflection at

124 B. Dieny the CoFe/OAF interface, the properties which would be obtained for a structure of the composition: OAF 20 nm/CoFe 1.2 nm/Cu 2 nm/CoFe 1 nm/NiFe 0.5 nm/NOL/NiFeCr 2 nm, are given below: RNOLb ¼ RCoFe=OAF ¼ 1

Rs ¼ 42:5 V

DR=R ¼ 36:1%

DR ¼ 15:3 V

(7) If the NOL is sufficient to prevent the structure from oxidation, then the capping metallic layer can be removed. The GMR properties then become: RNOLb ¼ RCoFe=OAF ¼ 1

Rs ¼ 44:7 V

DR=R ¼ 39%

DR ¼ 17:3 V

(8) If the roughness of the layer is very low, the thickness of the spacer layer could be reduced significantly. If we assume that the Cu spacer thickness can be reduced to 1 nm instead of 2 nm (independent of the problem related to the increase of the interlayer coupling), then the GMR amplitude in OAF 20 nm/CoFe 1.2 nm/Cu 1 nm/CoFe 1 nm/NiFe 0.5 nm/NOL would be: RNOLb ¼ RCoFe=OAF ¼ 1

Rs ¼ 63:8 V

DR=R ¼ 60%

DR ¼ 38 V

It becomes apparent that the GMR of spin valves can be potentially as large as that of (Co/Cu) multilayers with a large number of repeats. Indeed, if the shunting in the inactive part of the spin valve is reduced as much as possible and if the active part is sandwiched between two interfaces providing perfect specular reflection, then due to the mirror symmetry induced by the specular reflection, the spin valve becomes equivalent to an infinite multilayer. This ideal picture is, however, balanced by the consideration of the magnetic properties and in particular the properties of the pinned layer. However, the merit of this discussion is to underline the trends which should be followed to possibly improve the CIP GMR. At the moment, with known materials and in particular in the absence of suitable insulator antiferromagnet, spin valves seem to be close to their limit with 20% GMR amplitude. This is the leading reason why other technologies based on the use of CPP magnetoresistance are currently being explored. These may use MTJs, pure metallic spin valves, or metallic spin valves with NOL. These approaches are discussed in the following section.

2.6 2.6.1

Spin valves in magnetoresistive read heads: today’s technology and trends Principle of magnetic recording

In magnetic recording, the areal density of information stored in hard disk drives steadily increased at a rate of 30%/year from the introduction of the first RAMMAC disk drive by IBM in 1954 until 1992. This pace of increase accelerated in 1992 because of the technological change of readout technology from inductive to magnetoresistive. Since 1992, the areal density has increased by

Spin valves

125

60%/year. At the end 2001, demonstrations of recording density above 100 Gbit/in.2 were achieved (Zhang et al., 2002). This is 8 orders of magnitude larger than the density in 1954! In correspondence, the bit size has drastically decreased. At areal density of 100 Gbit/in.2, it is of the order of 50 nm £ 150 nm. The first magnetoresistive heads introduced in 1992 were based on the AMR of thin transition metal films, in particular Ni80Fe20. This technology was used until 1998 and was then replaced by the spin valves. The principle of a write/read head is illustrated in Fig. 2.29 which represents a schematic cross-section of a ‘vertical’ head. The head is divided in two parts: the writer, which is basically a submicronic electromagnet, and the reader. The writer essentially consists of a planar coil and a magnetic circuit which presents a gap, called the write gap, that is positioned just above the media. The stray field from this gap is the write field which is used to switch the magnetization of the storage media. The higher the saturation magnetization ðMsat Þ of the pole pieces, the higher the write field. Besides a high value of Msat ; various qualities are required for the pole piece materials, most importantly: a high permeability to insure low write current, high resistivity to reduce eddy current effects and thereby allow to work at high frequency (several 100 MHz), and good resistance to corrosion. Examples of materials which are being used in write heads are Ni80Fe20, Ni45Fe55, FeTaN, FeAlN, amorphous alloys (CoZrNb), or laminated materials such as FeN/SiO2, FeN/FeNiCo. Concerning the magnetoresistive reader, it essentially consists of a magnetoresistive element (a spin valve) electrically connected with conducting leads to a current source and a preamplifier. This MR element is sandwiched between two thick shields of soft magnetic materials such as

reader

writer

1∝m 1 µm

Fly height 10 nm,

MR

shield 2

shield 1

substrate

Planar coil

100 nm

disk rotating at 5000 to 10000 rpm.

Fig. 2.29 Schematic representation of the cross-section of a vertical head above a storage longitudinal media. ( For a colored version of this figure, see Plate 2.29, page 377.)

126 B. Dieny Permalloy, Ni80Fe20. The purpose of the shields is to increase the resolution of the head along the track by absorbing all the magnetic flux coming out of the media except just underneath the gap separating the shields (read gap) where the MR element is located. Because of the shields, the MR element only detects the transitions located right below the read gap. The narrower the read gap, the better the resolution along the track and the higher the areal density that can be read. In the CIP geometry which is presently used, the MR element is electrically insulated from the metallic shields by alumina layers, the thickness of which is between 20 and 10 nm. As the areal density increases, these insulating layers must be made thinner and thinner to reduce the gap width. This tends to make the heads more and more sensitive to electrostatic discharge (ESD) damage. Furthermore, in order to have a linear response from the MR element, the magnetization of the pinned layer is set perpendicular to the media, i.e. parallel to the vertical stray field emanating from the transition between adjacent bits. By contrast, the magnetization of the free layer is set perpendicular to this direction in the quiescent state. The stray field from the transition between bits then leads to a coherent rotation of the free layer magnetization towards parallel or antiparallel alignment with the magnetization of the pinned layer. This is illustrated in Fig. 2.30.

2.6.2

Biasing of spin-valve heads

A great advantage of spin-valve GMR compared to AMR is that spin valves intrinsically provide a linear response. The previously used AMR read heads intrinsically provided a quadratic response, thus requiring specific biasing schemes to linearize the signal. The linear response of spin valves can be understood as follows, assuming a coherent rotation of the magnetization of the free layer:

Fig. 2.30 Schematic representation of a biased standard spin valve in a magnetoresistive heads. Only the free and pinned layers have been represented together with the conducting leads. PM designates permanent magnet layers which produce a static horizontal stray field on the free layer in order to maintain it in a well-controlled single domain state. The magnetization of the pinned layer is set parallel to the field from the media whereas the magnetization of the free layer in the quiescent state as well as its easy axis of magnetization are set perpendicular to it. ( For a colored version of this figure, see Plate 2.30, page 377.)

Spin valves

127

The various energy terms which determine the orientation of the magnetization in the nominally free layer are –

– – – –

–

k 1 ) with the applied field to be sensed ðHÞ: The Zeeman coupling of its magnetization (M k 1 and the easy axis of magnetization of EH ¼ 2M1 H sinðfÞ; where f is the angle between M the free layer which lies perpendicular to the direction of the field from the media. The magnetic uniaxial anisotropy of the free layer: Ea ¼ 2K cos2 ðfÞ: The coupling with the magnetostatic field ðHdip Þ created by the pinned layer magnetization k 2 Þ on: Edip ¼ M1 Hdip sinðfÞ: ðM k 1 : Es ¼ 2NM12 cos2 ðfÞ; where N is the demagnetizing field The shape anisotropy acting on M coefficient of the free layer. k 1 and M k 2 through the spacer layer: Ec ¼ 2M1 HSV  The exchange-like coupling between M sinðfÞ; where M1 HSV is the amplitude of the coupling energy expressed per unit volume of magnetic material in the free layer [HSV is actually the free layer loop shift seen at the wafer level as, for example, in Fig. 2.9(c)]. k 1 to the magnetic field HJ created by the sense current J which The Zeeman coupling of M flows through the structure. The next section shows how this field can be calculated by using the semiclassical theory of GMR: EJ ¼ 2M1 HJ sinðfÞ: Minimizing the total energy leads to

sinðfÞ ¼

M1 ðH þ HSV þ HJ 2 Hdip Þ 2ðK þ NM12 Þ

or sinðfÞ ¼ ^1 at saturation. Using the linear relationship between the change of CIP resistance and the cosine of the angle between the magnetization in the free and pinned layer (Section 2.3.3.4), the above relation yields   M1 ðH þ HSV þ HJ 2 Hdip Þ RðHÞ ¼ Rp þ ðRap 2 Rp Þ 1 2 2ðK þ NM12 Þ or RðHÞ ¼ Rp ðRap Þ at, respectively, positive (negative) saturation. The resulting linear characteristic RðHÞ is drawn in Fig. 2.31 and compared with experimental characteristics obtained on spin-valve heads. The deviations from linearity observed on the experimental curves are mainly due to the effect of the permanent magnets located on both edges of the MR element. These magnets induce a transverse field on the magnetization of the free layer which was not taken into account in this simple modeling. It causes a non-uniformity in the rotation of the magnetization of the free layer. The susceptibility of the free layer is larger at the center of the MR element than at the edges where the magnetization is partly pinned by the interaction with the permanent magnets. This nonuniformity also contributes to the observed non-linearity. The offset field in the characteristics is given by Hdip 2 HSV 2 HJ : It can be adjusted to zero by several ways: (i) By using synthetic antiferromagnetic pinned layer of the form AP1 tAP1 /Ru/AP2 tAP2 ; it is possible to adjust the

128 B. Dieny

R(H)

(a)

Rap

Hdip-HSV-HJ Rp

2 4mA

1

∆V/Isense (Ω)

(b)

4 mA

0.1

0 0.5mA

∆V (mV)

−0.1 −20 −15 −10

−5

0

Field (Oe)

0

5

10

0.5 mA

−1 −2 −100

−50

0 Field (Oe)

50

100

Fig. 2.31 (a) Calculated linear response of a spin-valve sensor in a simple coherent rotation model. (b) Experimental transfer curves measured on a spin-valve head from Headway Technologies for different values of the sense current showing the influence of the sense current on the bias point. The sense current was varied by steps of 0.5 mA from 0.5 to 4 mA. The main curve shows the signal in mV versus transversal applied field whereas the inset shows the signal normalized by the sense current, i.e. the change of resistance of the MR element.

relative thickness of the two layers AP1 and AP2 in such a manner that the stray field from these two layers on the free layer exactly compensates HSV þ HJ : (ii) By adjusting the Cu spacer thickness, the interlayer coupling between the free and pinned layer can be tuned since this coupling oscillates as a function of the Cu thickness as shown in Fig. 2.12. However, the observation of these oscillations requires a very good structural quality of the samples. (iii) By setting the sense current to an appropriate value, it is also in principle possible to generate a magnetic field on the free layer to compensate Hdip 2 HSV : However, as will be shown further, in order to maximize the signal and signal to noise ratio (SNR), the density of current in spin valves must be as large as possible compatible with reasonable heating and electromigration. Therefore, a flexibility exists on the direction of the current but not so much on its amplitude. In real read heads, the three approaches mentioned above are used in a combined way to cancel the offset of the RðHÞ characteristics.

Spin valves 2.6.3

129

Current distribution and magnetic field due to sense current acting on the free layer

The semiclassical theory of GMR allows a calculation of the distribution of current and magnetic field throughout the spin-valve stack. These quantities are given by relations (2.4) and (2.5) in Section 2.2.2. As an example, Fig. 2.32 shows the profile of current and magnetic field through a spin valve of the composition: NiCr 5 nm/PtMn 8 nm/CoFe 2 nm/Ru 0.7 nm/CoFe 2.5 nm/Cu 2 nm/CoFe 1 nm/NiFe 2 nm/Cu 1 nm/TaO 2 nm (spin valve of Fig. 2.28). The result of the calculation shown in Fig. 2.32 was obtained for an average current density of 2 £ 107 A/cm2. Current densities in the range 2–4 £ 107 A/cm2 are typically used in MR heads. This implies that in some specific layers, in particular the low resistivity Cu spacer, the current density can be as high as 108 A/cm2. The magnetic field acting on the free layer due to the sense current can be quite significant, of the order of several tens of oersteds. This field depends

Cu CoFe NiFe Cu TaO

NiCr

PtMn

5

CoFe Ru CoFe

sensitively on the position of the free layer in the stack. It is weak in symmetric dual spin valves for

j(z)/<j>

4 3 2 1

Cu CoFe NiFe Cu TaO

0 30

HJ(z) (Oe)

20 10 0 -10

0

5

10

CoFe Ru CoFe

NiCr

-30 -40

PtMn

-20

15 z (nm)

20

25

Fig. 2.32 Calculated distribution of current and magnetic field due to the sense current through a spin valve of the composition: NiCr 5 nm/PtMn 8 nm/CoFe 2 nm/Ru 0.7 nm/CoFe 2.5 nm/Cu 2 nm/CoFe 1 nm/NiFe 2 nm/Cu 1 nm/TaO 2 nm. To calculate the magnetic field, an average current density of 2 £ 107 A/cm2 was assumed.

130 B. Dieny which the free layer is located at the plane of symmetry of the stack but can be as large as 40 Oe if the free layer is located at the top of the structure. It is therefore important to compensate this field by the stray field from the pinned layer and by the interlayer coupling through the spacer. 2.6.4

Signal-to-noise ratio in spin-valve element

We consider a spin-valve element of resistance R in a CIP MR head. t is the total thickness of the spin-valve stack, w its length parallel to the trackwidth and h its height perpendicular to the media. A current I flows in the plane of the spin valve. The main source of electronic noise in the MR element is the Johnson noise, which is the white noise of a resistance due to the Brownian motion pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of the electrons. The RMS Johnson noise voltage is given by VJohnson ¼ 4kB TRDf ; where kB is the Boltzmann constant, T the temperature, and Df the bandwidth. When a field is applied to the sensor, the signal amplitude can be written as DV ¼ DRI; where DR is the absolute GMR of the spin valve. Therefore, the SNR is given by SNR ¼

DV VJohnson


¼

DR R

 pffiffiffiffiffiffiffiffiffiffiffiffiffi power pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; 4kB TDf

where power ¼ RI 2 is the electrical power dissipated by Joule heating in the sensor. A direct conclusion from this relation is that the larger the power dissipated in the sensor, the larger the SNR. This is the reason why, in MR sensors, the current densities are as large as possible compatible with reasonable heating (working temperature , 1008C) and with electromigration (the sensor must withstand the current density for at least 5 years without degradation). Introducing the sheet resistance Rsh defined by R ¼ Rsh ðw=hÞ and the current density j ¼ I=ht; the SNR can be expressed as
SNR ðdBÞ ¼ 20 Log10

DV VJohnson

"


 ¼ 20 Log10

DR R

 pffiffiffiffiffiffiffiffiffiffiffiffi # jt Rsh wh pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi : 4kB TDf

With the following parameters corresponding to areal density of the order of 50 Gbit/in.2: DR=R ¼ 15%; Rsh ¼ 15 V; t ¼ 26 nm; w ¼ 0:3 mm; h ¼ 0:25 mm; j ¼ 4 £ 107 A=cm2 ; Df ¼ 300 MHz; the SNR is equal to 740, i.e. SNR (dB) ¼ 57. Besides Johnson noise, there are other sources of noise in a read head, in particular associated with the magnetic properties of the free layer [Barkhausen noise and noise due to thermal fluctuations within the free layer (Smith and Arnett, 2001)] or with the electronic noise from the electronic channel (noise from preamplifier) (Wang and Taratorin, 1999). Besides the SNR, another important parameter to estimate the performance of the read head is its spatial readout resolution parallel and perpendicular to the trackwidth. In the direction parallel to the trackwidth, the resolution is given by the effective length of the MR element. This length is influenced by the spacing between the leads, by the way the current penetrates into

Spin valves

131

the MR element and spreads over its entire thickness, by the position of the permanent magnets and the related stiffness that they induce at the edges of the free layer. Recently, the ‘lead overlaid’ design was introduced to inject the bias current in the part of the spin valve where the free layer has the highest susceptibility, in order to decrease this effective magnetic length as much as possible (Nakamoto et al., 2000). The limitation, in current technology, comes from the spatial resolution of the technology (lithography, etching), which is used to pattern the device. Along the track, the spatial resolution is determined by the read-gap width, which is the spacing between the two shields sandwiching the MR element. As already discussed, the width of this gap is the sum of the spin-valve thickness and of the two alumina layers, which insulate the MR element from the shields. The thickness of the MR element hardly can be decreased because all thicknesses in the stack have been optimized to maximize the MR ratio and provide suitable magnetic properties. Some improvements still can be achieved, such as increasing the grain size to allow a further decrease in the antiferromagnetic layer thickness or further improving the degree of specular reflection which results in a decrease in the optimal thickness of the free and pinned layers. However, the impact of these possible improvements on the thickness of the stack will be rather limited. It is also possible to further decrease the insulator layer thickness but it is more and more difficult to avoid shortage between the MR element and the shields and the devices become more and more sensitive to electrostatic breakdown. For these reasons, the CIP MR head technology seems to be close to its intrinsic limit. As a result, more and more R&D efforts are presently focused on CPP MR heads based on tunnel junctions or metallic layers as explained in the two following sections.

2.6.5

CPP heads based on magnetic tunnel junctions

In CPP heads, a key advantage is that the shields which are used to screen the influence of remote bit transitions on the sensing MR element can also serve as current leads as schematically represented in Fig. 2.33. The read gap of the head is then significantly narrowed since the

~30 nm

Shield 2

Shield 1

J

150nm or less CPP MR element

Fig. 2.33 Schematic representation of a CPP MR element in a CPP read head.

132 B. Dieny insulating layers between the shields and the MR element are no longer necessary, thus increasing the resolution of the head along the track. In such a CPP geometry, in order to match the impedance of the MR element with the impedance of the preamplifier, the level of resistance which is sought for the CPP MR element is in the range 10 –30 V. The diameter of the MR element must be smaller than the trackwidth in order to avoid crosstrack reading. For areal density above 100 Gbit/in.2, this imposes the diameter d of the CPP pillar to be smaller than 150 nm. Consequently, the resistance £ area ðRAÞ product of the MR element should range between 0.7 and 2 V mm2 for d ¼ 150 nm, between 0.3 and 1 V mm2 for d ¼ 100 nm and between 0.08 and 0.2 V mm2 for d ¼ 50 nm. Two types of CPP MR elements are presently under investigation for CPP read-head applications, MTJs and spin valves. ‘Standard’ tunnel junctions exhibit an RA product in the range 100 kV mm2 – 100 V mm2 and significant R&D efforts are under way to further decrease the RA product to the range 10–1 V mm2. Tunnel magnetoresistance of the order of 20% at low bias voltage with RA product of 10 V mm2 is presently obtained with alumina barrier prepared by natural oxidation of a 0.7 nm thick aluminum layer. At the other extreme are the metallic multilayers and, in particular, the CPP spin valves. The latter present an RA product typically in the range 0.02–0.05 V mm2. These values are too low for areal densities in the range 100–300 Gbit/in.2, but may become acceptable when the trackwidth will have decreased below 50 nm. At the moment, R&D efforts are focusing on increasing the RA product as well as the MR amplitude in these structures, for example, by introducing discontinuous NOLs in the stack in order to confine the current path [confined current path (CCP) approach]. In this section, we focus on the tunnel junctions. The use of CPP metallic spin valves will be discussed in the following one. The observation of large TMR amplitude at room temperature in MTJs has stimulated very strong interest in these derives (Moodera et al., 1995; Miyazaki and Tezuka, 1995; see also Chapter 3). Besides a basic research interest related to tunneling of spin-polarized electrons, several very important applications of these systems are under development: MRAMs (see Chapters 4 and 5), magnetoresistive read heads, and injectors of spin-polarized electrons into semiconductors. Although the physics of TMR and GMR is quite different, both effects are associated with a change in the relative orientation of the magnetization between a free and a pinned layer. Consequently, the shapes of the MR transfer curves are very similar in MTJs and in spin valves. An important difference, however, is that MTJs show non-linear IðVÞ characteristics and the TMR amplitude is sensitive to the bias voltage (Moodera et al., 1995). In MTJs based on alumina barriers, the TMR decreases with increasing bias voltage. It drops by a factor 2 at a typical value of 300 mV. In the low voltage regime, this decrease can be approximated by DR ðVÞ ¼ R




DR R


0

 V ; 12 Vc

Spin valves

133

where ðDR=RÞ0 represents the maximum MR obtained at low bias voltage and Vc is the voltage at which the TMR extrapolates to zero. The main source of noise in MTJs is the shot noise. This is caused by the discrete nature of the electrical current. The electrons tunnel one by one through the tunnel barrier according to Poisson statistics. This leads to noise, the RMS voltage of which is given by

Vshot

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
 eV : ¼ 2eVRDf coth kB T

At the temperature of interest for read-head application (around 50 –1008C), the coth term is very pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi close to unity so that Vshot ¼ 2eVRDf : It is then possible to estimate the SNR in a CPP TMR head. Let us assume that the MTJ sensor has a section wh; where w is the length parallel to the trackwidth and h the height perpendicular to the media. For a current I flowing through the MTJ, the SNR can be written as

SNR ¼

DV ¼ Vshot




DR R




 0

 V V 12 Vc pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : 2eVRDf

The SNR is maximum for V ¼ Vc =3 < 200 mV: Taking into account the geometry of the MTJ, the maximum SNR is then given by


DR SNR ¼ 0:27 R



pffiffiffiffiffiffipffiffiffiffiffi wh Vc pffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffi : 2eDf RA 0

This expression shows that to maximize the SNR, the TMR amplitude should be as large as possible. Furthermore, the TMR amplitude should decrease as weakly as possible as a function of increasing bias voltage, and the RA product should be as low as possible. Therefore, the RA product should be decreased not only to match the impedance of the preamplifier, as previously mentioned, but also to maximize the SNR. Assuming RA ¼ 1 V mm2 ; ðDR=RÞ0 ¼ 10%; w ¼ 120 nm; h ¼ 120 nm; Df ¼ 300 MHz; Vc ¼ 0:6 V; the SNR is equal to 256, i.e. SNR (dB) ¼ 48. This SNR is lower than the SNR calculated in Section 2.6.4 for CIP spin valves. This demonstrates the need to continue to lower the RA product and to increase the MR amplitude for ultrahigh density recording. Despite this lower SNR, the technological steps required for producing CPP heads are simpler at very small dimensions than for CIP heads, and this is a major advantage for areal density above 100 Gbit/in.2.

134 B. Dieny 2.6.6

CPP heads based on metallic multilayers

With tunnel junctions, increasing the SNR requires the lowering of the RA product. With aluminabased junctions, RA , 1 V mm2 has been achieved with a barrier about 0.5 nm thick. This is very near the limit of one atomic cell so that it seems difficult to reduce this value much further at least with alumina. R&D efforts are in progress for developing new types of insulating layers such as doped AlHfOx or AlZrOx barriers, HfO2 barriers (Wang et al., 2003; Zhang et al., 2003) MgO or TiO2 barriers. At the other extreme, however, metallic multilayers can offer a large CPP MR amplitude with a low RA product in the range 0.02 –0.05 V mm2. The dominant source of noise in these systems is again the Johnson noise, as in CIP metallic spin valves, rather than the shot noise. The pffiffiffiffiffiffiffiffiffiffiffiffiffi SNR is thus proportional to SNR / ðDR=RÞ power: A significant advantage of CPP heads compared to CIP spin valves is that the heat dissipation is much more efficient in the CPP geometry because the metallic pillar is directly connected to the shields and the shields constitute very efficient heat sinks. As a result, the electrical power which can be dissipated in the sensor is larger than in CIP geometry and this leads to a larger SNR. Intrinsically, the CPP GMR in metallic magnetic multilayers can be very large. CPP GMR values exceeding 100% were observed, for instance, in (Co/Ag) multilayers (Lee et al., 1995) at low temperature. These large amplitudes were, however, obtained in uncoupled or antiferromagnetically coupled multilayers for which high saturation fields were required or hysteresis effects were observed. For a read-head application, good control of the relative orientation of the magnetization in the successive magnetic layers is required as well as a high susceptibility of the free layer. This requires the use of CPP spin-valve stacks comparable with those developed for CIP GMR. The drawback is that the highly resistive antiferromagnetic or buffer layers comprising in the stack are now in series with the active part of the spin valves, instead of being in parallel in the CIP geometry. This significantly deteriorates the GMR amplitude. As an example, by using the semiclassical theory of CPP GMR (Valet and Fert, 1993), with the parameters derived from Table 2.1, it is possible to calculate that a CPP spin valves of the composition NiCr 5 nm/NiFe 2 nm/CoFe 1 nm/Cu 4 nm/ CoFe 3 nm/PtMn 12 nm/NiCr 5 nm sandwiched between Cu leads has a magnetoresistance DR=R ¼ 3:41% with AR ¼ 0:035 V mm2, ADR ¼ 0:0012 V mm2, whereas the active part of the spin valve alone, i.e. the stack of composition NiFe 2 nm/CoFe 1 nm/Cu 4 nm/CoFe 3 nm directly sandwiched between Cu leads, would have a magnetoresistance DR=R ¼ 59:1% with AR ¼ 0:0038 V mm2, ADR ¼ 0:0023 V mm2. Note that ADR is not conserved in this comparison because of the role played by spin accumulation at the outer edges of the active part of the spin valves. In order to reduce the detrimental effect due to the series resistance of the antiferromagnetic or buffer layers, the relative resistance of the active part of the spin valve must be increased. This can be achieved by introducing NOLs in the free and/or pinned layers or even in the non-magnetic spacer layer. These very thin NOLs, typically 0.5 –1 nm thick, are discontinuous. Their effect is to locally constrain the current paths through very narrow pinholes, thus increasing the local effective

Spin valves

135

resistance around the pinhole. This is equivalent to having a stack of variable cross-section, the cross-section being narrow in the active part of the stack and broad in the inactive part of the stack. By introducing such NOLs in CPP metallic spin valves, it has been shown that an increase by a factor 33 in ADR could be achieved at room temperature (Nagasaka et al., 2001). A question remains, however, on the reliability of such a structure considering the fact that an extremely high current density ( , 1010 A/cm2) may flow through these small pinholes. Alternatively, the resistance can be increased by laminating the free and pinned layer by insertion of very thin layers of non-magnetic material, for example, replacing a 3 nm thick CoFe layer by a multilayer of the composition (CoFe 1 nm/Cu 0.3 nm)2/CoFe 1 nm. The Cu layers are sufficiently thin to provide a strong ferromagnetic coupling between the successive CoFe layers so that they magnetically behave as a single layer (Oshima et al., 2002). However, as explained in Section 2.2.3, from a transport point of view each CoFe/Cu interface produces the same spindependent scattering as 20 nm of bulk Co. Therefore, laminating the free and pinned layers increases significantly the effective thickness of these layers. Another possibility to increase the resistance of the active part of the spin valves is to use magnetic materials with high resistivity and large scattering asymmetry. Concerning the choice of materials constituting the active part of the spin valve, it is interesting to compare the influence of the spin-diffusion length in the magnetic and non-magnetic layers. These influences are very different as illustrated in Fig. 2.34(a) and (b). Figure 2.34(a) shows the variation of the resistance and magnetoresistance versus spin-diffusion length in the magnetic layers in a spin valve of the composition NiCr 5 nm/F 5 nm/Cu 4 nm/F 5 nm/PtMn 12 nm/NiCr 5 nm. F is a magnetic material of bulk resistivity 20 mV cm and scattering asymmetry 0.5. We assume that the spin-diffusion length of this material can be varied. The CPP GMR is calculated using a code based on Valet and Fert theory extended to any spin-valve structure. Surprisingly, in such simple spin valves, the CPP GMR increases as the spin-diffusion length in the magnetic material is reduced. This phenomenon can be understood qualitatively within the two-channel model as follows. In parallel magnetic configuration, in order to observe a large GMR amplitude the resistance in this configuration must be as low as possible. Because of the scattering asymmetry between the two spin channels, most of the current flows in the channel associated with the spin-up electrons, which are assumed here to be weakly scattered. If the electrons are still polarized when they enter the highly resistive buffer or antiferromagnetic layer, these layers add a larger series resistance in the spin-up channel than in the spin-down channel because of the unequal electron flow in the two channels. When the electrons have become totally depolarized, the inactive layers (buffer and antiferromagnetic) can be considered as resistance added in series to the undifferentiated spin channel. As a result of this larger weight of the highly resistive non-magnetic layer on the spin-up channel, the overall scattering contrast between spin-up and spin-down channels is reduced. Consequently, it becomes clear that it is advantageous to use a magnetic material with a short spin-diffusion length in such geometry. Alternatively, it is also possible to introduce an additional depolarizing layer between the active part of the spin-valve and the outer inactive layers.

136 B. Dieny

(a)

6

5

0.034 4

3

0

5

10

15

A.R (Ω. µm2)

∆R/R (%)

0.038

0.03 20

lSF ferro (nm)

0.036

(b)

A.R (Ω. µm2)

∆R/R (%)

3

2

1

0

0

10

20

30

40

0.035 50

lSF NM spacer (nm)

Fig. 2.34 Calculated CPP magnetoresistance and resistance versus spin-diffusion length in the magnetic layer (a) and in the non-magnetic spacer (b) in a spin valve of the composition NiCr 5 nm/F 5 nm/NM 4 nm/F 5 nm/PtMn 12 nm/NiCr 5 nm. F is a ferromagnetic material of resistivity 20 mV cm and bulk scattering asymmetry b ¼ 0:5; NM is a non-magnetic spacer of resistivity 5 mV cm. In (a), the spin-diffusion length in the non-magnetic spacer was set to lSF NM spacer ¼ 50 nm. In (b), the spin-diffusion length in the ferromagnetic layers was set to lSF ferro ¼ 20 nm.

By contrast, the influence of the spin-diffusion length in the non-magnetic spacer is very different. As shown in Fig. 2.34(b), the MR drops rapidly as the spin-diffusion length is reduced. This is because spin memory is lost by the electrons as they travel from one ferromagnetic layer to the other. Clearly, it is preferable to use a non-magnetic spacer with long spin-diffusion length. An important point to consider in modeling the transfer curves of CPP heads is the magnetic field that is generated by the sense current. This field tends to induce a vortex configuration in the magnetic layers. This effect will tend to become less critical at small dimensions because for a given current density, the field is maximum at the outer edges of the pillar and its amplitude scales with the diameter of the pillar. Furthermore, the exchange energy required to create a vortex configuration increases rapidly as the diameter of the pillar decreases (Miltat, 1994).

Spin valves 2.6.7

137

Spin-transfer effect in CPP magnetoresistive heads

It has been predicted by Slonczewski (1996, 1999) and Berger (1996, 1999) that a spin-polarized current flowing throughout a magnetic layer exerts a torque on the local magnetization when the direction of spin polarization is not parallel to the local magnetization. This is because the polarization of the conduction electrons tends to become aligned with the local magnetization as the electrons enter the magnetic layer and there is an associated transfer of angular momentum. The produced torque is of the form aJ ½M ^ ðM ^ PÞ; where M is a unit vector parallel to the direction of the local magnetization and P a unit vector parallel to the direction of the current polarization (Slonczewski, 1996, 1999), and aJ is a prefactor proportional to the current density. This torque term is in addition to the conventional terms in the Landau –Lifshitz –Gilbert equation which determines the magnetization dynamics in thin films. Spin transfer can induce magnetic excitations in the magnetic layer and eventually lead to the switching of its magnetization orientation. These effects have been experimentally studied on very narrow metallic pillars, typically between 150 and 60 nm in lateral dimension, by various groups (Katine et al., 2000; Grollier et al., 2001; Urazhdin et al., 2003; Myers et al., 2002; Albert et al., 2002; Sun et al., 2002; Kiselev et al., 2003). The structures investigated had minimal complexity, i.e. they consisted of simple sandwiches comprising a non-magnetic spacer layer separating a thick and a thin magnetic layer (typically Co 20 nm/Cu 4 nm/Co 4 nm). The current densities required to observe currentinduced magnetization switching, or generation of magnetic excitations, are typically in the range 107 –108 A/cm2 which correspond to the current densities used in magnetoresistive heads. The question naturally arises whether these effects can also be encountered in CPP GMR heads. Measurements of CPP MR transfer curves were recently performed with a variety of sense current amplitudes on spin-valve metallic pillars developed for CPP heads (Lee et al., 2004). These structures comprise synthetic pinned layers of the form AFM/AP2/Ru/AP1, where AFM is an IrMn antiferromagnetic pinning layer, AP2 and AP1 are two CoFe-based ferromagnetic layers antiferromagnetically coupled through the Ru spacer. Both the free and pinned layers were laminated by insertion of ultrathin Cu layers in order to increase the CPP resistance and magnetoresistance. These measurements indicate that in addition to the usual magnetic field generated by the current, the spin polarization of the current traversing the free layer clearly influences the magnetic static and dynamic behavior of this layer. Very significant current-dependent shifts in the free layer hysteresis loops, as well as very large noise level for particular ranges of field and current, were observed. Figure 2.35 shows a typical set of MR hysteresis loops measured at various positive and negative sense currents on a 150 nm £ 150 nm pillar. The current density ranged from 4 £ 106 to 4 £ 107 A/cm2. Positive current corresponds to current flowing from the free to the pinned layer, i.e. electrons flowing from the pinned to the free layer. This sample had a resistance of about 5.1 V in the low resistance state, corresponding to an RA product of 0.11 V mm2 and a CPP GMR of 2.3%.

138 B. Dieny

1,0 Field

+4 mA

+5 mA

-2 mA

-4 mA

-5 mA

+7 mA

+8 mA

0,5 I=+2 mA

(+) to (-) (-) to (+)

+6 mA

0,0

(R-Rmin)/(Rmax-Rmin)

1,0 0,5

-6 mA HAP→P

HP→AP

0,0 1,0 0,5

+9 mA

+10 mA

0,0 1,0 -7 mA

-9 mA

-8 mA

-10 mA

0,5 0,0 -200

0

200

-200

0

200

-200

0

200

-200

0

200

External Field (Oe)

Fig. 2.35 Normalized ðRðHÞ 2 Rmin Þ=ðRmax 2 Rmin Þ CPP magnetoresistance curves measured at various positive and negative sense current at room temperature on a spin-valve pillar with synthetic pinned layer and laminated free and pinned layers [samples from Headway Technologies (Lee et al., 2004)]. The gray curves correspond to the branch of the loops measured with increasing field, the black curves are the measurements performed with decreasing field. In the observed range of field, only the free layer magnetization switches. On the loop measured at 2 6 mA, the transition fields at increasing ðHP!AP Þ and decreasing ðHAP!P Þ fields are indicated.

Several points can be made about these curves: (i)

There is a striking influence of the sense current on the shape of the MR response. This influence shows up as a current-dependent loop shift of the free layer and a very large noise level in some particular ranges of fields and currents. In the CIP geometry, the Oersted field commonly induces a bias of the hysteresis loop of the free layer. However, in CPP, the self field of the bias current has a cylindrical symmetry, which means that the observed loop shifts

unambiguously have a different origin. (ii) A close look at the curves measured at low currents indicates a very unusual inversion of the coercivity of the free layer in some ranges of current. At low positive current (between 2 and 5 mA) and also at large positive and negative current ðlIl . 8 mAÞ; the switching of the magnetization with increasing field (from the parallel state to antiparallel) occurs at a lower field than the switching with decreasing field (from antiparallel to parallel). This effect can be explained within Slonczewski’s theory of spin torque (Slonczewski, 1996, 1999) by arguing that the prefactor in the spin torque is larger in the antiparallel than in the parallel magnetic configuration.

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139

(iii) A sudden increase in coercivity is observed between 5 and 6 mA with the onset of large noise associated with magnetic excitations. As the positive current is further increased, the coercivity decreases and the range of fields over which the magnetic excitations are observed becomes narrower and narrower. The noise is telegraph noise associated with stochastic jumps between various trajectories of precession of the magnetization of the soft layer (Lee et al., 2004). All these effects are manifestations of spin transfer in CPP magnetoresistive heads. In spinelectronics devices such as MRAM, the ability to switch the magnetization of a magnetic layer with a spin-polarized current may provide a very useful way to write the binary information. In magnetoresistive read heads, by contrast, these effects should be reduced as much as possible. As long as spin transfer behaves like an effective field (the low current regime in which loop shifts are observed), its effect can be included in the adjustment of the bias point. However, if magnetic excitations are generated, such as observed at 6 mA in Fig. 2.35, this would have a detrimental impact on the head performances. In this case, techniques must be found to reduce the spin-transfer effect. For example, dual spin-valve stacks in which opposite spin-transfer effect are expected from the two pinned layers could be used. Increasing the Gilbert damping in the free layer can also help to reduce the magnetic excitations due to spin transfer since the critical current for the onset of these excitations is proportional to the damping constant (Li, 2003).

2.7

GMR MRAM

Besides their use in magnetoresistive heads, spin valves have also found a very promising application in non-volatile magnetic memories (MRAMs) (see also Chapters 4 and 5). This generation of GMR MRAM followed a previous generation which was based on the AMR of NiFe elements (Yoo et al., 1989; Pohm et al., 1991). The principle of GMR MRAM is illustrated in Fig. Top view : WL SL

Side view : WL SL

Fig. 2.36 Schematic representation of a GMR MRAM. The dark ellipses represent the pseudo-spin-valve memory elements interconnected in series by Cu leads along the sense lines (SL). The word lines (WL) are perpendicular to the sense lines and electrically insulated from them.

140 B. Dieny 2.36. By contrast with exchange-biased spin valves for magnetoresistive heads which comprise a soft free layer and a pinned reference layer, the spin valves developed for GMR MRAM applications comprise two ferromagnetic layers of different coercivities. These structures are named ‘pseudo-spin valves’. A typical composition is Ni80Fe20 4 nm/Cu 2.5 nm/Co70Fe30 3 nm in which the NiFe layer is the soft layer and Co70Fe30 the hard layer. The two magnetic layers have a uniaxial shape anisotropy with parallel easy axes. In GMR MRAM architecture, the GMR elements are organized in a two-dimensional array as illustrated in Fig. 2.36. The elements are located at the cross-points between two sets of parallel lines, word and sense lines. Along the sense lines, the GMR cells are connected in series. The word lines are located above the sense lines, perpendicular to them, and are electrically insulated from them. The information is stored as the orientation of the magnetization of the hard layer. In order to write the information in a selected cell, pulses of current are simultaneously sent through the sense line and word line which cross each other at the selected memory element (refer also to Chapter 1). These two perpendicular currents generate two perpendicular magnetic fields on the hard layer of the selected memory cell, one along the easy axis of magnetization (field generated by the bit line), and one along the hard axis (field generated by the word line). The other cells are subjected to only one or to none of these two fields. The principle of the write selectivity is very similar to the one used in TMR MRAM technology (see Chapters 4 and 5) and it is based on the Stoner –Wohlfarth asteroid. The simultaneous application of fields along the hard axis ðHy Þ and easy axis ðHx Þ reduces the amplitude of the Hx field required to switch the magnetization of a magnetic element presumed to be in single domain state. The easy axis switching field depends on the field applied along the hard axis through the relation:

Hx2=3 þ Hy2=3 ¼




2K Ms

2=3 :

Because of the combination of two perpendicular fields, it is possible to switch the magnetization of the hard layer in the selected memory element without switching any other element. In order to read the information of a given cell, a current is sent through the word line corresponding to the selected cell. Since many cells are connected in series along each word line, the read process must be a differential, two-step process. By sending a low amplitude pulse of current along the appropriate bit line, the soft layer of the selected cell can be oriented in a first predetermined direction. The generated easy axis field must be large enough to switch the soft layer of the cell, but not so large as to switch the magnetization of the hard layer. In this magnetic configuration, a first determination of the total resistance of the word line is performed ðR1 Þ: The magnetization of the soft layer is then switched to the opposite direction by sending an opposite pulse of current in the appropriate bit line. In this second magnetic configuration, the total resistance of the word line is again determined ðR2 Þ: The two values R1 and R2 are then compared. If R2 . R1 ; the selected cell was in parallel magnetic configuration in the first read step implying

Spin valves

141

that the hard layer magnetization is in the first predetermined direction of orientation of the soft layer magnetization. Similarly, the opposite is true if R2  R1 : Advantages of these memories are similar to the advantages of TMR MRAM (nonvolatility, radiation hardness, speed and durability). However, they cannot be made with high density. Indeed, due to the series connection of the GMR cells along the word lines, the readout signal scales as 1=N; where N is the number of cells along the word line. This drastically decreases the read margin if N becomes large, and consequently increases the risk of read errors and slows down the readout process (Pohm et al., 1994, 1996). Another problem of GMR MRAM which may be encountered is inherent to the magnetic properties of pseudo-spin-valve structures. In such sandwiches comprising two magnetic layers of different coercivities, it has been observed that when the magnetization of the soft layer is switched a large number of time without switching the hard layer, a progressive depolarization of the magnetization of the hard layer takes place. Although the effect has been clearly seen in the case of MTJs, it is also present in pseudo-spin valves since it has a magnetostatic origin and is therefore independent of the nature of the nonmagnetic spacer material (Mc Cartney et al., 1999). This derives from the magnetostatic stray field generated by the soft layer magnetization and affecting the hard layer at domain walls during the switching process. This inhomogeneous stray field nucleates small reversed domains in the hard layer, leading to the observed progressive depolarization. This effect may reduce the number of possible read events between each write. Demonstrations of MRAM density up to 1 Mbit have been performed by NVE (Brown and Pohm, 1994). However, due to the difficulty mentioned above, this technology did not undergo a very large expansion and is now surpassed by the TMR MRAM technology which does not have the limitations in terms of density and number of read cycles.

2.8

Conclusion

Spin valves were invented shortly after the discovery of GMR in antiferromagnetically coupled magnetic multilayers, with the goal of obtaining GMR at low fields. They are used as magnetic sensors in magnetoresistive heads for computer disk drives. Their transport properties have been studied both in CIP and CPP geometries. In CIP the characteristic scaling lengths are the elastic spin-dependent mean free paths, whereas in CPP the characteristic lengths are the spin-diffusion lengths. In magnetoresistive read heads, CIP GMR was introduced in disk drives in 1998. The optimization of CIP multilayer stacks has allowed the increase of CIP magnitude up to DR=R ¼ 20%; at the wafer level, by improving the overall structural quality of the stacks and enhancing the specular reflection of conduction electrons at the edges of the active part of the spin valves. The GMR in CIP spin valves could be increased further. However, this would be at the cost of magnetic properties that are suitable for practical application. Therefore, CIP spin-valve performance seems to be close to its limit. Consequently, more and more efforts are focused on new approaches,

142 B. Dieny in particular CPP spin valves comprising NOL introduced to locally confine the current paths (CCP approach). This increases the CPP resistance as well as the relative resistance of the active part of the spin valve. However, at the current densities used in magnetoresistive heads (up to 108 A/cm2), spin-transfer effects occur and these must be reduced and controlled for this particular application. On the other hand, these spin-transfer effects may turn out to be very useful as an alternative write scheme in magnetoresistive random access memories (MRAM), or to generate steady magnetization precession in RF components. The knowledge acquired over the past 14 years in the development of spin valves has benefited the field of MTJs and MRAM. Indeed, both GMR in spin valves and TMR in MTJs are associated with a change in the relative orientation of the magnetization in two magnetic layers. Most often, the magnetization of one of the layers is pinned by exchange anisotropy, whereas the magnetization of the other layer can switch or rotate relatively easily by application of a low magnetic field. Therefore, the same magnetic material engineering techniques can be used in MTJs as are used in spin valves, such as antiferromagnetic biasing layers, synthetic pinned layers, and the choice of appropriate buffer layers.

Acknowledgements I deeply acknowledge Headway Technologies and in particular Kochan Ju, Min Li, Simon Liao for a long collaboration on the optimization of spin-valve structures. I thank my colleagues at SPINTEC for fruitful discussions. I greatly acknowledge M. Johnson for his patient editing and for very careful reading of the manuscript.

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Color plates

reader

377

writer

Planar coil

Fly height 10nm,

:~

100nrn

disk rotating at 5000 to 10000 rpm.

Plate 2.29 Schematic representation of the cross-section of a vertical head above a storage longitudinal media. (See Fig. 2.29.)

t'

H = Field from media

Plate 2.30 Schematic representation of a biased standard spin valve in a magnetoresistive heads. Only the free and pinned layers have been represented together with the conducting leads. PM designates permanent magnet layers which produce a static horizontal stray field on the free layer in order to maintain it in a well-controlled single domain state. The magnetization of the pinned layer is set parallel to the field from the media whereas the magnetization of the free layer in the quiescent state as well as its easy axis of magnetization are set perpendicular to it. (See Fig. 2.30.)

Magnetoelectronics M. Johnson (Editor) Copyright q 2004 Elsevier Inc. All rights reserved.

Chapter 3 Spin-polarized tunneling Jagadeesh S. Moodera and Robert H. Meservey Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

3.1

Introduction

The field of spin-polarized electron tunneling has been greatly broadened in recent years because of advances in tunneling between ferromagnetic electrodes, the investigation of different materials as electrodes and barriers, and the development of the tunneling microscope and nanotechnology. In addition to new scientific understanding, applications of the technique to surface analysis and electronic devices have greatly increased interest in the field. In this chapter we start with earlier research that was mainly concerned with superconductors, and then attempt to describe the more recent and rapidly moving current research that is mainly concerned with ferromagnetic materials. General older references on tunneling are found in Wolf (1985) and Burstein and Lundqvist (1969). Spin effects in tunneling with superconductors have been described (Fulde, 1973). Spinpolarized electron tunneling was reviewed in 1994 (Meservey and Tedrow, 1994). Two reviews have described the research on spin effects in tunneling between ferromagnetic metals (Moodera et al., 1999a; Moodera and Mathon, 1999). Spin electronics, both theory and applications, have been reviewed (Gregg et al., 2002) and the field of spin-based sensors and memory devices was recently reviewed (Parkin et al., 2003). Various aspects of spin-dependent transport have been described (Maekawa and Shinjo, 2002) with articles on spin-polarized tunneling by T. Miyazaki, by S. Maekawa et al. and by S.S.P. Parkin. Tunneling was recognized as a consequence of quantum mechanics as early as 1927 and the early history has been described recently (Merzbacher, 2002). Interband tunneling in semiconductors (Esaki, 1969) became an area of interest in the 1950s. The first experiments that were done in metal-to-metal tunneling and that were correctly explained were probably measurements of the temperature dependence of electrical contacts (Holm and Meissner, 1932, 1933). This research made it clear that the current in copper-to-copper electrical switches usually tunnels through a thin copper oxide barrier. Also, it is interesting to note that these authors apparently observed electron pair tunneling between superconductors in 1932, although only in 1962 this effect was explained (Josephson, 1962) using the BCS theory (Bardeen et al., 1957). Giaever (1960a,b) described his classic measurements of the tunnel current between Al and Sn through a thin Al2O3 barrier as the temperature was lowered to 1.05 K. This tunneling result,

152 J.S. Moodera and R.H. Meservey and others that immediately followed (Shapiro et al., 1962), made graphic the concepts of the BCS theory, the energy gap and electron –phonon coupling. Figure 3.1 shows how the measurement of the dynamic conductance, dI=dV; of a superconductor/insulator/normal metal (S/I/N) junction reproduces the superconducting density of states, slightly broadened by the temperature (Tedrow and Meservey, 1973). This result contradicted a one-dimensional WKB treatment (Harrison, 1961), which predicted no density of states dependence of the tunneling current, but the experimental results were too clear to be denied. Theoretical analysis (Bardeen, 1961; Cohen et al., 1962) supported Giaever’s intuitive description. A flood of experimental and theoretical research in tunneling immediately followed, starting with superconductivity and becoming a broad and active field branching into studies of

Fig. 3.1 Superconductor –normal metal tunneling. (a) BCS density of states of superconductor as a function of voltage. (b) Function proportional to the temperature dependence of the Fermi function. (c) Convolution of (a) and (b) giving the theoretical conductivity of the tunnel junction as a function of V:

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153

metals, semimetals, semiconductors and magnetism. With the development of the tunneling microscope (Binnig and Rohrer, 1982a,b; Chen, 1993; Wiesendanger, 1994; Bode, 2003) and nanotechnology, the range again broadened and tunneling techniques can now study, and even arrange, individual atoms (Eigler and Schweizer, 1990; Crommie et al., 1993). In information technology applications, spin-polarized tunneling is a competitive technique for nonvolatile random access memory elements and read-head sensors. Many new developments can be expected in the field of magnetoelectronics.

3.2 3.2.1

Superconductive tunneling Spin effects in superconductors

Certain metals become superconducting below a critical temperature characteristic of the particular metal. In this macroscopic quantum state the metals have no electrical resistance for currents less than a critical value and exclude magnetic fields from their bulk, up to a critical orbital magnetic field, by generating nondissipative screening currents on their surface. The BCS theory of superconductivity describes the superconducting current carriers as pairs of electrons in time-reversed states ðþk "; 2k #Þ with not only opposite momenta, but also opposite spins. The orbital critical field is the magnetic field at which the diamagnetic screening currents destroy the antisymmetry of the pair momentum and increase the energy of pairs until their energy equals their energy in the normal state. It was soon pointed out (Clogston, 1962; Chandrasekar, 1962) that opposite spin pairing implied a paramagnetic critical field Hp ¼ D0 =ð2mÞ1=2 < 1:86Tc (teslas), where D0 is half the energy gap at zero field, Tc the critical temperature, and m the magnetic moment of the electron. Since this critical field had not been observed, it was suggested (Ferrell, 1959; Anderson, 1959) that the neglect of spin –orbit scattering might be important. The theory was revised (Abrikosov and Gor’kov, 1962a,b) to include this effect. Since spin –orbit scattering increases approximately as the fourth power of the atomic number, Z 4 ; the Abrikosov–Gor’kov (AG) theory implies that spin effects are only important in elements with low values of Z; like Al. Although Hp could not be seen in bulk Al, which has an orbital critical field of only 100 G, paramagnetic limiting effects could be observed in Al films 4 nm thick when the magnetic field was applied in the plane of the film. The remarkable increase of the orbital parallel critical field of superconducting Al films from about 100 G to 5 T as they are made thinner, together with an increase in the superconducting transition temperature from 1.1 to about 2.5 K, was essential for enabling the original spin-polarization measurements. The most dramatic evidence of paramagnetic limiting was the spin splitting of the quasi-particle states in a tunneling measurement (Meservey et al., 1970) as shown in Fig. 3.2 for an Al/Al2O3/Ag tunnel junction, where Ag is a normal metal and the superconducting Al film is 4 nm thick. The explanation of this result is that there is Zeeman splitting of the quasi-particle density of

154 J.S. Moodera and R.H. Meservey

Fig. 3.2 The measured conductance of an Al/Al2O3/Ag tunnel junction at various values of magnetic fields in the plane of the film. The applied magnetic fields in teslas are: a ¼ 0; b ¼ 1:5; c ¼ 2:24; d ¼ 2:99; e ¼ 3:72; f ¼ 4:31:

states peaks, with one spin direction increasing in energy whereas the other spin direction decreases in energy. The spin splitting of the superconducting density of states is obvious, but complete analysis of the tunneling conductance curves required the Maki theory (Maki, 1964a,b; 1966, 1969; Fulde and Maki, 1966). This theory starts with the AG extension of the theory of superconductivity and includes the effects of spin–orbit scattering and orbital and other sources of depairing of the superconductor. Fulde and coworkers (Fulde, 1973) applied the Maki theory to tunneling. For early detailed calculations see Meservey et al. (1975) and Bruno and Schwartz (1973). These results provided a source of tunneling electrons of high spin polarization P of either spin direction, where P ¼ ðN" 2 N# Þ=ðN" þ N# Þ: Here N" and N# are the number of tunneling electrons whose magnetic moments are parallel to the magnetic field or antiparallel, respectively. The Zeeman splitting is also shown schematically in Fig. 3.3, where Fig. 3.3(a) shows the spin-split BCS density of states of an ideal superconducting thin film in a parallel magnetic field in which the orbital screening currents and spin –orbit scattering are negligible. However, in Fig. 3.3 the counter-electrode is a ferromagnet, which has unequal densities of spin-up and spin-down electrons states, the kernels being represented in Fig. 3.3(b), so that an additional asymmetry is introduced. In a parallel magnetic field, the quasi-particle states with magnetic moments parallel to the magnetic field move to lower energy 2mH and those antiparallel to the field move to higher energy þmH: The measured conductance [Fig. 3.3(c)] at any energy (eV) is the convolution of the density of states (a) and the derivative of the Fermi function at energy eV (b), which gives the temperature-broadened density of quasi-particle states. In this idealized case it is clear that by choosing voltages corresponding to the inner peaks in conductance, a tunnel current of entirely spin up or spin down can be obtained.

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155

Fig. 3.3 (a) Magnetic field splitting of the quasi-particle density of states for a superconductor without spin – orbit scattering. (b) Spin- and temperature-dependent kernel in the tunneling current integral. (c) Spin-up conductance (dashed), spin-down conductance (dotted), and total conductance (solid line).

The effects of the Maki –Fulde theory were confirmed in Al, in amorphous Be and Ga and in V, VGa3,VN, VTi, Al(Pt), and Ba12xKxBiO3 (Meservey and Tedrow, 1994). The source of spinpolarized electrons from superconducting Al in a magnetic field led to many studies of superconductivity (Fulde, 1973; Meservey and Tedrow, 1994). An important result of measurements between two spin-split superconducting Al films was that there was no detectable spin scattering in tunneling through Al2O3 barriers (Meservey and Tedrow, 1994). Conservation of electron spin in the tunneling process is important in the analysis of many tunneling experiments. Tunneling measurements using superconductors have even provided a method of calculating Fermi-liquid corrections of the magnetic moment of quasi-particles in normal metals using a theory by Rainer (Tedrow et al., 1984; Alexander et al., 1985; Gibson et al., 1989; Gibson and Meservey, 1989). These Fermi-liquid corrections were made even more powerful by the use of a ferromagnetic counter-electrode (Tedrow et al., 1982).

156 J.S. Moodera and R.H. Meservey 3.2.2 3.2.2.1

Superconductor –ferromagnet tunneling Transition metals

Once the technique of producing almost purely spin-polarized tunnel currents of either spin direction from superconducting Al films was successful, it was applied to measure the apparent spin sub-band densities of states of the 3d ferromagnets. To do this the junctions were made by oxidizing the Al in laboratory air to form the tunnel barrier and then depositing the counterelectrode of Ni. By deconvolving the measured conductance vs voltage, the relative size of the tunnel currents in the two spin directions was obtained, giving the spin polarization of the tunneling current as P ¼ ½N" ðEF Þ 2 N# ðEF Þ=½N" ðEF Þ þ N# ðEF Þ;

ð3:1Þ

where N" ðEF Þ and N# ðEF Þ are the number of majority spin and minority spin electrons in the tunneling current near the Fermi energy. The first measurement of a Ni counter-electrode gave a value of P ¼ 7 ^ 1% (Tedrow and Meservey, 1971). Further measurements of the 3d metals, in which the tunnel barrier was formed by oxidizing the Al film in laboratory air before depositing the ferromagnetic counter-electrode, gave these values of spin polarization: PNi ¼ þ10 ^ 1%; PCo ¼ þ34 ^ 2%; PFe ¼ þ41 ^ 2%: These values have been reduced from those originally published (Tedrow and Meservey, 1973). An approximate correction for spin –orbit scattering has been made, and one Co junction with large scatter of data points has been discarded. The positive sign indicates that the tunneling electrons had predominantly majority spin, N". N# : This result was unexpected, particularly in the case of Ni where it was known that the density of states at the Fermi energy was overwhelmingly in the minority direction. Figure 3.4 shows recent measurements of the conductance of two Al/Al2O3/Ni junctions (Kim and Moodera, 2003) showing the effect on the conductance when the majority spin current is larger than the minority spin current. Figure 3.4(a) shows the tunneling conductance from an epitaxially grown (111) face of Ni with a spin polarization P ¼ þ25%: In Fig. 3.4(b), analysis of the tunneling curve for a junction with a polycrystalline Ni film deposited in an MBE system gave a value of P ¼ þ46%: This value is more than four times that obtained in the early measurements of junctions with counter-electrodes deposited in relatively poor vacuum conditions. It shows the inadequacy of the Stearns model for Ni discussed below (Stearns, 1977), and the extreme sensitivity of the Ni surface to contamination. Theorists had previously suggested that the tunneling probability of localized d electrons was very small and that electrons with an s-like character must carry most of the tunnel current (Gadzuk, 1969; Politzer and Cutler, 1972). It was also proposed (Hertz and Aoi, 1973) that the tunneling electrons were hybridized s –d electrons and included virtual spin wave emission. A later model (Chazalviel and Yafet, 1977) proposed hybridized s –d electron bands in an attempt to explain the spin polarization of field-emission data, the analysis of which is closely related

Spin-polarized tunneling

1.5 (a)

1.0

0.5

0.0

0.5

1.0

157

1.5

dI/dV (10 4Ohm 1)

8 6 4 2 T = 0.4 K 0 8 dI/dV (10 4Ohm 1)

(b)

6 4 2 T = 0.4 K 0 1.5

1.0

0.5

0.0

0.5

1.0

1.5

V(mV)

Fig. 3.4 Tunneling conductance as a function of voltage (with respect to Al) in various fields for (a) Ni(111)/Al2O3/Al junction: 0 T (closed circle), 3.3 T (closed square), 3.7 T (open square), and (b) Al/Al2Ox3/polycrystal Ni junction: 0 T (closed circle), 2.9 T (closed square), 3.2 T (open square). Symbols (solid lines) correspond to experimental data (calculated curves using Maki’s theory) showing a spin polarization of 25 and 46% for (111) oriented and polycrystalline Ni, respectively.

to the subject of this review. A transfer Hamiltonian method (Feuchtwang and Cutler, 1976; Nagy et al., 1979) was used to study tunneling in field emission, and also could be applied to junction tunneling. A model that gave clear numerical predictions of the polarizations based on the known band structure was proposed (Stearns, 1977). Although most of the d electrons were highly localized, this model noted that one of the d bands in Ni (and in Fe) which crosses the Fermi surface is nearly parabolic and has an effective mass close to that of a free electron. The exchange splitting of the majority and minority spin sub-bands of these ‘itinerant d electrons’, which resulted from s –d hybridization and were designated di electrons, is nearly the same as for the localized d bands. Stearns assumed that these di electrons dominated the tunnel current. The densities of states of majority and minority di were obtained from band structure calculations and from de Hass – van Alphen measurements (Gold et al., 1971; Baraff, 1973). Assuming (as had Bardeen with superconductors) (Bardeen, 1961) that the matrix elements determining the tunneling probability are independent of spin led to predicted values for the polarizations PNi ¼ 11%; PCo ¼ 33%; and PFe ¼ 43%; which agreed well with the measured values. The Stearns model also predicted that

158 J.S. Moodera and R.H. Meservey the polarization P should be approximately proportional to the magnetic moment m of these materials, as was found experimentally with many alloys of Ni, Co, and Fe. This approximate proportionality, taken from early experimental data, is shown in Fig. 3.5. Recently, Choy et al. (1999) have derived the proportionality of P and m for many 3d ferromagnets using a tight-binding approach, but it is clear that Ni and many Ni alloys do not have this proportionality. The original superconductor-to-insulator ferromagnetic junctions were made by depositing metallic Al, forming the Al2O3 barrier by oxidizing the Al surface in air that contained water vapor, and then depositing the ferromagnet. Recently, a different method has been developed to form ferromagnetic insulator/ferromagnetic (FM I/FM) junctions (Moodera et al., 1995; Miyazaki and Tezuka, 1995). One ferromagnet is deposited and covered with a thin coat (< 1 nm) of metallic Al. The Al is then oxidized to form the barrier; and finally the second ferromagnet (or a superconductor) is deposited as the counter-electrode. In forming the Al2O3 in this way, the surface of the original ferromagnetic electrode is not oxidized because the oxidation potential of Al is much higher than that of Ni, Co, or Fe. This also avoids the intermixing of the metal and the Al oxide, an effect that has been observed recently (LeClair et al., 2000a). Furthermore, vacuum conditions have been improved for recently fabricated junctions. New measurements led to these revised values (Moodera and Mathon, 1999) for the polarizations: PNi ¼ 46%; PCo ¼ 42%; and PFe ¼ 45%: The proportionality between the magnetic moment and polarization is no longer observed in many 3d metals and alloys. Iron is the only metal in which the old and new values are within the limit of experimental error. It is clear that the Stearns model (Stearns, 1977) is not sufficient to explain the newer results. One proposed model (Slonczewski, 1989) described the ferromagnet as

Fig. 3.5 Showing the proportionality of P vs m for transition metal ferromagnets.

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159

having free-electron-like wave functions with spin and included exchange energy splitting inside the ferromagnet and tunneling matrix elements. This model gave results which reduced to the Stearns density of states expression for the limiting cases of high barriers or large insulator thickness, and gave decreased polarization, and even a sign change, for thin or low barriers. The complete free energy tunneling expressions of this model have been solved numerically without approximations (MacLaren et al., 1997). Predictions of this free energy model have not been experimentally verified. Other theorists have emphasized the importance of including tunneling matrix elements that are appropriate for the boundary conditions at the ferromagnetic interface and for the type of measurement analyzed (Mazin, 1999; Nadgorny et al., 2000). Some recent theoretical proposals to explain the results of spin-polarized tunneling emphasize the importance of the interface effects between the ferromagnet and the barrier material and will be described in Section 3.5.

3.2.2.2

Transition metal compounds

Many compounds containing 3d transition metals are ferromagnetic and research is only beginning in this broad field. The Heusler alloys MnxSb12x were measured using a superconducting Al counter-electrode (Sullivan and Rogers, 1983) and a maximum value of P ¼ þ25% was found. The relationship that P was approximately proportional to the magnetic moment for different alloy compositions who also seen. NiMnSb, predicted by theory to have a value of P ¼ 100%; was measured by inverse photoemission to have a value of P approaching 100%. However, tunneling measurements have shown a value of P ¼ 30%; probably because the alloy composition at the metal surface at the tunnel barrier is off stoichiometry. A detailed discussion of compounds with the possibility of giving P ¼ ^100%; that is, half-metallic magnets can be found in Pickett and Moodera (2001). The superconducting tunneling conductance technique has been used (Worledge and Geballe, 2000a) to measure the spin polarization of conduction electrons in a ferromagnetic material very different from 3d metals. Measurements on high quality junctions of La0.67Sr0.33 MnO3/SrTiO3/Al gave a value of P ¼ þ72 ^ 1%: SrTiO3 was used as the barrier because the growth temperature of the ferromagnet, La0.67Sr0.33MnO3 (LSMO), was high. LSMO had previously been predicted to have P ¼ 100% (Pickett and Singh, 1997). A photoemission experiment (Park et al., 1998a) probing electrons near the Fermi surface, at T ¼ 40 K, measured a density of states of only majority spins, giving evidence that LSMO is a half-metallic ferromagnet. However, photoemission spectroscopy performed on this material might fail to detect the small number of conduction electrons that make up the tunneling current, and therefore the tunneling result may not be in conflict with spectroscopy data. In their tunneling experiment, Worledge and Geballe eliminated most of the orbital depairing found in previous measurements of S/I/FM junctions. This improvement allowed very high experimental precision and excellent fits to the

160 J.S. Moodera and R.H. Meservey

Fig. 3.6 Normalized conductance data for an LSMO/Al2O3/Al junction taken at H ¼ 3 T (solid line), and fit to Maki’s theory (dashed line) with T ¼ 0:31 K, D ¼ 0.39 mV, z ¼ 0:024; b ¼ 0:05; and P ¼ 72:0%:

theory, as shown in Fig. 3.6. In addition, these authors have cleared up an ambiguity in Maki theory in the calculation of the densities of spin states. Recently, CrO2/I/Al junctions were successfully made (Parker et al., 2002) and the tunneling conductance spin polarization was measured to be nearly 100%. The CrO2 (100) was grown by CVD on a TiO2 (110) substrate, and etched with a solution of Br dissolved in methanol. After etching, the sample was placed in a vacuum for the deposition of a thin Al film. Subsequently, the junctions were measured at 3He temperature (0.4 K) in a parallel magnetic field. The majority spin electron peak in the superconducting density of states was displaced as expected from Zeeman splitting. However, Fig. 3.7 shows that there was no minority peak up to a field of 2.5 T. The lack of a minority peak showed that the polarization of the tunneling electrons was very close to 100%, giving evidence that CrO2 could be a true half-metal ferromagnet. It is now of interest to know the detailed nature of the barrier, which apparently was composed of Cr2O3.

Fig. 3.7 Zeeman-split conductance curves of a CrO2/I/Al junction taken at 0.40 K with applied fields ranging from 0 to 2.5 T in increments of 0.5 T showing nearly full spin polarization of tunneling electrons in CrO2.

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The resistance of CrO2 could be controlled over a very wide range, with the following advantage. Excellent tunnel results were obtained for high resistance barriers, and good point contact Andreev reflection (PCAR) results were obtained at low resistances (Soulen et al., 1998). More recently, the spin polarization of SrRuO3 was measured (Worledge and Geballe, 2000b) using a superconducting counter-electrode and a negative polarization of P ¼ 29% was found as shown in Fig. 3.8. This is the first measurement to give a negative polarization using a superconducting counter-electrode. Using a spin-split superconducting film remains the most unambiguous method of measuring the spin polarization of the tunnel current from a ferromagnetic metal because of the long coherence length of superconductors and the complete understanding of the theory and experimental method of superconducting tunnel spectroscopy. Tunneling between magnetic materials, using FM/I/FM junctions, has the advantage that it does not require cryogenics nor does it need a high magnetic field. However, because of the very short coherence length of ferromagnetism in metals, the effect of the metal surface and the interface with the tunnel barrier must be known on the scale of a monolayer to obtain consistent results. In Section 3.5 we discuss some of the many FM/I/FM recent tunneling results and theoretical studies that have been developed to explain them. 3.2.2.3

Rare earth ferromagnets

The spin polarization of ferromagnetic rare earth metals has been measured using superconducting Al counter-electrodes (Meservey et al., 1980a). The tunnel currents for Tm, Dy, Ho, Tb, and Gd were all found to have positive polarization that was approximately proportional to the known magnetic moment of the s –d conduction electrons, of these elements, as shown in Fig. 3.9. In these rare-earth metals the 4f electrons are completely localized and therefore do not contribute to the

Fig. 3.8 Normalized data for SrRuO3/SrTiO3/Al junction at H ¼ 3 T (solid line), with a fit to the Maki theory (dashed line), showing that the spin polarization of SrRuO3 is negative. The inset shows the zero field data (solid line), with a theoretical fit (dashed line).

162 J.S. Moodera and R.H. Meservey

Fig. 3.9 Measured polarization P as a function of the magnetic moment of the conduction electrons for the heavy rare-earth elements. Each symbol represents a different sample. The solid line is the least-squares fit to the average of the points of each ferromagnetic element, and is constrained to pass through zero.

tunneling current, but they provide most of the magnetic moment. The s –d conduction electrons have smaller moments that are aligned with the f electron moments. In these ferromagnets the measured spin polarization is approximately proportional to the magnetic moment of the conduction electrons. This result eliminates the possibility that a spin flip might take place in the tunneling process.

3.2.2.4

Exchange proximity effect

Another remarkable effect of the Eu chalcogenides is their exchange-field coupling with the conduction electrons in an adjacent metal layer. In an important experiment (Tedrow et al., 1986), a layer of Eu was deposited on a thin Al film and then oxidized to form EuO. The quasi-particle density of states of the superconducting Al film was spin-split by a small magnetic field, and the splitting was greatly enhanced by the exchange interaction with the EuO, a ferromagnetic semiconductor. The same effect was seen with other rare earth oxides (Tkaczyk and Tedrow, 1987). This exchange proximity effect was also found when EuS was in contact with a thin superconducting Al film. For example, when EuS in contact with a 5 nm Al film is ferromagnetically aligned in a magnetic field of 0.5 T and the field is then removed, an effective field of more than 4 T, from the exchange interaction, acts on the Al film. This enables one to make a spin-polarization measurement with no applied field. Using a thin Al film in contact with a EuS film (Hao et al., 1991) it was shown that the phase transition from the superconducting state to the normal state of the Al, under the influence of the exchange field, was first order and that the exchange effect was inversely proportional to the Al film thickness, as predicted (de Gennes, 1966). This technique has allowed the observation of the paramagnetic critical field of superconducting Al in zero magnetic field, and shows promise as a source of spin-polarized electrons requiring a minimally small or zero applied magnetic field.

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3.3

163

Spin-filter effect

In the original work on spin-polarized tunneling, the polarization of the tunnel current derives from the spin imbalance of the density of states of spin-up and spin-down conduction electrons at the Fermi energy. The highest value of spin polarization P attained with transition metal alloys was about 50%. However, higher values of P can be obtained by using special barriers that have a different tunneling probability lTl2 for the two spin directions: lT " l2 . lT # l2 : For instance, EuS has a band gap of 1.65 eV and a Curie temperature of TC ¼ 16:6 K: The exchange splitting of the conduction band at 4 K is DEex ¼ 0:36 eV; so that the barrier heights are F#;" ¼ F0 ^ DEex =2 for spin-down and spin-up electrons, where F0 is the average barrier height at a temperature above TC : Since the tunneling probability varies exponentially with barrier height, the spin-up current can greatly exceed the spin-down current in a nonmagnetic metal/EuS/nonmagnetic metal tunnel junction. Figure 3.10 shows such a junction schematically. In a junction consisting of a normal Au electrode, a EuS barrier, and a superconducting Al spin detector, the measured spin polarization of the tunnel current in a field of 0.5 T (which saturates the susceptibility of the EuS) gave a value of P ¼ 80% as shown in Fig. 3.11. This result agreed within 5% of the value calculated using tunneling theory to determine the height and thickness of the barrier and the known band properties of EuS (Hao et al., 1990). Related studies of EuS using the techniques of field emission

Fig. 3.10 Schematic representation of the tunnel barrier for a Au/EuS/Al junction, at T p TC : W1 and W2 are the work functions of Au and Al, respectively. x is the electron affinity of EuS. The barrier heights at the Au and Al interfaces are shown as f1 and f2 at the bottom of the EuS conduction band (dashed line) at T . 16:7 K. The bottom of the two bands shown by the solid lines, separated by DEex ; are the barriers seen by the two spin orientations.

164 J.S. Moodera and R.H. Meservey

Fig. 3.11 Conductance vs voltage for a Au/EuS/Al junction at T ¼ 0:4 K for various values of H: Fitting the curves to theory gives P ¼ 80 ^ 5%: Curves were taken in increasing field. Hysteresis was observed in decreasing H; but is not shown.

(Mu¨ller et al., 1972; Kisker et al., 1976; Kisker et al., 1978), internal field emission, and resistance measurements (Esaki et al., 1967) also showed polarization effects. The spin-filter effect also can be seen by using the antiferromagnetic semiconductor EuSe ðTN ¼ 4:6 KÞ and driving it into the ferromagnetic state with a small magnetic field (Moodera and Meservey, 1993). In this latter state, the conduction band edge of the EuSe tunnel barrier is exchange split (similar to EuS) in the presence of an applied magnetic field, and shows nearly 100% spin polarization (Fig. 3.12). In addition, by using this barrier the exchange splitting can be

Fig. 3.12 Calculated electron-spin polarization due to spin filtering in EuSe barrier as a function of the applied magnetic field, deduced from the tunnel junction conductance data. Also shown is the junction resistance ðRJ Þ variation in the applied magnetic field.

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165

tuned by the magnetic field and the result is an increase of the spin polarization, as shown in Fig. 3.13. A junction magnetoresistance JMR < 80% (corresponding to a tunnel magnetoresistance TMR < 400%) has been observed (see Section 3.4.1). Junctions with EuS and EuSe barriers require liquid helium temperature for operation, whereas EuO has its ferromagnetic ordering temperature at 69.6 K, and this value of TC can be increased somewhat with dopants. The garnets, M3Fe5O12 (where M is a rare earth element) such as Y3Fe5O12, which is an insulator and is magnetic above room temperature, are also candidate materials for use as barriers. Another promising structure is a device with two spin-filter barriers (Worledge and Geballe, 2000c). Extending the spin-filter phenomenon, Worledge and Geballe have envisioned a magnetoresistive tunnel structure that takes advantage of this effect. In their proposed device structure (called a double spin-filter junction), two magnetic tunnel barriers are placed between three normal metal electrodes. The tunnel current through this structure would be higher (lower) when the magnetic moments of the two barriers are parallel (antiparallel). This could give rise to a change in the tunnel conductance by many orders of magnitude. Realizing such a structure in practice requires the ability to have two layers of magnetic insulators with different coercivities and different thicknesses, both of which are sufficiently thin to serve as tunnel barriers. The feasibility could be shown with Eu chalcogenides. However, observation of such an effect requires a large spin accumulation in the middle layer. This is very difficult with a metal, whereas it might be easier to achieve with a semiconducting layer as the middle electrode. Along this direction, there have been approaches to use a spin-filter material as the tunnel barrier in an MTJ to create a new kind of TMR device, analogous with an optical

Fig. 3.13 Tunnel conductance vs junction voltage bias in various applied fields for a high resistance tunnel junction, showing only up-spin peaks, indicating nearly 100% electron-spin polarization and nearly complete spin filtering in EuSe barrier.

166 J.S. Moodera and R.H. Meservey polarizer –analyzer. The resistance of such a device depends on the relative orientation of the FM electrodes with respect to the spin-filter material (Nasser and Moodera, 1998; LeClair et al., 2002). In an experiment on such a device, the resistance of Co/EuS/Gd junctions changed by over 100% at low temperatures in an applied field of 1 T. Spin-filter tunneling is being envisioned as one of the ways to achieve quantum computing (Bennett and DiVincenzo, 2000). The proposal (DiVincenzo, 1999) is schematically shown in Fig. 3.14 where the spin-filter property of the barrier is exploited to accomplish the process necessary for the quantum measurement. In this scheme the correlation of the electron wave function from one quantum dot to the adjacent one is by spin-dependent tunneling through the spin selective barrier. An applied gate voltage adjusts the energy level of the trapped electron allowing it to tunnel or not tunnel through the spin-filter barrier. In this way it is predicted that quantum coherence can be large and the coupling/uncoupling of the qubits can be achieved in a controlled manner. Then it is possible to measure the state of each qubit individually and reliably by electrical means, rather than by the extremely difficult task of magnetically measuring a single spin.

3.4 3.4.1

Ferromagnetic – ferromagnetic tunneling Early experiments by Jullie`re and others

Spin-polarized tunneling experiments between superconductors and ferromagnets showed that the conduction electrons tunneling from ferromagnetic metals are spin polarized with degrees of polarization that are characteristic of each metal. Based on these results and their analysis (Tedrow and Meservey, 1973), Jullie`re (1975a) proposed a model for spin-polarized tunneling between two

Fig. 3.14 Schematics of the spin-filter quantum measurement. Possible vertical and in-plane structures are shown. By adjusting the voltage one can decrease or increase the tunneling probability. Because of the exchange splitting of the conduction band barrier in the ferromagnet, spin-up electrons will tunnel through the barrier easily while spin down will not, depending on the applied voltage.

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ferromagnetic metal electrodes. In this simple model the fractional change in the dynamic conductance, ðGp 2 Ga Þ=Gp ; where the subscripts p and a signify parallel or antiparallel orientation of the magnetic moments of the ferromagnetic electrodes, is given by ðGp 2 Ga Þ=Gp ¼ 2P1 P2 =ð1 þ P1 P2 Þ:

ð3:2Þ

Here P1 and P2 are the spin polarizations of the conduction electrons in the two ferromagnetic electrodes. In practice, the fractional change in resistance is measured and has been defined in two ways: JMR ; ðRa 2 Rp Þ=Ra ¼ 2P1 P2 =ð1 þ P1 P2 Þ;

ð3:3aÞ

TMR ; ðRa 2 Rp Þ=Rp ¼ 2P1 P2 =ð1 2 P1 P2 Þ:

ð3:3bÞ

These definitions are related by TMR ¼ JMR=ð1 2 JMRÞ: In using these expressions, one should remember that in Eq. (3.2), G ¼ dI=dV; whereas in Eqs (3.3a) and (3.3b), R ¼ V=I: Therefore, these expressions only coincide when R is constant with voltage. Furthermore, the values of P1 and P2 are determined from superconductive tunneling at V < 0; but may be functions of V at higher voltages (Moodera et al., 1998; LeClair, 2002). In his experiments Jullie`re used Fe as the bottom electrode. The thin Fe film was next covered with an amorphous Ge (a-Ge) barrier, which was then exposed to oxygen to oxidize the Fe that was exposed through pinholes in the a-Ge (Jullie`re, 1975b). The top electrode was a thin Co film. One could expect JMR ¼ 29% for an Fe– insulator–Co tunnel junction, assuming PCo ¼ 40% and PFe ¼ 42%: At 4.2 K a magnetoconductance JMR ¼ 14% was observed at zero bias, a value which decreased with increasing bias voltage to less than 2% at 6 mV. Jullie`re interpreted the 14% JMR at zero bias to be FM/I/FM tunneling, as in Eq. (3.2) or (3.3a), whereas the large decrease in the JMR with increasing bias was attributed to spin-flip scattering. This simple model assumes that the tunnel currents of up and down spin channels contribute independently to the current, that the tunneling matrix element is independent of spin, and that the density of states is independent of energy. Despite these simple assumptions, recent experiments have shown Jullie`re’s model predicts fairly accurately the magnetoresistance observed with pairs of ferromagnetic electrodes in high quality junctions near V ¼ 0: Some years after Jullie`re’s experiment, measurements (Gibson and Meservey, 1985) were made with superconducting Al/a-Ge/FM junctions where the a-Ge was deposited at 80 K. In several junctions the a-Ge was treated with a plasma discharge of O2, N2, or H2. However, no spin polarization was seen in the tunnel conductance measurements of the junctions. Studies of Al/a-Si/FM junctions (Meservey et al., 1982) had detected spin-polarized currents in a few junctions, but the conductance background was too large to make quantitative analysis possible. Concerning Jullie`re’s original results on Fe/a-Ge/Co junctions, it is possible that the observed polarization was attributable to electrons tunneling through the Fe oxide. At a thickness of 10 nm, transport in the a-Ge barrier is probably in the variable range hopping regime in which

168 J.S. Moodera and R.H. Meservey the electrons tunnel between successive defect states. They would lose their spin memory more rapidly than in an a-Si barrier because of greater spin –orbit scattering. This conjecture would explain why the original results have never been reproduced. After the early research by Jullie`re, several groups attempted to observe tunneling between ferromagnetic films. In an experiment using a Ni/NiO/Co junction at 4.2 K, JMR < 2% was measured (Maekawa and Ga¨fvert, 1982). The JMR decreased rapidly as the temperature increased, and a much smaller value was observed at 77 K. Several other groups reproduced such effects, mainly with NiO, CoO, and Al2O3 barriers, and reported small changes in the JMR at low temperature (Suezawa and Gondo, 1982; Miyazaki, 2002; Kabani et al., 1990). A JMR of 7% at 4.2 K was observed in Fe/GdO/Gd tunnel junctions (Nowak and Rauluszkiewicz, 1992). These authors also observed the magnetic domain structure of the tunnel junctions, showing the coupling of top and bottom FM electrodes due to film roughness and domains. Although demonstration of spin-polarized tunneling between two ferromagnetic electrodes of a planar function appeared to be straightforward, it was not realized with any significant magnitude or reproducibility until 20 years after Jullie`re’s publication. The major roadblocks were (i) surface roughness of the FM electrodes, (ii) quality of the tunnel barrier, (iii) FM –I interface quality, (iv) FM electrodes, and (v) domain walls. We describe these problems in greater detail below, in no particular order. Although oxidizing the bottom FM electrode to create a native tunnel barrier on the surface of the film appears to be an obvious fabrication approach, this is not successful. It fails because oxides of the ferromagnetic transition metals are strongly paramagnetic at higher temperature, whereas at low temperature they are usually antiferromagnetically ordered. The presence of magnetic moments in the barrier can lead to spin scattering. A proper tunnel barrier, such as a thin Al2O3 (, 2 nm) layer that uniformly covers the surface of the bottom ferromagnetic film, can be fabricated if the first electrode is nearly atomically smooth. Forming the tunnel barrier by growing an ultrathin insulating layer over a rough surface is nearly impossible because of nonuniform coverage of the insulator over the bottom electrode. Even with a working junction of this kind, its stability will be a problem since the tunneling will take place only at a few hot spots, giving rise to enormous current densities in these regions and leading to premature junction breakdown. Furthermore, surface roughness of the bottom FM electrode will lead to dipolar, orange peel coupling of the two ferromagnetic electrodes (see also Chapter 2). Such a coupling will not allow independent switching of their magnetizations. The spin polarization of the tunnel current from ferromagnetic electrodes is extremely sensitive to surface and interface properties because of the short coherence length characteristic of the ferromagnetic state (see Section 3.5). The lack of symmetry at the surface has an effect on the surface magnetic moment. This has been treated extensively in the literature theoretically, and also has been observed experimentally. The effect of impurities or nonstoichiometry in or near the interface can change the tunnel process drastically. The interactions between the FM metal and the atoms of the barrier in the interface can have a profound effect related to their chemical bonds and

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their band structure (Meservey et al., 1980b, 1983; Moodera and Meservey, 1984). Because of this interface sensitivity, extreme care and precision in the formation of tunnel junctions with ferromagnetic materials are required to obtain a large JMR. The presence of magnetic domain walls will lead to coupling of the two FM electrodes and thus reduce the magnetic response of the junction. In this regard, it is helpful to minimize the thickness of the FM films. In fact, from early SPT experiments it can be seen that only a few monolayers of FM film near the tunnel barrier are required to obtain a good JMR (Meservey et al., 1980b, 1983; Moodera and Meservey, 1984). As long as the Curie temperature is sufficiently high, the junction will show good magnetoresistance. As a final note, it has been argued recently that inter-atomic bonding between states in the ferromagnet with those (such as Al and O) in the insulator, Al2O3, should influence not only the magnitude, but even the sign, of the spin polarization of the tunneling electrons (Tsymbal and Pettifor, 1998). 3.4.2

Recent experiments and basic properties

The possibility of observing a large and reproducible magnetoresistance in FM –I–FM tunnel junctions has existed since the Jullie`re experiment of 1975. However, the experimental breakthrough did not happen until 1995, when most of the problems mentioned in the previous section were carefully addressed. It was shown in CoFe/Al2O3/Co junctions that a large JMR of over 12% at room temperature could be obtained, consistently and reproducibly (Moodera et al., 1995). Since then, the research topic of TMR has been actively pursued in universities and national labs as well as industries, and over a thousand papers have appeared in the literature. Of great interest are basic research topics such as novel effects related to the physics of interfaces and spin tunneling. However, the main driving force is now applied research for using MTJs as high sensitivity read heads for ultrahigh density magnetic recording, the development of nonvolatile magnetic random access memory (MRAM) elements, and the possible development of spin-based logic circuits (Ney et al., 2003) (see Chapter 6). As described in the introductory text above, a standard magnetic tunnel junction is composed of two ferromagnetic conductors separated by an ultrathin insulator. Deposition of the junction materials can be done by thermal evaporation, sputtering, or by pulsed laser deposition. In all these methods it is important to keep the interfaces clean, to avoid inter-diffusion, and to ensure that the insulator is uncontaminated. A thermal evaporation technique was used to make the junctions reported in Fig. 3.15 and is briefly described below. Other techniques, such as sputtering, were typically adapted from this method and details can be found in the literature. Cryogenic evaporation through a shadow mask was employed to create the cross-geometry junction structure shown in the inset of Fig. 3.15. In general, a seed layer such as Si or SiO2 was initially deposited onto LN2 cooled glass substrates, followed by a deposition of the first FM film as a long strip. On top of the FM film a thin (about 1–2 nm) continuous film of Al was deposited and then plasma oxidized at room temperature to create the Al2O3 tunnel barrier. Cross strips of the

170 J.S. Moodera and R.H. Meservey

Fig. 3.15 Resistance of CoFe/Al2O3/Co junction plotted as a function of field H in the film plane, at 295 K. Also shown is the variation in the CoFe and Co film resistance. The arrows indicate the direction of magnetization orientation of the two films. Inset: schematic of the cross-strip geometry. The junction area is defined as the intersection of the two perpendicular electrodes (hatched), which are separated by a thin insulating layer.

top FM electrode were then deposited to complete the FM/I/FM junctions. The FM films were grown in the presence of an applied magnetic field to achieve a well-defined magnetization state and sharp value of coercive field, HC : The FM electrode strips were 1 mm wide and the effective junction area of 4 £ 1024 cm2 was defined by thick layers of Al2O3. The tunnel junction resistance ðRJ Þ ranged from less than 100 V to tens of kV depending on the Al film thickness and the duration of the glow discharge. The current –voltage ðI – VÞ characteristics of the junctions showed less than 20% increase in RJ as the temperature was decreased from room temperature to 4 K. The I – V data were fit to formulae found in Simmons (1963) or Brinkman et al. (1970) to deduce the barrier height. Average values were greater than 2.5 eV and values near 3.5 eV were found in some samples. It should be pointed out that deposition of the seed layer, the first FM film, and the Al barrier film at cryogenic temperature helped to form smooth films and thereby increased the junction yield and stability. Room temperature deposition also worked, although the yield was slightly lower. Other groups have employed etched Si with a variety of metal seed layers as substrates. Several insulating compounds have been tried as the barrier material and some of them, such as MgO, AlN, and Ga2O3 have been quite successful (Wang et al., 2001; Li et al., 2000; Bowen et al., 2001). The best barriers have been made when a thin metal layer is subsequently reacted to form an insulating compound, and plasma oxidation (dc or rf) is widely used. For ultrathin barriers, natural

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(or thermal) oxidation gives better control because it is a slower process. Furthermore, there may be an unknown mixture of O ions and O2 molecules present in the plasma. Reactive evaporation also works, although the yield and stability of the resulting junctions are not as good as other methods. With magnetic electrodes, it should be noted that oxidation of the bottom electrode itself should be avoided because magnetic oxides can lead to low surface polarization and/or spin scattering. The change in junction resistance DR as a function of the applied magnetic field H for a Co/Al2O3/Ni80F20 junction is shown in Fig. 3.15. The two stable and well-defined resistance states are distinctly seen. The JMR seen in this case, as defined with respect to the peak resistance, is 13.2%. The peak value of RJ shows a memory effect: the resistance first increased with increasing field to the value (at < 100 Oe) corresponding to the peak in RJ ; and then maintained this value when the field was reduced to zero. That is, two stable resistance states can be maintained at H ¼ 0; thus giving two nonvolatile memory states. The variation of RJ with the in-plane field H shown in Fig. 3.15 was predicted by Jullie`re and can be understood as follows. At high fields, the two FM films have their magnetization orientations aligned parallel in the applied direction of H (arrows in Fig. 3.15 indicate the direction of the magnetization orientations). Upon reversing the field, the magnetization M1 of the film with a lower HC aligns itself in the reversed field direction whereas the second electrode, with a higher HC ; remains magnetized in the original field direction. The result is an antiparallel configuration. As the field magnitude is increased further, the orientation, M2, of the second FM also aligns in the new field direction, resulting in parallel orientation of the two magnetizations. Thus, at high fields in either direction, in the parallel configuration, the tunneling probability (current) is high, whereas in the antiparallel configuration, the tunneling probability (current) is lowest. The rotation of the magnetization of one FM with respect to the other also supports this FM –I–FM tunneling model. When the sample is rotated in a magnetic field, with a magnitude higher than the coercivity HC of one electrode, the magnetization M1 of the magnetically softer film follows the field direction. This will change the relative orientation of the magnetizations of the two FM films – switching from parallel to antiparallel orientation gradually. The tunneling probability is affected accordingly, which is seen as the periodic variation of RJ as a function of angle. The maximum value of RJ corresponds to the antiparallel orientation of the magnetizations, whereas the parallel orientation corresponds to the minimum of the curve. When similar measurements are made at a field value higher than the peak field, RJ remains unchanged because both M1 and M2 follow the magnetic field direction and remain parallel to each other. Optimization of the tunnel barrier and improvement of the FM –I interfacial quality can give rise to better values of JMR as can be seen in Fig. 3.16. The change in RJ from 295 to 4.2 K was less than 15%. The JMR values obtained were 20.2 and 27.3%, at 295 and 1 K, respectively (Moodera et al., 1998). Assuming the polarization values for Co and Ni80Fe20 are 35 and 45%, respectively (as measured by the SPT technique with an Al superconductor described in

172 J.S. Moodera and R.H. Meservey

Fig. 3.16 Resistance vs applied magnetic field for a Co/Al2O3/Ni80Fe20 junction at room temperature and 77 K showing JMR values of 20.2 and 27.1%, respectively. Arrows indicate the magnetization orientation of the two FMs according to Julliere’s model.

Section 3.2), Julliere’s model [Eq. (3.2)] predicts a JMR of 27.2% in very good agreement with the values measured at low temperatures. The ratio of the junction resistance, RJ ; to the lead resistance over the junction area, RL ; is important in arriving at a value for JMR in magnetic tunnel junctions. When RJ is many times greater than the resistance of the lead ðRL Þ over the junction area, a four-terminal measurement gives the correct value of JMR. However, when RJ becomes comparable to RL in a cross-geometry structure, the measured RJ is lower than the real value due to nonuniform current flow in the junction area. As a result of this, the apparent junction resistance is incorrect and the JMR is inflated to large and spurious values, as high as 1000% (Moodera et al., 1998). Using a proper correction the actual JMR falls to values that are consistent with those obtained for junctions with a high value of RJ =RL : Accurate correction should be possible if this ratio is at least 4. Producing junctions with high, stable values of JMR depends critically on the quality of the tunnel barrier. A good insulating barrier shows little temperature dependence and is stable against thermal cycling to cryogenic temperatures and bias voltage cycling, as well as with time. It has an I – V characteristic similar to that of a standard tunnel junction (such as Al/Al2O3/Al, with Al in the normal state): ohmic at low bias voltage and the conductivity increases approximately as V 2 at higher bias. One unique feature of FM/I/FM structures is that any tunnel junction with at least one ferromagnetic electrode always seems to have a ‘zero bias anomaly’ at low temperature (discussed in Section 3.4.3 below). The optimum Al film thickness needed for the barrier has been extensively studied. In general, the Al thickness ranges from about 0.7 to 1.8 nm to achieve uniform coverage, depending on the type of FM electrodes. When the Al film is too thin, the FM surface is oxidized. This changes the characteristics of the ferromagnetic surface and of the barrier and may give rise to spin scattering, especially at room temperature. On the other hand, when the Al film is too thick, excess un-oxidized Al metal can be left behind to act as a nonmagnetic metal at the interface, thereby

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reducing the spin polarization of tunneling electrons and hence reducing the JMR. Recently, the desire to fabricate low resistance junctions for applications has driven a need to use thinner Al films, along with the use of ‘softer’ oxidation techniques like natural oxidation. It is customary to evaluate the barrier parameters using the tunneling theory equations of either Simmons (1963) or Brinkman et al. (1970), where expressions relate the tunnel current density ðJÞ to the applied dc bias ðVÞ; the barrier height (F) and the thickness ðdÞ: When referring to these original articles for details, the reader should note that the tunneling current depends not only on the barrier properties, but also on the density of states (DOS) of the electrodes and on possible inelastic tunneling processes, which are not explicitly considered in these tunneling theories. Hence, the value of F and d obtained by fitting the I – V data to these expressions are ‘effective’ values. With FM electrodes such as Ni80Fe20, Ni, or any of the half-metallic FMs, band structure features surely affect the tunneling properties. However, a complete and adequate theory does not yet exist. The creation of excitations such as magnons and phonons will change the shape of the I – V curve from ideal behavior. The presence of localized states (due to nonstoichiometry, impurity atoms or defects), of ‘pinholes’ in the barriers, or of an additional magnetic oxide barrier creates additional conductance channels. The tunnel conductance is then a sum of all the conductances of all available channels. Fitting the I – V data in such junctions can, at best, give resultant effective barrier parameters which differ from the intrinsic behavior of a clean barrier insulator. For example, RBS data (Sun et al., 1998) and XPS studies (Mitsuzuka et al., 1999) of the Al2O3 barrier material seem to indicate effects of nonstoichiometry in the barrier composition.

3.4.3

Bias voltage dependence

Metal/insulator/metal tunnel junctions are nonlinear elements whose I – V curve can be approximated by I ¼ aV þ bV 3 ; with the dynamic conductance ðG ¼ dI=dVÞ varying quadratically as a function of dc bias at voltages well below the barrier height (Simmons, 1963). However, for a junction having an FM electrode, the functional variation of G with V deviates from that of a ‘standard’ junction, such as Al/Al2O3/Al, in a number of important ways. In Fig. 3.17 the dynamic conductance variation with V; for a Co/Al 2 O 3/Ni 80 Fe 20 junction, shows an asymmetry, a common feature for junctions with dissimilar metal electrodes (Brinkman et al., 1970). This feature is associated with the metal from which the electrons are tunneling (the negative electrode) and is prominent with Ni and Ni alloy electrodes. Figure 3.18 shows dG=dV ¼ d2 I=dV 2 as a function of V for the same junction used in Fig. 3.17 and demonstrates the inelastic tunneling (IET) spectra measured in zero magnetic field, at several temperatures (Shang et al., 1998). The peak at , 110 mV in the IET spectra for the Al/Al2O3/Al junction (inset of Fig. 3.18) is a common feature for Al2O3 (or aluminum nitride, AlN) barriers and is caused by an Al–O (Al–N) bond-stretching mode. For magnetic junctions,

174 J.S. Moodera and R.H. Meservey

Fig. 3.17 Dynamic conductance G as a function of dc bias for parallel and antiparallel orientation of magnetizations, for a Co/Al2O3/Ni80Fe20 junction. Top: T ¼ 295 K. Bottom: T ¼ 1 K.

Fig. 3.18 Inelastic tunneling spectra (IETS) at three temperatures for the same junction measured in Fig. 3.17, measured at H ¼ 0: Similar spectra are seen for junctions where one electrode is an FM and the other electrode is Al. The inset shows an IETS spectrum of an Al/Al2O3/Al reference junction for comparison. Note that the sharp features (between 0 and ^ 200 mV) for all Al junctions were only seen at liquid He temperatures.

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175

the broad peak around 100 mV (present at room temperature also) and the sharp peak at 17 mV have been attributed to magnons generated in FM electrodes (Tsui et al., 1971). Near zero bias, the sharp decrease in conductance with decreasing T is usually seen in tunnel junctions when one of the electrodes is a transition metal and is called a resistance anomaly. This kind of zero bias anomaly is different from those described by the Appelbaum–Anderson model (Appelbaum, 1966; Anderson, 1966) which usually are conductance peaks that extend over a relatively small voltage range, are sensitive to magnetic fields and are associated with magnetic impurities in the barrier. The large zero bias resistance anomalies seen in FM/I/FM tunneling have a considerably larger voltage range and are comparatively insensitive to magnet fields. These features have been attributed to a decrease in the conduction electron density of states caused by charging effects (Giaever and Zeller, 1969), by localization effects (Altshuler et al., 1980; Bergmann, 1983) or by Kondo scattering (Kondo, 1964). The effective density of states of the conduction electrons is presumed to decrease because of an interaction with the more localized d states. Such resistance anomalies always seem to be present in tunnel junctions when at least one electrode is a 3d ferromagnetic metal and the other electrode is either a ferromagnet or a normal metal. When one electrode is a superconductor the conductance is zero for voltage less than the superconducting energy gap, and there is no effect of the anomaly near V ¼ 0: A complete theory of the Kondo scattering mechanism has been presented (Mezei and Zawadowski, 1971). Experiments and further references to the literature of the Kondo effect have been published (Bermon and So, 1978). The JMR of all FM junctions is observed to decrease with increasing values of applied voltage at all temperatures, irrespective of junction quality (Moodera et al., 1995; Lu et al., 1998; Beech et al., 1996; Zhang et al., 1997a). The bias voltage dependence of JMR of the junction used in Fig. 3.17 at 295, 77 and 1 K is shown in Fig. 3.19. The JMR decreases monotonically as lVl increases; the values of JMR normalized to their value at T ¼ 0 show clearly the temperature independence of the JMR bias variation. The magnitude of the decrease depends not only on the quality of the interfaces and barrier type, but also on the material of the FM electrode. In the best junctions the JMR decreases to about half its value at a bias of about 0.5 V or higher (Yu et al., 2003). However, junctions having nonideal interfaces or having transition metal oxide barriers such as NiO show a much larger dependence on the bias. Moreover, it has been observed that junctions with FM electrodes composed of Ni or Ni80Fe20 show a larger decrease in JMR than for junctions with electrodes composed of Co or CoFe.1 Measurements of the voltage dependence of JMR (Lu et al., 1998) have extended these results to other materials and have further studied the effect of barrier quality. There are many studies which show the characteristic decrease of JMR with increasing bias, and no studies have failed to show it. Various explanations have been offered for this universal dependence on bias voltage. Research suggested (Moodera and Kinder, 1996) that this bias dependence was intrinsic and 1

Observed in the authors’ lab, unpublished.

176 J.S. Moodera and R.H. Meservey

Fig. 3.19 JMR vs dc bias at three temperatures for the same junction measured in Fig. 3.17. Data shown are (a) the actual percentages and (b) percentages normalized at zero bias. The inset shows the JMR in the low bias region, displaying near constancy of JMR. The dashed line in (b) is the theoretically expected variation for an Fe– Al2O3 –Fe junction with a 3 eV barrier height.

possible causes were proposed: the creation of magnons, variation of the density of states in the ferromagnet with applied voltage, and decrease in the tunnel barrier height with voltage. Davis and MacLaren have proposed a variation of the free electron model (Slonczewski, 1989) in which relative changes in the densities of states and effective masses of majority and minority spin tunneling electrons are assumed to vary as a function of bias voltage (Davis and MacLaren, 2000). Such a model requires a detailed fit to the known band structure of the ferromagnetic metal electrodes. Theoretically, it has been shown (Zhang and White, 1998; Vedayev et al., 2001; Jansen and Moodera, 1998) that parallel conductance paths that do not conserve spin and tunnel through defect or impurity states in the barrier lead to a decrease in JMR. In a further study (Jansen and Moodera, 2000), the presence of Si impurities in an Al2O3 barrier was shown to lead to a modest decrease of JMR with increasing bias voltage, whereas Ni impurities in the barrier led to a large decrease of JMR with bias, presumably from spin scattering. Although impurities and defect states in the barrier can increase the bias dependence, these effects alone cannot provide a complete explanation. There is no indication at present that perfect insulators or vacuum barriers can eliminate the bias dependence effect. Experimentally, the decrease in JMR with increasing bias voltage has been attributed to the excitation of magnons (Moodera et al., 1998). This mechanism has theoretical support

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177

(Zhang et al., 1997a; Bratkovsky, 1997). The model of Zhang et al. assumes that additional electron tunneling channels are opened up by the creation of surface magnons, implying that the initial decrease of JMR with voltage will be linear, as is observed. This explanation is also appealing because the temperature dependence of the JMR seems to be explained convincingly by the excitation of surface magnons (Shang et al., 1998). Another explanation of the decrease of JMR with applied voltage suggested by Hong, Wu and Mills (2002) is based on the modification of the quasiparticle density of states by the self-energy of magnon emission and absorption. The observed asymmetry with voltage is explained by different magnon self-energies in different ferromagnets, but the curvature of the predicted decrease of JMR with voltage differs from the measurements. It appears that none of the possible causes of the bias voltage dependence of the JMR has been definitely proved or disproved.

3.4.4

Exchange biasing of tunnel junctions

The position of the MR peaks as a function of magnetic field is determined by the coercive fields of the FM electrodes. The coercive field, HC ; of the FM film is easily influenced by the film growth conditions. In order to obtain a good antiparallel alignment of the magnetization orientations M1 and M2 of electrodes F1 and F2, it may be necessary to exchange bias one of the FM films, using techniques similar to spin valve structure. One of the first reports of such a technique was the use of an FeMn layer (Sato et al., 1998) in Ni80Fe20/Co/Al2O3/Co/Ni80Fe20/FeMn junctions to exchange bias the top FM film, and JMR value of 24% was obtained (see Fig. 3.20). Subsequently, several other groups have reported realization of an effective spin valve structure in magnetic tunnel junctions using various materials such as PtMn, TbCo, and MnRh. These results are essentially an extension of the technique used in GMR studies of magnetic multilayers (see also Chapter 2).

Fig. 3.20 Resistance as a function of applied field for a Ni80Fe20/Co/Al2O3/Co/Ni80Fe20/Fe– Mn exchange biased junction after annealing at 3008C for 1 h. The magnetic electrode which is in contact with antiferromagnetic Fe– Mn alloy, is exchange biased has a higher coercivity. The counter magnetic electrode, which is magnetically softer, switches at lower applied field (see inset) (after Sato, 1998).

178 J.S. Moodera and R.H. Meservey 3.4.5

Temperature effects

3.4.5.1

Temperature dependence of magnetoresistance of magnetic tunnel junctions

The tunnel current of an M/I/M structure is not expected to show much temperature dependence. For example, in Al/Al2O3/Al junctions (with Al in the normal state) only a change of a few percent in the junction resistance is commonly observed as the temperature is reduced from 300 to 4.2 K. This is because neither the density of states in the metal nor the tunneling probability has significant temperature dependence between room temperature and 4.2 K. Tunneling theories predict a few percent change because of the temperature dependence of the Fermi function in metals. However, in junctions with either semiconducting electrodes or semiconducting barriers (as also seen previously with magnetic semiconductors) significant temperature dependence of the tunnel current can be expected and is observed. The same is true with magnetic tunnel junctions. A large temperature variation of both JMR and RJ is observed even in the highest quality MTJs, significantly more than the expectation based on the temperature dependence of the Fermi function and the magnetization. For transition metals and alloys, the bulk saturation magnetization increases by a few percent between 300 and 4.2 K, with a change of less than 1% below 77 K. However, values of RJ and JMR of Co/Al2O3/NiFe junctions, for example, increased by about 20 –30% as the temperature was reduced from 295 to 44 K, with negligible change from 77 to 1 K. Such an increase is common with good MTJs, suggesting that its origin is intrinsic. The temperature dependence of MTJs has been attributed to two causes: (i) the temperature dependence of surface/interface magnetization; and (ii) the presence of temperature-dependent spin scattering at the FM/I interfaces or in the barrier. Regarding the first mechanism, tunneling is extremely sensitive to the surface layer of the electrode and the interface with the insulator. The variation with temperature of the surface magnetization Ms ðTÞ is expressed by the well-known Bloch T 3=2 law, Msurface ðTÞ ¼ Msurface ð0Þ½1 2 aT 3=2 ; which describes the thermal spin wave excitation for T p TC : Here a is greater than 1 and is usually on the order of 2.5 or higher (Pierce et al., 1982). This gives a faster decrease of Msurface compared to Mbulk (a ¼ 1 in bulk) and a proportional decrease of the tunneling electron spin polarization. In phenomenological models (Shang et al., 1998; Jansen and Moodera, 1998), the observed tunnel conductance is assumed to be comprised of two parts: (A) direct elastic tunneling GT where spin is conserved, and (B) an inelastic tunnel conductance through electron states in the barrier, which is taken to be an unpolarized and independent of the relative orientation of the electrode magnetizations. Thus, the presence of this inelastic conductance channel in parallel with GT will reduce the JMR below its maximum possible value. The magnetoconductance DG ¼ Gðu ¼ 08Þ 2 Gðu ¼ 1808Þ; where u is the angle between the two magnetization vectors, is proportional to the product of the polarization of the two electrodes, DG / P1 P2 : Therefore, the temperature dependence of DG directly reflects the

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179

Fig. 3.21 Temperature dependence of the normalized DG for two representative ferromagnetic junctions. The solid lines are the fits to a theory based on thermal spin-wave excitations.

temperature dependence of the polarizations. A plot of DG vs T for two MTJs is shown in Fig. 3.21. The experimental data (symbols) are compared with the Bloch T 3=2 law for thermal spin-wave excitation for T p TC ; PðTÞ ¼ Po ð1 2 aT 3=2 Þ: The agreement is quite good, with Po and a taken from the measured values for Co and Ni80Fe20, supporting the validity of the above mechanism. Here a is a parameter that is extremely sensitive to the surface/interface and can take different values depending on the junction interface quality. Higher contamination at the interface can lead to a higher value of a and thereby causes a considerable decrease of P as the temperature increases. Bratkovsky (1997) has proposed a model wherein the roles of magnons, phonons, and inelastic tunneling processes are considered in order to explain the temperature dependence of the properties of MTJs. This model gives good fits to the data. In the theory by Zhang et al. (1997a) the temperature and bias dependence of JMR and RJ is mainly attributed to the emission or absorption of spin waves by tunneling electrons. Here, the spin-wave-assisted tunneling is an inelastic, higher order process with an associated tunneling matrix element that is smaller than that for direct elastic tunneling. Using an itinerant electron ferromagnet picture, MacDonald et al. (1998) considered the transfer of spectral weight at finite temperatures from a majority (or minority) spin quasi-particle peak to a shadow band peak located near the opposite spin quasi-particle energy. They also point out that the fraction of the spectral weight transferred is proportional to the suppression of the saturation moment at low temperatures. Assuming a phenomenological tunneling Hamiltonian for the MTJ they derive the tunnel conductance and JMR at finite T; allowing the temperaturedependent polarization to vary in proportion to the temperature dependence of the saturation magnetic moment. Their prediction is JMRðTÞ ¼ JMRðT ¼ 0Þð1 2 AT 3=2 þ · · ·Þ:

ð3:4Þ

180 J.S. Moodera and R.H. Meservey Here A is the product of {1 2 ½JMRðT ¼ 0Þ=2} with the sum of the T 3=2 coefficients for the relative magnetizations of the two ferromagnetic electrodes. The shadow band model of MacDonald et al. predicts a temperature dependence similar to that of the phenomenological approach taken by Shang et al. to explain the experimental temperature dependence of JMR, described previously. 3.4.5.2

Temperature stability and annealing effects

Tunnel junctions, despite being delicate and sensitive, have shown good structural stability during thermal treatment. An ideal tri-layer junction structure may deteriorate when heated because of the breakdown of the thin insulating barrier or diffusion of the electrode material into the barrier. On the other hand, when MTJs are annealed at temperatures less than about 600 K, they often show improvement in their JMR value and a slight increase in the junction resistance (Sun et al., 1998; Sousa et al., 1998). This increase has been attributed to improvement in the quality of the interfaces, and it is especially true in sputtered tunnel junctions that have high values of intermixing at the interfaces when unannealed. In other words, the FM/I interface becomes sharper because metal ions diffuse out of the insulating layer and into the adjoining FM electrode. In addition to this effect, defects such as oxygen vacancies in Al2O3, are annealed out because oxygen at the interfaces diffuses into the barrier to fill up these sites. Finally, the magnetic properties of the FM electrodes improve, making the coercive fields become sharper. As a result, the parallel and antiparallel magnetization states of the junction are better defined. Apart from annealing effects, MTJs show only a slow decrease of JMR values as the temperature increases above 300 K, retaining double-digit values even at 650 K (Cardoso et al., 2000; Schmalhorst et al., 2002). Furthermore, there is improvement in the bias dependence of MTJs up to this temperature. Above temperatures of about 700 K the degradation of the structure accelerates because of irreversible changes associated with diffusion of various layers into the barrier. These effects are more significant when the layers are rough (Cardoso et al., 2001). Another important effect is that the barrier insulator can begin to break down at higher temperatures (Schmalhorst et al., 2002). In some instances, additional barrier layers to block mass diffusion have been added to the structure to reduce this detrimental effect. As can be expected, the temperature stability of MTJs depends on the barrier thickness. Barriers that are only 2 –3 monolayers thick, which are used to obtain low resistance junctions for sensor applications, show relatively poorer thermal stability and lower breakdown voltage compared to thicker barriers (Cardoso et al., 2001; Parkin et al., 1999). This lack of stability has been attributed to oxidation of the bottom FM electrode in local regions of uneven barrier coverage of the FM surface. 3.4.6

Barrier dopant effects

Tunneling in MTJs provides a powerful opportunity to investigate a range of phenomena because electron spin is involved, in addition to electron charge. In other words, one can sensitively study

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the interaction of electron spin with matter, especially on an atomic scale. This can be accomplished, for example, by embedding sub-nanometer particles in the tunnel barrier, a field of study which has been barely explored. In principle, this should enable the study of exchange interactions between atoms or ions in an extremely low concentration regime, where other techniques are inadequate. The influence of barrier impurity atoms on spin tunneling in ferromagnetic junctions has been investigated by measuring the TMR. For that purpose, Co/Al2O3/Ni80Fe20 junctions were prepared with sub-monolayer amounts of Co, Ni, Pd, Cu or Si incorporated into the middle of the insulating oxide (Jansen and Moodera, 1998). The total tunnel conductance G of a doped barrier can be expressed as G ¼ Gt þ Gas þ Gex ; showing separate contributions to the tunnel current from direct, spin conserved; impurity assisted; and spin-exchange scattering, respectively. In the absence of spin flips, the tunnel conductances can be written as Gt ¼ G0 ð1 þ P1 P2 cos uÞ=2;

ð3:5Þ

where P1 and P2 are the spin polarizations of conduction electrons in electrodes 1 and 2, G0 is the total conductance in the absence of spin polarization and u represents the angle between the two magnetizations. Following Julliere’s definition and Appelbaum’s approach, the expression for JMR for the case of impurity-assisted tunneling is " 0

JMRas ¼ JMR

1 1 þ Ras ð1 2

# 1 2

JMR0 Þ

;

ð3:6Þ

and for the case of spin-exchange scattering it is, " 0

JMRex ¼ JMR

# 1 þ aRex ; 1 þ Rex ð1 2 12 ð1 2 aÞJMR0 Þ

ð3:7Þ

where JMR0 is the magnetoresistance for direct tunneling, a is the fraction of the conductance with asðexÞ spin flip in comparison to with no spin flip, and RasðexÞ ¼ G0 =G0 : During a tunneling event when a spin-flip event occurs in the barrier, the carrier is required to enter a spin-down empty state in electrode 2 and there is the associated possibility of exhibiting an inverse magnetoresistance. To a first approximation, the JMR is thus expected to go down linearly with decreasing values of the fraction a: Note that scattering at the Fermi energy is important here, since tunneling electrons originate from states in a narrow energy interval around EF : These issues have been discussed theoretically by several groups (Jansen and Lodder, 2000; Vedyayev et al., 2001; Inoue et al., 2002). As mentioned above, the dopants Ni, Co, Pd, Au, and Cu were introduced into the barrier at the sub-monolayer level. A significant reduction of JMR with increasing dopant content was observed, in almost all cases, as shown in Fig. 3.22. It is interesting to note that Co impurities show weaker JMR suppression than Cu impurities even though bulk Co is

182 J.S. Moodera and R.H. Meservey

Fig. 3.22 Normalized JMR vs thickness t of the layer of impurities present in the tunnel barrier. Data, measured at 77 K, are shown for Co (filled circles), Pd (open squares), Cu (open circles), and Ni (filled squares), together with a linear fit (solid lines).

ferromagnetic and Cu is nonmagnetic. Impurity suppression of JMR is strongly dependent on the spin state of the impurity ion. The weak influence of Co can be explained by the dominant presence of Co in a trivalent oxidation state which has no magnetic moment, whereas Ni and Cu ions were present in an oxidation state that has a magnetic moment. Thus, the data show that incorporation of a sub-monolayer level of dopants in the barrier of FM –I–FM junctions leads to severe reduction of the JMR as a result of spin scattering. The distinctly different effects of spin-exchange scattering and impurity-assisted tunneling on JMR can be seen by using dopants with well-defined magnetic or nonmagnetic ions. The strong presence of inelastic tunneling due to spin-exchange scattering was demonstrated in samples having Ni ion dopants by observation of significant temperature and bias dependence of the JMR and RJ values. The impurity-assisted tunneling that occurred in samples having nonmagnetic Si ions mainly gave rise to an elastic contribution, increasing the unpolarized conductance and reducing JMR slightly. The dependence of JMR on dopant thickness for Si and Ni dopants is shown in Fig. 3.23.

3.4.7

Half-metallic ferromagnets

The class of Heusler alloy compounds, NiMnSb and PtMnSb, and other compounds such as CrO2 and Fe3O4 are known as half-metallic ferromagnets (HMF) because they are the predicted to have an energy gap in the minority spin band at EF (de Groot et al., 1983; Schwarz, 1986; Pickett and Singh, 1996). There is high interest in these compounds because of fundamental physics issues as well as their potential for applications. However, most of these compounds are difficult to prepare, and it is even more difficult to maintain a good surface or interface with the barrier. In order for an HMF to be useful in spin-tunneling studies, the half-metallicity has to be maintained even at the last layer, contiguous with the interface. This has turned out to be rather challenging, as reported by several studies in the literature (Park et al., 1998a; Ristoiu et al., 2000). MTJs of the kind NiMnSb/ Al2O3/Ni80Fe20 have been partially successful in showing a JMR effect (Tanaka et al., 1999).

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Fig. 3.23 Normalized JMR (at 77 K) for Co/d-doped Al2O3/Ni80Fe20 tunnel junctions, as a function of thickness t for Si (filled squares) and Ni (open circles) dopants. Solid lines are fits based on Eqs (3.6) and (3.7) for Si and Ni, respectively.

The expected JMR value of such a junction is expected to be 62% for a fully polarized NiMnSb. However, these junction electrodes were prepared with epitaxial NiMnSb films and showed a JMR of only 20% at T ¼ 4 K; as shown in Fig. 3.24. The low JMR value that was observed can be explained as a result of a nonideal surface of NiMnSb, including effects such as surface reconstruction, defects (such as vacancies or compositional/chemical/structural disorder), or simple interface bonding (Orgassa et al., 1999; de Wijs and de Groot, 2001). One interesting outcome of this investigation was the observation of steps in RJ vs H plots resulting from the fourfold magnetocrystalline anisotropy in the NiMnSb epitaxial film (refer to Fig. 3.24). An MTJ of this kind, with four states rather than the usual two, would offer novel possibilities for programmable logic functions and nonvolatile memory (refer also to Chapter 5).

Fig. 3.24 Four-state magnetic tunnel junction NiMnSb/Al2O3/Ni80Fe20 junction. The NiFe magnetization is pinned 228 from the [100] axis. Each state reflects one of the four in-plane easy axes of the NiMnSb. The tunnel barrier is Al2O3 formed on an epitaxial NiMnSb film.

184 J.S. Moodera and R.H. Meservey Lu et al. (1996) and Viret et al. (1997) have observed extremely high values of low-field TMR, reaching 450% (that is, JMR ¼ 82%) at low temperature and low fields in LSMO/I/LSMO ˚ junctions (refer to Section 3.4.1 for the definition of JMR and TMR). The barriers were 30 –50 A thick layers of SrTiO3 (STO), PrBaCu2.8Ga0.2O7 (PBCGO) or CeO2. Using the value of spin polarization P ¼ 72% for LSMO, as measured by Worledge and Geballe (2000a), the Jullie`re model would predict a value of JMR ¼ 68%. The higher observed JMR value of 82% has been attributed to a higher polarization in LSMO, P . 72%: However, the temperature and voltage dependence of resistance and magnetoresistance of manganite-based junctions differs greatly from that of conventional transition-metal based tunnel junctions, indicating a more complex conduction mechanism than direct tunneling through the barrier (Sun et al., 1997; Viret et al., 1997; Park et al., 1998b). The large, negative TMR reported in an epitaxial Fe3O4 junction, shown in Fig. 3.25, is consistent with the predicted negative spin polarization in this half-metallic material, but is much smaller than the expected result of 2 100% (Hu and Suzuki, 2002). Despite extensive efforts to observe 100% polarization of tunneling electrons at room temperature in any of these half-metallic ferromagnets, it has not been achieved. To date, demonstrations of large values of JMR have only been at low temperatures. The interface and barrier quality play important roles, especially in these exotic compounds. Some examples of important effects are: a reduced ordering temperature of the surface magnetization, interface disorder, and the shunting of tunnel conductance by hopping processes. For MTJs with half-metals on both sides of the barrier and with ideal interfaces, the JMR effect would be 100% with the tunneling current either on or off. Even with a JMR value less than 100%, half-metal electrodes would still provide a much greater signal to noise ratio than with transition metal ferromagnets, making it possible to build devices that operate at lower voltages and higher speeds. However, even if the chemical integrity of the compound can be maintained at the surface, either surface reconstruction or chemical bonding with the barrier can be expected to strongly influence the half metallicity of the compound. Nevertheless, it should be possible to find a

Fig. 3.25 (a) Magnetization vs magnetic field hysteresis loop from an unpatterned Fe3O4/CCO/LSMO trilayer structure at 80 K, with magnetic field applied along the in-plane [001] direction. (b) Magnetoresistance vs magnetic field at 80 K for a junction of area 20 mm £ 20 mm.

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proper match of the materials to reach the goal of a totally spin-polarized tunnel current using half metals. 3.4.8

Observation of resonant effects in MTJs

In special situations, interesting quantum effects can be observed in MTJs. There have been several theoretical predictions of TMR oscillating as a function of nonmagnetic (NM) metal thickness in FM –NM–I– NM–FM junctions (Vedyaev et al., 1998; Mathon and Umerski, 1999). These calculations show that the interface layer behaves as a quantum well, leading to the formation of quantum well states (QWS) when resonance conditions are fulfilled. The occurrence of QWS at the Fermi energy is expected to enhance the TMR (Mathon and Umerski, 1999). In the case of an asymmetric structure, such as FM–NM –I–FM, the sign of the TMR is predicted to oscillate as the NM thickness increases, with the amplitude diminishing for sufficiently large thickness (Ortega et al., 1993). For example, calculation for Co/Cu/vacuum/Co junctions showed TMR oscillations should occur because the Cu conduction band matches well with the majority-spin sub-band of Co. The matching was poor for the minority-spin electrons, resulting in down-spin QWS in the Cu layer (Ortega et al., 1993). Such effects are observable when the QWS in one of the spin channels is long lived and the interlayer is atomically smooth. Scattering from impurities or diffuse scattering at the FM/NM interface can allow the QWS to evolve into propagating states. Spin asymmetry in the NM interlayer is then destroyed, leading to the decay of TMR. It should be noted that there are many studies of QWS, using giant magnetoresistance in magnetic multilayers (Parkin, 1991; Bruno and Chappert, 1991). Experiments have shown TMR oscillations, including the change of sign, in Co/Au/ Al2O3/NiFe junctions as shown in Fig. 3.26. These data show signs of QWS signature, although ˚ of Au (Moodera et al., the TMR decreased to low values at small thicknesses of about 4– 5 A ˚ 1999b). Up to a Au thickness of 5 A the TMR was positive, whereas it became negative for thicker ˚ no TMR was seen. In the range of Au thickness up to 8 A ˚, Au films. For Au thicknesses above 8 A the bias dependence showed similar sign changes, with TMR oscillating from positive to negative values as a function of bias. In an excellent study by Yuasa, Nagahama and Suzuki, clear ˚ of Cu. Having perfect epitaxial oscillations were seen in Co/Cu/Al2O3/NiFe junctions up to 29 A growth of Cu on Co led to smooth layers and contributed to dramatic effects (Yuasa et al., 2002) (see Figs 3.27 and 3.28). These results, along with the bias voltage dependence, matched very well with a model based on the Cu band structure (Bruno and Chappert, 1991).

3.5

Tunneling and the role of the interface

In the field of SPT, one of the most frequently asked questions is the sensing depth of the tunneling electrons. A few years after the first experiments, it was realized that SPT had extreme sensitivity in studying the thickness dependence of ferromagnetism in thin films.

186 J.S. Moodera and R.H. Meservey

Fig. 3.26 (a) The JMR at zero bias voltage and 77 K of a control junction and of junctions with 0.3, 0.6, and 0.7 nm thick Au interface layers. The curves are offset for clarity. The curves for 0.6 and 0.7 nm thickness are magnified 20 £ . (b, c) Dependence of the JMR on bias voltage for increasing thicknesses of the Au interface layer at T ¼ 77 K for (b) tNM # 0:3 nm and (c) tNM $ 0:4 nm.

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Fig. 3.27 (a) Schematic cross-section diagram of the magnetic tunnel junction (MTJ) with FM – NM– I –FM structure, in which electrons with different spin directions tunnel from the upper to the bottom electrodes. FM, NM, and I denote a ferromagnetic electrode, a nonmagnetic layer, and an insulating layer (tunnel barrier), respectively. The MTJs were prepared to have a Co(001) –Cu(001) – Al– O– Ni– Fe structure. (b) Fermi surface of face-centered cubic Cu. When conduction electrons are confined in the [001]-direction, quantumwell states with scattering vectors q1 and q2 can be created. ( For a colored version of this figure, see Plate 3.27, page 378.)

In a series of experiments that used ultrathin films of transition metals Fe, Ni and Co, the onset of magnetism in monolayer films was investigated, as well as interface sensitivity to tunneling (Tedrow and Meservey, 1975; Meservey et al., 1980b, 1981). In addition, the phenomenon of the magnetic proximity effect showed the importance of the hybridization of the electron states in

Fig. 3.28 Normalized TMR curves at T ¼ 2 K at a bias voltage of þ 10 mV for Co(001) –Cu(001) – Al– O ˚ and (b) 4.5 A ˚ . Rp denotes the ˚ ) –Ni80Fe20 junctions with Cu layer thickness ðtCu Þ of (a) 0 A (18 A tunnel resistance with parallel magnetization configuration. (c) TMR ratio at T ¼ 2 and 300 K at a bias voltage of þ 10 mV as a function of tCu : ( For a colored version of this figure, see Plate 3.28, page 378.)

188 J.S. Moodera and R.H. Meservey ultrathin magnetic films with states in the adjacent backing metal in dictating the magnetism at those few monolayers. The onset of spin polarization P; and of ferromagnetism as film thickness is increased is shown in Fig. 3.29 (Meservey et al., 1980b). The bulk values of polarization in both Fe and Co samples are reached by the time two monolayers of film are formed. The slow increase in P as a function of increasing film thickness is due to the incomplete coverage of the surface by the magnetic film at very small thickness. This results in direct tunneling current of unpolarized electrons from the nonmagnetic backing metal. The onset of P is significantly different for Ni (Fig. 3.30), perhaps because of band interactions between the metals. Since the bulk value of P is reached at 10 monolayers of Ni, the slow onset may be due to sp –d hybridization, mentioned above, or there may be intermixing during deposition. When a Ni film was backed with Au, the polarization approached the bulk value by about one or two monolayers of coverage, similar to Fe and Co. Further evidence of the interface sensitivity of SPT is provided by the sharp reduction of the polarized tunnel current upon introducing a monolayer of Au in between Fe and an Al2O3 barrier, shown in Fig. 3.31. It is interesting that a finite, although very small, polarization was detected when the Au film was ˚ thick. This has been attributed to spin accumulation in the Au (Moodera et al., 1989). 50 –100 A What is most important in the above experimental results is the sensitivity of the tunneling current to the interface layer, and the demonstration that the density of states on this last one or two monolayers adjacent to the tunnel barrier influences the tunneling electron characteristics. Appelbaum and Brinkman (1970) state: ‘…the fact is that as the effective range of the many-body interactions are typically a few Fermi wavelengths in the metal, the spectral function at the M/I

Fig. 3.29 The onset and development of spin polarization P for Co and Fe films as a function of film thickness for films with thicknesses of a few monolayers.

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Fig. 3.30 Measured electron-spin polarization P for Ni films of various thicknesses in contact with Al, Au, Mn, and Cr.

interface is greatly influenced by the boundary effects. Thus the tunneling in M/I/M junctions should be sensitive to the density of states of the electrodes within a few Fermi wavelengths ð< 3:5kF21 Þ of the interface.’. In the case of M/I/M or FM/I/FM tunneling, the density of states of the electrode material that is very close (within one to two monolayers) to the insulating barrier

Fig. 3.31 Measured polarization P vs average thickness d of a Au layer covering Fe for an Al/Al2O3/Au/Fe junction with Al superconductor. Solid line is P; calculated from the proposed model. The other lines are explained in the text.

190 J.S. Moodera and R.H. Meservey dominates the properties. The hybridization of the electrode wave function with that of the insulating layer may greatly influence the interfacial DOS, and the tunneling properties can be strongly dictated by this. In the case of superconductor junctions, the sensing length scale is on the order of superconducting coherence length, which can be several to many hundreds of nanometers. Because of these long dimensions, the sensing length scale is comparable with bulk for SC/I/SC tunneling, and is essentially unaffected by the interfacial modifications. The deterioration of spin polarization with interface modification is also proven in studies with MTJs (Moodera et al., 2000). Inserting an ultrathin layer of nonmagnetic metal such as Al, Au, Cu, Pt or Pd at the FM/I interface of Co/Al2O3/NiFe junctions causes the TMR to be dramatically reduced, irrespective of the metal. This is shown in Fig. 3.32. In all cases the TMR reached negligible values when just a few monolayers of the metal were inserted at the interface. All these studies clearly show the interfacial sensitivity for spin-dependent tunneling, as well as the sensing depth for the tunneling electrons. The spin information comes mostly from the last one or two monolayers of atoms near the interface. Such extreme surface localization might be modified in completely coherent tunneling with conservation of lateral momentum. In recent experimental work using well-characterized MTJs (LeClair et al., 2001b), the role of interfaces and the corresponding densities of states in spin tunneling has convincingly been shown (LeClair et al., 2001). The authors introduced a layer M (M ¼ Cu, Cr, Ru) at the interface of Co/M/Al2O3/Co junctions to show the importance of the interfacial density of states in spin

Fig. 3.32 Normalized JMR vs thickness t of the layer of different normal metal M impurities at the interface of Co/M/Al2O3/Ni80Fe20 junctions. Data, measured at room temperature, are shown for Ag (B), Au (A), Pt (X), and Cu (W) with lines to guide the eye. The inset shows spin transport through a normal metal: dependence of the JMR on the bias voltage for increasing thickness of the Au interface layer in a Co/Au/Al2O3 / NiFe tunnel junction at 77 K, for tNM $ 0:4 nm.

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Fig. 3.33 Normalized TMR as a function of Cr interlayer thickness for junctions dusted with only Cr, and Cr ˚ ), showing the near complete restoration of the original TMR. Lines are a guide to the eye. with Co (6.3, 10.0 A Inset: Co– Cr spin polarization deduced from the Julliere model (see text) as a function of Cr interlayer thickness for 10 K (triangles) and 295 K (circles). The line is a linear fit for 295 K.

tunneling. These metals were chosen because they strongly modify the interfacial density of states. The bias dependence of the tunnel conductance and TMR measurements were both used to show that the decay of TMR was related to the interfacial electronic structure. The TMR decay was ˚ , compared to Cu where the strongest for Cr and Ru, with a characteristic decay length of about 1 A ˚ decay length was about 2.6 A. This difference was attributed to stronger band mismatch of the majority d band in Co and Cr or Ru than the mismatch with Co and Cu, resulting in strong interband scattering from the Co s – p majority band to the d states of Cr. If an additional 2 –3 monolayers of Co was placed between Cr and Al2O3, the TMR was nearly restored to its original value, as shown in Fig. 3.33. These same junctions also showed zero bias anomalies in the conductance, which come about from the interfacial modification of the tunnel junctions. A two-band s – d model has been proposed to explain theoretically the strong interface sensitivity of the tunneling properties of MTJs (Bagrets et al., 2002). The authors’ aim was to investigate the influence of electron scattering at nonideal interfaces on the decrease of the TMR magnitude. They showed that the TMR can be substantially reduced, even down to zero value, due to interfacial inter-band scattering. This is related to the possibility that itinerant majority electrons can scatter into the strongly localized minority d sub-band, which has a larger density of states at the Fermi energy compared to majority spins.

3.6

Theoretical and experimental progress

Recently, there has been an enormous increase in the sophistication of the experimental preparation, analysis, and performance of magnetoresistance tunnel junctions, as well as theory.

192 J.S. Moodera and R.H. Meservey The free electron theories of Stearns (1977), Slonczewski (1989), and MacLaren et al. (1997) have been replaced by more realistic theories of the complex tunneling situation in FM/I/FM junctions. The effect of the interface between the ferromagnet and an insulating or semiconducting barrier has been considered by several groups. Calculations using a tight-binding technique (Tsymbal and Pettifor, 1997) made important predictions: when the lateral momentum is conserved, the polarization should depend strongly on covalent bonding between Co and the insulator that leads to a d-electron current and finally to a change in the sign of spin polarization. Studies of the atomic and electronic structure of Co/Al2O3/Co crystalline structures (Oleinik et al., 2000) showed that the metal– insulator interactions are important. These authors also applied their technique to an insulating barrier of SrTiO3 (Oleinik et al., 2001), suggesting that the bonding between Co and Ti, mediated by O, could change the sign of the polarization. Experimentally, a negative value of magnetoresistance has been reported (De Teresa et al., 1999) for a Co/SrTiO3/La0.7Sr0.3/MnO3 junction. Another measurement (Sharma et al., 1999) on functions using Ta2O3 as a barrier also showed negative magnetoresistance at some voltages. These results have not yet been reproduced. Crystalline materials have been analyzed (Butler et al., 1997; MacLaren et al., 1998), and crystalline systems with Fe electrodes and semiconductors Ge, GaAs, and ZnSe as barriers also have been analyzed (Butler et al., 2001). These material combinations may allow the epitaxial growth of MTJs. It has been suggested (Mavropoulos et al., 2000) that tunneling in epitaxial systems can be obtained from the complex band structure in the gap region using pseudo-potential techniques. The analysis assumes the ballistic regime, that is, the conservation of lateral momentum, and obtains surface densities of states peaks drastically different from those of the metal alone. In most cases, for sufficiently large film thicknesses, tunneling was found to be dominated by states with normal incidence on the interface. First-principles calculations of the tunneling magnetoconductance of epitaxial junctions have been based on the Kubo –Landauer formula together with realistic tight-binding bands fitted to an ab initio band structure of Fe and MgO. Calculations for Fe/MgO/Fe (Butler et al., 2001) matched wave functions across the barrier and obtained results showing that the tunneling depends strongly on the symmetry of the Bloch states in the metal and the evanescent states in the barrier. Different symmetry states decay at different rates, with quantum interference effects in the barrier. The largest values of TMR were predicted for thick barriers. The Fe/MgO/Fe system has been studied (Mathon and Umerski, 2001) using the Kubo formula with tight-binding bands. A value TMR ¼ 1200% was predicted, with the largest value again being for the largest MgO thickness. Note that JMR ¼ ðRa 2 Rp Þ=Ra ; which in this case equals 92%, may be a more intuitive measure of relative merit for these calculations. One result of these calculations is that for low barrier thicknesses, tunneling electrons with trajectories that are not perpendicular to the junction plane are important, but are less important at distances far from the interface. These authors point out the similarity between these calculations of Fe/MgO/Fe and those of Fe/ZnSe/Fe (MacLaren et al., 1999) even though the conductance is larger by a factor of 108 in the case of ZnSe compared with that of MgO because of the much smaller barrier height of ZnSe.

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A very interesting theory has been proposed (Mathon, 1997) that claims to apply for all distances of separation of ferromagnetic electrodes in a vacuum. This theory claims to describe giant magnetoresistance (GMR) in the limiting case with the metals in contact. It also claims to describe TMR in the limiting case of finite vacuum separation. It, too, is based on the Kubo – Landauer formula. When applied to Co(001) surfaces at low bias voltage, it predicts a negative polarization in the GMR region (metallic contact regime), but a positive value of polarization in the TMR region. These predictions approximate results measured with Co electrodes. Much of the theoretical analysis has used conservation of lateral momentum as an assumption. However, the experimental reality is that this conservation rarely exists. Kubo formalism and Green’s function methods have been used to analyze the effect of s –d scattering on TMR (Bagrets et al., 2002). These authors predict that quasi-free electrons can scatter into the localized d sub-bands, thereby reducing the TMR. An analysis of the TMR (Itoh et al., 2003) between Co electrodes, one of which has a layer of Cu, predicts oscillations of the TMR corresponding to those experimentally observed (Yuasa et al., 2002). Recently on the experimental side, there has been much research on Fe/MgO/Fe tunnel junctions. The ability to grow epitaxially Fe(001) on Mg(001) and vice versa had been shown by Urano and Kanaji (1998) and Vassent et al. (1996). An epitaxial Fe/MgO/Fe tunnel junction on an Fe(001) single crystal substrate showed a tunneling characteristic over much of its area (Wulfhekel et al., 2001). A TMR of 60% at 30 K was reported (Bowen et al., 2001) in an epitaxial Fe(001)/ MgO/FeCo(001) tunnel junction, much larger than the 13% reported (Yuasa et al., 2000) for an Fe(001)/amorphous-Al2O3/FeCo junction at 2 K. These authors also gave a value of TMR ¼ 42% for the 211 direction. The result of Bowen et al. was interpreted as a proof of the importance of the electronic structure of the entire electrode-barrier system in defining the spin polarization of tunneling electrons. However, this result is also expected from Jullie`re’s simple analysis, with the measured values PFe ¼ 45% and PFeCo ¼ 55% obtained by the superconducting technique (Moodera et al., 1999a). The TMRs of junctions with Fe electrodes that have a variety of different crystal directions have been measured (Yuasa et al., 2000) at 2 K and give values that range from 13% for Fe(100) to 42% for Fe(211). Fe/MgO/FeCo(100) junctions have been prepared (Mitani et al., 2003) using plasma oxidation and a value of TMR ¼ 23% was measured at 4.2 K. Recently, epitaxial Fe/ MgO/Fe junctions of high quality have been made (Faure-Vincent et al., 2003) and measurements gave a value TMR ¼ 100% (JMR ¼ 50%) at 80 K and 67% at room temperature. In fully epitaxial Fe(001)/MgO(001)/Fe(001) MTJs, Yuasa et al. observed a TMR of 88% at T ¼ 293 K (146% at T ¼ 20 K), the highest value yet reported (Yuasa et al., 2004). This value nearly equals the theoretical predictions for this system. One of the highest values of TMR that has been reported at room temperature (Wang et al., 2003; Lee et al., 2004) is TMR ¼ 72% (and 113% at 1 K) for CoFeB/Al2O3/CoFeB junctions made by DC magnetron sputtering, in which the CoFeB layers are amorphous. This value of TMR at 1 K corresponds to a spin polarization of 60% for CoFeB, using Jullie`re’s formula. Most importantly, the TMR stayed

194 J.S. Moodera and R.H. Meservey near 60% even at a junction bias of 0.5 V, showing the high application potential for this type of MTJ. One should also note that in this kind of junction, the tunneling can be expected to be incoherent since all three layers are amorphous (as opposed to the coherent tunneling in epitaxial Fe/MgO/Fe junctions). The exact nature of the ferromagnet interface layer is evidently of great importance. A layer of FeO between an Fe electrode and an MgO barrier has been detected using surface X-ray diffraction (Meyerheim et al., 2000). This result has also been reported using electron energy loss spectrometry (Oh et al., 2003). Calculations (Zhang et al., 2003) predict that a layer of FeO between Fe electrode and MgO barrier would reduce the conductance when the magnetic moments are in the parallel position, but have little effect when they are antiparallel, thus leading to a strong decrease in the TMR. The highly developed techniques of angular photoemission spectroscopy have recently been applied by Himpsel and coworkers (Himpsel et al., 1999; Altmann et al., 2000) to measure directly the dispersion relation of the itinerant electron states near the metal surface and close to the Fermi level in Ni, permalloy, and Fe. For Ni(100) and Ni(110) the free electron model implies spin polarizations of the density of states 5.5 and 4.8%, respectively, although the authors suggest other interpretations that might give values of P as high as 29%. These measurements provide strong support of the band structure calculations and demonstrate the power of angular photoemission and inverse photoemission in studying the electron states that are involved in tunneling. Although the review of this section does not attempt to cover the many developments of spin polarization using the tunneling or atomic-force microscopes, this field will be of great importance. In an early experiment (Wiesendanger et al., 1990), an image of the alternate spin terraces of antiferromagnetic Cr was shown. More recently, the problem of the bias dependence of tunneling through a vacuum barrier has been studied with a Co(0001) sample (Ding et al., 2003). They found very little dependence at large tunneling distances, and they conclude that the effect must be caused by the properties of the barrier, rather than magnons or other effects. A measurement technique using an atomic force microscope (Worledge and Abraham, 2003; Worledge and Trouilloud, 2003) for determining the properties of junctions themselves may shorten the time needed to evaluate magnetic tunnel junctions by eliminating process steps required for standard transport measurements. Considerable progress has been made in reducing the gap between theory and the limitations in producing perfectly characterized interfaces on the atomic scale. However, although many questions remain for the theoretically proposed structures and their experimental validation, the experimental results make clear that important applications are to be expected. 3.6.1

Some possible future directions

The formation of artificial tunnel barriers by the oxidation of a thin metal layer has progressively become a standard technique over the past few years. Improvement in barrier growth techniques

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now allows the study of double junction structures, FM1/I1/M/I2/FM2, where I1 and I2 are oxide barriers and M is a continuous metallic layer. These systems are likely to show a reduced bias voltage effect and are therefore promising for applications. Recent theoretical work suggests that their behavior may be richer than that of two junctions connected in series (Zhang et al., 1997b). Various types of double junctions have been grown, where M is a ferromagnetic metal with ˚ . However, the decrease of MR with increasing bias voltage was thickness larger than 30 A measured and was no better than the result expected from two junctions in series (Sun et al., 1998). A decrease of MR with increasing bias that is less than expected from two junctions in series has ˚ Co film as the middle layer M (Montaigne et al., 1998). This may be the been reported using a 20 A result of resonant/coherent tunneling contributions. Coulomb blockade effects can be expected in ultrasmall MTJs with low capacitance. One can expect to see an influence on the TMR as well as the charging effect. The presence of nanoparticles/islands in the barrier, nonmagnetic or magnetic, is predicted to affect the spintunneling phenomenon between the two FM electrodes. Oscillations of TMR as a function of bias, due to discrete charging effects in the Coulomb blockade regime, have been predicted in double junction MTJs consisting of two FM electrodes with a small FM metallic grain in the barrier (Barnas and Fert, 1998). The corresponding oscillation period is a function of the charging energy, and the oscillations are expected to disappear when both junctions have the same spin asymmetry. Similarly, enhanced TMR in MTJs in the Coulomb blockade regime has been theoretically predicted as a higher order tunneling effect. Some experimental results have been attributed to this phenomenon (Takahashi and Maekawa, 1998). Martinek et al. have reviewed the interesting interplay of ferromagnetism and discrete charging effect in the sequential tunneling, co-tunneling and strong coupling regimes in FM single electron transistor structures. This structure can be described as a small grain, or quantum dot, coupled by tunnel junctions to FM electrodes (Martinek et al., 2003). For quantum dots at low temperature, a Kondo resonance which significantly depends on the spin polarization of conduction electrons in the leads has been predicted. Spin polarization study of FM and AFM surfaces near atomic resolution has recently progressed rapidly with extensive work reported by the Wiesendanger group using spin polarized STM (see, for example, Bode, 2003). One can expect to see many new magnetic phenomena on an atomic scale using this powerful approach.

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204 J.S. Moodera and R.H. Meservey Wang, J., Cardoso, S., Freitas, P.P., Wei, P., Barradas, N.P., and Soares, J.C. (2001). Tunnel junctions with AlN barriers and FeTaN electrodes. J. Appl. Phys. 89, 6868. Wang, D., Nordman, C., Daughton, J.M., Qian, Z., and Fink, J. (2004). 70% TMR at room temperature for SDT sandwich junctions with CoFeB as free and reference layers. IEE Trans. Magnetics 40(4), 3269. Wiesendanger, R. (1994). Scanning Probe Microscopy and Spectroscopy: Methods and Applications, Cambridge University Press, Cambridge. Wiesendanger, R., Gu¨ntherodt, H.-J., Gu¨ntherodt, G., Gambino, R.J., and Ruf, R. (1990). Observation of vacuum tunneling of spin-polarized electrons with the scanning tunneling microscope. Phys. Rev. Lett. 65, 247. Wolf, E.L. (1985). Principles of Tunneling Spectroscopy, Clarendon Press, Oxford. Worledge, D.C. and Abraham, D.W. (2003). Conducting atomic-force-microscope electrical characterization of submicron magnetic tunnel junctions. Appl. Phys. Lett. 82, 4522. Worledge, D.C. and Geballe, T.H. (2000a). Maki analysis of spin-polarized tunneling in an oxide ferromagnet. Phys. Rev. B 62, 447. Worledge, D.C. and Geballe, T.H. (2000b). Negative pin-polarization of SrRuO3. Phys. Rev. Lett. 85, 5182. Worledge, D.C. and Geballe, T.H. (2000c). Magneto-resistive double spin filter tunnel junction. J. Appl. Phys. 88, 5277. Worledge, D.C. and Trouilloud, P.L. (2003). Magneto-resistance measurement of unpatterned magnetic tunnel junction wafers by current-in-plane tunneling. Appl. Phys. Lett. 83, 84. Wulfhekel, W., Klaua, M., Ullmann, F., Zavaliche, R., Kirschner, J., Urban, R., Monchesky, T., and Heinrich, B. (2001). Single-crystal magneto-tunnel junctions. Appl. Phys. Lett. 78, 509. Yu, J.H., Lee, H.M., Hayashi, M., Oogane, M., Daibou, T., Nakamura, H., Kubota, H., Ando, Y., and Miyazaki, T. (2003). Magnetic tunnel junctions with high magnetoresistance and small bias voltage dependence using epitaxial NiFe(111) ferromagnetic bottom electrodes. J. Appl. Phys. 93, 8555. Yuasa, S., Sato, T., Tamura, E., Suzuki, Y., Yamamori, H., Ando, K., and Katayama, T. (2000). Magnetic tunnel junctions with single-crystal electrodes: a crystal anisotropy of tunnel magnetoresistance. Europhys. Lett. 52, 344. Yuasa, S., Nagahama, T., and Suzuki, Y. (2002). Spin-polarized resonant tunneling in magnetic tunnel junctions. Science 297, 234. Yuasa, S., Fukushima, A., Nagahama, T., Ando, K., and Suzuki, Y. (2004). High tunnel magnetoresistance at room temperature in fully epitaxial Fe/MgO/Fe tunnel junctions due to coherent spin-polarized tunneling. Jpn. J. Appl. Phys. 43, L5. Zhang, S. and White, R. (1998). Voltage dependence of magnetoresistance in spin dependent tunneling junctions. J. Appl. Phys. 83, 6512. Zhang, S., Levy, P.M., Marley, A.C., and Parkin, S.S.P. (1997a). Quenching of magnetoresistance by hot electrons in magnetic tunnel junctions. Phys. Rev. Lett. 79, 3744. Zhang, X., Li, B.Z., Sun, G., and Pu, F.C. (1997b). Spin-polarized tunneling and magnetoresistance in ferromagnet/insulator(semiconductor) single and double tunnel junctions subjected to an electric field. Phys. Rev. B 56, 5484. Zhang, X.-G., Butler, W.H., and Bandyopadhyay, A. (2003). Effects of the iron-oxide layer in Fe– FeO– MgO –Fe tunneling junctions. Phys. Rev. B 68, 092402.

378

Color plates

(a)

(b) FM

"+:

~

........ .~ ......~ • ....

.ii +::

,,...

I

(NI.Fe)

(,~:))

FM ( ~ + ) )

l(iil)

~

(111),

Plate 3.27 (A) Schematic cross-section diagram of the magnetic tunnel junction (MTJ) with F M - N M - I - F M structure, in which electrons with different spin directions tunnel from the upper to the bottom electrodes. FM, NM, and I denote a ferromagnetic electrode, a nonmagnetic layer, and an insulating layer (tunnel barrier), respectively. The MTJs were prepared to have a C o ( 0 0 1 ) - C u ( 0 0 1 ) - A 1 - O - N i - F e structure. (B) Fermi surface of face-centered cubic Cu. When conduction electrons are confined in the [001 ]-direction, quantumwell states with scattering vectors ql and q2 can be created. (See Fig. 3.27.)

(a)

tcu = 0 A

1.08 ¢E=~ 1.06

==

~ 1.04

!

,=

8

+,--- 6~

1.00

i~!

o..

'r' ~-2o

o

;K'-- ~ q , --- T = ~'~" I~~~,'~:!~;l~,C~

I oo,) I

2o 4o

HImT] (b)

(c) 10

2

tcu = 4 . 5 A

0

~.~ 0.99 0.96

(A) (B)

tc.lA]

,-.- i . . : o , -40-2002040 H[ mT]

Plate 3.28 Normalized TMR curves at T = 2 K at a bias voltage of + 10 mV for Co(001)-Cu(001)-A1-O (18 A)-Ni8oFe2o junctions with Cu layer thickness (tcu) of (A) 0 A and (B) 4.5 ~,. Rp denotes the tunnel resistance with parallel magnetization configuration. (C) TMR ratio at T ----2 and 300 K at a bias voltage of + 10 mV as a function of tc,. (See Fig. 3.28.)

Magnetoelectronics M. Johnson (Editor) Copyright q 2004 Elsevier Inc. All rights reserved.

Chapter 4 Magnetoresistive random access memories James Daughton NVE Corporation, 11409 Valley View Road, Eden Prairie, MN 55344-3617, USA

4.1

Introduction and background

Magnetoresistive random access memory (MRAM) is potentially an ‘ideal’ memory because it has the properties of nonvolatility, high speed, unlimited write endurance, and low cost. These memories use the hysteresis of magnetic materials for storing data and some form of magnetoresistance for reading the data out. Because of the difficulty of separately connecting a large array of memory cells with complex integrated support circuits, the memory cells and support circuits are connected together on-chip. Early predecessors of modern MRAMs date from the 1960s when a magnetoresistive readout scheme was proposed for reading out the datum on a bit by detecting stray magnetic fields from the storage element (Naiman, 1965). About 20 years later, a cell was proposed which used the magnetoresistance of the storage element itself to determine its memory state (Schwee et al., 1982). However, only a small fraction of the cell contributed to the readout signal. The birth of modern MRAM concepts took place at Honeywell in the mid-1980s. Cells first used anisotropic magnetoresistance (AMR) materials (Pohm et al., 1987, 1988) and then giant magnetoresistance (GMR) (Daughton, 1992; Panning et al., 1999) materials for data readout, and were fabricated with integrated circuits. These approaches did not result in components with competitive read access times, because the readout signal levels were small, until the invention of the pseudo-spin valve (PSV) (Chen et al., 1996; Pohm et al., 1997). The next evolutionary step was the use of tunneling magnetoresistance (TMR) for higher speed memories (Daughton, 1997; Parkin et al., 1998; Naji et al., 2001). This technology is projected for production in the coming years. One approach used by Motorola (Freescale Semiconductor) is discussed in detail in Chapter 5. New MRAM developments are aimed at four current challenges: (1) overcoming problems associated with the uniformity of writing and disturb thresholds in two-dimensional (2D) memory selection configurations, (2) eliminating spurious magnetic storage configurations (magnetic vortices), (3) attaining stable magnetic cells at sub-100 nm dimensions, and (4) reducing the magnitude of write currents. Vertical GMR cells (Zhu et al., 2000), cells using Hall readout (Johnson et al., 1998), sandwich tunneling cells (Daughton, 2000), Ne`el/Curie point written cells (Beech et al., 2000), and spin momentum transfer written cells (Kiselev, 2004) each address one or

206 J. Daughton more of these issues. The potential impact of the new ‘SPINS’ technology (Wolf et al., 2001) on MRAM is briefly discussed. 4.1.1

MRAM history

Early MRAM (as opposed to serial memories like tape and disk) used the hysteresis of magnetic materials to store data (‘1’ or ‘0’) and used two or more current carrying wires, or straps, to write the data. Magnetic elements were arrayed so that only those which were to be written received a combination of magnetic fields above a write threshold, while the other elements in the array did not change storage states. A simple version of a 2D writing scheme of this type is illustrated in Fig. 4.1 (refer also to Chapter 1). Most of today’s MRAM concepts still use this writing technique. The magnetic elements that formed the cells of these early memories were typically magnetic cores or plated wires and inductive signals were used for reading out the storage state (‘1’ or ‘0’). A magnetic field, associated with a current in a wire, was used to ‘interrogate’ the memory element, and the polarity of a voltage induced in a sensing circuit depended on whether a ‘1’ or ‘0’ was stored. The signal was a transient, and attempts at memory miniaturization were frustrated because the magnetic flux was reduced and the readout signals were smaller for smaller elements. The first proposal for a magnetoresistive readout scheme was by Jack Raffel and his coworkers at MIT Lincoln Laboratory (Naiman, 1965). Their scheme stored data in a magnetic body, which in turn produced a stray magnetic field that could be detected by a separate magnetoresistive sensing element. The concept was not high density because it was difficult to get an external stray field from a small magnetic storage cell that was sufficiently large to be read by a magnetoresistive sensor, using the lithographic fabrication techniques available at that time. This idea of separating the magnetic storage element from the sensor has some similarity with schemes recently proposed for sensing magnetized bodies by Hall effect devices (Johnson et al., 1998).

Fig. 4.1 Two-dimensional writing architecture.

Magnetoresistive random access memories 207 The first technology that used a magnetic element for storage and also used the same element for magnetoresistance readout was the Cross-tie random access memory (CRAM) (Schwee et al., 1982). This cell used a slight difference in resistance of the element that depended on the presence or absence of a Block point to indicate a ‘1’ or ‘0’. There were difficulties in writing data to the cell reproducibly and consistently, and the difference in resistance between a ‘1’ and ‘0’ was only about 0.1% of the inherent cell resistance, resulting in an impracticably low signal. The first proposals for fabricating magnetic memory cells on a silicon support chip used inductive rather than magnetoresistive readout, but little of this work was published. The concept of integrating magnetic storage cells with support circuits was (and still is) important for MRAM because interconnections between an array of magnetic cells and the circuitry required to make a memory are too complex to be provided on separate chips.

4.1.2

Early MRAM

In the mid-1980s an advanced MRAM concept was developed at Honeywell and it has some common features with most modern versions: † writing using magnetic hysteresis; † reading using the magnetoresistance of the same body in which data are stored; † memory cells integrated with support circuits as a single integrated circuit (IC). Figure 4.2 illustrates the method of data storage and data reading in the MRAM cell. The cell consisted of two ferromagnetic films (NiFe, dark layers of the sense line in Fig. 4.2) sandwiching a poor conductor (TaN), with the composite film etched into stripes as shown. The self-field of a current of sufficient magnitude through the stripe magnetized the NiFe clockwise or counterclockwise when aided by the field from a current in an orthogonal strip line (word line in Fig. 4.2). Current in either strip by itself would not change the storage state. Thus, a single memory cell in a 2D array could be selectively written (Pohm et al., 1987, 1988; Daughton, 1992). Reading out the bit state of this cell depended on sensing the differential resistance of the cell when a sense current was passed through it. Because the sense current creates a magnetic field which opposes the magnetization in one storage state (counterclockwise magnetization), but is in the same direction in the other state (clockwise magnetization), the angle of rotation of the magnetization orientation was different for a ‘1’ or ‘0’. The magnetic material used was a cobalt – Permalloy alloy with a normal AMR ratio of about 2%. Despite improvements in reading methods (Pohm, Comstock, and Hurst, 1990; Pohm, Daughton, and Spears, 1990), the maximum differential resistance of the cell between a ‘1’ and a ‘0’ when it was read was about 1/4 of the 2% magnetoresistance, or about 0.5%. In prototype arrays with practical values of sense current, this gave differential sense signals of 0.5– 1.0 mV. This amplitude of sense signal allowed 16 Kbit

208 J. Daughton

Fig. 4.2 Early MRAM.

integrated MRAM chips to operate with a read access time of about 250 ns (Hurst and Granley, 1996). Write times for the MRAM were 100 ns, and could have been faster if needed. The discovery of GMR materials in 1989 (Baibich and Barnas, 1990) gave hope for higher readout signal amplitudes and faster read access time. In 1991, ferromagnetic films sandwiching a copper layer and etched into stripes showed a magnetoresistance ratio of about 6%. This materials configuration fits the aforementioned MRAM cell with little modification. Since the read access times tend to improve as the square of the signal level, normal scaling would indicate that the improvement of a factor of 3 in magnetoresistance would lead to improvement in read access time by a factor of 9. Read access times of under 50 ns were achieved for MRAM with GMR materials (Panning et al., 1999). However, this cell had serious limitations even with GMR materials. MRAM was still not as fast as semiconductor memory. Worse, there was a limit to the reduction of cell size because the cell would not work with sense lines narrower than about 1 mm. The reason was due to

Magnetoresistive random access memories 209 ‘magnetization curling’ at the edges of the stripe, which can be described as an unfortunate tendency for magnetization to orient along the stripe. Exchange coupling imposes limits on the length scale over which the magnetization can change directions. Near the center of a 1 mm stripe, the magnetizations of the two ferromagnetic layers in the sandwich tend to be oriented substantially along the axis of the stripe. Thus, data are stored very marginally. 4.1.3

Pseudo-spin valve MRAM

The invention of the PSV cell (Chen et al., 1996; Pohm et al., 1997) significantly improved readout signal levels, thus improving the read access time of MRAM while maintaining densities competitive with other solid-state memory technologies. In this design nearly all of the (approximately) 6% GMR was available for readout. Furthermore, the signal swing was ^ 6%, making the difference between a ‘0’ and ‘1’ about 12% of the cell resistance. This gave an improvement over the original mode of operation by a factor of 8, albeit with a more complex reading method, and put MRAM read access time on a much more even footing with semiconductor memory. Figure 4.3 illustrates the construction of a PSV cell. There are two magnetic layers that have mismatched properties so that one tends to switch at lower fields than the other. This can be done by using two magnetic films of the same material, but with different thicknesses. In that case, the thinner film switches at lower fields, or is the ‘soft’ film, and the thicker film switches at a higher field, and is the ‘hard’ film. The cell resistance is low (high) when the magnetization orientations of the hard and soft films are parallel (antiparallel). The soft film acts as a means of reading the stored state, and binary information is stored in the hard film. Without switching the hard film, the soft film can be manipulated to be parallel or antiparallel to the hard film. Figure 4.4 shows a sequence of two word fields which starts with a negative field and ends with a positive field. The resistance either rises or falls, depending on whether a ‘1’ or a ‘0’ is stored. With simple electronics,

Fig. 4.3 Pseudo-spin valve (PSV) cell. ( For a colored version of this figure, see Plate 4.3, page 379.)

210 J. Daughton

Fig. 4.4 Read mode for PSV.

the difference between the initial and final resistances can be sensed, and the polarity of this difference indicates whether a ‘1’ or ‘0’ is stored. In some MRAM designs the difference in readout signal level between a ‘1’ and a ‘0’ is not much larger than the sum of other circuit variations and array imbalances, such as variations due to line resistance, cell resistance, or transistor voltage drops. A two-step read process is then necessary. A GMR MRAM architecture that has many cells in series on each sense line is a case in point. The readout signals are not large enough to distinguish a ‘1’ from a ‘0’ with a single voltage reading, and some sort of ‘auto-zeroing’ is required. As will be shown in the next section, tunneling MRAM architectures with a signal single transistor per cell have achieved sufficiently high signal levels to allow a single pass read. PSV memory cells can be at least as narrow as 0.2 mm (Everitt et al., 1998) and, using a 2D memory organization, PSV memory is a dense MRAM scheme. A weakness is that the switching current amplitudes that are required push the limits for high-density integrated circuits. PSV memory could replace EEPROM or flash memory in applications where high density and/or fast writing is important. 4.1.4

Magnetic tunnel junction MRAM

The discovery of very high magnetoresistance in magnetic tunnel junctions (MTJs) (Miyazaki and Tezuka, 1995; Moodera and Kinder, 1996) opened the possibility of much higher signals for MRAM, and consequently much faster read times. The salient features of a modern MTJ are (see also Chapter 3): † magnetoresistance values over 40%; † wide range of junction resistance £ area products between 10 and 108 V mm2;

Magnetoresistive random access memories 211 † reduced magnetoresistance with increased bias voltage – commonly to 50% of maximum at 300–400 mV; † catastrophic breakdown of the barrier at 1–2 V. The high resistance of the junction itself does not permit readout voltages and write currents to share a common circuit, which is a disadvantage when compared with GMR memory cells. The result for 2D write selection architectures using MTJ cells is that a separate connection to the cell is required for reading. However, one of the electrodes in the tunneling device can be used as a write drive line, and this conserves area in the cell. In concept, a number of MTJs could be connected in series or in parallel to a common readout sensing system. This would conserve area, as in the case of GMR cells, but would reduce the effective signal level with respect to the background voltage and therefore slow the read access time. Most designs using MTJs are based on the electrical connection of a single MTJ to the electronic selection system for reading. Early designs used a diode instead of a transistor for read selection in order to reduce the area of the cell, but this proved impractical. Read selection is now commonly accomplished by connection of an isolation transistor between the cell and the sense electronics. While this adds area to the cell, the high readout signal from a single MTJ allows a single static voltage reading to determine memory state. The two-stage reading technique employed with PSVs is not required. A technique for reducing cell area by eliminating the select transistor (or diode) in the MTJ cell has been proposed (Zheng et al., 2001). Using additional electronic circuits connected to the periphery of the area, the readout signal of one specific cell in a 2D array may be determined by negating the effects of ‘sneak paths’. The additional electronics is very sophisticated and requires significant chip area to implement. However, with modern chemical mechanical polishing techniques, the required circuitry might be placed under the cells, thus requiring no net additional chip area at all. MTJ MRAM designs use a cell with a pinned ferromagnetic layer and a soft ferromagnetic storage layer on either side of a tunnel barrier. The two storage states are parallel or antiparallel alignments of the magnetization orientations of the pinned and storage layers. The storage layer in the cell is elliptical or has sharp or tapered ends and is longer than it is wide. The uniaxial magnetic anisotropy used for storage is primarily due to shape anisotropy, i.e. the difference in demagnetizing energies when the storage magnetization orientation is directed across the short axis of the cell and when the storage magnetization is directed along the long axis. On the other side of the tunnel barrier is a ‘pinned’ ferromagnetic layer in which the magnetization is permanently aligned in one direction along the long axis of the cell by virtue of a strong coupling to an antiferromagnetic material. The pinning can be enhanced by replacing the single pinned layer with a synthetic antiferromagnet layer (SAL) (Parkin et al., 1990). In ˚ ) layer, usually of ruthenium. A strong the SAL, two ferromagnetic layers sandwich a thin (6 –12 A antiparallel coupling is induced between the two ferromagnetic layers in the sandwich.

212 J. Daughton This structure is commonly referred to as a ‘synthetic antiferromagnet’. A schematic cross-section of such an MTJ SAL cell, along with the magnetic fields acting on the ‘free’ or unpinned layer, is illustrated in Fig. 4.5. One of these fields derives from ‘Orange peel’ coupling. Orange peel or Ne`el coupling is due to a correlation of roughnesses of the free layer and the pinned layer next to the barrier (refer also to Chapter 2). The use of a synthetic antiferromagnet greatly reduces stray magnetic field from the pinning layers. It is common to make the ferromagnetic layer next to the barrier slightly thicker than the other ferromagnetic layer in the synthetic antiferromagnet. This balances out the ‘Orange peel’ coupling with a small stray field from the ferromagnetic layers, thereby making the storage states in the cell symmetric with respect to applied fields. The switching characteristics of the soft or storage layer roughly obey the Stoner –Wohlforth switching model, and this permits a 2D write selection array architecture. The intrinsic cell switching speed is limited by the dynamics of thin film switching to a few nanoseconds. For readout, a bias limited to 150 mV and applied across a tunnel junction with 30% magnetoresistance generates a difference signal between a ‘1’ and a ‘0’ of 45 mV. This signal level is on the order of that used for DRAM readout and also about the same as the differential signal on internal nodes in an SRAM cell. Thus, with proper resistance and capacitance values in the cell, the intrinsic speed of MTJ elements configured into a DRAM type architecture (see Fig. 4.6) or a flip-flop like cell (see Fig. 4.7) should be comparable to semiconductor memory cells (Daughton, 1997). MTJ memory appears to be nearly ready for commercial production. Specific development of MTJ memories is covered in Chapter 5. The ‘toggle mode’ for writing a synthetic antiferromagnet that is described therein is a breakthrough method of overcoming cell margins required for 2D write selection.

Fig. 4.5 Structure of synthetic antiferromagnetic layer MTJ cell.

Magnetoresistive random access memories 213

Fig. 4.6 ‘DRAM-like’ MRAM.

4.2 4.2.1

MRAM developments Improving write select margins

Magnetic memory cells, such as magnetic cores, have traditionally used selection schemes for reading and writing that do not require a transistor or diode in the memory cell, but which do place

Fig. 4.7 ‘SRAM-like’ MRAM.

214 J. Daughton restrictions on uniformity and ‘disturb’ sensitivity of the cell. These restrictions are the focus of this section. Figure 4.1 is a diagram showing a typical 2D write selection scheme. Selected cells receive both Ix and Iy currents, and are switched into the desired memory states. The current amplitudes must be selected so that Ix or Iy separately do not disturb the memory state of stored data. Bits on the same x line or y line that are not being written are subjected to ‘half-select’ currents which might disturb the data. If very large currents are used to insure the writing of worst case cells, then the half-select currents are also large and tend to disturb the most disturb-sensitive cells. The half-selected memory states are not nearly as stable as stored bits, and they provide the majority of projected cell failures in time (Beech et al., 2000). In addition to half-select currents, these cells must withstand stray magnetic fields from neighboring cells, fields from leakage currents, stray environmental fields, and thermal agitation. Thus, the requirements for uniformity and appropriate design margins present challenges in manufacturing the 2D magnetic arrays. Many MRAM schemes also use a 2D selection scheme for reading data. Both the original MRAM concept developed at Honeywell and the PSV concept use magnetic 2D selection schemes for reading, and the read process thereby introduces further disturb conditions. MTJ memories use diodes or transistors to select a memory cell for reading with a small current, and thus do not have significant disturb conditions for reading. However, they still have the constraints of 2D magnetic selection for writing. A further complication in achieving appropriate write select margins is the presence of magnetic anomalies, or vortices, in the ferromagnetic element. These vortices cause inconsistent magnetic behavior, and result in the inability to write reproducibly or to read a cell correctly. Magnetic simulations and measurements have confirmed this behavior (Zhu et al., 2000). The effects of magnetic anomalies make it extremely difficult to get satisfactory write/disturb margins. There are several developments besides the ‘toggle mode’ of operation (refer to Chapter 5) which could help improve the margins for write selection. One is to use a different memory organization for writing by incorporating one transistor per cell for write selection. A second approach is to eliminate ‘vortices’ in order to tighten the statistical distributions of write currents.

4.2.1.1

Transistor write select

Figure 4.8 depicts a ‘one-dimensional (1D) selection’ scheme for both reading and writing a magnetoresistive memory cell. A large current of either polarity (positive current for a ‘1’ and negative current for a ‘0’) is passed through a select transistor and through the memory cell during the write process. For readout, a lower current amplitude is used to generate a voltage across the cell, higher or lower depending on the datum stored and the magnetoresistance of the cell. This voltage is then sensed and compared to a reference in order to determine the memory state. In this architecture, the transistor provides the selection of the memory cell, and not the 2D magnetic switching properties of the cell. A very large current can be used to write to the cell and a much smaller current can be used to read the cell, thus potentially providing large margins.

Magnetoresistive random access memories 215

Fig. 4.8 Cross-section of 1T1MTJ cell.

Of course, it is important to use as small a current as possible to reliably write the cell so as to reduce the size of the transistor needed for selection. There is still a 2D array of cells, but the transistors take the burden of cell selection rather than placing severe constraints on the magnetic switching properties of the cell. The scheme is quite similar to that used for DRAM, where a transistor is used to write a charge state, and then to detect charge on a capacitor. Figure 4.9 shows a hypothetical implementation of this architecture for an array using ‘spin valve’ cells. Two ferromagnetic films sandwich a conducting layer, and one of the two magnetic films is ‘pinned’ with an antiferromagnet across a stripe when it is etched from a sheet of the composite materials. A magnetic field created by a current through the stripe can be used to magnetize the unpinned magnetic film in either of two directions, depending on the direction of the current. Then a smaller current through the stripe can be used to sense the value of resistance – higher if the films are oppositely magnetized and lower if they are magnetized in the same direction. A large current amplitude can be used for writing, without disturbing other cells, and a much lower current amplitude can be used for sensing. This would suggest that large margins can

Fig. 4.9 A spin valve cell used in a one transistor one-dimensional architecture.

216 J. Daughton be achieved. In practice, this particular cell has problems with demagnetization fields in cells with micron dimensions and smaller. Furthermore, the cell would be large due to the size of the transistor needed to pass a large write current. A better cell for write select (Daughton, 2000) is shown in Fig. 4.10. This cell uses spindependent tunneling for a higher readout signal level and to minimize demagnetizing effects. Neither Permalloy film in the trilayer sandwich is ‘pinned’. A current driven through the sandwich can magnetize it into either of two magnetic states, clockwise or counterclockwise, depending on the direction of current. With no magnetic field (no current) applied, the magnetization orientations of the films are antiparallel and lie across the axis of the stripe. A tunnel barrier is deposited on top of the trilayer sandwich, and a pinned synthetic antiferromagnet (SAL) is deposited on top of the barrier. The top layer of the synthetic antiferromagnet is pinned by coupling to an antiferromagnet. The synthetic antiferromagnet is comprised of two ferromagnetic layers sandwiching a thin ruthenium layer, a structure which has very strong antiparallel coupling. The synthetic antiferromagnet therefore produces very little stray magnetic field and, similarly, the unpinned Permalloy trilayer sandwich also produces very little stray magnetic field. The spin tunneling current between the top Permalloy layer and the pinned SAL is then either relatively high or low depending on the direction of magnetization of the Permalloy. Spin-dependent tunneling

Fig. 4.10 Sandwich/tunneling cell.

Magnetoresistive random access memories 217 has demonstrated about 40% magnetoresistance with 100 mV across the barrier, and thus a signal of approximately 40 mV could be obtained. The barrier resistance is usually sufficiently large to limit the read current to about 20 mA, while the current needed to set the magnetization in the cell (the write current) should be about 2.5 mA for a cell having a width on the order of a micron, and about 0.75 mA for a cell 0.4 mm wide. For those values, the disturb current would be about 1/100 of the write current, and it follows that large margins can be achieved. An improvement to the sandwich/tunneling cell makes use of a strong antiparallel coupling between two ferromagnetic layers and is shown in Fig. 4.11. The antiparallel coupling can be induced by depositing a thin interlayer of a selected material, typically ruthenium, between the two ˚ of ruthenium is used, ferromagnetic layers in each sandwich. If an interlayer of approximately 9 A there is an antiparallel coupling field between the two ferromagnetic layers of several thousand oersteds. The relatively high resistance of the very thin ruthenium layer forces most of the current into the Permalloy layers, which reduces the field conversion efficiency of the cell to some extent. In very small cells, this efficiency loss is more than compensated by the increased stability of the cell and by the elimination of demagnetizing and stray magnetic field effects during switching. Cells of this type have been fabricated and tested at NVE Corporation (Pohm et al., 2001). The key potential advantage for these memories is a relaxation of the margin requirements for cell write currents in comparison with 2D selection schemes. Memory performance should be

Fig. 4.11 SAF sandwich cell.

218 J. Daughton as high as for MTJ memories, but densities will be lower because of the size requirement for the write transistor. This is especially true when compared with the PSV-based memories. However, for many small, niche memories, the overhead space required for pads and peripheral electronics is much larger than the space required by the memory cells. In such applications the write transistor selection scheme could be especially useful. 4.2.1.2

Eliminating vortices

Several methods have been suggested for eliminating magnetic vortices in a ferromagnetic thin film element. One is ‘C-State Storage’, an approach using cell shape to solve the half-select disturb problem (Arrott, 2001). By shaping the cell so that a flat boundary is formed parallel to the major axis, as shown in Fig. 4.12, a magnetization configuration is forced which, according to simulations, is much less sensitive to half-select disturb fields applied along the major axis. If experimentally verified, this approach could markedly improve the yield of MRAM processing. A second structure which may circumvent vortices (Zhu et al., 2000) is shown in Fig. 4.13. Ferromagnetic films of a few nanometers thickness are separated by thin copper layers, and alternating magnetic layers have significantly different thicknesses. When a bit (write) current is passed vertically through the stack, a circumferential magnetic field is created that can magnetize these magnetic films, with the thinner magnetic layers switching at lower currents (fields) and the thicker layers switching at higher currents (fields). With all the layers magnetized clockwise (or counterclockwise), the resistance of the stack is lower than when alternate layers are oppositely magnetized. The current-perpendicular-to-the-plane (CPP) GMR (refer to Chapter 2) is in general larger than current-in-plane (CIP) GMR, so that for a given current through the stack the signal amplitude can be usable, even though the cell itself has relatively low resistance due to its shape. In order to attain a 2D read/write select organization, a pair of parallel word lines lying on the outside edge of the cell carry currents in opposite directions, and an orthogonal pair of lines carrying similar currents is placed on the opposite side of the cell, as shown in Fig. 4.14. With currents flowing through both pairs of word lines, a ‘tipping’ field is created which lowers the bit

Fig. 4.12 Stable C-state magnetization configuration. ( For a colored version of this figure, see Plate 4.12, page 379.)

Magnetoresistive random access memories 219

Fig. 4.13 Vertical GMR cell.

current thresholds for switching. Thus, a 2D selection scheme is possible where the word currents by themselves, or the bit currents by themselves, cannot write the hard (thicker) film layer, but the combination of the two currents can. One way to read out data from such a cell is to switch the soft (thin) layer from one state to the other while observing the resistance. At some intermediate value of word current and sense current where the soft (thin) layers can be switched, but the hard (thick) layers are not, the resistance of the sense line is observed as the sense current is reversed. In this way, the orientation of the hard layer can be determined in the same manner as described earlier for the PSV. The primary advantage of this cell is, potentially, its density. According to extensive numerical simulations, the clockwise/counterclockwise storage mode does not create vortices for cells with sizes down to less than 100 nm diameter (approximately 30 nm inside diameter),

Fig. 4.14 Vertical GMR cell write configuration. ( For a colored version of this figure, see Plate 4.14, page 379.)

220 J. Daughton which is smaller than demonstrated PSV and MTJ cells. The vertical, CPP GMR should be higher than for the CIP GMR used in PSVs (refer to Chapter 2), and the signal from this cell is projected to be sufficient despite the relatively low cell resistance which is imposed by its shape. Data confirming the small achievable size for vertical GMR cells have not been published. In most cells, there are design constraints associated with both writing and reading which interrelate. The data stored in the cells described earlier were read by the magnetoresistive properties of the magnetic material in the cell itself. An alternative is to detect the sense of the stray field from a magnetic cell with a Hall effect device fabricated in an underlying semiconductor (Johnson et al., 1998). A 2D write selection scheme is used to write magnetic cells that can produce large external fields. The scheme is illustrated in Fig. 4.15 (see also Chapter 6). In order to get high signals, a large Hall effect is desired, and prototype implementations have generally used GaAs or InSb in order to achieve a large Hall coefficient. This would be a cost disadvantage compared with Si-based MRAM. One big advantage of this scheme is that no electrical interconnections are required between the magnetic array and the sensing circuitry. This gives the designer the option of separate optimizations of the writing and sensing aspects of the memory and eliminates any interactive effects. 4.2.2

Extending density/reducing write currents

MRAM may potentially be an ideal memory, offering nonvolatility, fast read and write, and excellent write durability. However, in order for this potential to be realized, MRAM must take

Fig. 4.15 Hall read-out MRAM cell. ( For a colored version of this figure, see Plate 4.15, page 380.)

Magnetoresistive random access memories 221 advantage of the lithographic processing capabilities available in the semiconductor industry. According to the International Technology Roadmap for Semiconductors, the lithography used in advanced manufacturing for memory in the future is shown in Table 4.1. MRAM as presently being developed may not be able to utilize this lithography because of thermal stability and write current requirements for cells with features with dimensions below about 0.1 mm. In any working memory, the energy stored in a device has to be much higher than kT; where k is Boltzmann’s constant and T is the absolute temperature, in order to avoid excessive thermal failure rates. Over the past few years, manufacturers of hard disk drives have dealt with this same consideration in the form of the ‘superparamagnetic limit’ for disk storage density. There is presently a large research program in hard drive development called ‘HAMR’, or heat-assisted magnetic recording (McDaniel, 2004), which is similar in intent to the thermally assisted MRAM discussed in this section. There are very stringent reliability requirements for modern memory components. Failure rates of about one failure per billion hours are required. Fundamental failure rates are determined by the ratio of the effective storage energy of the cell to kT: In memories where 2D write selection is used, the ‘half-selected’ cells are most vulnerable. Although a low fraction of the cells are halfselected at any one time, those cells determine the failure rates due to thermal upset. For a cell with a given area and a given internal field (magnetization) to define the ‘1’ and ‘0’ states, an energy density can be found, and the necessary thickness (volume) of the magnetic material can be calculated. The magnetic field (write current) needed to switch the cell can then be determined. Adding film thickness can increase the stored energy and promote cell stability. However, analysis shows that for cells with minimum features below about 0.1 mm, the current required to switch a stable cell may be impracticably high. Table 4.2 shows the thickness of ferromagnetic film and the required write current as a function of lithographic feature size for a 2D memory using shape anisotropy to achieve bistable storage states. This assumes a maximum operating temperature of 778C, a thermal relaxation time of 1029 s, a 16 Mbit chip with 511 þ 1023 elements half-selected, and an allowable error rate of 10210 h21. Note that the required current increases as the cell area decreases, which is not a desirable scaling characteristic. In addition, it has been found that the ˚ are more susceptible to formation of vortices. Therefore, other films thicker than about 30 A

Table 4.1 International technology roadmap for semiconductors – lithography, cell size and chip capacity for start-up production of DRAM through 2010 (2001 edition) Year

2003

2005

2007

2010

Lithography (mm) Cell size (mm2) Capacity (Gbit)

0.1 0.06 1

0.08 0.0384 2

0.065 0.025 4

0.045 0.012 8

222 J. Daughton

Table 4.2 Film thickness and current as a function of cell width for cells meeting stability criterion Cell width (mm)

˚) Thickness (A

Digit current (mA)

Write current (mA)

0.09 0.06

59 72

4.8 5.6

3.9 6.1

solutions must be found to keep MRAM on a density improvement timetable similar to other solidstate memories. One possible solution is to make a cell from a round, ‘unbalanced SAF’, as shown in Fig. 4.16, to which additional matched SAF pairs are added. Since there is no shape anisotropy, many layers could be added without increasing the write current above that needed to overcome material anisotropy, and greater stability is achieved with more layers. Furthermore, each of the ˚ , thus reducing the risk of vortices. Although this idea has magnetic layers can be thinner than 30 A promise, stability would require a very thick stack to achieve practical values of field-induced anisotropy (limited to about 20 Oe) when the minimum lithographic feature is less than 0.1 mm. Two developments which could lead to higher density and lower write currents are magnetic/thermal writing and spin momentum transfer writing. 4.2.2.1

Thermal/magnetic writing

Heating a ferromagnetic element to a temperature that exceeds a Curie, Ne`el, or blocking temperature, in conjunction with coincident magnetic fields from a write current, can result in a

Fig. 4.16 High storage energy cell.

Magnetoresistive random access memories 223 write process with smaller currents that can scale to widths less than 0.05 mm. By heating magnetic materials in MRAM cells above their ordering temperatures, the fields needed to write the bit state may be greatly reduced, but the cells can be thermally stable at normal operating temperatures (Beech et al., 2000). Figure 4.17 illustrates the basic idea of thermally aided storage. Magnetization as a function of temperature changes rapidly near the Curie temperature TC of a ferromagnetic material. If the ambient temperature range of the silicon chip is 0 –1008C, then selfheating currents could raise the temperature of the cell to the Curie point, approximately 2008C. The required currents would depend on the silicon substrate temperature. For example, more current would be required if the substrate temperature was 08C than if the substrate temperature was 1008C. The antiparallel exchange coupling in an antiferromagnet follows much the same relationship shown in Fig. 4.17, and when a ferromagnetic layer is pinned by an antiferromagnetic layer having a Ne`el temperature of about 2008C, the same sort of operation could be anticipated. Figure 4.18 shows two cells, one using a low Curie point storage layer (Fig. 4.18(a)) and the second using the pinning of a ferromagnetic film by an antiferromagnet with a suppressed Ne`el temperature (Fig. 4.18(b)). The low Curie point layer is designed with shape anisotropy to provide stability. The Ne`el cell should not require shape anisotropy. The effective storage field due to the antiferromagnetic coupling between the antiferromagnet and the ferromagnet can be on the order

Fig. 4.17 Curie point writing concept.

224 J. Daughton

Fig. 4.18 Magneto-thermal cells.

of 5000 Oe as compared to 20 Oe for the field-induced HK of a normal film, or about 100 Oe for the effective HK of a cell using shape anisotropy. The storage energy per unit volume is at least 50 times higher for the Ne`el cell which would allow for a higher areal density for MRAM. Figure 4.19 schematically illustrates a 2D selection scheme where a resistive element is added in series with the x-select lines to provide local heating, as well as magnetic field, to a cell. It would be possible to make all or part of each y-select line resistive so as to add a second component of heating to the elements. The magnetization orientation of a pinned layer in a spin valve cell or spin-dependent tunneling memory cell in this array can be switched by heating the

Fig. 4.19 Thermal/magnetic selection.

Magnetoresistive random access memories 225 cell above the blocking temperature and cooling with the magnetization set in the desired direction by write fields. Consider a simple model calculation. The blocking temperature of FeMn is about 2258C. For coincident thermal write, the sense and word lines must each provide a temperature rise of 1258C. For a 50 V memory cell (10 V contact resistance and 2 squares of PSV magnetoresistive material ˚ thickness, current at 20 V/square), and using standard thermal constants for silicon oxide of 300 A amplitudes of only 1 mA are required. Next, assume that the thermally written memory cells are ˚ of thermal oxide for insulation. The thermal conductivity built on top of a silicon wafer with 300 A of silicon is more than 100 times greater than SiO2 and can be treated as a heat sink. The thermal conductivity of SiO2 is 0.014 W/cm 8C and the thermal diffusivity is 0.006 cm2/s. From the governing thermal diffusion equation, it can be shown that, to a first approximation, the heating and cooling of the assumed memory cell is characterized by a 1.6 ns time constant. Thus, it is seen that with appropriate dielectric thickness, heating and cooling can be done in a few nanoseconds. A second and probably more desirable cell architecture is shown in Fig. 4.20. In this structure, the heating is provided by current through a select transistor that serves to select the cell from an array of cells for both reading and writing. A minimum sized transistor can be used as long as the required current for heating is less than about 100 mA. This current switching capacity holds even as the IC technology scales to higher densities. The thermal vias need only be moderately good electrical

Fig. 4.20 Low curie point cell. ( For a colored version of this figure, see Plate 4.20, page 380.)

226 J. Daughton conductors, and must be poor thermal conductors. The thermal conductivity of the surrounding dielectric should also be low in order to concentrate the heat on the magnetic storage element. There are a number of possible designs for the cell that is contained between the thermal vias. A double tunnel junction is a good example and is illustrated in the figure. There are two pinned layers on the upper and lower sides of tunnel barriers. A single magnetic storage layer, composed of a low Curie point material, is between the tunnel barriers. The thermal time constant for the thermal vias is roughly proportional to the square of the thermal path lengths, thus favoring short thermal paths. However, the temperature rise is inversely proportional to the path length for a given power dissipation. This necessitates a compromise in path length and dictates material thermal properties. For 0.05 mm lithography, assuming it is desired to heat and cool in about 5 ns, path lengths of about 0.05 mm would be required. The thermal via material should have a thermal diffusivity of 0.003 cm2/s and a thermal conductivity of about 0.01 W/cm 8C. Magnetization reversal modeling has shown that the low Curie temperature material can be switched reliably into stable storage states at temperatures less than 408C below the Curie point. The switching field is independent of the film thickness, which may be made sufficiently thick to give adequate shape anisotropy (and storage energy) at operating temperatures to achieve very low failure rates (Daughton, 2002). It has been shown that the digit write field required scaled as width23/2, and the required current amplitude scaled roughly as width21/2. The required magnetic fields can be attained with a few milliamperes of current, depending on the field efficiency of the ‘cladded’ digit line (Durlam et al., 2002). The cell illustrated in Fig. 4.20 is smaller than conventional MTJ cells because no additional contact is needed for a readout sense signal. This cell should achieve packing densities equal to or greater than DRAM using the same lithography, provided that thermal switching currents are less than 100 mA and that compatible materials can be found.

4.2.2.2

Spin momentum switching

It was pointed out in this chapter that the requirement for high current amplitudes for switching very dense MRAM cells is a potential problem. It has been verified that spin-polarized currents can be used to switch magnetic films (Katine et al., 2000), and projections indicate that this phenomenon could be a way to lower the amplitude of switching currents. Current passing through a pinned (fixed) ferromagnetic layer was shown to switch the magnetization orientation of a thin, free ferromagnetic layer to the same magnetic state as the fixed layer. Current densities of approximately 107 A/cm2 were used. Figure 4.21 shows that a current density less than 0.5 £ 106 A/cm2 has been used to switch a structure that is essentially a memory element (Kiselev, 2004). The test results shown in Fig. 4.21(d) were obtained by using a DC bias field to center the R – H characteristic. Note that the equivalent external magnetic field necessary for switching was several hundred oersteds. Projections for the current amplitudes necessary to switch small cells (,0.05 mm diameter) indicate that much less current can be used in this mode of switching than in

Magnetoresistive random access memories 227

Fig. 4.21 Spin momentum transfer writing.

the conventional mode of using magnetic fields generated by currents. It is important to note that a cell made for spin momentum transfer writing could be similar to the very simple cell envisioned in Fig. 4.20. The combination of thermally assisted writing with spin momentum switching could achieve very low switching currents. 4.2.3

New spintronics effects – potential MRAM enhancements

There are three areas of spintronics research (Wolf et al., 2001) which may have a high impact on the MRAM technology: higher magnetoresistance materials, spin momentum switching, and ferromagnetic semiconductors. Spin momentum switching was discussed in the previous section. The magnetoresistance readout signal level from MRAM cells depends on the spin polarization of conduction electrons in the materials, i.e. the percentage of conduction electrons with spin polarization aligned in one direction. In theory, the magnetoresistance can be ‘on–off’ if the polarization is 100%. Theoretical predictions for the band structures of Heusler alloys and chromium dioxide predict 100% polarization for these materials, but this has not yet been demonstrated in magnetoresistance devices. Tunneling devices using manganates have demonstrated conduction ratios of 7 : 1 (Jo et al., 2000) at 77 K. Akinaga has demonstrated magnetoresistive ratios of 1000 : 1 on thin layers of manganese antimonide (Akinaga, 2002). Constricted contacts have also demonstrated very large magnetoresistance (Chopra and Hua, 2002). Large values of magnetoresistance would make the MRAM faster, and could give the designer additional latitude in improving speed/die size (cost) tradeoffs (see also Chapter 3).

228 J. Daughton There is an intense research effort on the topic of ferromagnetic semiconductors. Thus far, the magnetic properties of the materials are not suitable for magnetic storage, and progress is still needed to raise the Curie point of the materials above room temperature. If suitable magnetic properties are obtained for these materials at room temperature and above, these materials would represent a significant opportunity to improve MRAM density by integrating the storage cell with active devices.

Acknowledgements Some of this work was supported by contracts with agencies of the Department of Defense and with the National Science Foundation.

References Akinaga, H. (2002). Magnetic switch effect in metal/semiconductor hybrid granular films – extra huge magnetoresistive effect at room temperature. J. Magn. Magn. Mater. 239(1 –3), 145– 148. Arrott, A. (2001). High selectivity for magnetic random access memory using C-states. Paper EC-11 04 Presented at MMM Conference, Seattle, November 15, 2001. Baibich, M. et al. (1990). Giant magnetoresistance of (001) Fe/(001) Cr magnetic superlattices. Phys. Rev. Lett. 61(21), 2472. Barnas, J. et al. (1990). Novel magnetoresistance effect in layered magnetic structures: theory and experiment. Phys. Rev. B 42(13), 8110. Beech, R. et al. (2000). Curie point written magnetoresistive memory. J. Appl. Phys. 87(9), 6403. Chen, E. et al. (1996). Submicron spin valve MRAM cell. J. Appl. Phys. 81, 3992. Chopra, H. and Hua, S. (2002). Ballistic magnetoresistance over 3000% in Ni nanocontacts at room temperature. Phys. Rev. B 66, 020403R. Daughton, J. (1992). Magnetoresistive memory technology. Thin Solid Films 216, 162– 168. Daughton, J. (1997). Magnetic tunneling applied to memory. J. Appl. Phys. 81(8), 3758. Daughton, J. (2000). Advanced, MRAM concepts. Paper Presented at Nonvolatile Memory Symposium, Washington DC, November 16, 2000. Daughton, J. and Pohm, A. (2003). Design of Curie point written MRAM cells. J. Appl. Phys. 93(10), 7304. Durlam, M. et al. (2002). A low power 1 Mbit MRAM based on 1T1MTJ bit cell integrated with copper interconnects. Proceedings of the VLSI Symposium 2002. Everitt, B. et al. (1998). Pseudo spin valve MRAM cells with sub-micrometer critical dimensions. IEEE Trans. Magn. 34(4), 1060 – 1062. Hurst, A. and Granley, G. (1996). Projected applications, status, and plans for Honeywell high density, high performance nonvolatile memory. Proceedings of the 1996 Nonvolatile Memory Technology Conference, Albuquerque, NM, 1996. Jo, J. et al. (2000). Very large magnetoresistance and coherent switching in half-metallic manganite tunnel junctions. Phys. Rev. B 61, R14905. Johnson, M., Bennett, B., and Yang, M. (1998). Hybrid ferromagnetic semiconductor nonvolatile memory. IEEE Trans. Magn. 34(4), 1054 – 1059.

Magnetoresistive random access memories 229 Katine, J. et al. (2000). Current-driven magnetization reversal and spin-wave excitations in Co/Cu/Co pillars. Phys. Rev. Lett. 84, 3149. Kiselev, S. et al. (2004). Spin transfer-driven magnetic switching and precession. Presentation at Nanomagnetics Workshop, Cornell University, May 14, 2004. McDaniel, T. (2004). Ultimate limits to thermally assisted magnetic recording. Presentation at American Physical Society Meeting, March 25, 2004. Miyazaki, T. and Tezuka, N. (1995). Giant magnetic tunneling effect in Fe/Al2O3/Fe junction. J. Magn. Magn. Mater. 139, L231. Moodera, J. and Kinder, L. (1996). Ferromagnetic –insulator –ferromagnetic tunneling: spin-dependent tunneling and large magnetoresistance in trilayer junctions. J. Appl. Phys. 79(8), 4724 – 4729. Naiman, M. (1965). Proceedings of the 1965 Intermag Conference, Paper 11-2. Naji, P. et al. (2001). A 256Kbit, 3.0 Volt 1T1MTJ nonvolatile magnetoresistive random access memory. ISSCC Digest of Technical Papers, February, 2001, p. 122. Panning, G. et al. (1999). Honeywell technology and product overview and plans. 1999 GOMAC Conference, Monterey, CA, March 8 –11, 1999. Parkin, S., More, N., and Roche, K. (1990). Oscillations in exchange coupling and magnetoresistance in metallic superlattice structures: Co/Ru, Co/Cr, and Fe/Cr. Phys. Rev. Lett. 64(19), 2304– 2307. Parkin, S. et al. (1998). Exchange biased magnetic tunnel junctions and application to non-volatile magnetic random access memory. J. Appl. Phys. 85, 5828. Pohm, A. et al. (1987). Threshold properties of 1, 2, and 4 mm multilayer MR memory cells. IEEE Trans. Magn. 23(5), 2575. Pohm, A. et al. (1988). The design of a one megabit non-volatile M-R memory chip using 1.5 £ 5 mm cells. IEEE Trans. Magn. 24(6), 3117. Pohm, A. et al. (1997). Bias field and end effects on the switching thresholds of ‘pseudo spin valve’ memory cells. IEEE Trans. Magn. 33(5), 3280. Pohm, A., Beech, R., and Daughton, J. (2001). High speed, low energy, SDT memory cells using sandwich type free layers. Paper EC-04 Presented at MMM Conference, Seattle, November 15, 2001. Schwee, L. et al. (1982). The concept and initial studies of a crosstie random access memory (CRAM). J. Appl. Phys. 53(3), 2762. Wolf, S. et al. (2001). Spintronics: a spin-based electronics vision for the future. Science 294, 1488 – 1495. Zheng, Y. et al. (2001). Switch free measurement of MTJ MRAM arrays. Paper EC-02 Presented at MMM Conference, Seattle, November 15, 2001. Zhu, J., Zheng, Y., and Prinz, G. (2000). Ultrahigh density vertical magnetoresistive random access memory. J. Appl. Phys. 87(9), 6668.

Color plates

379

HWORD

< iSENSE

f f


0

k F, min (c) ηk0

kF, min k0

kx kF, max kx δk x

Fig. 6.18 Energy dispersion and Fermi surface diagrams describing Rashba effect and current-induced nonequilibrium spin magnetization. (a) Energy dispersion along kx ; showing spin-split subbands. (b) Fermi surface in equilibrium. (c) Nonequilibrium Fermi surface displaced by positive bias current I þ . Solid (dotted) arrows represent down (up) spin states.

312 M. Johnson to the Hamiltonian, ~ z; Hso ¼ aðs~ £ kÞ·^

ð6:2Þ

where s~ is the Pauli spin matrix. The electron energy dispersion relation is EðkÞ ¼ ð"2 k2 =2mp Þ ^ ak:

ð6:3Þ

As plotted for kx in Fig. 6.18(a), the spins are degenerate at kx ¼ 0 and spin splitting increases linearly with lkx l up to the Fermi energy EF : For kx . 0 there are more carriers with spin down than up, and the opposite is true for kx , 0: The Fermi sea is a paraboloid of revolution about the E-axis, and the Fermi surface is a pair of concentric circles [Fig. 6.18(b)] with radii kF;max and kF;min : The spin eigenstates, determined by the Rashba term and denoted by arrows, are along ^^y for momentum states kx [Fig. 6.18(a)]. More generally x and y are not good quantum numbers and the spin eigenstates have a rotational form implied by Fig. 6.18(b) (Silsbee, 2001; Hammar et al., 2000a,b). A system with a circular Fermi surface is ideal for Shubnikov–de Haas measurements, and the Fermi surface depicted in Fig. 6.18(b) was first deduced from beat patterns in Shubnikov– de Haas oscillations (Luo et al., 1990). The Rashba spin –orbit effect has several important consequences. First, if a carrier is injected into such a 2DEG with a known spin orientation, the orientation will randomize very ~ p because the magnitude of the effective field is large, rapidly. The spin precesses rapidly around H p ~ changes with any scattering event that alters momentum. The result is that but the direction of H spin relaxation is rapid. Second, the Rashba effect can be modulated by varying an externally applied gate voltage. This permits novel studies of the Fermi surface of a 2DEG (Nitta et al., 1997) and is the concept that underlies the original device idea of Datta and Das (1990). Third, the unusually strong spin –orbit effect can be used to generate a population of nonequilibrium spinpolarized electrons. In turn, this population can be detected using a ferromagnetic film as a spin-sensitive electrode. The result is a technique, called ‘current-induced nonequilibrium magnetization’, that can characterize the spin transport properties of an individual ferromagnetic – 2DEG interface (Hammar et al., 1999, 2000a; Hammar and Johnson, 2001). Given the difficulties associated with the experimental development of an SI FET, studies of the component parts of the device are very useful. Current-induced nonequilibrium magnetization is described in the following way. Referring first to Fig. 6.18(b), which describes the equilibrium condition, the total number of up-spin and down-spin carriers is equal for zero bias current ðI ¼ 0Þ: However, the situation changes when a bias current flows. A positive current imposed along the x^ -axis of a 2DEG channel displaces the Fermi sea (and circles) to the right by dkx [dotted lines of Fig. 6.18(c)]. For the branch kx . 0; up-spin (down-spin) carriers are added near kF;min ðkF;max Þ: The chemical potentials of both spin subbands, EF;" and EF;# ; are raised, but EF;# is raised more than that of EF;" because the incremental area of the Fermi sea at kF;max is larger than that at kF;min : Similarly, for the branch kx , 0;

Broader digital electronics applications of magnetoelectronics

313

down-spin (up-spin) carriers are depleted at 2lkF;min l ð2lkF;max lÞ: As a result, the Fermi surface tilts upward towards þkx [Fig. 6.18(a)] (Hammar and Johnson, 2000; Hammar et al., 2000b). For negative bias current, the tilt slope reverses. This relative difference eDV ¼ EF;" 2 EF;# represents a nonequilibrium population of spinpolarized electrons. The magnitude DV can be measured by appealing to the spin injection technique, and using a ferromagnetic electrode F as a spin-sensitive potentiometer. Two experimental geometries have been used for this measurement, and they are described with the aid of Fig. 6.19. A 2DEG mesa structure is patterned into a channel of width w, where w is typically 1–10 mm, and has four ohmic contacts S1–S4 [Fig. 6.19(a), top view]. A cross-sectional view of a (a)

F1 y Hy

F

x

S4

S1 2DEG

w

S2

F2

S3

(b) Permalloy

SiN

In0.45Al0.55As Al0.6Ga0.4Sb 4 ML InAs Al0.6Ga0.4Sb

50 nm F (metal) 5 nm 7.5 nm barrier (doping) (insulator) 12.5 nm

InAs

15nm

Al0.6Ga0.4Sb

200 nm

AlSb

>2.0 µm

SQW barrier (insulator)

Fig. 6.19 (a) Schematic top view of device geometry for detecting current-driven nonequilibrium spin magnetization. (b) Cross-section of planarized device structure.

314 M. Johnson typical heterostructure is shown in Fig. 6.19(b). The SQW is formed at the 15 nm thick InAs layer that is sandwiched between the two insulating layers of AlGaSb. The carrier density in the 2DEG is electron doped from 4 ML of InAs grown near the middle of the top, confining AlGaSb layer. The InAlAs cap layer is effective for reducing hole leakage current. The relatively high resistance of the F –I–2DEG interfaces, approximately constant for the temperature range 4 K , T , 295 K, implies the top insulating layers form a low transmission barrier for transport. The resistivity of the ferromagnetic metal electrode is about 30 mV cm and that of the 2DEG is about 150 mV cm. However, the resistivity of the barrier was about 10 V cm, about five orders of magnitude larger. Therefore, ‘resistance mismatch’ is not important and the interface resistance dominates spin transport (refer to Chapter 1) (Johnson and Byers, 2003). The carrier density, mobility, and sheet resistance at 77 K (296 K) were determined from a Hall measurement (before processing) to be 8:7 £ 1011 cm22 ð1:3 £ 1012 cm22 Þ; 75 000 cm2/V s (25 000 cm2/V s), and 80 V/square (190 V/square), respectively, with weak temperature dependence below 77 K. To pattern the device structure, the 2DEG mesa is formed by optical lithography (Hammar et al., 2000a) and an Ar ion mill dry etch. Next, the InAs SQW is undercut with a selective wet etch [Fig. 6.19(b)]. The sample is then planarized with SiN prior to dissolving and removing the photoresist. This planarization prevents accidental contact to the SQW at a mesa side wall, and presents a smooth surface for the ferromagnetic films, thereby promoting single domain behavior. Ferromagnetic electrode F is fabricated by optical lithography with a width that varies from 1.5 to 2.5 mm, followed by e-beam deposition of Ni0.8Fe0.2 or Fe0.1Co0.9, and liftoff. The planarization was accurate within the rms roughness of the sample surface, as determined by AFM. MFM images at room temperature showed continuous magnetization in the sample region in the remanent state. Referring again to the top view [Fig. 6.19(a)], the ferromagnetic electrode spans the 2DEG channel and contacts are available at either end, F1 and F2. In the potentiometric geometry, bias current ^I is driven along the 2DEG channel from S1 to S4 and F is used as an open circuit spin-sensitive potentiometer by connecting an infinite impedance voltmeter between F2 and S2. The externally applied magnetic field Hy is swept over a range that is larger than the coercivity of F, changing its magnetization orientation from 2M^y to þM^y: Referring to Fig. 6.18(a), the voltage difference DVF measured by F as the difference between voltages associated with the two magnetization states ^My is DVF ¼ P1 DV;

ð6:4Þ

where P1 is the fractional polarization of carriers in F (Hammar and Johnson, 2000). This measurement of the spin subband chemical potentials of the 2DEG can also be made by using a diode geometry, injecting bias current through the F –2DEG interface and measuring the interfacial conductance for the two magnetization states ^My : Referring to Fig. 6.19(a), bias current I is applied from terminal S1 to F1 and voltage V is measured from terminal F2 to S4. The diode geometry has the advantage of demonstrating both spin injection and detection simply by changing the bias polarity, and demonstration that spin-polarized current can be

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315

transmitted across a ferromagnetic metal –2DEG interface is important. The potentiometric geometry has pedagogical advantages: (i) it is a conceptually straightforward spin detection experiment in which an open circuit voltmeter measures a spin-dependent voltage and (ii) the geometry is simple, with current flowing through the channel under F but zero current flowing in F. Data from both geometries show the same effect (Hammar and Johnson, 2000; Hammar et al., 2000a) with quantitative agreement. The measured voltages were linear with I in the experimental range 10 mA # I # 200 mA and examples of data sets for a device with a channel width W ¼ 15 mm and ferromagnetic electrode width WF ¼ 2:3 mm are presented in Fig. 6.20 as resistances RP and RI for the potentiometric and diode (or interface) geometries, respectively. For the data set shown as the bottom trace in Fig. 6.20, the hysteretic voltage is associated with the hysteresis of F and the difference IDRP ¼ ½V 2 V0 ðHy . 40 OeÞ 2 ½V 2 V0 ðHy , 40 OeÞ < 40 mV (for a bias current of 100 mA) is identified as VðIþÞlMþ 2 VðIþÞlM2 ¼ DVF [Fig. 6.18(a) and Eq. (6.4)]. The symmetry of the hysteretic voltage was observed to reverse when the bias polarity is reversed, consistent with the predicted change in the sign of the slope. The data set shown in the top trace of Fig. 6.20 represents a measurement in the diode geometry, under the same conditions. This simplified discussion has used a single slice of the Fermi sea [Fig. 6.18(a)]. However, the experiments involved samples having width on the order of a micron or more and carrier trajectories having a range of values of ky : A recent theory (Silsbee, 2001) gives a complete and rigorous nonequilibrium calculation that averages electrochemical potential differences over the Fermi surface. The key parameters are the relative shift h / kF;max 2 kF;min [also proportional to a, refer to Fig. 6.18(a)] and the fractional polarization m of carriers in F (this parameter is called P elsewhere in this chapter). It predicts that differences of resistance DR should be approximately the

660.5 0.2

RI (Ω)

∆RP (Ω)

661.0

0.0 −0.2 −0.4 −200

−100

0 Field (Oe)

100

200

Fig. 6.20 Examples of data, T ¼ 4 K: Top trace, right axis: RI : Bottom trace, left axis: DRP : Solid lines: sweep field Hy up. Dotted lines: sweep Hy down. Positive bias current (symmetry reversal for negative bias current is not shown).

316 M. Johnson same for interface and potentiometric measurements, DRI < DRP : It further predicts that the resistance modulation should be proportional to the resistance Rl of a length ‘ (with ‘ an electron mean free path) of the 2DEG channel, Rl ¼ R2DEG ð‘=WÞ; so that the ratio DRP =Rl is approximately constant for device structures with similar values h and m. In the limit of low junction conductance and narrow F electrodes, WF p W; this theory makes the quantitative prediction: DRP ¼ lmlh: Rl

ð6:5Þ

Referring to Fig. 6.20, the observation that DRI ¼ DRP is consistent with the Silsbee theory. Quantitatively, the measured values of DR can be compared with Eq. (6.5). Using accepted values of m ¼ 0:4 ^ 0:05 (Nadgorny et al., 2000), a value h # 0:1 is deduced, which lies in the range proposed by theory (Silsbee, 2001). The data show a weak temperature dependence in the range 4 K , T , 300 K and weak dependence on the magnitude of the interface resistance (Hammar and Johnson, 2001; Johnson, 2001), in further confirmation of the theory. The converse of this nonequilibrium effect has also been reported (Ganichev et al., 2001). Multiple and single quantum well heterostructures were irradiated with circularly polarized light. A nonequilibrium population of spin-polarized electrons was thereby generated with a net spin orientation that depended on the helicity of the incident light. The spin –orbit Rashba coupling generated an electric dc current with a direction that varied as the orientation (spin-up or spindown) of photo-induced electrons was changed. Finally, a consideration of symmetry arguments has resulted in a minor modification of the Silsbee theory of current-induced nonequilibrium magnetization (Silsbee, 2003a,b). The Onsager reciprocity relations (Onsager, 1931; Casimir, 1945) imply that the junction resistance between a ferromagnet and a nonmagnetic material cannot change when the magnetization orientation of the ferromagnet is reversed. These relations are not relevant to the potentiometric geometry, but they do pertain to the diode geometry (Silsbee, 2003a). When considering this, Silsbee has noted that shifts of spin subband chemical potential can alter the steady-state current paths in the 2DEG in the vicinity of the F film. Thus, changes in the voltage detected in the diode geometry, DVI ; do not imply the interface resistance itself has changed, and the Onsager relations are not violated. 6.3.1.3

Electrical spin injection and detection in a 2DEG channel

Following these studies of spin transport across a single interface, electrical spin injection and detection in a high mobility 2DEG was experimentally demonstrated by fabricating two F/2DEG junctions, of the form shown in Fig. 6.19(b), on a common channel. Narrow channels, about 900 nm wide, were defined on an InAs SQW heterostructure using optical lithography and an Ar ion mill dry etch. The chip was backfilled with SiN to planarize the surface at the level of the mesa and to cover the side edges of the 2DEG.

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F2

317

F1

S1

S2

LX

X x= 0

Fig. 6.21 Top view of nonlocal geometry for spin injection and detection.

Figure 6.21 shows a top view of the experimental geometry. Two ferromagnetic metal electrodes, F1 and F2, were fabricated on a common InAs channel (six separate channels were connected in parallel for improved signal-to-noise ratio; not shown in Fig. 6.21). The interelectrode spacing Lx was on the order of magnitude of the carrier mean free path, a few microns. Using the nonlocal geometry of the original spin injection experiment (Johnson and Silsbee, 1985, 1988a,b) (refer to Chapter 1), spin-polarized electrons were injected from F2 into the 2DEG and the injected current was grounded at terminal S1. Detecting electrode F1 was grounded at S2, and acts as a spin-sensitive potentiometer. Ballistic and quasi-ballistic spin-polarized electrons that are injected at the F2/2DEG interface have initial trajectories to the left and right in equal numbers. Carriers with initial trajectories to the right eventually scatter, and all the current is drained at ground. Since there is no net current in the region x . 0; the entire portion of the channel to the right of the injector is a constant potential surface. In the absence of nonequilibrium spin effects, the detecting circuit would measure zero voltage. Injector F2 was fabricated with Permalloy and had a relatively small coercivity, HC2 < 30 Oe: Detector F1 was fabricated with FeCo and had a relatively large coercivity, HC1 < 70 Oe: By applying an external field Hy in the film plane and parallel to the easy magnetization axis of the ferromagnetic films, the relative magnetization orientation of injector and detector was manipulated between parallel and antiparallel. An example of electrical spin injection and detection is seen in the data shown in Fig. 6.22, taken at a temperature of 4.2 K using a sample with Lx ¼ 10:6 mm: The baseline resistance of about 0.36 V is two orders of magnitude smaller than the channel resistance Rch ¼ 52 V; demonstrating the effectiveness of the nonlocal geometry. The overlapping dips that appear in the

318 M. Johnson

0.40

R (Ω)

0.38

0.36 sweep up sweep down

0.34

0.32 −800

−400

0 H y (Oe)

400

800

Fig. 6.22 Examples of data showing detection of electrical spin injection. The sample has a separation of Lx ¼ 10:6 mm between injector and detector. Solid lines: sweep field down. Dotted lines: sweep field up. The hysteretic dips are characteristic of spin injection and detection.

range 2200 Oe , Hy , þ200 Oe have the qualitative shape that is characteristic of spin injection (Hammar and Johnson, 2002). Data were also taken on a sample with an interprobe separation of Lx ¼ 3:2 mm. Hysteretic dips that were qualitatively similar to those of Fig. 6.22 were observed, and the amplitude was substantially larger. From the amplitude dependence of these two probe separations, an upper bound of the spin-dependent mean free path was estimated to be L ¼ 4 mm. It is interesting to note that the spin-dependent mean free path is longer than the electron mean free path, Ls . ‘: The reason is that the measurement averages over many electrons having a variety of trajectories. A fraction of the carriers have trajectories along x^ and are in spin eigenstates. These electrons have very long spin-dependent mean free paths. The magnitude of the spin injection effects diminished by about 20% at an elevated temperature of 150 K. Data at higher temperatures could not be taken because of failure of the wire bonds. The magnitude and temperature dependence agree with a recent theory of spin-dependent transport in quantum wells of III–V heterostructures (Hall et al., 2003) (Lau et al., 2001). These data demonstrate the electrical injection of spin-polarized electrons across a low transmission barrier and into a high mobility 2DEG channel, and their subsequent detection by a ferromagnetic electrode. The nonlocal geometry is similar to that of the Datta –Das device (Datta and Das, 1990), and realization of an SI FET is plausible. While the spin injection effects have been small, shrinking the device to the nanometer dimensions of a technologically viable device may increase the magnitude significantly.

Broader digital electronics applications of magnetoelectronics 6.3.2

319

Bipolar spin-polarized transport in semiconductors

The field of spin-polarized transport in metals and semiconductors has been devoted, almost entirely, to passive systems that are studied in a linear response regime. An exception is ‘charge – spin coupling’ in Johnson–Silsbee theory of spin injection and spin accumulation (Johnson and Silsbee, 1985, 1987, 1988a). As described in Chapter 1, a thermodynamic force H p is associated ~ This force can drive currents of with a nonequilibrium population of spin-polarized electrons, M: nonequilibrium spin, either in bulk materials, or forwards or backwards across a F–N interface. Following the principle of ‘charge –spin coupling’, the properties of charge and spin inhabit the same carrier, the electron, and therefore the force H p (which is proportional to nonequilibrium ~ also drives electric currents, either in the bulk or forwards or backwards across magnetization, M) an F –N interface. If one describes an F1 –N–F2 structure in analogy with an emitter –base – collector device (Johnson, 1993), the resulting interfacial currents of the form Jeb and Jbc are somewhat analogous with currents in a semiconductor bipolar transistor (Sze, 1981). One important difference is that effects of ‘charge – spin coupling’ in an all-metal F1 –N– F2 system are well described by linear response. Semiconductor diodes and bipolar transistors, of course, are characterized by carrier populations that have exponential dependence on several parameters. This intrinsically nonlinear response is the source of such useful characteristics as current and power gain. Interesting questions can be asked: can one generalize the equations of motion for electrons and holes in semiconductors to include spin-polarized currents, spin accumulation, and effects of charge–spin coupling? If this is accomplished, are there predictions of interesting nonlinear effects such as magnetoresistance, current gain, or power gain? Both questions can be answered in the affirmative, following the important theoretical work (Zutic et al., 2001, 2002; Fabian et al., 2004) described in this section. After the derivation of a general theory described below, it will be reasonable to assume that the spin lifetime of holes, typically less than 1 ps (Hilton and Tang, 2002), is very short. With strong spin –orbit interaction in a valence band, the spin relaxation time and momentum relaxation time are approximately the same (Meier and Zakharchenya, 1984). The spin relaxation time is so short that transport is dominated by electrons, and the spin-dependent structure of the valence band is much less important than that of the conduction band. A semiconductor system generalized to include the effects of equilibrium and nonequilibrium spin can have several material components, including a nonmagnetic and a magnetic semiconductor. A magnetic semiconductor (Munekata et al., 1989; Dietl, 2002) is characterized by intrinsic spin splitting (Zeeman or exchange) of the carrier bands. Zeeman splitting can be enhanced significantly when carriers have large g-factors. In the case of narrow band semiconductors, values of g for bulk InSb and InAs are 250 and 215, respectively, at room temperature. Exchange splitting can also be realized by using a ferromagnetic semiconductor (Ohno, 1998) such as GaMnAs. Spin splittings are on the order of 10 meV in ferromagnetic semiconductors.

320 M. Johnson A semiconductor with magnetic impurities is another system of great interest. In this example, the semiconductor may be doped with a density Na ðrÞ of acceptors and a density Nd ðrÞ of donors. Densities Na and Nd are constants for material that is doped with spatial homogeneity. More generally, the doping may be spatially inhomogeneous. In this case, the variable r refers to position in some convenient coordinate system. In examples used later in this section, the coordinate system is chosen to have x along a cross-sectional cut, normal to the growth plane. The semiconductor may also be doped with magnetic impurities, whose presence leads to large g-factors for the electrons and holes, gn ðrÞ and gp ðrÞ; respectively. Values of g can be as large as 500 at cryogenic temperature. For example, g has a value of < 500 in Cd0.95Mn0.05Se at 1 K (Tsui et al., 2003). Once again, the magnetic doping may be spatially homogeneous such that gn and gp are constants. More generally, the magnetic doping may be spatially inhomogeneous. It is already apparent that spin-polarized bipolar transport in semiconductors is much more subtle and complex than unpolarized transport. In this second example, the spin splitting derives from the application of a homogeneous external field, B, which causes a Zeeman splitting. Following the notation of Zutic et al. and introducing subscript l for spin (l ¼ 1 ;"; l ¼ 21 ;#Þ; the Zeeman energy shift of electrons is 2lqzn ðrÞ ¼ 2lgn ðrÞmB B=2;

ð6:6Þ

and the Zeeman energy shift of holes is

lqzp ðrÞ ¼ lgp ðrÞmB B=2;

ð6:7Þ

where mB is the Bohr magneton, q is the proton charge, and z can be described as a spin-dependent electric potential. The charge currents for up- and down-spin carriers result from an electric field that comprises both applied and built-in (deriving from charge inhomogeneities) fields, E ¼ 7f; nonuniform magnetic potentials z, and electron (hole) densities n ( p) (Zutic et al., 2001): Jnl ¼ qmnl nl E þ qDnl 7nl 2 qlmnl nl 7zn ;

ð6:8aÞ

Jpl ¼ qmpl pl E 2 qDpl 7pl 2 qlmpl pl 7zp ;

ð6:8bÞ

where m and D are carrier mobility and diffusion coefficient, respectively. The third term, proportional to l7z; describes a magnetic drift which forces carriers with opposite spin orientation (l ¼ 1 or 21) to go in opposite directions. Using Eqs (6.8a) and (6.8b) and introducing a change of variables, the current densities for charge and spin, J ¼ J" þ J# and Js ¼ J" 2 J# ; respectively, are Jn ¼ sn E 2 ssn 7zn þ qDn 7n þ qDsn 7sn ;

ð6:9aÞ

Jp ¼ sp E 2 ssp 7zp 2 qDp 7p 2 qDsp 7sp ;

ð6:9bÞ

and Jsn ¼ ssn E 2 sn 7zn þ qDsn 7n þ qDn 7sn ;

ð6:10aÞ

Jsp ¼ ssp E 2 sp 7zp 2 qDsp 7p 2 qDp 7sp ;

ð6:10bÞ

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321

where n ¼ n" þ n# ; sn ¼ n" 2 n# : The electron charge and spin conductivities are defined as sn ¼ qðmn n þ msn sn Þ and ssn ¼ qðmsn n þ mn sn Þ; respectively, where mn ¼ ðmn" þ mn# Þ=2 and msn ¼ ðmn" 2 mn# Þ=2; and similar definitions are used for diffusion coefficients. Analogous notations and definitions are used for holes. Equations (6.9) and (6.10) are a generalization of the Johnson– Silsbee magnetotransport equations (Johnson and Silsbee, 1987; see also Chapter 1) and reflect the spin –charge coupling in bipolar transport in inhomogeneous magnetic semiconductors. Note that a spatial variation in spin density, as well as in q7z (which describes magnetic drift), can cause charge currents. Conversely, spin currents can flow as a result of spatial variations of carrier densities and gradients of f: Next, stationary continuity equations for electrons and holes are derived. Assuming that generation and recombination of electrons and holes are mostly due to interband processes and that electrons (holes) with a given spin can recombine with holes (electrons) of arbitrary spin, the continuity equations are 7·

Jnl n 2 n2l 2 ls~n ¼ þwnl ðnl p 2 nl0 p0 Þ þ l ; q 2T1n

ð6:11Þ

7·

Jpl pl 2 p2l 2 ls~p ¼ 2wpl ðpl n 2 pl0 n0 Þ 2 ; q 2T1p

ð6:12Þ

where n0 and p0 are the equilibrium carrier densities, w is the interband recombination rate (assumed generally to be spin dependent), and T1 is the spin relaxation time. Note that spin relaxation equilibrates electron spin populations, while preserving the nonequilibrium electron density. It follows that, for a nondegenerate semiconductor, s~n ¼ an0 n; where an0 ¼ sn0 =n0 ¼ tanhðqzn =KB TÞ is the fractional density of polarized electrons in equilibrium, with KB the Boltzmann constant and T the temperature. These generalized equations are quite powerful. The distributions of charge and spin in a magnetic (or nonmagnetic) semiconductor under applied bias V can be determined from Eqs (6.9) –(6.12) and Poisson’s equation, 7·e E ¼ r; where r ¼ qðp 2 n þ Nd 2 Na Þ and e is the dielectric constant of the semiconductor. These equations are too complicated for analytic solution, but they can be solved numerically for a variety of interesting structures. 6.3.2.1

Spin diodes

Following the principle of working from less complex to more complicated structures, and deriving device components that can be used to build more complicated devices, a good starting point is an analysis of a magnetic p–n junction (Zutic et al., 2001, 2002). The reasonable simplification that electrons are magnetically active, but not holes ðzp ¼ 0Þ; is now employed. In Fig. 6.23, up-spin and down-spin electrons are represented by arrows, but holes are presumed to have random spin orientation [because of rapid relaxation (Hilton and Tang, 2002)] and are represented by open circles. Spin injection is the process of interest from a device having a

322 M. Johnson

Fig. 6.23 Band-energy schemes for magnetic p – n junctions with magnetically active electrons (arrows). Holes (circles) are unpolarized. (a) Electrons from the magnetically active n-region (discernible by the conduction band split) can be injected into the nonmagnetic p-region only at large bias. (b) Spin extraction from a magnetic p-region, where electrons are minority carriers, is similar. (c) If there is a nonequilibrium population of spinpolarized majority electrons and the p-region is magnetic, a giant magnetoresistance and spin voltaic effects arise. (d) The former can be observed in a scheme, where electron spin is injected from a magnetic heterostructure N into the nonmagnetic n-region, which forms a p – n junction with the magnetic p-region.

magnetic n-side [Fig. 6.23(a)], and spin extraction can be studied with a device having a magnetic p-side [Fig. 6.23(b)]. For the purpose of numerical simulations, Zutic et al. choose some specific parameters for their device. The GaAs p–n junction has a length of 12 mm (x ¼ 0 is at the far left of the device) and is doped with a Na ¼ 3 £ 1015 cm23 acceptors (Nd ¼ 5 £ 1015 cm23 donors) to the left (right) of x ¼ 6 mm: The doping profile is constant for regions except the space–charge region, x ¼ 6 ^ 0:1 mm; where a linear gradient is assumed. Magnetism and spin splitting of the conduction band are achieved by doping with magnetic impurities, following the profile of Na ðxÞ and Nd ðxÞ; in order to create large g-factor values and induce a Zeeman splitting that is proportional to an applied field, B. Other parameters for GaAs at room temperature are the electron and hole diffusivities, Dn ¼ 10Dp ¼ 103:6 cm2 =s; electron and hole mobilities, mn ¼ 10mp ¼ 4000 cm2 =V s; intrinsic nonmagnetic carrier density, ni ¼ 1:8 £ 106 cm23 ; recombination rate, w ¼ 0:33 £ 1025 cm3 =s; spin relaxation time, T1 ¼ 0:2 ns; minority diffusion lengths, Ln ¼ 1 mm; Lp ¼ 0:25 mm; and the electron spin diffusion length in the n (p) region is Lsn ¼ 1:4 mm ðLsp ¼ 0:8 mmÞ: The calculated built-in voltage (for B ¼ 0) is 1.1 V. Spin injection from n to p is schematically described in Fig. 6.23(a). An external field (having a value that gives qz ¼ 0:5KB T; for the results discussed in Fig. 6.24) causes spin splitting of the magnetic n-region, and the up-spin subband is more heavily populated with carriers. At low bias, below the built-in value of 1.1 V, there is no significant spin injection. While there are

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323

exponentially more up-spin carriers in n, the barrier for crossing the space –charge region is exponentially larger for up-spin electrons than for down-spin. These two exponential factors cancel and no net spin current flows through the space –charge region. The same result follows from analogous reasoning for spin extraction from a magnetic p-region [Fig. 6.23(b)] at low bias. As the bias voltage increases, the barrier for crossing the space –charge region is reduced and the two exponential factors are no longer balanced. Spin injection and extraction become large and both processes are sensitive to the spin relaxation time, increasing further if T1 increases. These results are demonstrated in Fig. 6.24, where the fractional density of spin-polarized electrons, a ¼ s=n is plotted for a variety of values of bias. A nonlinear spin injection (and extraction) process is an example of an important and interesting result that derives from the fully general formalism of Zutic et al. The current through the magnetic p–n junction also depends on magnetic field, because the spin splitting in the magnetic material is proportional to B. In the pedagogical process of Fig. 6.23(a), increasing the magnitude of B causes an increase in the spin splitting and a larger population of up-spin electrons. For the high bias regime, with V larger than the built-in voltage, the density of spin-polarized carriers crossing to the p-region increases exponentially. In other words, the transport current, and therefore properties such as conductance and resistance, are sensitive to external field and an exponential magnetoresistance is predicted.

Fig. 6.24 Calculated spin polarization profiles for different forward bias and spin relaxation rates. Spin injection (top) from the magnetic n-side into the nonmagnetic p-side occurs only at large bias. Bias values of the different traces are given in volts. The largest injection in the graph is for V ¼ 1.5 V, with the spin relaxation time increased to 100 T1 : Similar behavior is observed for spin extraction from the nonmagnetic n-region into the magnetic p-region (bottom). The magnetic splitting is qz ¼ 0:5KB T:

324 M. Johnson Figure 6.23(c) and (d) depicts another mechanism for the observation of a large magnetoresistance. If a large nonequilibrium population of polarized electrons is induced in the nonmagnetic n-region, the opposing exponential factors are again thrown out of balance and a large spin injection effect can be expected. In Fig. 6.23(d), the nonequilibrium population of up-spins is induced in n by spin injection from an appropriate magnetic region labeled N. This figure also shows how an exponential, giant magnetoresistance could be observed if the magnetization orientation of p can be independently manipulated to be parallel or antiparallel with that of N. The authors predict that this structure could also be used to observe a spin-voltaic effect: appropriate spin populations can induce a nonzero current flow at zero voltage bias (Zutic et al., 2001).

6.3.2.2

Spin bipolar transistor

Having derived some understanding of magnetic p–n junctions, the more complex and interesting device to consider is an MBT (Fabian et al., 2004). Figure 6.25 is a schematic diagram of a nonmagnetic (n)/magnetic (p)/nonmagnetic (n) transistor in an emitter – base– collector configurations, and the following discussion offers a qualitative description of the operation principles. Forward bias applied from the base to the emitter lowers the barrier for electrons to cross from the emitter to the base. Reverse bias from the base to collector increases the energy barrier for electron transport. A steady-state population of nonequilibrium spins is maintained in the emitter by spin injection, using optical pumping of circularly polarized light (depicted) or electrical spin injection from a ferromagnetic electrode (not shown). The nonequilibrium spins are created and maintained within a spin diffusion length of the emitter –base depletion layer. Spin-polarized transport from the emitter to the base generates a nonequilibrium spin population (spin accumulation) in the base, with a value that depends on the spin splitting in the base, and therefore depends on magnetic field. The important question is whether current gain in the device can be controlled by this ‘source’ spin accumulation. If carrier recombination in the base is negligible, the base current is formed mostly by holes that flow to the emitter. By contrast, the collector current entirely derives from nonequilibrium electrons injected from the emitter to the base, and then to the collector. The gain is then proportional to the ratio of the electron and hole nonequilibrium densities in the junction region between the emitter and base. The nonequilibrium hole density dpbe cannot be controlled, but the injected electron density is sensitive to both the spin splitting qzb and the density of polarized spins in the emitter, dae : Increasing the external field causes qzb to increase, and therefore, the equilibrium population of the electrons in the base increases. Maximizing the product dae a0b ; where a0b is the equilibrium spin-polarized carrier density in the base, lowers the barrier for the more populated spin state and optimizes electron transport across the base –emitter junction. The result is a current gain b that is sensitive to the spin splitting qz; and therefore sensitive to the external magnetic field. Results of numerical calculations for GaAs and Si npn transistors, using generic parameters, are shown in Fig. 6.26, where b is plotted as a function of qz=KB T: The ‘spin’ dependence of gain is relatively small for the GaAs device. However, a fairly large

Broader digital electronics applications of magnetoelectronics

forward

reverse P

N emitter

325

N

base

je

E

collector jc

jb

P wc Vbe Vbc wb