Spintronics - The Journal of Physical Chemistry B (ACS Publications)

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J. Phys. Chem. B 2005, 109, 14278-14291

FEATURE ARTICLE Spintronics Mark Johnson Materials Physics DiVision, NaVal Research Laboratory, Washington, D.C. 20375 ReceiVed: February 9, 2005; In Final Form: May 6, 2005

Thin ferromagnetic films can be lithographically patterned and incorporated into magnetoelectronic devices that have applications in digital electronics. Their bistable magnetization states are adaptive to application as memory cells in nonvolatile, magnetic random access memories (MRAM). Prototype MRAM chips are characterized by rapid, low energy switching and excellent durability. This novel approach to integrated memory is expected to have immediate impact in the niche market of high performance, embedded memory. Research in the field is confronting several issues associated with the reproducibility of device behavior and scaling device structures to the nanometer dimensions of competing silicon devices. If successful solutions are found, the technology could challenge large segments of the semiconductor memory market. Another research effort is aimed at the development of a spintronic device with power gain. Such a device would enable new kinds of logic architectures, as well as novel on-chip combinations of memory and logic. Our studies investigate the dynamics of high-speed magnetization switching processes. We are also studying charge and spin transport in high mobility semiconductor heterostructures, with the ultimate goal of creating a spin-injected field effect transistor.

Overview Semiconductor technology is an extremely successful industry, and has transformed society in many ways. Indeed, the reproduction, dissemination, and storage of information has led to a present era that is rightly called the “information age.” In digital semiconductor electronics, binary information is encoded and transmitted as voltage pulses, and memory is achieved by storing charge on a capacitor. Semiconductor devices have been miniaturized to nanometer dimensions, and the minimum feature size, f, of devices in production today is less than 100 nm. Complicated information processing systems can be integrated on a few small chips, or even a single chip, and functions of information manipulation can be performed quickly and inexpensively. Although the technology is extraordinarily successful, there are weaknesses. For example, capacitors are intrinsically leaky and on-chip semiconductor memory is volatile. Information stored in high density, low cost dynamic random access memory (DRAM) must be refreshed every few ms, and data are lost whenever the system is powered down. Nonvolatile semiconductor memory, based on a “floating gate” device structure described below, has achieved high density, low cost, and a market success of roughly $16 billion in sales in 2003. These devices, however, have problems and weaknesses of their own. Write and erase times are very slow, creating relatively high energy requirements, and endurance is limited to roughly a hundred thousand write/erase cycles. In parallel with the rapid development of semiconductor technology, the recent past has seen several significant advances of basic and applied research in the area of magnetic materials. Magnetic domains in thin film magnetic media can be made to 10.1021/jp0580470

have two bistable magnetization states. This has been exploited by the magnetic recording industry, which itself has been a highly successful technology for several decades. Information storage using magnetic media is characterized by high density and nonvolatility. However, media storage requires moving parts, and the constraints of mechanical systems impose limitations that include slow access to the stored data and a relatively large footprint with high power and poor reliability: how many of us have suffered through at least one head crash in our professional lifetimes? As one example of important applied research, ferromagnetic materials were lithographically patterned to form sensitive magnetic field sensors. In particular, after the introduction of anisotropic magnetoresistance (AMR) read heads in 1993, the areal density of data recorded with magnetic media began to increase by 60% per year. As an example of important basic research, new understanding of transport phenomena associated with spin polarized electrons led to the development of new kinds of device structures. By applying fabrication techniques to these novel structures, integrated devices with nanometer dimensions have been developed. Such devices were first used in magnetic recording technology. After the introduction of giant magnetoresistance (GMR) read heads in 1998, the areal density of magnetic media data increased by about 100% per year. This extraordinary rate, higher than the rate of Moore’s law for semiconductor technology, diminished slightly by 2004. Lithographically patterned ferromagnetic elements can be made to have intrinsically bistable magnetization states. It is natural to assign binary values of “1” and “0” to these two states and to use the magnetic element in a cell for nonvolatile digital

This article not subject to U.S. Copyright. Published 2005 by the American Chemical Society Published on Web 06/28/2005

Feature Article

Mark Johnson received his Ph. D. in Physics from Cornell University in 1986. He was a Postdoctoral Fellow at the University of California at Berkeley and a Visiting Scholar at Stanford University, and then became a Member of Technical Staff and Principal Invesitgator at Bell Communications Laboratory, New Jersey, in 1990. He joined the Naval Research Laboratory as a Research Physicist and Principal Investigator in 1995. His thesis work, which included both theoretical and experimental studies of the transport dynamics of spin polarized conduction electrons in metals, was among the earliest in the field now called Spintronics and provided a framework for his continuing research interests. Current topics include spin polarized transport in novel materials systems such as semiconductors and semimetals, the fabrication and characterization of nanometer-sized conductors and semiconductors, static and dynamic studies of magnetism in nanometer particles and elements, and the application of magnetoelectronic devices to biotechnology.

storage in an integrated memory application. It is also natural to ask if there may be other applications for magnetic materials and devices in the field of integrated digital electronics. The relatively new research field that is devoted to novel device structures that utilize spin polarized electrons is called “spintronics” or “magnetoelectronics”. The focus of basic research is understanding the physics of transport phenomena of spin polarized carriers. Applied research is focused on integrated digital electronics. Magnetoelectronic circuits can be described as having signals that are inductively coupled, current driven, and latching. This is a paradigm shift from semiconductor electronics, which is characterized by signals with transient levels that are capacitively coupled and voltage driven. Magnetoelectronic circuits typically have the following characteristics. The switching speed is determined by the rate of reversal of the magnetization orientation of the ferromagnetic element and is on the order of 1 ns in present prototypes. Typical input (write) currents are 1-10 mA, the energy of a single magnetization switching event is on the order of 100 pjoules, retention of the latched state is tens of years, and durability of the switching process is more than 1015 cycles. Digital applications of magnetoelectronics are driven by nonvolatile memory, and the relevant comparison is with the dominant semiconductor nonvolatile memory technology.1 The CMOS approach to nonvolatile memory, nonvolatile random access memory (NVRAM), is based on the capacitance of a “floating gate” in a field effect transistor (FET). 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.2 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

J. Phys. Chem. B, Vol. 109, No. 30, 2005 14279 dielectric, however, is that charging times (write times) and discharging times (erase times) are quite long, on the order of 10 µs 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, 10-7 joule and 10-5 joule, respectively. Furthermore, charge carriers tunneling at high voltage eventually degrade the dielectric, and floating gate cells have limited durability, 105 to 106 cycles. The performance advantages of the spintronic approach to nonvolatile memory are now apparent.3 Because of the intrinsic bistability of ferromagnetic elements, magnetoelectronic devices are natural nonvolatile memory cells. Magnetic switching times (read, write, and erase times) are a few ns, 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 per bit is about 10-10 joule, which is smaller than floating gate energies by 10-3 (10-5). Furthermore, magnetoelectronic cells have nearly infinite durability and endurance and are not susceptible to radiation damage. Thus, spintronic technology can offer improvements by several orders of magnitude over CMOS floating gate NVRAM in categories of speed, energy consumption, and durability. In fact, prototype magnetoelectronic memories (MRAM) have performance superior to static random access memory (SRAM), which is the CMOS memory family having the highest performance characteristics.4 If MRAM can be manufactured with a high packing density, it is plausible that spintronics can make a significant penetration in the growing nonvolatile memory market. The promise of realizing these advantages, and of having a market impact of some few billion dollars, has been the true driving force for the field. The goal of this article is first to present a background description of magnetoelectronics that is sufficient to permit a basic understanding of the technology. Several areas of research and development that are necessary to the success of spintronics are then identified. Next, we review our theoretical and experimental work relating to three of these key topics. Finally, a survey of topics in the related field of magnetic semiconductor spintronics is outlined and references are provided. Some Background Whereas semiconductor electronics relies on the manipulation of charge, spintronics is based on spin, a quantum mechanical property of electrons, and utilizes the manipulation and transport of spin polarized carriers. In a transition metal ferromagnet, such as Fe, Ni, or Co, the 4s and 3d conduction bands are intersected by the Fermi energy EF. As shown schematically in Figure 1a, the narrow 4s band has free electron characteristics and has distinct but equal down-spin and up-spin subbands, as required by the Pauli exclusion principle. The 3d band, however, has down- and up-spin subbands that are split and shifted by the exchange energy, Uex. For pedagogical simplicity, the 4s band can be ignored but the itinerant electrons in the 3d band have interesting properties. The spontaneous magnetization of the material arises because there are more down-spin than up-spin electrons. By definition, the down-spin (up-spin) subband in Figure 1a is called the majority (minority) spin subband. The concept that an electric current in a transition metal ferromagnet could be composed of spin-polarized carriers had its origin about 70 years ago. By calculating scattering rates for up-spin and down-spin itinerant electrons in the 3d band, Mott5 deduced that the carriers would have a net spin polarization P. More generally, an Einstein relation6 can be used to

14280 J. Phys. Chem. B, Vol. 109, No. 30, 2005

Johnson interface. Quantitatively, their results gave values of P ≈ 10% to 45% for Ni, Fe, and Co.9 While these experiments used a superconducting Al film as a detector of polarized spins, Julliere10 quickly realized that a second ferromagnetic film could perform the same function. His ferromagnet-insulator-ferromagnet (F1-I-F2) magnetic tunnel junction (MTJ) structure has become the dominant spintronic device and is described in greater detail below. Figure 1b shows the free electron-like conduction band of a nonmagnetic metal (N) such as copper or aluminum. Johnson and Silsbee recognized that spin subband conductances in a nonmagnetic metal were also independent and unique11 because spin-flip scattering events, which can transfer an up-spin to a down-spin state and vice versa, are rare. Their spin injection experiments showed that spin polarized electrons driven across a ferromagnet-nonmagnetic material interface (F-N) could diffuse into N over large distances, on the order of a hundred microns in bulk metals12,13 and on the order of one micron in metal films.14 They also demonstrated spin detection, the converse of spin injection, by showing that the resistance of a ferromagnet-nonmagnetic metal-ferromagnet (F1-N-F2) structure depended on the relative magnetization orientations of the two ferromagnetic layers. Although unrelated to classical magnetoresistance, this is called a magnetoresistance measurement because the magnetization orientations of F1 and F2 are controlled by an external magnetic field. It follows that the resistance of the device structure is also a function of magnetic field. This effect was soon exploited in thin film trilayer sandwiches15 and multilayers.16 It became generally known as the giant magnetoresistance effect (GMR), and the trilayer structure was called the “spin valve”. The characteristic magnetoresistance of a GMR device is defined as the difference of resistance between device configurations having antiparallel and parallel magnetization orientations, divided by the resistance with antiparallel orientation

MR )

Figure 1. Density of states diagrams for (a) transition metal ferromagnets and (b) nonmagnetic metals. Each spin subband has a unique conductance, gv or gV. Electric current in a transition metal ferromagnet is spin polarized because of the intrinsic difference between gv and gV in the 3d band.

relate the electrical conductance of a metal, g, to the density of states at the Fermi level, N(EF). The net polarization of current in the ferromagnet is then expressed phenomenologically as

P ) (Jv - JV)/(Jv + JV) ) (gv - gV)/(gv + gV) * 0 where Ji are the spin subband partial currents and gi are the spin subband conductances. The fact that each spin subband of the 3d band has a unique conductance, gv * gV (Figure 1a), is implicit in this expression. The experimental verification of Mott’s idea came about 30 years ago. Tedrow and Meservey7,8 fabricated planar tunnel junctions using thin superconducting (S) aluminum films, aluminum oxide tunnel barriers (I), and a ferromagnetic (F) metal counter electrode and performed low-temperature tunneling spectroscopy. Without describing the detailed technique, they could interpret their tunneling conductance curves to deduce the net polarization P of the tunnel current crossing the F-I-S

∆R Ranti - Rpar ) Ranti Ranti

(1)

The MR of spin valves reached values of 10% by the early 1990s, much larger than the typical value of anisotropic magnetoresistance (AMR), which is intrinsic to all transition metal ferromagnets, of 2 to 3%. During the excitement over the development of spin valves, Julliere’s magnetic tunnel junction work was nearly forgotten. He observed a MR value of about 14% at low temperature, and no effect at room temperature. In 1995, Moodera and Meservey17 applied techniques for the fabrication of superconducting Josephson junctions18 to the fabrication of MTJs. Using thin aluminum oxide tunnel barriers, their MTJs were stable at room temperature and they measured MR values of about 12%. Although the MR value decreases as the bias voltage across the barrier increases, low bias MR values of MTJs are presently about 60%, much larger than those of spin valves, and MTJs are now the dominant spintronic device. The Basic Idea This section discusses the basic approach of magnetoelectronic technology. We begin by describing the operation of an integrated magnetoelectronic device cell.1 Figure 2a shows a patterned ferromagnetic element, which will often be denoted simply as F and which is typically composed of a transition metal ferromagnet such as Ni, Fe, or Co, or alloys such

Feature Article

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Figure 2. (a) The lithographically patterned thin ferromagnetic film F has uniaxial magnetization anisotropy axis along x and has a width equal to a lithographic minimum feature size f. (b) The hysteresis loop that describes the magnetization of F as a function of field H externally applied along the x axis. (c) Integrated magnetoelectronic devices are made by fabricating write wires and using write currents that are inductively coupled to F, enabling device input. (d) For an integrated device, output is achieved by incorporating the F element in a magnetoelectronic device. In this sketch of a planar magnetoresisive device, the top and bottom layers are ferromagnetic films. For a magnetic tunnel junction (spin valve), the intermediate layer is a thin dielectric tunnel barrier, D (nonmagnetic metal, N). (e) Magnetoresistive response of symmetric magnetic tunnel junction or spin valve. (f) Memory effect of a symmetric magnetic tunnel junction or spin valve. The condition H ) 0 represents nonpowered status, and the bistable states represented by R ) R0, R0 + ∆R are intrinsically nonvolatile.

as Ni0.8Fe0.2 (Permalloy). When fabricated with an appropriate magnetic anisotropy, the magnetization M B lies along a uniaxial anisotropy axis (xˆ in Figure 2a), and has two stable orientations, along positive (right) and negative (left) xˆ . The vector magnetization M B is denoted in 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 Figure 2b. Starting at the top right (H . 0), M B is positive, pointing to the right. As the field H is decreased, M B follows the dotted line, and the dotted arrow denotes H decreasing from positive to negative values. At H ) 0, M B still points to the right and the value of M at H ) 0 is called the remanent magnetization, MR. Continuing to follow the dotted line, the field decreases further until H ) - |HC|, the field value defined as the coercive field, where M B reverses orientation and becomes negative, pointing to the left, for values H < - |HC|. 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 switching (or saturation) 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 Figure 2b, the remanent magnetization is the same as the saturation magnetization, MR ) MS. The hysteresis loop of Figure 2b graphically demonstrates the bistability of element F. Using digital electronics phrasing, F can be described as a latching, two state device component. The magnetization state of a ferromagnetic element, such as that depicted in Figure 2a, 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 xˆ . Integrated applications require methods for device input and output. The former refers to means for addressing the element and setting a bit state. Figure 2c is a perspective view of a ferromagnetic element, similar to that sketched in Figure 2a, along with an integrated “write wire”. In real applications, cells are embedded in a two-dimensional array of rows and columns and must be addressed using bit and word lines that 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

14282 J. Phys. Chem. B, Vol. 109, No. 30, 2005 carrying a write current, IW, a magnetic field H B circulates around the write wire with clockwise orientation. When the write wire covers the length of F, the magnitude of H B is approximately constant near the surface of the write wire and of F, and H decays weakly in the direction normal to the interface. Thus, current IW provides a 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 on the order of 1 ns,19,20 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 Figure 2c, a current pulse of positive polarity, +2IW, corresponds to a “0” and a current pulse of negative polarity, -2IW, corresponds to a “1”. A subtle but important point is that the amplitude of the write pulse is set at +2IW. This permits unique addressability of individual cells in a two-dimensional array. The amplitude of the write pulse applied to any row i or column j is set to provide half the required switching field value, RIW ) Hs/2, where R is a constant of proportionality for the inductive coupling. The field provided at cell (i, j) is then 2RIW ) 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, and is one of the key technological issues for magnetoelectronics. Device output requires that the magnetization orientation of element F must be communicated to the external world, preferably in a nondestructive way: The bit value must be sensed by some “read out” process. To do this, F is incorporated as one of the ferromagnetic components in a magnetoelectronic device. Figure 2d shows a schematic view of a generic sandwich device. Each ferromagnetic layer has thickness of a few nm. For an MTJ (spin valve), the intervening layer is a thin dielectric tunnel barrier, D (nonmagnetic metal layer, N). Figure 2e shows a generic magnetoresistance effect for an MTJ or spin valve. When the magnetization orientations M1 and M2 are parallel, there is a relatively high device conductance (low resistance) associated with transport in the minority spin subbands of both F1 and F2 (refer to Figure 1a). When the magnetization orientations are antiparallel, the device conductance requires transport between the minority subband of one ferromagnet and majority subband of the other, and this conductance is less than conductance between two minority spin subbands.1 The magnetoresistance trace of Figure 2e can be understood by referring to Figure 2b and considering two F layers characterized by loops with different values of coercivity, HC1 < HC2. For large values of negative field H, M1 and M2 are parallel and point along the negative xˆ axis. As H is increased to zero (solid line in the figure), the orientation is unchanged. As H is increased further, the orientation of F1 begins to change at a value H ) HC1, and at a slightly higher field M1 and M2 are antiparallel and the resistance is relatively high. At a higher field value, H > HC2, M1, and M2 are again parallel, aligned along the positive xˆ axis, and the resistance diminishes to the relatively low value. As the field is reduced to negative values (dotted line in the figure), the same process occurs on the negative field side of the hysteresis loops. The field sweep can be stopped at HC1 < H < HC2, a field such that M1 and M2 are antiparallel because M1 has switched to point along positive xˆ but M2 still points along negative xˆ (Figure 2f). The external field H can then be reduced to zero. The antiparallel state is maintained unless H is driven negative with a value H < - |HC1|, where M1 reverses back to point along negative xˆ and is again parallel with M2. This is called a

Johnson memory effect21 and represents the bistability of F when it is incorporated in an integrated magnetoelectronic device. Practical magnetoelectronic devices are similar to the generic device of Figure 2d but incorporate some tricks of magnetic engineering. For example, the magnetization of one of the ferromagnetic layers is typically “pinned,” which means that it is given such a large coercivity that its orientation never changes. The second ferromagnetic layer, which we have denoted as the binary information layer F, has a magnetization that can flip its orientation and is called the “free” layer. As another example, the hysteresis loop of either the pinned or free layer may be shifted so that it is not symmetric with zero field. This technique is called magnetic biasing. Some Key Issues Having a basic understanding of the magnetoelectronic approach, several categories of current research can be described. One important category relates to the output characteristics of the magnetoelectronic device at the core of the cell. These characteristics are determined by device design and the physics of spin transport. At the present time, magnetic tunnel junctions (MTJs) have the best device characteristics. One key issue is to increase the available readout voltage by increasing the MR. At the same time, the junction resistance R must be relatively low for good impedance matching to the on-chip sense amplifiers that detect the readout voltage. Another reason to keep R low is that the junction capacitance C combines with R to diminish high-speed pulses with an RC time constant. One successful MTJ fabrication technology17 uses aluminum oxide barriers and transition metal ferromagnetic electrodes. A thin layer of Al is deposited on the first F layer and wets the surface. This is oxidized to form the aluminum oxide barrier layer, with a thickness of approximately 0.7 nm. The second F layer is then deposited on top of the barrier. This technique has proven to be remarkably reliable and reproducible, and the junctions have MR values greater than 60% at low bias. The readout levels of aluminum oxide MTJs are adequate, but higher output is always desirable. Recently, MTJs with transition metal ferromagnetic electrodes have been fabricated with MgO barriers.22,23 The MR values at room temperature are quite high, up to 200%,24,25 and this has become a topic of high interest. If the fabrication technique can be implemented on a production line, with reliability and reproducibility, this technique will likely be used for future generations of MRAM. A second category relates to the magnetic properties of the F elements. There are many relevant properties, and many topics of interest. For the pinned layer of a cell, the endurance and durability of the cell depend on a pinning force that is strong and does not degrade with time. Several research topics involve the design and fabrication of magnetic multilayers that have exchange forces that adequately pin the pinned layer. For the free layer, one key issue is to design ferromagnetic elements that have low values of switching field, Hs, so that the write current amplitudes are minimized. A related issue is to design the element to have a highly square hysteresis loop. Furthermore, the magnetization state of the free layer must have good thermal stability, the switching between states must be as rapid as possible, and these characteristics must be maintained as the dimensions of the ferromagnetic element shrink. In other words, the characteristics must “scale” as the feature size f is reduced. One research approach has been to design magnetic multilayers with highly reproducible properties.4 We have used a more pedagogical approach, and our studies of the switching dynamics of individual, patterned ferromagnetic elements are

Feature Article described in a section below. An entirely different approach has exciting possibilities. This technique begins by recognizing that the energy associated with the magnetic field of a write pulse is negligible compared with the joule heating dissipated in the write line. The inductive write process is therefore intrinsically inefficient, and a method of “direct writing” is desirable. Theorists predicted26,27 that electrical current that was spin polarized by one ferromagnetic film and injected into a second, contiguous ferromagnetic film could transfer spin angular momentum to the second ferromagnetic film and rotate its magnetization. After experimental verification,28 this effect has become known as “spin torque switching.” Although it requires high current densities, this may be a technique for efficient switching when cells have been scaled down to feature sizes below 100 nm, and this is an active area of research. A third category relates to the architecture of magnetoelectronic memories. The topics involve electrical engineering and the design of cells that have optimal write and read properties while effects of cross-talk between cells are minimized.4 One issue relates to optimizing cell isolation while minimizing cell area. Magnetoelectronic memory devices are characterized by a finite resistance. A typical cell incorporates a field effect transistor to isolate that cell from the array and thereby prevent the bias current applied to a target cell from dissipating to contiguous cells. However, this isolation device adds significantly to the cell area and novel addressing schemes are under research. A fourth category relates to the development of new applications for magnetoelectronic devices. For example, magnetoelectronic reprogrammable logic is a topic of increasing interest.3,29 If Boolean logic operations can be performed with magnetoelectronic devices, then a generic chip could be manufactured and sectors of the chip could be dynamically apportioned to perform logic or memory functions.30 New applications require new architectures, but of greater importance, they are facilitated by the development of new device structures. In particular, the magnetoelectronic devices used for memory and for magnetic field sensing, the MTJ and the spin valve, are passive devices. A capacitor is also a passive device, and such devices work well for memory applications. However, information processing applications require passing output signals from one device to subsequent devices, known as fanout, and this demands that each device cell must have power gain. The development of a magnetoelectronic device with power gain is a key issue in this research category. A proposal for a spin-dependent p-n junction, leading to spin-dependent diodes and transistors, is one approach.31 A second approach involves the development of a spin-injected field effect transistor (SI FET).32 Both approaches require the ability to spin inject from a ferromagnetic electrode into a semiconducting material, and there has been a lot of theoretical and experimental work on this issue.33 It should be noted that neither form of spindependent transistor would be superior to MTJs and spin valves for memory and sensing applications, and their development would not necessarily lead to immediate applications. However, the development of a spin-dependent device with power gain would enable new frontiers of applications. Our research has involved both theory and experiment. After discussing switching dynamics, we will describe a nonequilibrium thermodynamic theory for deriving the equations of motion of charge and spin in general ferromagnetic/nonmagnetic material systems and use these equations to calculate details of spin injection across a ferromagnetic metal/nonmagnetic semiconductor interface. We will then show experiments that

J. Phys. Chem. B, Vol. 109, No. 30, 2005 14283 demonstrate the injection and detection of spin polarized electrons in a high mobility, single quantum well (SQW) channel. Switching Dynamics One problem that limits magnetoelectronic device development is reproducibility of the magnetization switching threshold of the free ferromagnetic element. Successful operation of the inductive half-select write processes described in the Introduction requires that repeated application of single write pulses Iw must fail to alter the magnetization state, i.e., fail to “disturb” the bit. Referring to Figure 2b, the hysteresis loop of each element must be sufficiently square that local application of field Hs/2 will not alter the magnetization orientation. At the same time, application of two simultaneous write pulses must create the desired orientation with an extremely high success rate. The shape and characteristic saturation value Hs of each loop must reproduce within a narrow margin for each switching event in the expected lifetime of many billion events. Furthermore, a more stringent requirement is that the loops for all elements must be identical within tight margins for all the elements on a chip, from chip to chip across a wafer, and from wafer to wafer within a production run. Finally, the magnetization reversal should be as rapid as possible in order to achieve the highest performance. Figure 3a shows the patterned thin film ferromagnetic element F introduced earlier in Figure 2. Integrated write wires are sketched with an exploded view as a reminder that magnetic field will be applied to F by using current pulses through integrated write wires. This element has been fabricated to have a uniaxial anisotropy axis along its long axis. This is called the easy magnetization axis (e.a.) because the characteristic switching field along this axis is relatively low. The transverse axis is called the hard magnetization axis (h.a.) because the switching field along this axis is relatively high. Sending a current pulse Iea (Iha) through the wide (narrow) write wire of Figure 3a applies a magnetic field pulse Hea (Hha) along the easy (hard) magnetization axis. Switching between the bistable magnetization states of F can be discussed by assuming the magnetization behaves as a single domain, and is therefore a dipole moment M B with magnetization magnitude M. The total magnetic energy E of such a dipole in an external magnetic field H B is the sum of the anisotropy energy EK and the dipolar (Zeeman) energy,34

E ) EK - M B ‚H B ) Ksin2θ - M Hcos(θ - φ)

(2)

In this equation, θ (φ) is the angle of magnetization M B (external field H B ) measured with respect to the easy magnetization axis (the xˆ axis in Figure 3a). In the absence of magnetic field, H ) 0, the total energy is just the anisotropy energy and has the shape of the double-well potential shown in Figure 3b. The magnetization orientation has stable states along the easy axis, either positive (θ ) 0) or negative (θ ) π) along the xˆ axis. The energy barrier Eb between the wells is provided by the anisotropy energy, Eb ) K, the energy required to overcome the uniaxial anisotropy. The anisotropy energy is a property of the material and is proportional to the volume of the element, K ∝ Vol. A condition for the stability of the bistable states is that the thermal energy of element F must be much less than the barrier height, KBT , Eb, where KB is Boltzmann’s constant. This condition may impose limits (often called the superparamagnetic limit) when the feature size f becomes the order of a few nm.

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Johnson

Figure 3. Magnetization states of F represented with potential energy diagrams. (a) The element F has a uniaxial anisotropy axis along its long axis. This is the easy magnetization axis (ea) and the transverse direction is the hard magnetization axis (ha). (b) The bistable magnetization states are represented as a double-well potential. The height of the barrier between wells is proportional to the anisotropy energy. (c) Application of an easy axis field Hea tilts the potential. (d) Application of an hard axis field Hha diminishes the barrier between wells. (e) Simultaneous application of easy and hard axis fields results in effective switching. (f) Ideal Stoner-Wohlfarth switching astroid. The box represents error bars for the point at (Hea,S, 0).

Application of an external field H B changes the shape of the total energy plot. For a field along the easy axis, Hea (refer to Figure 3a), M B‚H B ) MHcosθ. The double well is tilted, but the energy barrier is unchanged because cosπ/2 ) 0 (Figure 3c). For a field along the hard axis, Hha, M B ‚H B ) MHsinθ. Because the Zeeman energy has the same symmetry as EK, the total energy plot has no tilt but the energy barrier is diminished, E′b < Eb (Figure 3d). We note that effective switching can be achieved by application of a sufficiently large field along the easy axis. However, a sufficiently large field applied along the hard axis creates a single well, and the magnetization orientation can fall along either easy axis direction when the hard axis field is removed. We also note that a combination of fields Hea and Hha permits effective switching (Figure 3e). The magnetization switching described above is characterized by a two-dimensional curve plotted in the space defined by easy and hard axis fields. An expression is written for the potential energy of the element as a function of the angle of magnetization orientation, with respect to an anisotropy axis, and in the presence of an external field applied in the film plane. The energy minima are found by differentiating the potential energy with respect to angle and setting the second derivative to zero. For a patterned thin film element with in-plane and uniaxial magnetization anisotropies, the magnetization switching is described by

[ ] [ ] Hea Hea,S

2/3

+

Hha Hha,S

2/3

)1

(3)

where Hea,S and Hha,S are the switching (saturation) field values for the easy and hard directions. This is called the Stoner-Wohlfarth35 switching astroid and is sketched in Figure 3f. To interpret this curve, consider the simple case where Hha ) 0. Then the value of switching field required for the field along the easy axis is (Hea/Hea,S)2/3 ) 1, or equivalently Hea ) Hea,S, which satisfies the definition of Hea,S. Regions inside the astroid represent field values for which successful switching does not occur, and regions outside the astroid represent successful magnetization switching. For inte-

grated operations, only two quadrants are needed (for example Hha g 0), and choosing appropriate field magnitudes for easy and hard axis fields corresponds to picking an operating point in the two-dimensional space of Figure 3f. Here the statistics of reproducible switching become crucially important. The operating point denoted as “a” in Figure 3f might be an optimal choice if, for example, cell geometry determines that easy axis fields can be supplied with lower current than hard axis fields. However, point “a” cannot be used if there is an error associated with the distribution of switching events, within a device or from device to device, such as that represented by the box in Figure 3f. In this case, the easy axis field to be used during switching overlaps with the error bars for Hha ) 0, and there is a chance that the easy axis field alone can switch the magnetization of an element. This would be a “bit disturb” event in the half-select process. It follows that operating point “b” is a better choice and will work as long as the error bars that represent the switching distribution in the vicinity of “b” are sufficiently narrow. Since the write process is performed using fast pulses, the dynamics of magnetization reversal in patterned F elements is a topic of high interest. Our group has participated in a series of experiments to study magnetization reversal by measuring the evolution of switching astroids for different shapes, durations, and rise times of switching pulses. Experiments performed in collaboration with the University of Alberta19,20,36 have used the pump-probe apparatus sketched in Figure 4. Current pulses with amplitudes of order 10 mA are electronically generated and applied to transmission lines connected to the sample (Figure 4a). The write wires are fabricated underneath the patterned F element (Figure 4b) so that linearly polarized laser pulses can be reflected from the surface of F and recorded by a detector. Because of the polar Kerr effect, the polarization axis of a reflected pulse is shifted by a small rotation that is proportional to the magnetization of F. The detector splits the reflected pulses into components and measures the Kerr rotation. Using standard delay lines and triggers, the laser “probe” pulse can be synchronized to arrive at a variable time measured relative to the arrival time of either current pulse. The measurements are

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Figure 4. (a) Schematic depiction of the pump-probe apparatus used for polar Kerr measurements of magnetization reversal. (b) Schematic top view of the sample. The ferromagnetic element F is fabricated on top of the write wires so that it is optically accessible to the probe pulses.

repeated at a KHz rate to accumulate and average data for each point of time, and the relative probe arrival time is gradually and systematically changed to sweep through a time period that spans the switching process. In this way, the magnetization orientation of F can be recorded as a response to the magnetic field pulses. An example of such a set of switching experiments is shown in Figure 5. Figure 5a depicts the amplitude, rise time, duration, and fall time of the two pulses. The data of Figure 5b show the Kerr rotation corresponding to the x-component of the magnetization of the element. The top and bottom curves are vertically displaced and use scales on the right-hand axis. The middle trace shows a normalized Kerr signal with an initial value of -1, corresponding to orientation along the negative x direction. The final value of +1 indicates that the magnetization has switched to an orientation along the positive x direction. The top and bottom curves have comparable initial values, indicating initial orientations along the -x direction. In all cases, pulse arrival time is about t ) 0.45 ns. The top curve represents the magnetization response to a hard axis pulse (Hea ) 0). The two peaks are understood by recognizing that the magnetization rotates twice, in a phenomenon related to ferromagnetic resonance, before returning to its initial state along the negative x axis. This trace describes the half-select response of elements on a word line or bit line, but not at the intersection of a chosen word and bit line. The final magnetization state (bit state) of these elements has not changed, although the dynamic state is clearly altered. It is plausible that

Figure 5. (a) Profiles of the easy and hard axis field pulses used for the data below. (b) Time-resolved magnetooptic measurements of the x component of the polar Kerr effect. Top trace: Hard axis pulse only. Middle trace: Simultaneous arrival of both hard and easy axis pulses. Bottom trace: Hard axis pulse arrives about 170 ps before easy axis pulse. Courtesy of M. Freeman and A. Krichevsky, U. Alberta.

a single pulse of different shape or duration could have a probability of changing the final magnetization state and disturbing the bit. The middle trace represents the simultaneous application of the easy and hard axis pulses described with Figure 5a. The magnetization has switched in a fashion resembling a step function, with a rise time of about 180 ps. The bottom trace represents the application of hard and easy axis pulses where the arrival of the latter is delayed by about 170 ps with respect to the former. The magnetization goes through several rotations before settling into a switched state. While the end result is a successful switching event, it is clear that the dynamic state is susceptible to fluctuations. This trace demonstrates that reliable switching relies on accurate pulse timing as well as appropriate shape and amplitude. These studies were extended by measuring the probability of magnetization reversal as functions of easy and hard axis field amplitude and duration. These sets of experiments mapped

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Johnson

Figure 6. Experimentally measured switching astroids for a variety of pulse durations. Courtesy of M. Freeman and A. Krichevsky, U. Alberta.

out switching astroids for a variety of pulse durations, and examples of such astroids are shown in Figure 6. Easy and hard axis pulses were applied to the write wires under a ferromagnetic element F that was shaped like an ellipse and had dimensions of 3.0 microns and 1.0 micron along the long and short axes. The 15 nm thick film was composed of Permalloy (Ni0.8Fe0.2). The duration of the hard axis pulse was slightly longer than that of the easy axis pulse, and the pulses were synchronized so that the hard axis pulse always arrived 1 ns before the easy axis pulse. The pulse durations were chosen such that the hard axis pulse was present throughout the duration of the easy axis pulse, and restrictions of pulse shaping required that the hard axis pulse was 1 to 2 ns longer than the easy axis pulse. The duration of both easy and hard axis pulses had different values, and data for easy axis pulse durations of 0.5, 2.0, 5.5 and 7.0 ns are shown in the figure. The amplitudes of the easy and hard axis pulses were systematically varied, for combinations of pulses, from -75 Oe to + 75 Oe. The magnetization state of F was measured 20 ns after pulse arrival. This time is at least 10 ns beyond the duration of dynamic states that occur during switching, and these measurements represent the final magnetization state of the element. In the color code of Figure 6, blue represents the x-component of the magnetization along the original magnetization orientation. Red represents the x-component of magnetization pointing along the opposite direction, and thereby indicates that a magnetization orientation switching event has occurred. Green and yellow represent intermediate values of the x-component of magnetization. This choice of color mapping means that the color of the x-component of the Kerr signal inverts for the two quadrants of positive easy axis field in comparison with the two quadrants of negative easy axis field. However, this color convention results in a plot that can be easily compared with a Stoner-Wohlfarth astroid. For each set of data in Figure 6, a blue region extends vertically from top to bottom of the plot. This means that

application of only a hard axis field fails to cause magnetization reversal, as discussed above. The data for the shortest pulse duration, 0.5 ns, show the shape of a blue astroid set against a red background. There are large regions of green and yellow near the top and bottom vertices. These regions correspond to dynamic states that ultimately result in poor or inconsistent switching. It is interesting that regions can be found, for example, near |Hea| ) 60 Oe and |Hha| ) 40 Oe, where halfselect operations could be performed. We note that the baseline error of the color plots is about 3%, and it follows that such half-select operations would have 97% efficiency. This is far below stringent industrial requirements, which might require fewer than one bit disturb in a million events. Nevertheless, within the accuracy of the experiment there is evidence that half-select processes can be used with pulses as short as 500 ps. As pulse duration increases, the width of the blue astroid decreases because smaller amplitudes of easy axis pulse are required to cause a successful switch. The widths of the yellow and green regions at the top and bottom of the plot also decrease. A Stoner-Wohlfarth astroid has been drawn over the blue region in the plot of the longest pulses (duration of 7.0 ns). While there is still considreable uncertainty at low amplitudes of easy axis field (near Hea ) 0 Oe), the blue astroid becomes an approximation of the Stoner-Wohlfarth curve. Half-select switching could be performed using amplitudes in the vicinity of |Hea| ) 35 Oe and |Hha| ) 35 Oe. Understanding the details of the dynamic states that result in the yellow and green regions in the plots of Figure 6 is a continuing effort of basic research, and simulations of the magnetization reversal process are becoming an important tool. For applications, the results of Figure 6 show evidence that reliable switching of patterned ferromagnetic elements might be possible on time scales of a few ns or less.

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Figure 7. Schematic of the spin injected FET proposed by Datta and Das.

and antiparallel with that of the source. The operation of this device is similar to that of a spin valve or MTJ. When the magnetization orientations of the source and drain are aligned parallel (antiparallel), the source-drain conductance is relatively high (low). Binary information is stored as the state of the drain, and can be written using integrated write wires. The information can be accessed by addressing the cell with an appropriate gate voltage, and the binary state then can be read as a low or high conductance value. This device structure is attractive for memory applications because cell storage and cell isolation can be achieved while using a single device, and cell size is thereby reduced.

Spin Injection into Semiconductors

Theory

The leading magnetoresistive device families, the spin valve and the magnetic tunnel junction, involve ferromagnetic and nonmagnetic metal films and/or thin insulating tunnel barriers. These passive devices are compatible with CMOS technology to the extent that these layers can be grown on silicon. Passive devices are adequate for memory applications if the output voltages are sufficiently large and reproducible to allow reliable readout. Active devices, which have power gain, are of greater utility and form the backbone of semiconductor electronics. Power can be provided using a third terminal and an external power source, and standardized output levels can be transmitted to successive devices. Such stabilized output levels are a key attribute of an improved device, and transmission of these levels, known as device fanout, is necessary for any kind of information processing beyond memory. Recently, research has sought to integrate spintronics directly with semiconductors by incorporating a semiconductor material in the device structure. The invention, creation, and/or discovery of an active magnetoelectronic device would enable new applications, such as reprogrammable logic, and would move the field of spintronics onto a new plateau of functionality. If logic and nonvolatile storage functions could be performed by the same magnetoelectronic device, new kinds of chips could be produced. High speed logic and high density storage could be accomplished with a single chip. Furthermore, sectors of the chip could be dynamically apportioned to perform logic or memory according to changing needs. This topic of basic research is highly active. The development of a magnetic bipolar diode (MBD), a magnetic bipolar transistor (MBT), and a spininjected field effect transistor (SI FET) are approaches that are presently viable. The third approach (SI FET) can be described as application of the spin injection technique12 to the semiconducting channel of an FET.32 In the structure proposed by Datta and Das (refer to Figure 7), a ferromagnetic source and drain are connected by a two-dimensional electron gas (2DEG) channel, with the source-drain distance Lx on the order of an electron ballistic mean free path. The magnetizations of both source and drain are oriented along the axis of the channel, the xˆ axis. A relativistic effect34 causes the spin polarized injected carriers to precess during their trajectories, and the precession rate can be modulated by a gate voltage, VG. The source-drain conductance is maximum (minimum) when the spins enter the drain with alignment parallel (antiparallel) with those in the drain. This original proposal of Datta and Das can be modified to result in a binary, digital magnetoelectronic device. The magnetization of the source is pinned to lie along a chosen direction and the magnetization of the drain has uniaxial anisotropy and orientations that can be switched between parallel

The development of an MBD, MBT, or SI FET involves the electrical injection of spin polarized carriers from a ferromagnetic material into a nonmagnetic semiconductor. One line of research has focused on using magnetic semiconductors as spin injectors.33 This field has been extremely active over the last five or six years, and a survey of some key historical contributions is outlined at the end of this article, However, magnetic semiconductors are not viable at room temperature. Ferromagnetic metal films, by contrast, have Curie temperatures well above room temperature, have low values of switching field, and can be lithographically fabricated using standard processes. However, metals and semiconductors are different kinds of materials, characterized by very different carrier densities, resistivities, and diffusion constants. It is not obvious that spin polarized electrons in a ferromagnetic metal can be effectively transported across an interface and into a semiconductor. Our research has involved both theory and experiment, and we begin with theory. The theoretical work is an exercise in statistical mechanics. The tensor formalism of Johnson and Silsbee6 was developed for diffusive charge and spin transport in three dimensions. For this review, vector quantities will be denoted with bold face in order to avoid confusion with tensor notation. Following an entropy production calculation, currents of charge (Jq), heat (JQ), and magnetization (JM) in a bulk ferromagnetic (F) or nonmagnetic (N) material are related to gradients of voltage (∇V), temperature (∇T), and magnetization potential (∇-H*) by the general equations of motion:6

() Jq JQ JM

(

a′′kB2T eEF 2 2 a′′kB T a′kB2T )-g eEF e2 µBT kB pµB p′ EF e e 1

[]

pµB e µB kBT p′ EF e

[ ]

2

2

µB

ζ

2

e

2

)

( ) ∇V ∇T ∇ - H*

(4)

with g ) 1/F being the bulk conductivity. The magnetization potential H* is defined as -H* ≡ M ˜ /χ - H ) M ˜ /χ (with χ the susceptibility) where we simplify to the case of zero external field H. The nonequilibrium magnetization, M ˜ ) M - M0, with M0 the thermal equilibrium value (M0 ) 0 in N), arises from transport effects such as spin injection. For the simple case ∇T ) 0, ∇(-H*) ) 0, eq 4 gives JM ) (pµB/e)Jq. Here p ) (Jv - JV)/(Jv + JV) ) (gv - gV)/(gv + gV) is the fractional spin polarization of carriers defined earlier, Jv and JV are the spin subband partial currents, and gv and gV are the spin subband conductivities (note that g is synonymous with σ, which is more commonly used). Following an Einstein rela-

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Johnson

tion,6,11 the conductivity and current density are proportional to the density of states at EF, Ji ∝ Ni(EF). In a nonmagnetic material N, the spin subband densities of states at the Fermi level are equal, Nv(EF) ) NV(EF) (refer to Figure 1b), the spin subband conductivities are equal, gv ) gV, and pn ) 0. In a ferromagnetic metal, Nv(EF) * NV(EF) and pf * 0, so that values of pf for transition metal ferromagnets are typically 0.4 to 0.5.38 The other kinetic coefficients Lij in eq 4 have been estimated from a free electron model. The fractional polarization constant p′ would be associated with spin flow driven by thermal gradients, and constants a′ and a′′ can be related to the thermal conductivity κ and thermopower .6 Finally, L33 ) ζ(µB/e)2 describes self-diffusion of nonequilibrium spins and ζ ≈ 1 (ζ ) 1 for noninteracting electrons). Thus, a current of spin polarized electrons in a nonmagnetic material is given by

µB2 JM,n ) g 2 ∇(H*) e

(5)

The same approach can be applied to a discrete system, and interfacial currents of charge (Iq), heat (IQ), and magnetization (IM) are related to differences, across an interface, of voltage (∆V), temperature (∆T), and magnetization potential (∆(- H*)):

() Iq IQ IM

(

kB2T e 2 kB2T2 akB T ) -G e e2 ηµB µBT kB η′ e  e 1

[]

2

ηµB e µB kBT η′  e µB2 ξ 2 e

[ ]

2

)

( ) ∇V ∇T ∇ -H*

(6)

with G ) 1/Ri the intrinsic conductance of the interface. The kinetic coefficients L′13 ) L′31 are identified in a manner similar to those of eq 4. Polarization parameter η describes the fractional polarization of current crossing the interface, η ) (Iv - IV)/(Iv + IV) ) (Gv - GV)/(Gv + GV). The interface may be characterized by spin asymmetry and, in general, η e pf. Using eqs 4 and 6, charge-spin coupling effects at the interface between a ferromagnetic and nonmagnetic material can be studied. Because of the large differences in resistivity between ferromagnetic metals, nonmagnetic metals, and semiconductors, these are often called “resistance mismatch” effects. They were first derived by Johnson and Silsbee,6 and the physical principles are described with the aid of Figure 8. Equation 4 is written for transport in F and N, and eq 6 is written for the interface region, defined as a volume with a thickness of an electron mean free path l on either side of the physical interface, x ) 0 ( l (Figure 8a). Far away from the interface, the current in F is polarized with the value in bulk, JM,f ) pf(µB/e)Jq. The current in N, far from the interface, is unpolarized, JM,n ) 0. At the interface (x ) 0 in Figure 8), polarized current JM is injected into N and creates spin accumulation M ˜. The density M ˜ n in N decays exponentially away from the interface with characteristic length δs,n, driven by self-diffusion and the L33 term of eq 6. This term also drives the diffusion of M ˜ back across the interface into F, where the nonequilibrium spin density M ˜ f decays with characteristic length δs,f. The population of nonequilibrium, spin polarized electrons near the interface is depicted in Figure 8a with gradations of gray shading. The associated magnetization potentials, H/n ) (M ˜ /χ)n and H/f ) (M ˜ /χ)f, are shown in Figure 8b. Since χf differs from χn, it follows that H/n is discontinuous at the interface, H/n(x ) 0) * H/f (x ) 0).

Figure 8. Flow of charge and spin currents, Jq and JM, near the interface between a ferromagnetic material (F) and nonmagnetic material (N). (a) Model system. x ) 0 at the F-N interface. Gradations of gray shading on either side of x ) 0 represent populations of nonequilibrium spin polarized electrons near the interface. (b) Magnetization potential, H* ∝ 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 the value in bulk of F by the backflow of polarized spins, an effect determined by “resistance mismatch.”

The back diffusion of nonequilibrium spins has several consequences. Away from the interface, current flow is Ohmic and a plot of V(x) shows slopes proportional to Ff and Fn in F and N, respectively (Figure 8c). Since charge and spin both reside on the same carrier, the backflow of polarized spins across the F-N interface is also a backward flow of charge. This negative charge current must be overcome by the imposed current Jq, causing the appearance of an effective interface resistance, Reff ) [pf(µB/e)H/f ]/Jq, in addition to the intrinsic interface resistance Ri (Figure 8c). Furthermore, the backflow of polarized spins cancels a portion of the polarized current JM,f. As JM approaches the interface, the fractional polarization is diminished from the bulk value, pf (Figure 8d). 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 is6,39

JM )

[

ηµB 1 + G(pf/η) rf (ξ - η2)/(ζf - pf2) Jq e 1 + G(ξ - η2)[(rn/ζn)+ rf/(ζf - pf2)]

]

(7)

where rf ) δfFf, rn ) δnFn and recall ξ, ζf, ζn ≈ 1. Interfacial spin transport is governed by the relative values of the intrinsic interface resistance Ri ) 1/G, along with 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 µΩ cm × 5 nm ∼10-11 Ω cm2 (ref 40) (nearly temperature independent), and rn ≈ 2 µΩ cm × 1 µm ∼2 × 10-10 Ω cm2 at cryogenic temperature14 (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

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Figure 9. (a) Micrograph of F1-2DEG-F2 sample. Six narrow channels are connected in parallel. (b) Top view of nonlocal geometry for spin injection and detection. (c) Cross-sectional view of the high mobility, single quantum well 2DEG sample.

by a contact resistance Rc. The latter represents the low resistance limit, and a typical value is Rc ≈ 10-9 Ω cm2.41 Since all of these values fall within a range of two decades, all terms in eq 7 will be important for the general case. For the limiting case G f ∞, eq 7 takes the simplified form6

JM ) pf

[

µB 1 J e q 1 + (r /r )(1 - p 2) n f f

]

(8)

and the injected polarization is reduced from that in the bulk of F by the factor

[1 + (rn/rf)(1 - pf2)]-1 ) (1 + M′)-1

(9)

Using the above estimates for rf and rn, M′ can be as large as M′ ∼ 20 for metal films, and consequently JM may be reduced to a small fraction of pf. When N is a semiconductor, M′ could be much larger. But this is valid only for the condition Ri , rn, rf.39 In the opposite regime, Ri . rf, rn, transport is dominated by Ri, eq 7 reduces to

JM ) η(µB/e)Jq

(10)

and the polarization is given by the interfacial parameter η. In summary, metals and semiconductors are obviously different material classes and their carriers have very different characteristics. If a perfectly conducting interface is achieved between a ferromagnetic metal (F) and a nonmagnetic semiconductor (S), these differences can reduce the polarization of injected current to nearly zero. Fortunately, zero resistance F-S interfaces are never achieved. The finite resistance of any real F-S structure is large enough to permit efficient spin injection. Experiment - Injection and Detection Using the theoretical insight that derived from the thermodynamic model, spin transport across a single F-S interface was studied42-44 and the fractional polarization of interface current was found to be on the order of 10%. Next, electrical spin injection and detection in a high mobility 2DEG was experimentally demonstrated by fabricating two F-S junctions, of the form shown in Figure 9c, on a common 2DEG channel. Figure 9b shows a schematic top view of the experimental geometry. Two ferromagnetic metal electrodes, F1 and F2, were fabricated on a common InAs channel. In the actual device, six separate channels were connected in parallel for improved signal-to-noise (Figure 9a). Narrow channels, about 900 nm

Figure 10. Examples of data showing detection of electrical spin injection. The sample has a separation of Lx ) 10.6 µm between injector and detector. Solid lines: sweep field down. Dotted lines: sweep field up. The hysteretic dips are characteristic of spin injection and detection.

wide, were defined on an InAs single quantum well (SQW) heterostructure using optical lithograophy 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. The interelectrode spacing Lx was the order of magnitude of the carrier mean free path, a few microns. Using the nonlocal geometry of the original spin injection experiment,12 spin polarized electrons were injected from F1 into the 2DEG and the injected current was grounded at terminal S1. Detecting electrode F2 was grounded at S2, and acts as a spin-sensitive potentiometer. Ballistic and quasi-ballistic spin polarized electrons that are injected at the F1-2DEG 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 F1 was fabricated with Permalloy and had a relatively small coercivity, HC1 ≈ 30 Oe. Detector F2 was fabricated with FeCo and had a relatively large coercivity, HC2 ≈ 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 Figure 10, taken at a temperature of 4.2 K using a sample with Lx ) 10.6 µm.45 The baseline resistance is nearly zero, demonstrating the effectiveness of the nonlocal geometry. The overlapping dips that appear in the range -200 Oe < Hy < +200 Oe have the qualitative shape that is characteristic of spin injection. Data were also taken on a sample with an interprobe separation of Lx ) 3.2 µm. Hysteretic dips that were qualitatively similar to those of Figure 10 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 Λs ) 4 µm. 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.46 These data demonstrate the electrical injection of spin polarized electrons across a resistive barrier and into a high mobility 2DEG channel, and their subsequent detection by a ferromagnetic electrode. While spin injection resistances have been small, shrinking the sample structure to the nanometer

14290 J. Phys. Chem. B, Vol. 109, No. 30, 2005 dimensions of a technologically viable device may increase the magnitude of spin transport effects, and realization of a spin injected FET is plausible. Further Survey of Spintronics Topics The terms “spintronics” and “magnetoelectronics” are broadly used to describe research that involves spin polarized conduction electrons. For example, the research and development of spin valve read-heads is an area often considered to be included within the description of these terms. As another example, the field of optical measurements on magnetic semiconductor structures is also included. In this field the typical experimental device is a spin-injected light emitting diode (SI LED), and measurements of the emission of polarized light are made for a variety of experimental conditions. Dilute magnetic and ferromagnetic semiconductors have magnetic properties at cryogenic temperatures. The focus of this article is the field of magnetic devices that are used for room-temperature applications in integrated digital electronics. However, the area of magnetic semiconductor spintronics has generated a lot of excitement and has been very popular. Several of the key developments of this area can be mentioned, along with reviews that can be used by those readers who wish to explore further. The study of the optical properties of semiconductors and their relationship to the spin states of the carriers has a long and rich history.47 The group of “diluted magnetic semiconductors” (DMS) usually refers to the family of II-VI compound semiconductors that include a small concentration of magnetic II dopants, for example of the form A1-x MnxBVI. These fascinating materials, which also have a long research history, display a range of magnetic effects including spin glass ordering at low temperature and large Zeeman splittings of electronic levels, and are often probed using measurements of a giant Faraday rotation.48 One of the real breakthroughs for the field of magnetic semiconductors was the discovery of ferromagnetic order, at low temperature, in a III-V compound semiconductor,49 Mn-doped indium arsenide.50 The magnetization curve of a Mn-doped gallium arsenide compound showed clear and square hysteresis at 5 K.51 These developments caused an intense and new interest in this field by the end of the 1990s, and several important results were achieved in the short span of a few years. The spin diffusion length of photoexcited carriers in GaAs was measured with optical probes52,53 and was found to be the order of microns in MBE-grown heterostructures and tens of microns in bulk samples. Shortly after this, several independent experiments demonstrated that spin polarized electrons could be injected into a nonmagnetic semiconductor from a II-VI magnetic semiconductor54,55 or from a ferromagnetic III-V semiconductor.56 These experiments used a spin injected LED device structure at cryogenic temperatures. The flow of spin-polarized current across a magnetic semiconductor-nonmagnetic semiconductor interface was inferred from the detection of circularly polarized flourescent radiation generated in the nonmagnetic semiconductor. Although no effects were seen above 50 K, the efficiency of injection of polarized carriers was high, and the success of these experiments motivated further interest in the field. Magnetic semiconductor spintronics has enjoyed tremendous popularity since these seminal experiments. At the present time, there are no magnetic semiconductors with magnetic properties near room temperature, and there are no viable device applications. However, understanding of this class of materials has made great progress, and there is some interest in cryogenic applications such as quantum computing.57

Johnson Summary The invention and development of novel magnetoelectronic devices has revolutionized the magnetic recording industry and has permitted explosive growth of the density of recorded information. Magnetoelectronic devices are being developed for integrated electronics applications. Market entry in this domain would represent a paradigm shift for conventional semiconductor electronics, and would initiate tremendous growth of magnetoelectronics as a multidisciplinary field. Our research in the past several years has focused on a few key issues that the technology must overcome. This review article has reviewed several of the physical concepts, revealed by basic research, that make this new field possible. It has also provided a critical review of significant technological hurdles. Many exciting topics of basic and applied research were mentioned. Some of these, at the leading edge of research, can be listed: (i) the development and study of novel tunnel barrier materials for MTJs, for example MgO; (ii) the development of novel magnetic multilayers that enable fast magnetization switching with high stability and low energy, and the detailed study of the switching dynamics of such layers; (iii) the application of these materials to novel device geometries and structures, such as current perpendicular to the plane (CPP) spin valves or lateral spin injection devices;58 (iv) the development and study of new kinds of magnetization switching techniques, for example spin torque switching; (v) the study of spin injection, detection, and spin transport modulation in semiconductors, with an especially keen interest in silicon; and (vi) the magnetic properties of patterned ferromagnetic elements at nm size scales. References and Notes (1) Johnson, M. Introduction to Magnetoelectronics in Magnetoelectronics; Johnson, M., Ed.; Elsevier Scientific, Ltd.: Oxford, UK, 2004. (2) Sharma, A. K. Semiconducting Memories: Technology, Testing and Reliability; IEEE Press: New York, 1997. (3) Johnson, M. Magnetoelectronic Memories Last and Last.... I.E.E.E. Spectrum Magazine 37 no. 2, 33 2000. (4) Akerman, J. et al. Magnetic Tunnel Junction based Magnetoresistive random access memory, in Magnetoelectronics; Johnson, M., Ed.; Elsevier Scientific, Ltd.: Oxford, UK, 2004. (5) Mott, N. F. Proc. R. Soc. A 1936, 153, 699. (6) Johnson, M.; Silsbee, R. H. Phys. ReV. B 1987, 35, 4959. (7) Tedrow, P. M.; Meservey, R.; Fulde, P. Phys. ReV. Lett. 1970, 25, 1270. (8) Tedrow, P. M.; Meservey, R. Phys. ReV. Lett. 1971, 26, 192. (9) Tedrow, P. M.; Meservey, R. Phys. ReV. B 1973, 7, 318. (10) Julliere, M. Phys. Lett. 1975, 54A, 225. (11) Johnson, M.; Silsbee, R. H. Phys. ReV. B 1988, 37, 5312. (12) Johnson, M.; Silsbee, R. H. Phys. ReV. Lett. 1985, 55, 1790. (13) Johnson, M.; Silsbee, R. H. Phys. ReV. B 1988, 37, 5326. (14) Johnson, M. Phys. ReV. Lett. 1993, 67, 3594. (15) Binasch, G.; Grnberg, P.; Saurenbach, F.; Zinn, W. Phys. ReV. B 1989, 39, 4828. (16) Baibich, M. N. et al. Phys. ReV. Lett. 1988, 61, 2472. (17) Moodera, J. S.; Kinder, L. R.; Wong, T. M.; Meservey, R. Phys. ReV. Lett. 1995, 74, 3273. (18) Gurvitch, M.; Washington, M. A.; Huggins, H. A. Appl. Phys. Lett. 1983, 42, 472. (19) Zelakiewicz, S.; Johnson, M.; Krichevsky, A.; Freeman, M. R. J. Appl. Phys. 2002, 91, 7331. (20) Choi, B. C.; Ballentine, G. E.; Belov, M.; Hiebert, W. K.; Freeman, M. R. Phys. ReV. Lett. 2001, 86, 728. (21) Johnson, M. Science 1993, 260, 324. (22) Butler, W. H. et al. Phys. ReV. B 2001, 63, 054416. (23) Mathon, J. J.; Umerski, A. Phys. ReV. B 2001, 63, 220403R. (24) Parkin, S. S. P. et al. Nat. Mater. 2004, 3, 862. (25) Yuasa, S. et al. Nat. Mater. 2004, 3, 868. (26) Berger, L. Phys. ReV. B 1996, 54, 9353. (27) Slonczewski, J. J. Magn. Magn. Mater. 1996, 159, L1. (28) Katine, J. A. et al. Phys. ReV. Lett. 2000, 84, 3149. (29) Das, B.; Black, W. C., Jr. J. Appl. Phys. 2000, 87, 6674.

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