IEEE TRANSACTIONS ON DEVICES, VOL. 54, NO. 5, MAY 2007 907 Spintronics Michael E. Flatté, Member, IEEE

(Invited Paper)

Abstract—Investigations of the dynamics of -polarized elec- tronic current through and near materials with spin-dependent electronic structures have created a rich new field dubbed “spin- tronics.” The implications of spintronics research extend deep into the realm of fundamental material properties, yet spintronics applications have also revolutionized the magnetic-storage indus- try by providing efficient room-temperature magnetic sensors. Control of nonequilibrium spin-polarized populations of through and near magnets has led to the dominance of linear (resistive) spintronic devices for magnetic readout in commercial . Rapid progress in understanding the funda- mental of nonlinear spin-polarized electronic transport in metals and semiconductors suggests new applications for spin- tronic devices in fast nonvolatile memory as well as logic devices, with or without magnetic materials or magnetic fields. Ongoing study of the interaction between such spintronic elements and optical fields, particularly in semiconductors, promises the future development of optical spintronic devices. Index Terms—Magnetoelectronics, Rashba fields, spin coher- ence, spin electronics, Spin , spin relaxation times, spin , spin transport, spintronics, .

Fig. 1. (a) High-resistance and (b) low-resistance geometry of CIP GMR. The I. INTRODUCTION spacer region is a nonmagnetic metal. (c) High-resistance and (d) low-resistance geometry of CPP GMR (if the spacer region is a nonmagnetic metal) or TMR N 1988, during an investigation of the properties of multi- (if the spacer region is an insulator). Arrows indicate the magnetization I layers of magnetic and nonmagnetic metallic materials, a direction of the magnetic layers. For applications, one ferromagnetic layer is dramatic dependence of the electrical resistance on the mag- typically “pinned” through shape anisotropy and may be exchange-biased [10] and the other layer is reoriented by the external magnetic field. netization orientation of neighboring layers (parallel or anti- parallel) was reported and named “giant ” (GMR) [1], [2]. Within a couple of years the “spin valve” on spin-dependent electronics, which came to be called “spin- had been introduced [3], with two metallic magnetic layers tronics.” Within this field of spintronics (in its area of over- separated by a nonmagnetic spacer. Shortly thereafter, room- lap with magnetoelectronics), a fundamental physics discovery temperature magnetic-field sensors had been made [4] from came to drive a large commercial sector (2005 sales exceeding spin valves which were superior to previous state-of-the-art $3 billion) within a decade of discovery. devices based on anisotropic MR (AMR). IBM introduced The initial discovery of GMR was for a configuration (shown GMR-based magnetic media read heads into its commercial in Fig. 1(a) and (b) for a spin valve) called “current-in-plane” disk-drive products in 1997, and soon, all disk-drive companies GMR (CIP GMR). Shortly thereafter, a simpler experimental were offering GMR-based read heads instead of AMR-based geometry was investigated (Fig. 1(c) and (d), called the “current heads. Out of a field treating the effects of magnetic fields perpendicular-to-plane” (CPP) configuration [5], [6]), which on electronic transport (“magnetoelectronics,” which includes yielded a much larger value than in CIP GMR of the MR AMR and many other effects) was rapidly born a field focusing (the percent difference in resistance for parallel and antiparallel orientations of the two ferromagnetic regions in the spin valve). In each of these configurations, the two ferromagnetic regions are separated by a region of nonmagnetic metal, typically with a higher conductivity than either of the two ferromagnetic Manuscript received December 1, 2006; revised January 24, 2007. This work was supported by the Office of Naval Research. The review of this paper was layers. Motivated by earlier low-temperature measurements of arranged by Editor H. Morkoc. small magnetic-field effects on the tunneling resistance be- The author is with the Department of Physics and Astronomy, Department tween ferromagnetic layers [7], it was found that replacing of Electrical and Engineering, and Optical Science and Technology Center, The University of Iowa, Iowa City, IA 52242-1479 USA. the nonmagnetic metal in the CPP-GMR geometry with an Digital Object Identifier 10.1109/TED.2007.894376 insulating tunnel barrier can yield large values of the MR at

0018-9383/$25.00 © 2007 IEEE 908 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 54, NO. 5, MAY 2007 room temperature [8]. This effect, referred to as “tunneling sential for calculations of spin transport and magnetooptical MR” (TMR), can exceed a factor of three at room temperature effects. For ordinary calculations of charge transport, the spin- [9]. Applications of such structures in magnetic-field sensors dependent character of these eigenstates is neglected. The rely on the reorientation of the magnetization of one of the two discovery of GMR itself, however, is evidence that, in some layers in a small magnetic field (the other layer is “pinned” circumstances, the spin-dependent character of electrical trans- through shape anisotropy and may be exchange-biased [10]) port can have a sufficient effect on ordinary charge transport and electrical detection of the change in resistance. The sensor to be easily detected. To identify the principal characteristics can be placed in a magnetic-storage read head, and the small of spin-dependent electronic structure important to spintronics, magnetic field can come from an encoded bit on magnetic the relevant materials can be grouped into several classes, based media (such as in a ). Alternatively (such as in on whether they are magnetic or nonmagnetic and whether they magnetic random-access memory, or MRAM), the spin valve are metals or insulators (including semiconductors). itself can be used as a magnetic bit, with the two-memory states corresponding to antiparallel and parallel configurations. A. Magnetic Metals In the initial MRAM designs, a small magnetic field generated by a current pulse in an integrated wire (or pair of wires) is The common starting point for most analyses of spin trans- used to “write” the memory state, and readout is performed by port is the “two-channel” conduction approximation, originally measuring the resistance of the spin valve. developed for magnetic metals [24], [25] and, subsequently, The discovery of these spin-dependent effects in metallic applied to heterostructures of magnetic and nonmagnetic metals electrical transport has spawned a wide range of further inves- [26], [27]. This approach models the current as carried inde- tigations and has united previously distinct subfields of physics pendently by spin-up and spin-down carriers, with a separate [11]–[21] into the new field of spintronics. This includes spin- conductivity for each. The spin-up and spin-down carriers can dependent transport in semiconductors, spin-dependent tunnel- independently reach a local equilibrium but may be out of equi- ing through insulators, and spin-transport effects driven by the librium with each other. The rate of spin-flip processes, which spin–orbit interaction in semiconductors, oxides, and metals. couple the two channels, is much smaller than the ordinary The investigation of equilibrium and transient spin-dependent scattering rate characterizing the spin-conserving momentum phenomena using optical techniques, a rich field in the 1970s relaxation of nonequilibrium spin-up or spin-down distribu- [12], has blossomed again, particularly for magnetic insulators tions. Thus, even though metals often have mean free paths and nonmagnetic semiconductors. The discovery of semicon- much shorter than a nanometer, the spin-diffusion length can ductors that can become ferromagnetic upon dilute with range from several nanometers in strongly scattering magnetic magnetic atoms [15], [22], [23] may connect all these areas materials to several micrometers in metals lacking magnetic by providing electrical control of magnetic properties, spin- impurities or strong spin–orbit scattering. dependent transport, and strong magnetooptical effects, such as In this two-channel model, the bulk conductivity of spin-up Faraday rotation. The new areas of semiconductor spintronics and spin-down carriers is determined separately by the density have yet to have a commercial impact, although the properties of states at the Fermi energy EF for spin-up and spin-down found in these systems are unique and numerous theoretical carriers, so device proposals have been put forward. Here, some of the unifying themes of spintronics will be 2 σ↑(↓) = e N↑(↓)(EF )D↑(↓) (1) explored, including various regimes of spin transport in mag- netic and nonmagnetic metals, semiconductors and oxides, where D↑ ↓ is the diffusion constant for spin-up (spin-down) spin-dependent optical properties such as Faraday rotation, and ( ) carriers. The response of such a material to an applied electric electrical control of magnetic properties and spin lifetimes. The field is to flow a spin-polarized current, with a polarization treatment begins with a discussion in Section II of the spin- (defined below) that is determined by the conductivities dependent electronic properties of materials, including those characterizing spin transport and spin persistence (spin conduc- J↑ − J↓ σ↑ − σ↓ tivities and spin lifetimes), then continues with the coupling Pcurrent = = . (2) J↑ + J↓ σ↑ + σ↓ of optics to spin (Section III), proceeds to the behavior of spin-dependent electrical transport (Section IV), and concludes with some discussion of the roadblocks remaining for some Another important quantity describing the properties of mag- of the more long-term device applications (Section V). For netic metals is the change in chemical potential associated with more extensive treatments of these issues, reviews treating an excess of spin-polarized carriers spintronics can be found in [17] and [18], and topical treatments of individual aspects can be found in [13]–[16], [19]–[21]. ∂µ↑(↓) = N↑(↓)(EF ). (3) ∂n↑(↓)

II. SPIN-DEPENDENT ELECTRONIC One of the successes of spin-transport theory and experiment PROPERTIES OF MATERIALS is the ability to generate regions of “spin accumulation” in As with ordinary charge-transport problems, an understand- magnetic and nonmagnetic materials. In metals, the density of ing of the eigenenergies and eigenstates of a material is es- excess carriers of one spin direction is usually several orders FLATTÉ: SPINTRONICS 909 of magnitude lower than the background density of carriers, so The transport of carriers within a magnetic metal is also the resulting change in the conductivity (which is dependent on influenced by the spin–orbit interaction. In any material with the density of states at the Fermi energy), for either spin-up or a spin–orbit interaction, the eigenstates are not factorable into a spin-down carriers, is negligible. spinor and an orbital wavefunction. As a consequence, when The spin-dependent conductivity, the spin-dependent den- carriers move in a preferred direction, such as through the sity of states at the Fermi energy, and the spin-flip time τsf flow of charge current, there is an influence on the trajectory phenomenologically describe most bulk transport phenomena of the carriers depending on whether their spin is oriented in metals. The applicability of this simple phenomenological in one direction or another. The effect is a transverse force model is due to the central role that the Fermi surface plays with opposite sign for spin-up and spin-down carriers. In a in metallic electronic transport. The electronic structure deep magnetic metal, as the conductivities of spin-up and spin-down within the band has little effect on the properties of charge carriers are different, the ordinary charge current is composed transport or spin transport through these materials. In spintronic of different numbers of spin-up and spin-down carriers moving structures such as the CIP GMR spin valves, however, in which with different velocities. As carriers of one spin orientation the mean free path of carriers is longer than the thickness of the are deflected toward one side of the wire, and of the other are nonmagnetic metal layer separating the ferromagnetic layers, deflected toward the other side, the consequence of spin–orbit the spin-up and spin-down conductivities must be determined entanglement is a Hall voltage across the wire and a spin accu- for the structure as a whole and cannot be constructed simply mulation (of opposite signs) on the two sides of the wire. This from the spin-resolved conductivities of the bulk-constituent transverse charge current, called the anomalous Hall effect, materials. originates either from a difference in the scattering process from The spin-flip time τsf , in combination with the conductivities an impurity for spin-up and spin-down carriers (so-called “skew above, determines the diffusion length for an accumulation of scattering” [32]) or from the change in the form of the position one spin direction or the other relative to the background. These and velocity operators in a material with spin–orbit interaction spin-diffusion lengths can be quite short (a few nanometers (so-called “side-jump” [33]–[36]). in permalloy [28]) but as long as micrometers in clean noble metals such as gold [29], copper, or silver [30]. The addition B. Nonmagnetic Metals of impurities that increase the spin–orbit coupling or that increase mutual spin-flip scattering events with an impurity The properties of nonmagnetic metals can be described with can decrease the spin-diffusion length to a the same phenomenological quantities as magnetic metals, few nanometers in copper or silver [30] and likely limit the although nonmagnetic metals will have identical conductivities spin-diffusion lengths in magnetic materials as well. and densities of states at the Fermi energy for spin-up and spin- The majority spin direction of carriers is commonly defined down carriers. This does not, however, preclude the existence in magnetic metals as the spin direction parallel to the bulk of significant spin-dependent transport in nonmagnetic metals. magnetization. In a Stoner model [31], the electronic structure The clearest example of this effect is the . of spin-up carriers can be determined from that of spin-down The origin of the effect can be the same as the anomalous carriers by displacing the electronic structure of the spin- Hall effect described above for magnetic metals, but as an down carriers by a momentum-independent energy. For a free- equal number of spin-up and spin-down carriers are moving electron carrier dispersion relation the Stoner model implies in the nonmagnetic material, there is no Hall voltage, only that the carriers with high conductivity have a spin direction two counterpropagating spin currents of opposite polarization parallel to the magnetic moment, which is not always the case in [37], [38]. The spin Hall effect was first identified in transport real structures with more complex band structures (particularly in nonmagnetic semiconductors [39]–[41] but has since been in magnetic semiconductors). The direction of the magnetiza- demonstrated in aluminum [42]. The phenomenon often is seen tion usually does not play a direct role in metallic spin transport, as an accumulation of spins pointing along one direction on one except in how it affects the relative orientation of high- or low- side of a wire and of spins pointing along the other direction conductivity spin channels to an applied magnetic field. on the other side of the same wire. The size of the effect in Other electronic properties of the metal often have signifi- aluminum [42] is similar to that predicted in [43] and [44]. As cantly less of an effect on transport. As an example, the Fermi this effect has been observed at room temperature, now in ZnSe momentum (which has not been specified above) does not materials [45], perhaps the Spin Hall effect will prove useful significantly influence bulk electronic transport independently eventually for routing packets of spin, for communications, or of the transport parameters introduced above, although it can for logic. play an important role in determining the tunneling through Another important consequence of the correlation between an interface. During tunneling, the wave functions of the metal spin and orbit is spin relaxation in nonmagnetic metals. The must be matched with those of the insulating material, and thus, nonmagnetic metals of interest are predominately centrosym- the Fermi momentum (and band character) of the carriers at the metric elemental crystals or random alloys. In the absence of an Fermi level in the metal may play an important role. Another applied magnetic field, all states in the electronic spectrum of exception is the mean free path, which plays an important role such materials appear in (at least) doubly degenerate pairs. As in CIP GMR as it determines the range over which the two the spin and orbital degrees of freedom are entangled for these ferromagnetic layers of the spin valve can communicate with states, it is proper to refer to this degeneracy as “pseudospin each other. degeneracy,” although it is often referred to as spin degeneracy 910 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 54, NO. 5, MAY 2007 in the literature. Pseudospin degeneracy can be derived from true ferromagnetic semiconductor. In the meantime, substantial the dual requirements of time-reversal (Kramers) symmetry and progress on elevating the Curie temperature of Ga1−xMnxAs inversion symmetry (to above 170 K) was achieved by subjecting the samples to extended low-temperature postgrowth anneals [53], [54], Es(k)=E−s(−k)(Time reversal symmetry) (4) which appear to substantially reduce the density of undesirable interstitial Mn. Es(k)=Es(−k)(Inversion symmetry) (5) Extensive characterization studies have been done on some imply materials that are clearly ferromagnetic semiconductors, such as Ga1−xMnxAs, and include magnetotransport, bulk magneti- Es(k)=E−s(k)(Pseudospin degeneracy) (6) zation, and magnetooptics (magnetic circular dichroism) [17], and as a result, the mechanism of has begun where s is the pseudospin direction. The carriers in a metal to become clear. When the magnetic dopant Mn is substituted are scattered from one momentum state to another on fem- for Ga, the Mn acts as a relatively shallow acceptor (113-meV tosecond timescales. As the entanglement of spin and orbit binding energy). Due to the exchange interaction between the differs slightly for different momentum states, each time a core spin and the hole, the bound hole has its spin aligned transition from one momentum state to another occurs, there antiparallel to the core spin of the Mn. When the density of Mn is a finite probability of flipping the spin. This process, called dopants becomes high enough, the wave functions of neighbor- the Elliott–Yafet process [46], [47], limits spin lifetimes in ing acceptor states can overlap. Through the double-exchange sufficiently pure copper [48] and many other nonmagnetic mechanism [55], the energy is substantially lowered if the hole metals. spins are oriented parallel, which drives the ferromagnetic state. Recently, the anisotropic energetics of the interaction between Mn pairs were visualized directly through scanning tunneling C. Magnetic Insulators and Semiconductors microscope experiments [56], verifying predictions made ear- Some of the largest MR effects measured to date have been lier [57] that also explained the anisotropy of the individual Mn found at low temperature in tunnel junctions involving ferro- acceptor state [58], [59]. When the density of Mn becomes large magnetic insulators [49]–[51]. These materials exhibit spin- enough, the atomic details of the alloy can be smoothed away split band-edge energies of the order of a couple hundred of and the true spatial distribution of the Mn dopants replaced millielectronvolts. Thus, the barrier for spin-up and spin-down by a mean-field exchange interaction. Calculations based on carriers to tunnel through the insulating barrier differs by much such mean-field theories [52], [60], [61], in which the double- more than kBT and may be highly magnetic-field-dependent. exchange model approaches a “Zener” limit [52], for such Although these rare earth magnetic insulators are not mag- “hole-mediated ferromagnetic semiconductors,” have proved netically ordered at room temperature, their existence has successful at explaining the Curie temperatures, easy axes, prompted considerable exploratory research looking for room- magnetooptical properties, and magnetoelastic constants. Some temperature magnetic insulators that permit spin-preserving properties, such as the optical conductivity [62], still appear transport through a conduction-band barrier (spin-preserving challenging to explain based on either the single-Mn models Fowler–Nordheim tunneling). Such a room-temperature mag- or the mean-field models. netic insulator would very likely be a . The importance of holes in mediating the ferromagnetic state The ideal magnetic semiconductor would be a material that suggests that it should be possible to modify the properties of was ferromagnetic above room temperature, exhibited a spin- the magnetic material by reducing the number of holes (through split band structure, had high-mobility carriers, and could be gating). Such an effect would be extremely challenging (if controllably doped (preferably from n-type to p-type). One not impossible) to achieve in a magnetic metal because of the approach to look for such materials is to add magnetic dopants very high carrier concentration but has been demonstrated for to nonmagnetic semiconducting hosts [22], [23]. Success in these hole-mediated ferromagnetic semiconductors. Both the growing ferromagnetic In1−xMnxAs and Ga1−xMnxAs (which Curie temperature [63] and the coercive field [64] have been are not ferromagnetic at room temperature) and the prediction changed with a gate field. Very large MRs have also been found of room-temperature ferromagnetism in other doped semicon- when tunneling through regions of depleted Ga1−xMnxAs, a ductor hosts [52], strongly motivated researchers to explore magnetic semiconductor [65]. Here, the electronic structure of other potential hosts. Many of the subsequent reports of high- the depletion edge of a doped magnetic semiconductor was temperature ferromagnetic semiconductors in the literature, assumed to remain spin-split, as that of a magnetic insulator, however, have not been confirmed, probably due to the potential for in bulk when the carriers are depleted from Ga1−xMnxAs; formation of different combinations of the dopants and host the material does not stay ferromagnetic. elements than intended. Many of these different phases have The current limitations of Ga1−xMnxAs and other hole- ferromagnetic transition temperatures well above room tem- mediated ferromagnets for technological applications are the perature but are metal inclusions or clusters embedded in the relatively high level of doping required to get a high Curie material, instead of true magnetic semiconductors. It has proven temperature (corresponding to Mn concentrations near 10%), very challenging, in some cases, to differentiate the signal of the extremely short lifetimes of optically injected carriers [66], a sample with small regions of metallic phases embedded in and the Curie temperatures below room temperature. As these nonmagnetic semiconductors from that of a sample with a materials must be grown at relatively low temperatures (com- FLATTÉ: SPINTRONICS 911 pared to optimal temperatures for nonmagnetic semiconduc- would have an infinite lifetime from this mechanism (again, tors), control of the doping profile sufficient to grow magnetic ignoring the pseudospin nature of the states). For a zincblende bipolar devices has proved a great challenge, although there crystal, however, it is impossible to choose a global quantiza- is a recent report of success in fabricating a magnetic p-n tion axis, because the direction of the crystal magnetic field diode [67]. varies with k. The effective field for k(110) is perpendicular to the field for k(110), so no global quantization axis exists [71]. An unusual special case exists to this rule, for there is a D. Nonmagnetic Insulators and Semiconductors global quantization axis for (110)-grown zincblende quantum Just as the correlation of spin properties and orbital ones wells. led to the Spin Hall effect and finite spin lifetimes in nonmag- The presence of this effective internal magnetic field implies netic metals, these same phenomena can arise in nonmagnetic that the of a population of carriers will de- insulators and semiconductors. Transport through or within phase due to the variability of the internal field with momen- these materials, however, can also involve the electronic struc- tum. D’yakonov and Perel’ [72] have developed a theory for ture far from the Fermi surface, so the number of potential the spin lifetime in bulk zincblende semiconductors based on parameters required to describe spin transport can be far greater dephasing by the effective crystal magnetic field [B(k) in (7)]. than those required for metals. A derivation based on the density matrix formalism is viewable Recently, it was predicted that the tunneling process through in [12]. Thus, the spin lifetime in a material is closely connected MgO barriers would be extraordinarily spin-selective, and sub- to the structure of B(k), which itself is closely connected to the sequently, the MR measured in tunnel junctions involving this nature of the inversion asymmetry of the material. For example, material greatly exceeded the expected result from the spin po- the presence of the global quantization axis for (110)-grown larization of the metallic contacts [9], [68]. The prediction was zincblende quantum wells produces an exceptionally long spin based on first-principles calculations of the electronic structure lifetime for spins oriented parallel to that direction [73]–[76]. of Fe–MgO–Fe structures. The very large magnetoresistive As the inversion asymmetry of a material can be controlled, effect in such structures (exceeding a factor of three change in either in growth through the introduction of composition gradi- resistance [9]) persists even to room temperature and can also ents or after growth through the application of electric (gate) be used as an efficient spin injector from a magnetic metal into fields, this mechanism of spin relaxation provides a direct GaAs at room temperature [69], [70]. handle for tuning the spin lifetime. The effective magnetic field As most semiconductors do not have a center of symmetry, B arising from these effects is known simply as the “Rashba” the consequences of the spin–orbit interaction can be quite field [77], [78] and has the form different than in nonmagnetic metals. Even in the absence of an applied magnetic field, the pseudospin states of nonmagnetic B = αE × k (9) zincblende semiconductors, such as GaAs and other III–V semiconductors, are not degenerate [71]. Pseudospin states of where E is an effective electric field arising from the combina- the electron are split at finite k by the relativistic transformation tion of the effects above (compositional gradients or asymmetry of internal electric crystal fields into magnetic fields in the rest and applied external electric field), k is the carrier’s crystal frame of the moving electron. The splitting is described by the momentum, and α depends on the strength of the spin–orbit Hamiltonian interaction in the material. For (110) zincblende quantum wells, this Rashba field destroys the global quantization direction H = gµB(k) · S = Ω(k) · S (7) causing the spin lifetime to shorten [79], potentially by several orders of magnitude. Reductions of a factor of ten in the spin where B(k) is the effective crystal magnetic field, Ω(k) is the lifetime in a GaAs/AlGaAs quantum well [80] and of a factor resulting Larmor precession vector, g is the g factor, and µ is the of four in the spin lifetime in an InAs/AlSb quantum well [81] Bohr magneton. For direct-gap semiconductors, the effective have been observed experimentally through the application of crystal magnetic field vanishes at the conduction minimum an electric field. (k = 0), because Kramers degeneracy (4) requires that − − B(k)= B( k). (8) III. OPTICAL COUPLING TO THE SPIN Despite this, within 100 meV of the band edge in GaAs, The photon itself couples only weakly to the spin; however, this internal magnetic field approaches 1000 Tesla, which far the spin–orbit interaction permits spin-selective optical tran- exceeds the ability of a magnetic field applied from a typical sitions to occur even through electric-dipole interactions. The laboratory magnet to split the electronic spin states. details of such transitions depend on the electronic structure From (8) it is apparent that an ensemble of spins in such of the specific material, and most optical experiments to probe a material will experience a varying effective magnetic field, spin dynamics have been performed on direct-gap zincblende depending on the carrier momentum, that will cause spins in semiconductors. For these materials, the conduction band has the ensemble to precess differently from one another (a phe- s-like symmetry and the valence band has p-like symmetry. nomenon referred to as dephasing). As a spin only precesses in The crystal field of the semiconductor does not further split a transverse field, if B(k) were parallel to a fixed direction for the electronic states in the conduction or valence band at the all k, then a macroscopic magnetization oriented along that axis Γ point. Instead, the splitting that occurs is due to the spin– 912 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 54, NO. 5, MAY 2007 orbit interaction, which splits the six p states into a four- the carriers lose their spin polarization through spin relaxation fold degenerate J = 3/2 multiplet and a J = 1/2 doublet. The or decoherence, the transmission of the OCP pump will rise and valence-band edge corresponds to the J = 3/2 multiplet, and that of the SCP pump will decay, so the spin lifetime can be the individual states are labeled heavy hole and light hole up determined from the decay time (T1) of the SCP–OCP signal. and down. The heavy-hole states correspond to orbital angular One elegant method of probing the spin dynamics of op- momentum parallel to the spin and are tically injected carriers is Faraday rotation. In this technique product states of spin and orbit. The light-hole states, however, [93], the real index of refraction is measured, rather than the are not product states and consist of one-third spin antiparallel transmission coefficient. The difference in transmission coef- to orbital momentum along with two-thirds spin perpendicular ficients implies that the real indexes for SCP and OCP light to orbital momentum. will be different. Thus a linearly polarized probe pulse will An electric-dipole transition will be a spin-conserving tran- have its polarization axis rotated (Faraday rotation), and this sition and, if it involves circularly polarized light, will either rotation can be sensitively detected with a crossed polarizer. change the orbital angular momentum by +1(σ+) or −1(σ−) By applying a magnetic field transverse to the light-propagation along the axis of propagation (taken to be +ˆz). A σ+ photon direction, the spin population can be forced to precess, yielding will thus generate a heavy hole of Jz =+3/2 and an electron oscillatory Faraday rotation angles which directly indicate the of Sz = −1/2 or a light hole of Jz =+1/2 and an electron of Larmor precession frequency of the spin as well as the trans- ∗ Sz =+1/2, although the probability of the first process is three verse spin ensemble decoherence time T2 . Measurements via times larger than the probability of the second. Thus, circularly this technique identified very long spin-coherence times, even polarized light will generate an optically excited density of at room temperature, in II–VI semiconductor materials [94]. spin-polarized conduction electrons [12], with a maximum The spin-coherence times at low temperature, in commercial polarization of 50% wafers of GaAs, were found to exceed 100 ns [95]. Spatially resolved Faraday-rotation measurements also clearly showed n↑ − n↓ that packets of spin-polarized carriers in semiconductors could Pdensity = . (10) n↑ + n↓ be moved from one region of the semiconductor to another [96] or from one semiconductor material (such as GaAs) to another Similarly, spin-polarized electrons recombining with unpolar- (such as ZnSe) [97]. Observations of the decay of an optically ized holes will generate circularly polarized light with a po- induced spin grating, created by interfering two cross-polarized larization of 50%. In a quantum well, the light-hole states are pulses of light propagating at an angle to each other through the typically of higher energy than the heavy-hole states due to sample, also indicated that spin-polarized carriers could move quantum confinement (and possibly strain). In this situation, without losing their spin orientation [98]. in which the light-hole states are not optically accessed, the The very rapid spin relaxation possible in some semicon- polarization generated or detected can approach 100%. These ductor quantum wells has led to the proposal of spin-based spin-dependent selection rules are further modified in quantum optical switches [99]. Spin relaxation times shorter than 1 ps dots, where they can be very sensitive to the size, shape, and have been found in GaSb quantum wells [92], whose optical strain of the dot [82]. transitions have a wavelengths near 1.55 µm. Recently, even Time-resolved nonlinear optical techniques have provided faster optically switched transitions have been achieved using direct measurements of the evolution of a population of spins, the excitation of virtual spin-polarized excitons [100]. once they have been injected into a nonmagnetic semiconduc- Potential optical applications of ferromagnetic semicon- tor. In most bulk and quantum-well structures, the spin relax- ductors include switchable magnetooptical elements, such as ation times for holes are very short [83] due to the much greater Faraday isolators. A Faraday isolator uses the time-reversal- spin–orbit entanglement in the p-type valence bands than in the symmetry breaking of the Faraday effect to generate one-way s-type conduction bands. In time-resolved photoluminescence transmission. These devices are often used to isolate laser the electrons recombine with unpolarized holes, and the degree cavities from the remainder of an optical circuit. For commu- of circular polarization of the light determines the remaining nications wavelengths, the material commonly used is yttrium polarization of the electrons [84]–[89]. Another approach relies iron garnet, which provides a large Faraday rotation and low on the saturation of the optical transition used to generate optical loss. Use of a switchable ferromagnet would permit the the spin-polarized carriers once the spin-polarized carriers are one-directional transmission of a Faraday isolator to be turned present. A second pulse (the probe) incident on the material ON or OFF, or the direction of the allowed transmission to be with the same circular polarization (SCP) as the initial pulse changed dynamically. (the pump) will be transmitted through the sample more than it would have been without the pump [90]–[92]. To distinguish IV. TRANSPORT spin-dependent properties from ordinary band-filling effects, the experiment is also done with a probe of the opposite circular For most cases of simple macroscopic-charge-current flow, polarization (OCP) than the pump. For bulk materials with such as current flow in metals, transport is analyzed assuming selection rules near 50%, the transmission probability of the that the charge carriers are in a local equilibrium. In this probe with OCP will still be modified by the pump but less than framework, all the complex dynamics of an ensemble of charge the probe with the SCP. For quantum wells, the transmission of carriers are ignored, and the local properties are summarized by an OCP pump can be negligible right after the pump pulse. As a small number of parameters: local chemical potential; electric FLATTÉ: SPINTRONICS 913 potential; conductivity; and temperature. Charge transport is A. Incoherent Spin Transport then analyzed by relating the current J directly to the local 1) Formalism: A spin-polarized electron, through interac- change in the chemical potential  − φ by µ tion with external fields or its surroundings, can flip its spin, so the spin polarization of a current is not conserved in a J = σ∇(µ − φ) (11) spintronic circuit. Thus, the flow of spin-polarized current should be characterized by parameters, such as the spin-flip time (and related spin-diffusion length), describing aspects of where  is the chemical potential for electrons measured µ the steady-state transport that are not subject to the same strict relative to the electric potential, φ is the electric potential, conservation rules as charge current. and σ is the conductivity. In systems such as semiconductors The treatment here begins with some general considerations that can sustain large deviations of the local charge density that apply to both metals and semiconductors, and then specifies from equilibrium, the conductivity is separated into the carrier what approximations are commonly introduced to treat spin density and mobility and must be found self-consistently along transport in metals or semiconductors. Incoherent spin transport with the solution of the Poisson equation. Conservation of is usually considered either by introducing separate quasi- charge requires that, in steady-state transport, every electron chemical potentials for spin-up and spin-down carriers (an passing into an element of a circuit must pass out. Solution of approach common in the metallic community) or by introduc- (11) for the boundary conditions appropriate for a given voltage ing drift-diffusion equations that separately track spin-up and drop will produce a full description of the current distribution spin-down carrier densities and currents. These two approaches in response to an applied voltage. are, however, very closely related [105], as illustrated here for Spin transport requires a new descriptive framework. The charge flow. In the steady-state transport of a single charge spin of an electron can be altered through interaction with species, the continuity equation and conservation of charge external fields or the surroundings and, hence, is not a con- lead to served quantity for the carriers. Furthermore, the spin, as a quantum–mechanical quantity, cannot be fully described ac- ∇· cording to its projection along a single quantization axis. An J =0 (12) ensemble of spins with no spin-polarization along the zˆ axis could simply be an unpolarized ensemble or could be an and thus the current can be written as the gradient of a scalar ensemble that is fully polarized in the +ˆx direction. potential The theoretical treatment of spin transport simplifies con- siderably if a single quantization axis can be selected and J = ∇ξ = σ∇(−φ + µ). (13) the spin polarization in transverse directions can be neglected.

In this situation, referred to as incoherent spin transport, a For nondegenerate carriers µ = kBT ln(n/no), and (13) can quasi-chemical potential can be introduced for each of the two be written as spin directions of a spin-1/2 particle, a spin-up quasi-chemical potential, and a spin-down quasi-chemical potential. The term J = σE +(σkT/n)∇n = σE + eD∇n (14) “quasi-chemical potential” refers to a model where the spin- up carriers are considered to be in local equilibrium with other where n is the carrier density (n is the equilibrium carrier spin-up carriers (and the same for spin-down carriers) but spin- o density), k is Boltzmann’s constant, T is the temperature, E up and spin-down carriers are not in equilibrium with each other B is the electric field, e is the magnitude of the electric charge, (the two-channel model of Section II). This is a very similar and D is the diffusion constant. The far right expression of model to that used to describe nonequilibrium transport of (14) also holds in the degenerate regime, if n/n 1. Thus electrons and holes in semiconductors. Considerable progress o one can use either the chemical-potential expression or the has been made in analyzing incoherent spin transport, for it drift-diffusion equations to calculate the current in a general is remarkably similar to the two-band model for transport in situation. When either of these equations is combined with the semiconductors [101], [102]. Thus, equations that apply to Poisson equation relating the local deviation from equilibrium the transport of electrons and holes can at times be simply of the charge density to the electric field converted into equations that apply to the transport of spin-up and spin-down carriers. e ∇·E = − (n − n ) (15) If a single quantization axis cannot be defined, then the  o system is in the realm of coherent spin transport. One ap- proach to the theory of coherent spin transport is to con- a full solution is possible. sider the evolution of the spin-density matrix through the Frequently, the expressions in terms of quasi-chemical poten- system instead of merely considering the evolution of the tials are used when the carrier density is sufficiently high that diagonal (spin-up and spin-down) elements. In some limit- the conductivity can be considered independent of the nonequi- ing situations, evolution equations for the macroscopic spin librium spin-polarized carriers (as is the case in metals). Under (treated as a classical vector quantity) of the ensemble have these conditions, (13) can be solved for ξ with the appropriate been developed and successfully applied to situations of boundary conditions (continuity of current and a given voltage interest [96], [103], [104]. drop across the structure), and it is not necessary to consider 914 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 54, NO. 5, MAY 2007 the carrier density as a separate variable to be determined self- [17]. To include the possibility of spin imbalance in both the consistently. When the carrier density is low enough that the conduction and valence bands, four currents are required as spin-polarized carriers markedly change the conductivity of the follows: material (as can be the case in semiconductors), then σ in (13) ∇ must be determined self-consistently, requiring solving for the je↑ = en↑µe↑E + eDe↑ n↑ (21) carrier density in addition to the chemical potential and the je↓ = en↓µe↓E + eDe↓∇n↓ (22) electric field. In these situations, it is easier to use drift-diffusion − ∇ equations, which can be written without the chemical potential jh↑ = ep↑µh↑E eDh↑ p↑ (23) as a separate quantity to be determined. jh↓ = ep↓µh↓E − eDh↓∇p↓. (24) The essential modification to the charge transport expres- sions of (12)–(14) for spin transport is to consider the possibil- The evolution in time and space of these four currents and the ity of spins flipping from up to down or down to up as follows: electric field comes from the four continuity equations

∂n↑ ∂n↑ = −∇·je↑ +Γe↑↓n↓ − Γe↓↑n↑ (16) −e = −∇·j ↑ − eΓ ↓↑n↓ Γ ↑↓n↑ ∂t ∂t e e +e e

∂n↓ − eGe↑ + eR↑↑n↑p↑ + eR↑↓n↑p↓ (25) = −∇·j ↓ − Γ ↑↓n↓ +Γ ↓↑n↑. (17) ∂t e e e ∂n↓ −e = −∇·j ↓ + eΓ ↓↑n↓ − eΓ ↑↓n↑ In steady state the left-hand sides vanish. Within metals the ∂t e e e expressions can be further simplified by considering charge- − eGe↓ + eR↓↑n↓p↑ + eR↓↓n↓p↓ (26) neutral perturbations to the carrier density. Such perturba- ∂p↑ tions naturally satisfy the Poisson equation with ∇·E = 0, as e = −∇·j ↑ + eΓ ↓↑p↓ − eΓ ↑↓p↑ ∂t h h p ∆n↑ = −∆n↓. Substituting into (16), (17) yields + eGh↑ − eR↓↑n↓p↑ − eR↑↑n↑p↑ (27) 2 ∆n↑(Γe↓↑ +Γe↑↓) ∇ ∆n↑ = . (18) ∂p↓ D e = −∇·jh↓ − eΓh↓↑p↓ + eΓh↑↓p↑ ∂t − − For small perturbations ∆n↑ is proportional to µ↑,sowe + eGh↓ eR↑↓n↑p↓ eR↓↓n↓p↓ (28) can define a chemical-potential difference between spin-up and and the Poisson equation relating the local deviation from spin-down carriers µs such that [106], [107] equilibrium of the charge densities to the electric field ∇2 µs µs = 2 (19) e L ∇·E = − (∆n↑ +∆n↓ − ∆p↑ − ∆n↓). (29)  2 where L = D/(Γe↓↑ +Γe↑↓). The chemical potential for each spin direction is continuous across an interface in the absence Here, Γ are rates for spin relaxation of electrons and holes, of an interfacial resistance [106]. The presence of an interfacial G are generation rates for electron–hole pairs, R are their resistance can be absorbed into an effective chemical-potential recombination rates, and  is the dielectric constant. discontinuity determined by the spin-resolved current through Varying magnetic-band edges can be considered within this the interface. formalism by permitting the effective electric field to differ for For spin-dependent transport in semiconductors, however, different bands and spin directions [111], [112]. This can pro- the density dependence of the conductivity can have a dramatic duce unusual drift effects in magnetic heterostructures, includ- effect on the transport [108]–[110]. Equation (19) is modified ing effects analogous to grading the base-doping concentration by the presence of an electric-field-dependent term describing in a bipolar transistor [113]. carrier drift and is simpler to express in terms of the carrier 2) Applications of Incoherent Spin-Transport Theory: The density. For a nondegenerate distribution of carriers mechanism for GMR in the CIP and CPP geometries (Fig. 1) is quite different. For the CIP geometry, the MR comes from − 2 eE (n↑ n↓) enhanced spin scattering of carriers moving through the non- ∇ (n↑ − n↓)+ ·∇(n↑ − n↓) − =0. (20) 2 magnetic spacer when they can interact with two regions of op- kBT L positely oriented ferromagnetic material. If the spin scattering For degenerate carriers the energy scale appearing in the new for carriers of one spin direction is greater than for carriers of drift term of (20) is related to the Fermi energy rather than the the opposite spin when those carriers are within either the fer- thermal energy. The consequence of this new drift term is a romagnet or at the ferromagnet–nonmagnetic-metal interface, different upstream and downstream diffusion length for carri- then for antiparallel ferromagnetic layers and thin spacer layers, ers, similar to the different upstream and downstream diffusion the carriers of both spin directions will experience a strong lengths for packets of minority carriers in semiconductors. spin scattering. This occurs when the spacer layer is thinner Fully general drift-diffusion equations for carrier motion in than a mean free path, so a carrier in the nonmagnetic metal a semiconductor describe the combined motion of electrons spacer can sample the spin-dependent scattering coming from and holes in the presence of electric and quasi-electric fields, both layers. When the top and bottom layer of ferromagnet are including the effects of space-charge fields on carrier motion oriented parallel to each other, however, the scattering of one FLATTÉ: SPINTRONICS 915 spin direction is even larger but that of the other spin direction effort is underway, motivated by the discovery of coherent is very small. In the two-channel model, the high conductivity spin-transport phenomena in both magnetic multilayers and of the weakly scattered spin direction for the parallel-layer nonmagnetic semiconductors. Recently, the linear nature of geometry dominates over the two lower conductivity channels metallic transport in magnetic multilayers was given a new twist for the antiparallel-layer geometry. Various origins of the spin- from the discovery of “spin torque.” In this effect, the flow dependent scattering have been considered, first in approximate of current through a CPP spin-valve structure with nonparallel models that achieved qualitative agreement [26], [27], [114], ferromagnetic layers can cause the magnetization of the layers [115], and then, in first-principle calculations that achieved to precess or reorient [130], [131]. In one configuration, the first quantitative agreement [116]. ferromagnetic layer injects a spin-polarized distribution into the For the CPP geometry the MR comes instead from the nonmagnetic metal and that spin-polarized distribution retains matching conditions of (19) at the two interfaces [106], [117], its polarization transverse to the orientation of the second ferro- [118]. Trying to force a spin-polarized current into the nonmag- magnetic layer. Upon scattering from the second ferromagnetic netic metal produces a spin-accumulation region in the metal layer, or entering into it, the transverse component is changed, (corresponding to spin injection [119]) and that accumulation and as a result, the magnetization of the second ferromagnetic decays away from the interface over a length scale given by the layer experiences a torque [132]. Switching of small magnetic spin-diffusion length. As a result, the current flowing in the non- domains via this effect has been achieved, although the currents magnetic metal is still spin polarized. If the current reaches the required are large [133], [134]. This mechanism may replace second ferromagnetic layer prior to the spin-diffusion length, the applied magnetic fields required to reorient memory ele- then the current, still spin polarized, will find it easier to flow ments in MRAM with spin-polarized electrical currents. into a ferromagnetic layer oriented parallel to the first. Thus, Coherent transport within nonmagnetic semiconductors in a the voltage drop across the sandwich will be smaller for parallel magnetic field has been directly visualized using spatially re- ferromagnetic layers than for antiparallel layers. solved pump–probe measurements [96]. Coherent spin preces- For TMR, the resistance of each channel can be indepen- sion is also possible without an external magnetic field through dently determined assuming that the resistance is proportional the effect of the internal spin–orbit field that produces spin to the product of the densities of states on the two sides. decoherence in noncentrosymmetric semiconductors. These in- Then for parallel layers of the same ferromagnetic mater- ternal magnetic fields can cause spin precession during the 2 2 −1 ial, the resistance is proportional to [N↑(EF ) + N↓(EF ) ] , coherent propagation of spin packets over micrometers in non- and for antiparallel layers, the resistance is proportional to magnetic semiconductors [103], [104], [135], [136]. −1 [2N↑(EF )N↓(EF )] . Some of these results can be understood by a natural gener- The mechanism for MR in the CPP geometry requires the alization of the two-channel spin-transport theory to precessing flow of a spin-polarized current in the spacer region, which im- geometries [101], [103]. A more complete diffusive transport plies an accumulation of spin-polarized carriers within the non- theory that tracks properly how spin polarization along one magnetic spacer (spin injection). The amount of spin injection, axis can evolve into a spin polarization along a perpendic- however, is sensitively dependent on the relative conductivity ular axis is grounded best as the evolution of a spin density of the magnetic and the nonmagnetic materials [120]. The high matrix [137]. In the diffusive regime within such a theory, resistance of a semiconductor material, relative to a magnetic there naturally arise distinct length scales for the dynamics of metal, leads to a negligible spin-injection efficiency. Initially, the spin polarization parallel and perpendicular to an applied this obstacle was overcome by using a high-resistance magnetic magnetic field. metal, either a magnetically polarizable semiconductor [121] or a ferromagnetic semiconductor [122], and detecting the circular C. Transistor Structures polarization of the optical illumination in a so-called “spin light-emitting diode.” Optical techniques have also been used to Once spin-polarized distributions can be generated, moved demonstrate incoherent spin transport under large electric fields through magnetic and nonmagnetic semiconductor materials, in nonmagnetic-semiconductor structures [123]. manipulated, and detected, it is natural to explore the poten- Subsequently, a high-resistance spin-selective barrier was tial to use such distributions in multiterminal devices such as proposed as a route around the spin-injection obstacle . The first such three-terminal device proposed was [124]–[126]. The size of the required barrier is substantially a semiconductor device using coherent spin transport that had reduced relative to the expressions in the study in [124]–[126] incoherent charge inputs and outputs [138] and subsequent by nonlinear drift-diffusion effects in semiconductors [109], devices have extended the proposed range of device mechanism [110]. Convincing success in spin injection through a high- and device functionality. Since the proposal in [138], metallic resistance barrier into a semiconductor was achieved a couple three-terminal devices (where a third contact is made to the of years later [127]–[129] and has since reached 70% efficiency spacer layer in a CPP GMR configuration) [139] and hybrid at room temperature with an MgO barrier [69]. devices, in which the base of a transistor is replaced by a spin valve [140], have been built. Purely semiconductor proposals include unipolar spin transistors [102], [113], [141], B. Coherent Spin Transport magnetic p-n diodes [67], [111], [112], magnetic bipolar tran- The formalism for coherent transport is much less developed sistors [142], [143], and other spin field-effect transistors [76], than for incoherent transport; however, an intense research [144], [145]. 916 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 54, NO. 5, MAY 2007

Fig. 2. Schematic comparison of a MOSFET and a spin-based FET. The MOSFET works by controlling the height of the barrier, which is up in (a) and down in (b). The barrier height and width is largely determined by the desired ON–OFF current ratio and leakage current. The spin-based FET considered here works by controlling the nature of the initial state moving past fixed barriers; if the carriers in the base are fully spin polarized, the transistor is (c) OFF, otherwise the transistor is (d) ON.

It is reasonable to question, however, whether there is any likely to permit much more flexibility in the device design advantage to using spin-based devices to perform transistor ac- than is possible using only incoherent charge inputs and out- tion rather than charge-based devices. After all, several decades puts for a and a charge potential on the gate. of extensive worldwide research and development have been Although specific device configurations have not been ex- devoted to optimizing . Is it realistic to expect that tensively proposed, some capabilities that should prove use- spin-based devices could compete? ful include the ability to generate spin-polarized distributions This question is best addressed separately, depending on in the absence of magnetic fields and magnetic materials whether the inputs of the spin device are incoherent charge [148], [149], to manipulate [103], [104], [150] and inter- inputs or not. For devices with incoherent charge inputs, the fere [151] those distributions through transport, and to route minimum switching energy identified initially by Landauer spins in different directions based on their spin polarization [146], Ebit = kTln2 ∼ 23 meV, still applies. Although the [39]–[41]. Thus, many of the required elements have already device itself does not function by modifying the pathways for been experimentally demonstrated for a logical architecture charge motion, Landauer’s argument itself analyzes the modi- based on the coherent motion and manipulation of spin. fication of a charge on the gate of a transistor with incoherent As the most developed and analyzed proposals for com- charge inputs and outputs, independent of the mechanism for petitive spin-logic devices are based on spin transistors with transistor action once that charge is established. The condi- incoherent charge input, output, and gates, a deeper compari- tions for deriving this universal form for the switching energy, son of these with charge transistors is in order. Perhaps spin however, require that the switching is done slowly. As the transistors will be able to approach this fundamental limit in size shrinks and the required speed increases for charge-based smaller and faster transistors than charge-based transistors. To devices along the semiconductor roadmap [147], it is not clear analyze this hypothesis, Fig. 2 shows a schematic comparison that this fundamental limit will be reached. At the final node of of the two transistor mechanisms. On the left is the mechanism the 2003 roadmap, in 2018, the switching energy required for for operation of a charge transistor. Here, a barrier is raised and low-standby-power (LSTP) devices is 1500 eV/µm. Even for a lowered to turn the drain current OFF and ON. The barrier has to gate width comparable to the 10-nm gate length, the switching be sufficiently high and thick to maintain a large ON–OFF ratio energy would be approximately three orders of magnitude for the drain current, however the higher and thicker it is, the larger than the fundamental limit. larger the threshold voltage and the capacitance, and thus, the The static-power dissipation is another challenge in im- larger the gate switching energy will be. proving transistor-device performance that is related to the The spin field-effect transistor, however, does not function by dynamic-power dissipation (from gate switching) in CMOS raising or lowering a barrier. As shown in Fig. 2(c) and (d) for devices. Static-power dissipation in CMOS originates from one version of the spin field-effect transistor [76], the barrier is source–drain leakage, which can be minimized by making identical in both the ON and OFF configurations. The key is that the energetic barrier for the flow of carriers high and thick. the barrier is thick and high for carriers of one spin polarization This solution for static-power dissipation, however, degrades and is nonexistent for carriers of the opposite spin polarization. the dynamic-power-dissipation performance. Power dissipa- Carriers of one orientation are injected into the base region and, tion from source–drain leakage is intrinsic to the MOSFET then, cannot proceed until they flip their spin. If the spin lifetime mechanism and, thus, would be considerably different for spin in the base is very long, then the amount of current flowing out transistors. the drain is very small, whereas if the spin lifetime in the base Using the spin polarization of the input and output current is short, then the drain–current is large. to encode information and the ability to generate an effec- Modification of the spin lifetime to a length appropriate for tive gate bias that is spin-dependent (through the generation the “ON” configuration requires a substantially smaller electric of spin accumulation) to manipulate that information appears field than raising or lowering the barrier for the MOSFET. A FLATTÉ: SPINTRONICS 917

1-meV spin splitting can cause a spin to completely reorient interlayer exchange,” Phys. Rev. B, Condens. Matter, vol. 39, no. 7, by precession in only 1 ps. Generating this spin relaxation pp. 4828–4830, Mar. 1989. [3] B. Dieny, V. S. Speriosu, S. S. P. Parkin, B. A. Gurney, D. R. Wilhoit, and indirectly via applying an electric field and producing a Rashba D. Mauri, “Giant magnetoresistive in soft ferromagnetic multilayers,” field to relax the spins through the spin–orbit interaction implies Phys. Rev. B, Condens. Matter, vol. 43, no. 1, pp. 1297–1300, Jan. 1991. that a larger voltage is required; for the structure in [76], [4] J. Daughton, J. Brown, E. Chen, R. Beech, A. Pohm, and W. Kude, ≈ “Magnetic field sensors using GMR multilayer,” IEEE Trans. Magn., a Vth 100 mV is sufficient to reduce the spin lifetime to vol. 30, no. 6, pp. 4608–4610, Nov. 1994. 10 ps. The threshold voltage of an LSTP-CMOS MOSFET in [5] W. P. Pratt, S.-F. Lee, J. M. Slaughter, R. Loloee, P. A. Schroeder, and 2018 is four times larger. The capacitance of the structure in J. Bass, “Perpendicular giant of Ag/Co multilayers,” Phys. Rev. Lett., vol. 66, no. 23, pp. 3060–3063, Jun. 1991. [76] can also be considerably smaller than the capacitance of [6] S. F. Lee, W. P. Pratt, R. Loloee, P. A. Schroeder, and J. Bass, “‘Field- LSTP-CMOS, yielding an estimated power-delay product 500 dependent interface resistance’ of Ag/Co multilayers,” Phys.Rev.B, times smaller. Estimates of the leakage current based on the Condens. Matter, vol. 46, no. 1, pp. 548–551, Jul. 1992. [7] M. Julliere, “Tunneling between ferromagnetic films,” Phys. Lett. A, long spin lifetimes observed in semiconductor quantum wells vol. 54, no. 3, pp. 225–226, Sep. 1975. yield a leakage current six times smaller than LSTP-CMOS. [8] J. S. Moodera, L. R. Kinder, T. M. Wong, and R. Meservey, “Large Thus a spin-transistor design, with incoherent charge inputs, magnetoresistance at room temperature in ferromagnetic thin film tunnel junctions,” Phys. Rev. Lett., vol. 74, no. 16, pp. 3273–3276, Apr. 1995. outputs, and gates, could be significantly superior [152] to [9] S. S. P. Parkin, C. Kaiser, A. Panchula, P. M. Rice, B. Hughes, LSTP-CMOS even at the end of the roadmap node in 2018. M. Samant, and S.-H. Yang, “Giant tunnelling magnetoresistance at Of course, significant material advances would be required, room temperature with MgO (100) tunnel barriers,” Nat. Mater.,vol.3, no. 12, pp. 862–867, Dec. 2004. including the development of highly efficient spin-selective [10] W. H. Meiklejohn and C. P. Bean, “New magnetic anisotropy,” Phys. barriers and the demonstration of a much larger range of spin- Rev., vol. 102, no. 5, pp. 1413–1414, Jun. 1956. lifetime tuning than achieved to date. [11] C. P. Slichter, Principles of Magnetic Resonance.NewYork:Harper& Row, 1963. [12] F. Meier and B. P. Zachachrenya, Optical Orientation: Modern Problems in Condensed Matter Science, vol. 8. Amsterdam, The Netherlands: V. C ONCLUSION North Holland, 1984. [13] G. Prinz, “Magnetoelectronics,” Phys. Today, vol. 48, no. 4, pp. 58–63, The new field of spintronics was born in the intersection Apr. 1995. of magnetism, electronic transport, and optics. It has achieved [14] G. Prinz, “Magnetoelectronics,” Science, vol. 282, no. 5394, pp. 1660– commercial success in some areas and is advancing toward 1663, Nov. 1998. [15] H. Ohno, “Making nonmagnetic semiconductors ferromagnetic,” additional applications that rely on recent fundamental discov- Science, vol. 281, no. 5379, pp. 951–955, Aug. 1998. eries. The field is sufficiently broad that there is no single [16] D. D. Awschalom, M. E. Flatté, and N. Samarth, “Spintronics,” central obstacle to the application of these fundamental physical Sci. Amer., vol. 286, no. 6, pp. 66–73, Jun. 2002. [17] D. D. Awschalom, N. Samarth, and D. Loss, Eds., Semiconductor principles to new devices. Some of the advances that might Spintronics and Quantum Computation, Heidelberg, Germany: be most helpful would be room-temperature demonstrations Springer-Verlag, 2002. of: 1) a carrier-mediated ferromagnetic semiconductor whose [18] M. Ziese and M. J. Thornton, Eds., Spin Electronics, ser. Lecture Notes in Physics, vol. 569. Heidelberg, Germany: Springer-Verlag, 2001. density could be modified over a broad range by a gate [19] S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, field; 2) the injection of nearly 100% spin-polarized current S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, from a ferromagnetic metal into a nonmagnetic semiconductor; “Spintronics: A spin-based electronics vision for the future,” Science, vol. 294, no. 5546, pp. 1488–1495, Nov. 2001. 3) a nonmagnetic material with a gate-tunable or optically [20] A. H. MacDonald, P. Schiffer, and N. Samarth, “Ferromagnetic tunable Spin Hall effect, such that the Spin Hall conductiv- semiconductors: Moving beyond (Ga,Mn)As,” Nat. Mater., vol. 4, no. 3, ity could be tuned from positive to negative; 4) gate-tunable pp. 195–202, Mar. 2005. [21] T. Jungwirth, J. Sinova, J. Mašek, J. Kuera, and A. H. MacDonald, spin lifetimes over several orders of magnitude; 5) high- “Theory of ferromagnetic (III,Mn)V semiconductors,” Rev. Mod. Phys., efficiency minority carrier transport through a ferromagnetic vol. 78, no. 3, pp. 809–864, 2006. [22] H. Munekata, H. Ohno, S. von Molnár, A. Segmüller, L. L. Chang, and semiconductor (such as electrons through Ga1−xMnxAs); 6) a L. Esaki, “Diluted magnetic III–V semiconductors,” Phys. Rev. Lett., ferromagnetic semiconductor with very low optical loss; and vol. 63, no. 17, pp. 1849–1852, Oct. 1989. 7) spin transport in Si or SiGe devices. These are, of course, [23] H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. Endo, S. Katsumoto, and only a small selection of the possible areas that would have a Y. Iye, “(Ga,Mn)As: A new diluted magnetic semiconductor based on GaAs,” Appl. Phys. Lett., vol. 69, no. 3, pp. 363–365, Jul. 1996. tremendous effect on spintronics research and on achieving the [24] N. F. Mott, “The electrical conductivity of transition metals,” Proc. R. devices described here (and others). Soc. Lond. A, Math. Phys. Sci., vol. 153, no. 880, pp. 699–717, 1936. [25] A. Fert and I. A. Campbell, “Two-current conduction in nickel,” Phys. Rev. Lett., vol. 21, no. 16, pp. 1190–1192, Oct. 1968. ACKNOWLEDGMENT [26] R. E. Camley and J. Barnas,´ “Theory of effects in magnetic layered structures with antiferromagnetic coupling,” Phys. The author would like to thank D. D. Awschalom, Rev. Lett., vol. 63, no. 6, pp. 664–667, Aug. 1989. [27] J. Barnas,´ A. Fuss, R. E. Camley, P. Grünberg, and W. Zinn, “Novel N. Samarth, and G. Vignale for helpful conversations. magnetoresistance effect in layered magnetic structures: Theory and experiment,” Phys. Rev. B, Condens. Matter, vol. 42, no. 13, pp. 8110– REFERENCES 8120, Nov. 1990. [28] S. Dubois, L. Piraux, J. M. George, K. Ounadjela, J. L. Duvail, [1] M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, and A. Fert, “Evidence for a short spin diffusion length in permal- G. Creuzet, A. Friederich, and J. Chazelas, “Giant magnetoresistance loy from the giant magnetoresistance of multilayered nanowires,” of (001)Fe/(001)Cr magnetic superlattices,” Phys. Rev. Lett., vol. 61, Phys. Rev. B, Condens. Matter, vol. 60, no. 1, pp. 477–484, no. 21, pp. 2472–2475, Nov. 1988. Jul. 1999. [2] G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn, “Enhanced mag- [29] M. Johnson, “Spin accumulation in gold films,” Phys. Rev. Lett., vol. 70, netoresistance in layered magnetic structures with antiferromagnetic no. 14, pp. 2142–2145, Apr. 1993. 918 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 54, NO. 5, MAY 2007

[30] Q. Yang, P. Holody, S.-F. Lee, L. L. Henry, R. Loloee, P. A. Schroeder, [56] D. Kitchen, A. Richardella, J.-M. Tang, M. E. Flatté, and A. Yazdani, W. P. Pratt, and J. Bass, “Spin flip diffusion length and giant magnetore- “Atom-by-atom substitution of Mn in GaAs and visualization of their sistance at low temperatures,” Phys. Rev. Lett., vol. 72, no. 20, pp. 3274– hole-mediated interactions,” Nature, vol. 442, no. 7101, pp. 436–439, 3277, May 1994. Jul. 2006. [31] E. C. Stoner, “Collective electron ferromagnetism. II. Energy and spe- [57] J.-M. Tang and M. E. Flatté, “Multiband tight-binding model of local cific heat,” Proc. R. Soc. Lond. A, Math. Phys. Sci., vol. 169, no. 938, magnetism in Ga1−xMnxAs,” Phys. Rev. Lett., vol. 92, no. 4, p. 047 201, pp. 339–371, 1939. 2004. [32] J. Smit, “The spontaneous Hall effect in ferromagnetics I,” Physica, [58] A. M. Yakunin, A. Yu. Silov, P. M. Koenraad, W. V. Roy, J. D. Boeck, vol. 21, no. 6–10, pp. 877–887, 1955. J. H. Wolter, J.-M. Tang, and M. E. Flatté, “Spatial structure of an indi- [33] J. M. Luttinger, “Theory of the Hall effect in ferromagnetic substances,” vidual Mn acceptor in GaAs,” Phys. Rev. Lett., vol. 92, no. 21, p. 216 806, Phys. Rev., vol. 112, no. 3, pp. 739–751, Nov. 1958. 2004. [34] L. Berger, “Side-jump mechanism for the Hall effect of ferromag- [59] A. M. Yakunin, A. Yu. Silov, P. M. Koenraad, J.-M. Tang, M. E. Flatté, nets,” Phys. Rev. B, Condens. Matter, vol. 2, no. 11, pp. 4559–4566, W. V. Roy, J. D. Boeck, and J. H. Wolter, “Spatial structure of Mn–Mn Dec. 1970. acceptor pairs in GaAs,” Phys. Rev. Lett., vol. 95, no. 25, p. 256 402, [35] L. Berger, “Application of the side-jump model to the Hall effect and 2005. Nernst effect in ferromagnets,” Phys. Rev. B, Condens. Matter,vol.5, [60] M. Abolfath, T. Jungwirth, J. Brum, and A. H. MacDonald, “Theory no. 5, pp. 1862–1870, Mar. 1972. of magnetic anisotropy in III1−xMnxV ferromagnets,” Phys.Rev.B, [36] S. K. Lyo and T. Holstein, “Side-jump mechanism for ferromagnetic Hall Condens. Matter, vol. 63, no. 5, p. 054 418, Feb. 2001. effect,” Phys. Rev. Lett., vol. 29, no. 7, pp. 423–425, Aug. 1972. [61] T. Dietl, H. Ohno, and F. Matsukura, “Hole-mediated ferromagnetism [37] M. I. D’yakonov and V. I. Perel’, “Current-induced spin orientation of in tetrahedrally coordinated semiconductors,” Phys. Rev. B, Condens. electrons in semiconductors,” Phys. Lett. A, vol. 35, no. 6, pp. 459–460, Matter, vol. 63, no. 19, p. 195 205, May 2001. Jul. 1971. [62] K. S. Burch, D. B. Shrekenhamer, E. J. Singley, J. Stephens, [38] J. E. Hirsch, “Spin Hall effect,” Phys. Rev. Lett., vol. 83, no. 9, pp. 1834– B. L. Sheu, R. K. Kawakami, P. Schiffer, N. Samarth, D. D. Awschalom, 1837, Aug. 1999. and D. N. Basov, “Impurity band conduction in a high temperature fer- [39] Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Ob- romagnetic semiconductor,” Phys. Rev. Lett., vol. 97, no. 8, p. 087 208, servation of the Spin Hall effect in semiconductors,” Science, vol. 306, 2006. no. 5703, pp. 1910–1913, Dec. 2004. [63] H. Ohno, D. Chiba, F. Matsukura, T. Omiya, E. Abe, T. Dietl, [40] J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, “Experimen- Y. Ohno, and K. Ohtani, “Electric-field control of ferromagnetism,” tal observation of the Spin Hall effect in a two-dimensional spin-orbit Nature, vol. 408, no. 6815, pp. 944–946, Dec. 2000. coupled semiconductor system,” Phys. Rev. Lett., vol. 94, no. 4, [64] D. Chiba, M. Yamanouchi, F. Matsukura, and H. Ohno, “Electrical ma- p. 047204, 2005. nipulation of magnetization reversal in a ferromagnetic semiconductor,” [41]V.Sih,R.C.Myers,Y.K.Kato,W.H.Lau,A.C.Gossard,and Science, vol. 301, no. 5635, pp. 943–945, Aug. 2003. D. D. Awschalom, “Spatial imaging of the Spin Hall effect and current- [65] C. Rüster, T. Borzenko, C. Gould, G. Schmidt, L. W. Molenkamp, induced polarization in two-dimensional electron gases,” Nat. Phys., X. Liu, T. J. Wojtowicz, J. K. Furdyna, Z. G. Yu, and M. E. Flatté, vol. 1, no. 1, pp. 31–35, Oct. 2005. “Very large magnetoresistance in lateral ferromagnetic (Ga,Mn)As wires [42] S. O. Valenzuela and M. Tinkham, “Direct electronic measurement of with nanoconstrictions,” Phys. Rev. Lett., vol. 91, no. 21, p. 216 602, the Spin Hall effect,” Nature, vol. 442, no. 7099, pp. 176–179, Jul. 2006. Nov. 2003. [43] S. Zhang, “Spin Hall effect in the presence of spin diffusion,” Phys. Rev. [66] B. Beschoten, P. A. Crowell, I. Malajovich, D. D. Awschalom, Lett., vol. 85, no. 2, pp. 393–396, Jul. 2000. F. Matsukura, A. Shen, and H. Ohno, “Magnetic circular dichroism [44] R. V. Shchelushkin and A. Brataas, “Spin Hall effects in diffusive normal studies of carrier-induced ferromagnetism in Ga1−xMnxAs,” Phys. Rev. metals,” Phys. Rev. B, Condens. Matter, vol. 71, no. 4, p. 045 123, Lett., vol. 83, no. 15, pp. 3073–3076, Oct. 1999. Jan. 2005. [67] P. Chen, J. Moser, P. Kotissek, J. Sadowski, M. Zenger, D. Weiss, and [45] N. P. Stern, S. Ghosh, G. Xiang, M. Zhu, N. Samarth, and W. Wegscheider, “All-electrical measurement of spin injection in a mag- D. D. Awschalom, “Current-induced polarization and the Spin Hall ef- netic p-n junction diode,” Phys.Rev.B, vol. 74, no. 24, p. 241 302 (R), fect at room temperature,” Phys. Rev. Lett., vol. 97, no. 12, p. 126 603, Dec. 2006. Sep. 2006. [68] W. H. Butler, X.-G. Zhang, T. C. Schulthess, and J. M. MacLaren, “Spin- [46] R. J. Elliott, “Theory of the effect of spin-orbit coupling on magnetic dependent tunneling conductance of Fe|MgO|Fe sandwiches,” Phys. Rev. resonance in some semiconductors,” Phys. Rev., vol. 96, no. 2, pp. 266– B, Condens. Matter, vol. 63, no. 5, p. 054 416, Jan. 2001. 279, Oct. 1954. [69] X. Jiang, R. Wang, R. M. Shelby, R. M. Macfarlane, S. R. Bank, [47] Y. Yafet, “g factors and spin-lattice relaxation of conduction electrons,” J. S. Harris, and S. S. P. Parkin, “Highly spin-polarized room- Solid State Phys., vol. 14, pp. 2–98, 1963. temperature tunnel injector for semiconductor spintronics using [48] S. Schultz and C. Latham, “Observation of electron spin resonance in MgO(100),” Phys. Rev. Lett., vol. 94, no. 5, p. 056 601, 2005. copper,” Phys. Rev. Lett., vol. 15, no. 4, pp. 148–151, Jul. 1965. [70] G. Salis, R. Wang, X. Jiang, R. M. Shelby, S. S. P. Parkin, S. R. Bank, and [49] L. Esaki, P. J. Stiles, and S. von Molnár, “Magnetointernal field emission J. S. Harris, “Temperature independence of the spin-injection efficiency in junctions of magnetic insulators,” Phys. Rev. Lett., vol. 19, no. 15, of a MgO-based tunnel spin injector,” Appl. Phys. Lett., vol. 87, no. 26, pp. 852–854, Oct. 1967. p. 262 503, 2005. [50] J. S. Moodera, X. Hao, G. A. Gibson, and R. Meservey, “Electron-spin [71] G. Dresselhaus, “Spin–orbit coupling effects in zinc blende structures,” polarization in tunnel junctions in zero applied field with ferromagnetic Phys. Rev., vol. 100, no. 2, pp. 580–586, Oct. 1955. EuS barriers,” Phys. Rev. Lett., vol. 61, no. 5, pp. 637–640, Aug. 1988. [72] M. I. D’yakonov and V. I. Perel’, “Spin relaxation of conduction elec- [51] X. Hao, J. S. Moodera, and R. Meservey, “Spin-filter effect of ferromag- trons in noncentrosymmetric semiconductors,” Sov. Phys.—Solid State, netic europium sulfide tunnel barriers,” Phys. Rev. B, Condens. Matter, vol. 13, no. 12, pp. 3023–3026, 1972. vol. 42, no. 13, pp. 8235–8243, Nov. 1990. [73] M. I. D’yakonov and V. Y. Kachorovskii, “Spin relaxation of two- [52] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, and D. Ferrand, “Zener model dimensional electrons in noncentrosymmetric semiconductors,” Sov. description of ferromagnetism in zinc-blende magnetic semiconductors,” Phys.—Semicond., vol. 20, no. 1, pp. 110–112, 1986. Science, vol. 287, no. 5455, pp. 1019–1022, 2000. [74] R. Winkler, “Spin orientation and spin precession in inversion- [53] K. W. Edmonds, K. Y. Wang, R. P. Campion, A. C. Neumann, asymmetric quasi-two-dimensional electron systems,” Phys. Rev. B, N. R. S. Farley, B. L. Gallagher, and C. T. Foxon, “High-Curie- Condens. Matter, vol. 69, no. 4, p. 045 317, Jan. 2004. temperature Ga1−xMnxAs obtained by resistance-monitored anneal- [75] Y. Ohno, R. Terauchi, T. Adachi, F. Matsukura, and H. Ohno, “Spin ing,” Appl. Phys. Lett., vol. 81, no. 26, pp. 4991–4993, Dec. 2002. relaxation in GaAs(110) quantum wells,” Phys. Rev. Lett., vol. 83, no. 20, [54] K. C. Ku, S. J. Potashnik, R. F. Wang, S. H. Chun, P. Schiffer, pp. 4196–4199, Nov. 1999. N. Samarth, M. J. Seong, A. Mascarenhas, E. Johnston-Halperin, [76] K. Hall, W. H. Lau, K. Gündogdu,˘ M. E. Flatté, and T. F. Boggess, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Highly enhanced “Nonmagnetic semiconductor spin transistor,” Appl. Phys. Lett., vol. 83, Curie temperature in low-temperature annealed [Ga,Mn]As epilayers,” no. 14, pp. 2937–2939, Oct. 2003. Appl. Phys. Lett., vol. 82, no. 14, pp. 2302–2304, Apr. 2003. [77] E. I. Rashba, “Properties of semiconductors with an extremum loop I. [55] P. W. Anderson, “Theory of magnetic exchange interactions: Exchange Cyclotron and combinational resonance in a magnetic field perpendic- in insulators and semiconductors,” Solid State Phys., vol. 14, pp. 99–214, ular to the plane of the loop,” Sov. Phys.—Solid State, vol. 2, no. 6, 1963. pp. 1109–1122, 1960. FLATTÉ: SPINTRONICS 919

[78] Y. A. Bychkov and E. I. Rashba, “Oscillatory effects and the magnetic [102] M. E. Flatté and G. Vignale, “Unipolar spin diodes and transistors,” Appl. susceptibility of carriers in inversion layers,” J. Phys. C, Solid State Phys. Lett., vol. 78, no. 9, pp. 1273–1275, Feb. 2001. Phys., vol. 17, no. 33, pp. 6039–6045, 1984. [103] S. A. Crooker and D. L. Smith, “Imaging spin flows in semiconductors [79] W. H. Lau and M. E. Flatté, “Tunability of electron spin coherence in subject to electric, magnetic and strain fields,” Phys. Rev. Lett., vol. 94, III–V quantum wells,” J. Appl. Phys., vol. 91, no. 10, pp. 8682–8684, no. 23, p. 236 601, 2005. May 2002. [104] S. A. Crooker, M. Furis, X. Lou, C. Adelmann, D. L. Smith, [80] O. Z. Karimov, G. H. John, R. T. Harley, W. H. Lau, M. E. Flatté, C. J. Palmstrøm, and P. A. Crowell, “Imaging spin transport in lat- M. Henini, and R. Airey, “High temperature gate control of quantum eral ferromagnet/semiconductor structures,” Science, vol. 309, no. 5744, well spin memory,” Phys. Rev. Lett., vol. 91, no. 24, p. 246 601, 2003. pp. 2191–2195, Sep. 2005. [81] K. Hall, K. Gündogdu,˘ J. L. Hicks, A. N. Kocbay, M. E. Flatté, [105] C. Kittel and H. Kroemer, Thermal Physics. New York: Freeman, 1980. T. F. Boggess, K. Holabird, A. Hunter, D. H. Chow, and J. J. Zinck, [106] P. C. van Son, H. van Kempen, and P. Wyder, “Boundary resistance of “Room-temperature electric-field controlled spin dynamics in (110) InAs the ferromagnetic–nonferromagnetic metal interface,” Phys. Rev. Lett., quantum wells,” Appl. Phys. Lett., vol. 86, no. 20, p. 202114, May 2005. vol. 58, no. 21, pp. 2271–2273, May 1987. [82] C. E. Pryor and M. E. Flatté, “Accuracy of circular polarization as a [107] S. Hershfield and H. L. Zhao, “Charge and spin transport through measure of spin polarization in quantum dot qubits,” Phys. Rev. Lett., a metallic ferromagnetic–paramagnetic–ferromagnetic junction,” Phys. vol. 91, no. 25, p. 257 901, 2003. Rev. B, Condens. Matter, vol. 56, no. 6, pp. 3296–3305, Aug. 1997. [83] T. Uenoyama and L. J. Sham, “Hole relaxation and luminescence polar- [108] A. G. Aronov and G. E. Pikus, “Spin injection into semiconductors,” Sov. ization in doped and undoped quantum wells,” Phys. Rev. Lett., vol. 64, Phys.—Semicond., vol. 10, no. 6, pp. 698–700, 1976. no. 25, pp. 3070–3073, Jun. 1990. [109] Z. G. Yu and M. E. Flatté, “Electric-field dependent spin diffusion and [84] R. J. Seymour and R. R. Alfano, “Time-resolved measurement of the spin injection into semiconductors,” Phys. Rev. B, Condens. Matter, electron-spin relaxation kinetics in GaAs,” Appl. Phys. Lett., vol. 37, vol. 66, no. 20, p. 201202 (R), Nov. 2002. no. 2, pp. 231–233, Jul. 1980. [110] Z. G. Yu and M. E. Flatté, “Spin diffusion and injection in semiconductor [85] T. C. Damen, K. Leo, J. Shah, and J. E. Cunningham, “Spin relaxation structures: Electric field effects,” Phys. Rev. B, Condens. Matter, vol. 66, and thermalization of excitons in GaAs quantum wells,” Appl. Phys. no. 23, p. 235 302, Dec. 2002. Lett., vol. 58, no. 17, pp. 1902–1904, Apr. 1991. [111] I. Žutic,´ J. Fabian, and S. Das Sarma, “Spin-polarized transport [86] M. Kohl, M. R. Freeman, D. D. Awschalom, and J. M. Hong, “Femtosec- in inhomogeneous magnetic semiconductors: Theory of magnetic/ ond spectroscopy of carrier-spin relaxation in GaAs−AlxGa1−xAs nonmagnetic p-n junctions,” Phys. Rev. Lett., vol. 88, no. 6, p. 066 603, quantum wells,” Phys. Rev. B, Condens. Matter, vol. 44, no. 11, Jan. 2002. pp. 5923–5926, Sep. 1991. [112] J. Fabian, I. Žutic,´ and S. D. Sarma, “Theory of spin-polarized bipolar [87] S. Bar-Ad and I. Bar-Joseph, “Exciton spin dynamics in GaAs het- transport in magnetic p-n junctions,” Phys. Rev. B, Condens. Matter, erostructures,” Phys. Rev. Lett., vol. 68, no. 3, pp. 349–352, Jan. 1992. vol. 66, no. 16, p. 165 301, Oct. 2002. [88] J. Wagner, H. Schneider, D. Richards, A. Fischer, and K. Ploog, “Ob- [113] M. E. Flatté and G. Vignale, “Heterostructure unipolar spin transistors,” servation of extremely long electron-spin-relaxation times in p-type J. Appl. Phys., vol. 97, no. 10, p. 104508, May 2005. δ-doped GaAs/AlxGa1−xAs double heterostructures,” Phys.Rev.B, [114] P. M. Levy, S. Zhang, and A. Fert, “Electrical conductivity of magnetic Condens. Matter, vol. 47, no. 8, pp. 4786–4789, Feb. 1993. multilayered structures,” Phys. Rev. Lett., vol. 65, no. 13, pp. 1643–1646, [89] M. Oestreich, S. Hallstein, A. P. Heberle, K. Eberl, E. Bauser, and Sep. 1990. W. W. Rühle, “Temperature and density dependence of the electron [115] A. Barthélémy and A. Fert, “Theory of the magnetoresistance in Landé g factor in semiconductors,” Phys. Rev. B, Condens. Matter, magnetic multilayers: Analytical expressions from a semiclassical ap- vol. 53, no. 12, pp. 7911–7916, Mar. 1996. proach,” Phys. Rev. B, Condens. Matter, vol. 43, no. 16, pp. 13 124– [90] A. Tackeuchi, S. Muto, T. Inata, and T. Fuji, “Direct observation of 13 129, Jun. 1991. picosecond spin relaxation of excitons in GaAs/AlGaAs quantum wells [116] W. H. Butler, X.-G. Zhang, T. C. Schulthess, D. M. C. Nicholson, using spin-dependent optical nonlinearity,” Appl. Phys. Lett., vol. 56, J. M. MacLaren, V. S. Speriosu, and B. A. Gurney, “Conductance and no. 22, pp. 2213–2215, May 1990. giant magnetoconductance of Co|Cu|Co spin valves: Experiment and [91] R. S. Britton, T. Grevatt, A. Malinowski, R. T. Harley, P. Perozzo, theory,” Phys. Rev. B, Condens. Matter, vol. 56, no. 22, pp. 14 574– A. R. Cameron, and A. Miller, “Room temperature spin relaxation 14 582, Dec. 1997. in GaAs/AlGaAs multiple quantum wells,” Appl. Phys. Lett., vol. 73, [117] M. Johnson, “Analysis of anomalous multilayer magnetoresistance no. 15, pp. 2140–2142, 1998. within the thermomagnetoelectric system,” Phys. Rev. Lett., vol. 67, [92] K. C. Hall, S. W. Leonard, H. M. van Driel, A. R. Kost, E. Selvig, and no. 25, pp. 3594–3597, Dec. 1991. D. H. Chow, “Subpicosecond spin relaxation in GaAsSb multiple quan- [118] T. Valet and A. Fert, “Theory of the perpendicular magnetoresistance in tum wells,” Appl. Phys. Lett., vol. 75, no. 26, pp. 4156–4158, 1999. magnetic multilayers,” Phys. Rev. B, Condens. Matter, vol. 48, no. 10, [93] S. A. Crooker, J. J. Baumberg, F. Flack, N. Samarth, and D. D. pp. 7099–7113, Sep. 1993. Awschalom, “Terahertz spin precession and coherent transfer of angular [119] M. Johnson and R. H. Silsbee, “Spin-injection experiment,” Phys. Rev. momenta in magnetic quantum wells,” Phys. Rev. Lett., vol. 77, no. 13, B, Condens. Matter, vol. 37, no. 10, pp. 5326–5335, Apr. 1988. pp. 2814–2817, Sep. 1996. [120] G. Schmidt, D. Ferrand, L. W. Molenkamp, A. T. Filip, and [94] J. M. Kikkawa, I. P. Smorchkova, N. Samarth, and D. D. Awschalom, B. J. van Wees, “Fundamental obstacle for electrical spin injection from “Room-temperature spin memory in two-dimensional electron gases,” a ferromagnetic metal into a diffusive semiconductor,” Phys. Rev. B, Science, vol. 277, no. 5330, pp. 1284–1287, Aug. 1997. Condens. Matter, vol. 62, no. 8, pp. R4790–R4793, Aug. 2000. [95] J. M. Kikkawa and D. D. Awschalom, “Resonant spin amplification in n- [121] R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, type GaAs,” Phys. Rev. Lett., vol. 80, no. 19, pp. 4313–4316, May 1998. and L. W. Molenkamp, “Injection and detection of a spin-polarized [96] J. M. Kikkawa and D. D. Awschalom, “Lateral drag of spin coherence in current in a light-emitting diode,” Nature, vol. 402, no. 6763, pp. 787– gallium arsenide,” Nature, vol. 397, no. 6715, pp. 139–141, Jan. 1999. 790, 1999. [97] I. Malajovich, J. J. Berry, N. Samarth, and D. D. Awschalom, “Persistent [122] Y. Ohno, D. K. Young, B. Beschoten, F. Matsukura, H. Ohno, and sourcing of coherent spins for multifunctional semiconductor spintron- D. D. Awschalom, “Electrical spin injection in a ferromagnetic semi- ics,” Nature, vol. 411, no. 6839, pp. 770–772, Jun. 2001. conductor heterostructure,” Nature, vol. 402, no. 6763, pp. 790–792, [98] A. R. Cameron, P. Riblet, and A. Miller, “Spin gratings and the measure- Dec. 1999. ment of electron drift mobility in multiple quantum well semiconduc- [123] D. Hägele, M. Oestreich, W. W. Rühle, N. Nestle, and K. Eberl, “Spin tors,” Phys. Rev. Lett., vol. 76, no. 25, pp. 4793–4796, Jun. 1996. transport in GaAs,” Appl. Phys. Lett., vol. 73, no. 11, pp. 1580–1582, [99] Y. Nishikawa, A. Tackeuchi, S. Nakamura, S. Muto, and N. Yokoyama, Sep. 1998. “All-optical picosecond switching of a quantum well etalon using spin- [124] E. I. Rashba, “Theory of electrical spin injection: Tunnel contacts as a polarization relaxation,” Appl. Phys. Lett., vol. 66, no. 7, pp. 839–841, solution of the conductivity mismatch problem,” Phys. Rev. B, Condens. Feb. 1995. Matter, vol. 62, no. 24, pp. R16 267–R16 270, Dec. 2000. [100] E. J. Gansen, K. Jarasiunas, and A. Smirl, “Femtosecond all-optical [125] D. L. Smith and R. N. Silver, “Electrical spin injection into semicon- polarization switching based on the virtual excitation of spin-polarized ductors,” Phys. Rev. B, Condens. Matter, vol. 64, no. 4, p. 045 323, excitons in quantum wells,” Appl. Phys. Lett., vol. 80, no. 6, pp. 971– Jul. 2001. 973, Feb. 2002. [126] A. Fert and H. Jaffrès, “Conditions for efficient spin injection from [101] M. E. Flatté and J. M. Byers, “Spin diffusion in semiconductors,” Phys. a ferromagnetic metal into a semiconductor,” Phys. Rev. B, Condens. Rev. Lett., vol. 84, no. 18, pp. 4220–4223, May 2000. Matter, vol. 64, no. 18, p. 184 420, Oct. 2001. 920 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 54, NO. 5, MAY 2007

[127] A. T. Hanbicki, B. T. Jonker, G. Itskos, G. Kioseoglou, and A. Petrou, [143] J. Fabian, I. Žutic,´ and S. D. Sarma, “Magnetic bipolar transistor,” Appl. “Efficient electrical spin injection from a magnetic metal/tunnel barrier Phys. Lett., vol. 84, no. 1, pp. 85–87, Jan. 2004. contact into a semiconductor,” Appl. Phys. Lett., vol. 80, no. 7, pp. 1240– [144] J. Schliemann, J. C. Egues, and D. Loss, “Nonballistic spin-field-effect 1242, Feb. 2002. transistor,” Phys. Rev. Lett., vol. 90, no. 14, p. 146 801, Apr. 2003. [128] V. F. Motsnyi, J. D. Boeck, J. Das, W. V. Roy, G. Borghs, E. Goovaerts, [145] X. Cartoixa,` D. Z.-Y. Ting, and Y.-C. Chang, “A resonant spin lifetime and V. I. Safarov, “Electrical spin injection in a ferromagnet/tunnel transistor,” Appl. Phys. Lett., vol. 83, no. 7, pp. 1462–1464, Aug. 2003. barrier/semiconductor heterostructure,” Appl. Phys. Lett., vol. 81, no. 2, [146] R. Landauer, “Irreversibility and heat generation in the pp. 265–267, Jul. 2002. process,” IBM J. Res. Develop., vol. 5, no. 3, pp. 183–191, 1961. [129] C. Adelmann, X. Lou, J. Strand, C. J. Palmstrøm, and P. A. [147] International Technology Roadmap for Semiconductors. (2003). Crowell, “Spin injection and relaxation in ferromagnet–semiconductor Semicond. Ind. Assoc., San San Jose, CA. [Online]. Available: heterostructures,” Phys. Rev. B, Condens. Matter, vol. 71, no. 12, http://public.itrs.net p. 121 301 (R), 2005. [148] Y. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Current [130] L. Berger, “Emission of spin waves by a magnetic multilayer traversed induced spin polarization in strained semiconductors,” Phys. Rev. Lett., by a current,” Phys. Rev. B, Condens. Matter, vol. 54, no. 13, pp. 9353– vol. 93, no. 17, p. 176 601, 2004. 9358, Oct. 1996. [149] A. Y. Silov, P. A. Blajnov, J. H. Wolter, R. Hey, K. H. Ploog, and [131] J. Slonczewski, “Current-driven excitation of magnetic multilayers,” N. S. Averkiev, “Current-induced spin polarization at a single hetero- J. Magn. Magn. Mater., vol. 159, no. 1/2, pp. L1–L7, Jun. 1996. junction,” Appl. Phys. Lett., vol. 85, no. 24, pp. 5929–5931, Dec. 2004. [132] M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, M. Seck, V. Tsoi, and [150] Y. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Elec- P. Wyder, “Excitation of a magnetic multilayer by an electric current,” trical initialization and manipulation of electron spins in an L-shaped Phys. Rev. Lett., vol. 80, no. 19, pp. 4281–4284, May 1998. strained n-InGaAs channel,” Appl. Phys. Lett., vol. 87, no. 2, p. 022 503, [133] E. B. Myers, D. C. Ralph, J. A. Katine, R. N. Louie, and R. A. Buhrman, Jul. 2005. “Current-induced switching of domains in magnetic multilayer devices,” [151] Y. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Electron Science, vol. 285, no. 5429, pp. 867–870, Aug. 1999. spin interferometry using a semiconductor ring structure,” Appl. Phys. [134] J. A. Katine, F. J. Albert, R. A. Buhrman, E. B. Myers, and D. C. Lett., vol. 86, no. 16, p. 162107, Apr. 2005. Ralph, “Current-driven magnetization reversal and spin-wave excitations [152] K. Hall and M. E. Flatté, “Performance of a spin-based insulated gate in Co/Cu/Co pillars,” Phys. Rev. Lett., vol. 84, no. 14, pp. 3149–3152, field effect transistor,” Appl. Phys. Lett., vol. 88, no. 16, p. 162 503, Apr. 2000. Apr. 2006. [135] Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Coher- ent spin manipulation without magnetic fields in strained semiconduc- tors,” Nature, vol. 427, no. 6969, pp. 50–53, Jan. 2004. [136] B. A. Bernevig and S.-C. Zhang, “Spin splitting and spin current in strained bulk semiconductors,” Phys. Rev. B, Condens. Matter, vol. 72, no. 11, p. 115 204, Sep. 2005. [137] Y. Qi and S. Zhang, “Spin diffusion at finite electric and magnetic fields,” Michael E. Flatté (M’01) received the A.B. de- Phys. Rev. B, Condens. Matter, vol. 67, no. 5, p. 052407, Feb. 2003. gree in physics from Harvard University, Cambridge, [138] S. Datta and B. Das, “Electronic analog of the electro-optic modulator,” MA, in 1988, and the Ph.D. degree in physics from Appl. Phys. Lett., vol. 56, no. 7, pp. 665–667, Feb. 1990. the University of California, Santa Barbara (UCSB), [139] M. Johnson, “Bipolar spin switch,” Science, vol. 260, no. 5106, pp. 320– in 1992. 323, Apr. 1993. He was a Scholar in Residence at iQUEST, UCSB, [140] D. J. Monsma, R. Vlutters, and J. C. Lodder, “Room temperature- during the academic year 2000–2001. After post- operating spin-valve transistors formed by vacuum bonding,” Science, doctoral positions in the Institute for Theoretical vol. 281, no. 5375, pp. 407–409, 1998. Physics, UCSB, and in the Division of Applied [141] M. Deutsch, G. Vignale, and M. E. Flatté, “Effect of electrical bias on Sciences, Harvard University, he joined the faculty spin transport across a magnetic domain wall,” J. Appl. Phys., vol. 96, of The University of Iowa, Iowa City, where he no. 12, pp. 7424–7427, Dec. 2004. is currently a Professor in the Department of Physics and Astronomy and [142] M. E. Flatté, Z. G. Yu, E. Johnston-Halperin, and D. D. Awschalom, the Department of Electrical and Computer Engineering. He is also cur- “Theory of semiconductor magnetic bipolar transistors,” Appl. Phys. rently the Associate Director of the Optical Science and Technology Center, Lett., vol. 82, no. 26, pp. 4740–4742, Jun. 2003. The University of Iowa.