Spintronics and Spin Current

Transcription

1 Spintronics and Spin Current Spintronics and Spin Current Shun-Qing Shen Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong Conventional electronics completely ignores the electron spin, which provides us an unprecedented chance and new starting point to explore the future of modern semiconductor and information industry. Spintronics, or spin based electronics, aims at exploiting the subtle and mindbendingly esoteric quantum properties of the electron to develop a new generation of electronic devices. In this paper the motivation, physics fundamentals, and scope of spintronics will be briefly addressed. The spin current, one of the essential concepts in spintronics, will be discussed in details: the introduction and definition, physical effects, and recent experimental progresses of spin current. Key words: spintronics, spin current, electron spin. 1. SPINTRONICS More than eighty years ago, a UK genius physicist, Paul A. M. Dirac, synergized theories of quantum mechanics and Einstein s relativity to establish a new mechanics relativistic quantum mechanics. A straightforward and also amazing consequence from the theory is that an electron possesses an intrinsic angular momentum, called spin [see Table 1]. Since then it is realized that an electron possesses spin as well as the mass and elementary charge. Establishment and development of quantum mechanics brings us to a new stage to explore the constituents and structures of materials in Nature. Especially it becomes possible to have quantitative not qualitative knowledge of energy band structures of electrons in solid. This provides a solid foundation for the invention of semiconductor transistor and establishment of semiconductor industry. Until 1970s electronic micro-processors and resistances in circuits were compacted into an integrated circuit in a semiconductor chip. Since then semiconductor industry entered a fast track of development, and the number of transistors and resistances in a unit area doubles in every 12 to 18 months. The trend predicted by the Moore law summarizes the development of semiconductor and information industry. It makes the electronic computer, a huge machine, smaller and smaller, and to be part of everyday life. This rapid development also makes the size of transistors in the semiconductor chips approach the size of nanometers. As a single transistor cannot be smaller than a single atom, it becomes an insurmountable obstacle in the modern industry. Meanwhile, the Joule heating of the electronic devices with finite size effect is another obstacle. When people begin to think about the future of semiconductor industry, it is surprisingly found that almost all electric products just utilize electron charge to transfer energy and information. Spin as an intrinsic quantity in an electron is completely ignored except in some magnetic materials or degeneracy of energy bands, which provides a possible Shun-Qing Shen route and chance for the development of semiconductor industry. Spintronics or spin-based electronics aims exploiting the subtle and mind-bendingly esoteric quantum properties of the electron to develop a new generation of electronic devices. It has important impacts on information industry meanwhile it also provides new research subjects in the field of condensed matter physics and material science. Simply speaking, the driving force behind spintrions can be summarized in one sentence: conventional electronics has ignored electron spins completely [1]. In everyday electronic products, the orientation of electron spins Fundamentals of Electron Spin 1. Except for its mass and elementary charge, an electron has an intrinsic angular momentum, called spin. 2. Each spin has two arbitrary orientations, and its magnitudes are ± ħ / 2 (ħ is Planck constant). When all electron spins in solid align along the same direction, a ferromagnet forms. 3. In a magnetic field, an electron has different energies when electron spin is parallel or anti-parallel with the field. 4. Directional motion of electrons circulates an electric charge. In a conventional electric circuit, electron spins of charge carriers are random, and the current does not exhibit spin properties. 5. Directional and coherent motion of electron spin circulates a spin current, which will carry or transport information and control quantum spin in an spintronic device. Table 1: Fundamentals of electron spin. AAPPS Bulletin October 2008, Vol. 18, No. 5 29

2 Highlight of the Issue are completely random, 50% electrons has spin-up and other 50% has spin down. In another word, electron spin exhibits no role in the electronic devices. Discovery of giant magneto-resistance (GMR) in multilayer ferromagnetic thin films in 1988 marks the beginning of a new era. Magneto-resistance (MR) in metal is not new to physicists [2, 3]. When a metal is subjected to a magnetic field, the Lorentz force or the Hall effect will change the direction of motion of charge carriers, and leads to the change of resistance in the sample. When a charge carrier rotates around the field, it has no contribution if there is no scattering; once the carriers are scattered with each other or by impurity, the initial velocity of the carriers will determine the next cyclotron orbits. The longer the relaxation time (lower resistance) is, the larger the effect on the resistance in the field. Usually the MR ρ / ρ (H / ρ ) 2 (ρ is the resistance and H is the magnetic field). The MR in a good metal such as iron and cobalt is about %. Such a small MR has been already applied to design the magnetic sensor to readout the records in magnetic hard disk. In 1988 Baibich et al. [2] discovered that the MR in FeCr magnetic multilayers reaches at 50% at 4.2K, which is almost ten times of the highest record at that time. In the experiment the iron layers of 30 to 60 Å are separated by the cobalt layers of 9 to 60 Å. The magnetic iron layers are coupled antiferromagnetically. An external magnetic field about 20KOe makes the iron layers magnetized along the same direction, and the resistance in the sample is much smaller than the case without an external field. The magnetic coupling between the iron layers are determined by the thickness of non-magnetic cobalt layers. In 1990 Parkin et al. [4] found the oscillatory interlayer coupling with the thickness of the interlayers, which indicates that the GMR is controllable. The GMR does not relay on the direction of electric current to the orientation of magnetization, but is determined by the relative orientation of the magnetization in ferromagnetic layers. One of the key characteristics is that the thickness of the intermediate layer should be shorter than the mean free path of electrons (about 10 nm). It indicates that the two ferromagnetic layers determine the mechanism of spin-dependent scattering. When the magnetizations in the two layers are parallel to each other the mean free path increases. Oppositely when the magnetizations in the two layers are antiparallel to each other the mean free path decreases. As a result, the resistance of the system varies with the relative orientation of magnetizations in the two ferromagnetic layers. Soon after its discovery GMR has been applied to design the sensitive magnetic sensor, and increased the sensitivity to detect the magnetization drastically. Since then people began to realize the importance of quantum spin and its transport in research and applications in electronic devices. Later the tunneling magneto-resistance (TMR) was found to be much larger than GMR, and has extensive applications in commercial products [5]. After the discovery of GMR, Supriyo Datta and Biswajit Das at Purdue University, USA proposed a new type of spin field effect transistor [6]. This transistor consists of two ferromagnetic electrodes, i.e., a source and a drain. The conducting channel connecting the two electrodes is a two-dimensional electron gas in semiconductor heterojunction with strong spinorbit coupling. The injected electron from the ferromagnetic source should be spin polarized, and the effect of impurities on electron spins can be ignored in the range of spin coherent length. A gate voltage is applied on the conducting channel to control the electron spin procession via the spin-orbit coupling, and further to control the spin orientation of electrons when it reaches at the interface of the drain. When the electron spin arriving at the drain is parallel to the magnetization in the drain, the electrons enter the drain with a small resistance. Oppositely it will be reflected at the interface. In this way, the switch on and off of the transistor are realized. The conventional transistor utilizes the gate voltage to cut off the current between the source and drain, in which a larger voltage is required to change the direction of motion of electro than to change the orientation of electron spin. Comparing Datta-Das transistor and conventional transistor, the two transistors have almost the same structure, and use the gate voltage to control the current. However, the former is to use the gate voltage to control the spin orientation of electron, and the later is to use the gate voltage to change the direction of motion of electrons. Comparing these two procedures, the energy to change the spin orientation is much smaller, and the time is much shorter, and the efficiency is much higher. The novel and creative idea has attracted extensive attentions. It has already processed the key characteristics of modern spintronic devices: (1) it relies on spin polarized carriers or electron spins; (2) the moving electron spin can transport coherently and tunnel through the interfaces; (3) the spin coherent time of carriers is long enough to implement the desirable operations. Unfortunately, nearly twenty years has passed and this transistor has not yet been realized in any laboratory in the world until now. The two examples, GMR in metallic thin film and semiconductor field effect transistor, intrigues extensive research interests, and are two milestones in the development of spintronics. Rapid development and application of metallic spintronic devices become an important driving force in the study of spintronics. The GMR can be understood in two-channel theory of spin transport, which does not require the coherence of electron spin. Recent experiments such as, such as the current-induced magnetization procession and spin Hall effect in metals and semiconductors require coherence of electron spin. On the other hand, spin coherence lengths of electrons in semiconductors are much longer than those in metal, and we expect that more applications can be realized in semiconductors. In the studies of spintronics, simply speaking, there are three basic topics: 30 AAPPS Bulletin October 2008, Vol. 18, No. 5

3 Spintronics and Spin Current (1) spin injection: it is the first step to implement physical operation in spintronic device; (2) spin manipulation: it is crucial to control electron spin to realize desired physical operation efficiently by means of external fields; and (3) spin detection: it is necessary to measure the physical consequences of spin coherent states in spintronic devices. Spintronics is a practical science. As the electron spin can be understood only in the theory of relativistic quantum mechanics, it contains various basic topics, which are ignored in traditional theory of semiconductors. Studies of spintronics will provide new chances to explore quantum mechanics. In the present paper, we do not intend to overview the present status of spintronics. We focus on spin current, a counterpart of electric current, and address its definition, physical effect, and recent experimental measurements over the last few years. 2. SPIN CURRENT AND SPIN-OR- BIT COUPLING An electron carries elementary charge e. Coherent motion of electron may circulate an electric current, which can transport energy and information. Though electrons also possess intrinsic spins, the spin orientations of the charge carriers in traditional electronic devices are completely random. It does not exhibit any spin relevant effect except for trivial degeneracy. Before we introduce the concept of spin current, let us recall how to define electric current in a many-body theory. In principle, the Hamiltonian for a many-body system can be written as H = i,σ 1 2m (P i e c A σ) 2 + i j V ij, where the first term is the kinetic energy, and the second term is the interactions of electrons with each other or with the environments. From the Hamiltonian, the velocity operators of electrons are v σ = (P i e i c A σ)/ m c H, where e A σ σ =, is the spin index. In order to define an spin current we introduce an spin-dependent vector potential A σ. If we have the energy eigenvalues for the system, E (A, A ), an electric current is calculated from the formula j e = e (v + v ) = e ( E / A + E / A ). It is known that the vector potential A σ for an electromagnetic field is independent of spin, A = A. It concludes that the electric current is also independent of spin, v = v. Usually we just have electric current but no spin current. However, if the spin-dependent velocities for electrons are not equal, for example, v = v, it is found that there is no electric current j e 0, but (v v ) 0. This quantity has nothing to do with an electric current: it is relevant to the collective motion of electron spin. Consider the spin unit ћ / 2, the spin current is defined as j s = ћ 2 (v v ). We should emphasize that when we say spin-up and down, we have already specified the polarization orientation. Thus a spin current is determined by both the moving direction and the spin polarization of electrons. In theory, if the vector potential is spin-dependent, A A, it is highly possible for the system to circulate a spin current. How does the vector potential become spin-dependent in a many-body system? From physical origin of electron spin, it is a relativistic quantum effect according to the Dirac theory. It is well known that the electron spin interacts with a magnetic field, i.e. the Zeeman energy splitting. For an electron in an electric field, the electron spin is coupled with the field through the so-called spin-orbit coupling. People first realize the spin-orbit coupling in atomic physics, which can be understood in a classical picture. When an electron rotates around the nucleon, relatively from the standpoint of electron, the nucleon carrying a positive charge rotates around the electron. The moving nucleon generates a ring-like electric current. According to the Biot-Savart law, the ring-like current will induce a perpendicular magnetic field on the electron. The Zeeman energy of the electron spin and the induced magnetic field leads to the spin-orbital coupling. Taking into account the relativistic quantum correction, the result is V = 1 1 V 2m 2 c 2 r r S (r p ) = 1 2m 2 c 2 ( V p ) S, where V is the Coulomb potential that the electron experiences. This effect makes electron spin S and momentum p coupling together in an electric field V. From the point of view of relativistic quantum mechanics, the effect originates from the interference between the electron and positron. The factor 2mc 2 reflects the energy gap between electron and positrons, which magnitude is about 1 MeV. Usually the effect is very tiny, and emerges in atomic systems, such as the atomic light spectrum. Though the spin-orbital coupling is very small in a single atom, it will be magnified in some crystal systems. Due to the periodicity of crystal electrons in solid may form the band structure in the reciprocal vector space. If the system does not possess some inversion symmetries, the spin-orbital coupling of electron near some regimes will be magnified. For example, in a two-dimensional electron gas of InGaAs/ InAlAs heterostructure, the electrons near the Gamma point experiences strong coupling, i.e., Rashba spin-orbit coupling H R = λ( p σ ) z, and the coupling coefficient has dimension of velocity with a typical magnitude of order λ ~ 10-4 c (c the light speed) [7]. It is proportional inversely to the energy gap between the conduction and valence bands in semiconductors, which has the order of ev. Comparing with the energy gap between the electron and positron, it is smaller than 6 orders. In other words, the coupling has been magnified to 6 orders. The energy splitting caused by the coupling has been observed experimentally. In such a kind of system with spin-orbit coupling, the velocity of an electron is given by v = m 1 ( p + e c A σ), (A mc σ = λ e z σ ). We observe that the coupling will generate a spin-dependent vector potential [8]. From the definition of spin current, this vector potential makes it possible to circulate a spin current. A spin current is a second-rank pseudotensor, J s α = ћ 2 {σα, v}, which is given by not only the flow direction of electron spin but also spin orientation. Different spin orientations may produce different AAPPS Bulletin October 2008, Vol. 18, No. 5 31

4 Highlight of the Issue physical effects. Generally speaking, in an operation of time reversal, t t, the velocity v v and the charge e e. An electric current j e = ev will change its sign, j e j e. As for the spin current, the spin σ σ and the spin current will be invariant in a time reversal, j s α j sα. This property determines the low dissipative or even dissipativeless. It can be understood from the equation of motion of a simple harmonic oscillator with a damping term, mẍ = kx + λẋ. The energy dissipation comes from the damping term λẋ. When λ = 0, the total energy of the oscillator is conserved, and the equation of motion is invariant under time reversal. However, the damping term breaks the symmetry, and the system becomes dissipative. However, it is still an open issue whether the spin current is dissipativeless or not. In the spin Hall effect, the spin current induced by the electric current is dissipativeless, but the electric current itself is dissipative. Generally speaking, the coupling between the spin current and system crystal is rather weak, and has no direct coupling with phonon. This is one of the advantages of the spin current. Unlike the electric current, a spin current is not conserved, according to the definition. It is determined by the fact that the electron spin itself is not conserved. In modern physics, a conservation law is governed by symmetry. For example, a translational invariance of a system leads to the conversation of momentum, and the U(1) symmetry leads to the conservation of current. There are several mechanisms, which breaks the conservation of a spin current, such as magnetic impurities scattering, spin-orbit coupling, and nuclear spin. This characteristic brings us a lot of debates on the proper definition of spin current [9]. Since the electron spin is not conserved in solid, the key point is the physical consequences of the defined current. Whether the defined current is physical should be checked by the measurable phenomenon or effect directly related to the current. The answer about this question is quite positive based on the experimental progresses over last few years. Another issue is that a spin current cannot be transported for a long distance. Its possible application will be limited in some mesoscopic devices or circuits. The scale of spin current should be limited within a distance of spin decoherence. For a typical semiconductor material, it is about several to hundred micron meters. Recent experimental data indicates the spin coherence length can be tuned by an external field or become a quite long along some axis. It will be a new task for material scientists to look for a material with a super-long coherence length. 3. PHYSICAL EFFECTS OF SPIN CURRENT In order to apply a spin current in a device, first of all, we should know the physical effects of spin current. Over last few years we have extensively investigated general properties of spin current. Especially, spin Hall effect makes the spin current an essential subject in condensed matter physics Electric Field Induced by Spin Current By Biot-Savart law, an electric current may induce a magnetic field in the space surrounding it. Correspondingly, can a pure spin current induce an electric field? The answer is yes! Associated with the electron spin, there is a magnetic moment. According to Sun, Guo and Wang [10], for a spin current, it also accompanies a corresponding magnetic moment current. It has been well known that a single moving magnetic moment is equivalent to an electric dipole, it therefore follows that a moving magnetic moment may induce an electric field. To estimate the field, a simple way is to assume that a spin current consists of two positive and negative magnetic charges ± q mc moving in opposite directions. The two magnetic charges are separated by a distance δ. When δ 0 + and q mc +, we may have a magnetic dipole m = q mc δm^ (m^ is the polarization direction). Thus the spin current can be regarded phenomenalogically as a group of moving magnetic dipoles. Each magnetic dipole may generate a magnetic field. Under the Lorentz transformation, it can be transferred into an electric field. The electric field is given by E = μ 1 4π J mdv R 3(m^ 3R(R ^ m) R 2 ). This field is very small, but still measurable Spin Transverse Force In electrodynamics, it is known that an electric current experiences a transverse Lorentz force in a magnetic field, F = j c B. Correspondingly, can a spin current experience a classic force in an electric field? The present author gave a positive answer [8]. In a non-relativistic quantum mechanical limit, the spin-orbit coupling may contribute an anomalous velocity, which depends on spin and the external field, δv e = 4m 2 c 2 σ ε. From the Heisenberg equation of motion and the correspondence principle, we have a quantum mechanical analogue of Newton s second law. For a given quantum state, we find that m dv dt e 2 ε = 4m 2 c J 2 s ε ε in which the spin current is polarized along ε the electric field, J s = ћ 4 {v, σ ε / ε}. Just like the electric current, the spin current in a many-body system is a macroscopic quantity. The force is very similar to the Lorentz force, but it is proportional to the square of electric field. For a free electron, the force is very tiny. However, to control an electron spin, the force is not so small, and can produce measurable effects. For example, it can be regarded as the physical origin of zitterbewegung (wriggle) of Dirac particles. It was suggested that the effect can be observed in semiconductors, and even photonic crystals. For example, the energy gap between the positron and electron is 2mec 2 =1.06 MeV, but a typical energy gap between conduction band and valence band in a semiconductor is about one ev. Spin-orbit coupling is reversely proportional to the energy gap. As a result, it is possible that spinorbit coupling is enhanced 6 orders due to the band structure in semiconductors 32 AAPPS Bulletin October 2008, Vol. 18, No. 5

5 Spintronics and Spin Current comparing a Dirac free electron, and can induce an observable consequence. For a Rashba system, H R = λ( p x σ y p y σ x ), which is equivalent to an system subjected to an perpendicular field, and the motion of electron id confined in the plane. The spin transverse force is F = 4m 2 λ 2 J z s ẑ. ћ Spin Current and Spin Accumulation A straightforward consequence of spin current is the spin accumulation near the physical boundary. Usually the charge accumulation can induce an electric field or force on a charge, the spin accumulation does not induce an analogue field or force in the space. It depends on the diffusion process to reach at equilibrium. Thus the spin diffusion length and spin relaxation time are two key factors in the problem in the spin accumulation. General speaking, a spin current J s α and spin density distribution S α (r) can be described by a continuity equation [11], α S + J α t s = S α τ ρ τ s where ρ τ is the spin torque density. For a steady state, the spin density deos not evolve with time, and spin current and spin torque density are uniform in the bulk. However, near the boundary the spin current should vanish. Thus from the bulk to the boundary, J s α becomes non-zero, and induces anon-uniform distribution for spin density S α (r) 0. Physically, we introduce the spin-dependent chemical potential to describe the spin diffusion process, and the diffusion equation for the spin has the form [12] 2 (μ (r) μ (r)) = μ (r) μ (r) D 2 where D is the diffusion constant. The solution of this equation is determined by the boundary condition and the distribution of spin current. Generally speaking, the spin density is proportional to the spin current, and decays in an exponential law e r / D. The diffusion length is the range of the spin accumulation Scattering Effect of Spin Current A pure spin current is invariant under time reversal. When it is scattered by spin-dependent scatterers, such as the impurities or spin dependent band structure, it induces an electric current or potential. The simplest example is the scattering of the spin current through a spin dependent barrier potential. The spin-up barrier potential is higher than the one with spin down, the transmission coefficient for electron with spin up T is less than the transmission coefficient for electron with spin down T. Assume a pure spin current consist of two beams of moving electrons of spin up and down. The resulting electric current is proportional to the difference (T T ). Spin current may induce an electric current via an inverse spin Hall effect. The scattering mechanism can be classified as an intrinsic and extrinsic one. The external mechanism originates from the Mott scattering by the magnetic impurity [13]. Generally, the impurity potential possesses the spin-orbit coupling, i.e., LS coupling, V =ξ(r)l S. If the orientation of an angular momentum is specified, electrons with different spins, due to different expectation values of L S, will be scattered in opposite directions, that the scattering is asymmetric, which was noticed by the British physicist Mott in Thus the spin current can induce a transverse electric current by impurities. For a sample of strip geometry, the confinement of the boundary will accumulate extraneous charges near the boundary and induce a Hall voltage. Another mechanism originates from the spin-dependent band structure or spin-orbital coupling in the band structure [14]. For a Rashba system, the spin current will experience a spin transverse force under the spin-orbit coupling, F = 4m 2 λ 2 J z ћ 2 s z, within the spin relaxation time τ, it has a transverse drift velocity 4mλ v y = 2 J z s τ, and forms an Hall current. ћ 2 Further investigation illustrates that the spin orientation of spin current and symmetry of the spin-orbital coupling play a decisive role of the scattering of spin current, especially in mesoscopic systems. For example, spin current with in-plane polarization may generate quite different scattering effects [15]. 4. GENERATION AND DETEC- TION OF SPIN CURRENT Over the last few years, research works on generation and measurement of spin current have made breakthrough in either theoretically or experimentally. In theory, Hirsch rediscovered the spin Hall effect, that impurity scattering of electric current may induce a pure spin current [16]. Furthermore, Murakami et al. [17] and Sinova et al. [18] predicted that the spin-orbit coupling of the band structures may also produce an intrinsic spin Hall effect. These works stimulate extensive discussions on spin currents. Several experiments have been reported to inject and detect spin current. Here we briefly introduced these experiments. However, we do not intend to summarize recent theoretical progresses in this field Spin Hall Effect and Electrical Spin Injection Spin Hall effect provides a convenient and efficient way to generate spin current by electric means. When an electric field is applied to a system with spin-orbit coupling or magnetic impurities, the electrons with different spins will be deflected to opposite directions, and a paramagnetic system may generate a pure spin current perpendicular to the electric field, and its polarization is perpendicular to either the electric field and the flow direction. Early theorists predicted that the spin current is caused by the asymmetric scattering of electrons with up and down spins in impurity potentials, which is named as extrinsic spin Hall effect [13, 16]. Recently it was demonstrated that the spin-orbit coupling in the band structure of electrons can also lead to the perpendicular spin current even without impurity scattering, which is called intrinsic spin Hall effect [17, 18]. In the quantum Hall regime, the competition between the Zeeman splitting and spin-orbit coupling leads to the resonant spin Hall effect, in which a small current may induce a finite spin current AAPPS Bulletin October 2008, Vol. 18, No. 5 33

6 Highlight of the Issue [19] and spin polarization [20]. This effect converts an electric current into a spin current. Conversely, the spin current can also generate an electric current according to the Onsager relation. The first experimental report comes from D. Awschalom s group of UCLA, USA on optical measurement of GaAs and InGaAs thin film [21]. An electric field of order mvμm 1 is applied to a strip of μm 2. Then the spin distribution near the sample edge is scanned by the Kerr rotation method. It is observed that the spin accumulations near the two edges of the sample are opposite, and depend on the electric field. This is in a good agreement with theoretical prediction of spin Hall effect. As the GaAs sample does not break the structural inversion symmetry, the observed effect should be contributed by the scattering of impurity potentials. On the other hand, the spin accumulation is also always caused by the spin diffusion. The range of spin accumulation is determined by the spin diffusion length, which is also given by the impurity scattering. This experiment does not measure the spin current directly, but the spin accumulation which is believed to be caused by spin current. In the mean time, Dr. Wunderlich s group [22] from the Cambridge University, British reported their observation of spin light emitted diode of p-n junction which consists of two edges of one layer of two-dimensional (2D) electron gas and one layer of 2D hole gas. The 2D hole gas possesses a strong spin-orbit coupling because of lacking structural inversion symmetry. When an electric current flows the layer, the charge carriers near the two edges will recombine, and emit a photon. The light polarization of photons is determined by the spin polarization of the charge carriers. They reported the experimental measurement that the light polarization is determined by the direction of electric current. Theoretical calculation indicates that the observation can be understood very well from the spin current induced by the spin-orbit coupling of the band structure. So the mechanism is believed to be intrinsic. The group [23] from National Taiwan University observed the spin Hall effect in InGaN/GaN superlattice by measuring the polarization of lateral photoluminescence spectra to determine the spin polarization caused by spin Hall current. They also studied the strain dependence of the effect Nonlocal Spin Injection and Reciprocal Spin Hall Effect Lateral nonlocal geometric spin injection and detection dated back to Johnson and Silsbee [24] first reported that spin injection and detection in lateral nonlocal geometries can be shaped easily into multiterminal devices with output signals which are only determined by spin. They performed the experiment in non-magnetic aluminum strip contacted to two ferromagnetic electrodes. Spin polarized current were injected into aluminum strip from one of ferromagnetic electrodes which results in a non-equilibrium spin accumulation in the interface of aluminum strip and the ferromagnetic electrodes. The spin accumulation defuses away from the interface. The magnitude of spin accumulation at Al was detected by measuring the voltage at the interface of the second ferromagnetic electrode. In 2001 Jedema et al. [25] implemented the spin injection and detection in thin film devices at room temperatures. The relevant techniques have been applied to various systems. In 2006, Valenzuela and Tinkham [26] utilized this technique to inject and electrically detect spin current. The experiment was performed in a cross-bar shaped Al system. A ferromagnetic electrode is connected to the Al strip to inject spin polarized current by means of magnetic tunneling effect. The spin polarized current will induce a spin accumulation at the interface which leads to spin splitting of the chemical potential. The spin accumulation diffuses away and non-uniform distribution of chemical potentials may generate spin polarized current along the strip with electric current. On other side of Al strip there is no electric current. As the spin dependent chemical potential is distributed continuously in space, the chemical potentials with different spins are equal but have opposite sign. Owing to the diffusion procedure, the chemical potentials will decays exponentially in spin diffusion length. The distribution will induce a pure spin current. Measurement of spin current is performed by using the reciprocal spin Hall effect in which the spin current will be scattered by magnetic impurities or the spin-orbit coupling in the energy band of conduction electron, and induce a transverse Hall current. Spin current was detected by measuring the Hall electric current. It is worth noting that the experiment was performed at room temperatures because it is based on the diffusion principle. Saitoh et al. [27] and Kimura et al. [28] observed the spin Hall effect in Al and Pt systems, respectively. The Onsager relation between spin Hall effect and reciprocal spin Hall effect was confirmed experimentally. The measured spin Hall conductance is 4 orders of what measured in semiconductors. Very recently a much large spin Hall resistance of up to 2.9mΩ was measured in perpendicularly spin polarized FePt/Au devices, which was attributed to the large spin Hall angle in Au through the skew scattering mechanism [29] Optical Spin Injection Let us start with a brief introduction of the pure spin current induced by a light normally incident on the x-y plane of a C 2v 2EDG with a Rashba coupling H SIA = -λ(k x σ y k y σ x ), with k the momentum of electron and λ the spin-orbit coupling constant. A pure spin current is defined by j αβ = (v α σ β +σ β v β )/2, with v the velocity and σ the spin Pauli matrices of electron. The states with equal energy in the conduction band are represented by a pair of spin-dependent concentric circles of radii k + and k -. For example, for an electron with k along the x-axis, the four degenerated states are k +, >, k -, >, -k -, >, and -k +, >, respectively, where > and > are the two eigenstates of spin σ y, respectively, and k + k - =2m*α/ћ 2 with m* the effective mass. The two degenerate states on the same concentric circle, for example 34 AAPPS Bulletin October 2008, Vol. 18, No. 5

7 Spintronics and Spin Current k +, > and -k +, >, have opposite velocities v ± =±(ћ k + /m*-α/ћ), but carry equal spin current, j xy = (ћ 2 k + /m*-α)/2. Thus the pair contributes a null electric current, but a finite spin current of ћ 2 k + /m*-α. The total spin current is determined by the band structure and optical excitation processes. In a steady optical excitation process, the spin current is proportional to the spin relaxation time and the transition rates to the bottom of spin-dependent conduction bands. The contribution from the holes in valence bands is negligible since their spin relaxation time is typically short. Assuming the inter-band depahsing is fast, the injection rate of spin current can be calculated using the Fermi Golden rule [15] or the solution of semiconductor optical Bloch equations [30]. A linerar polarized light can be decomposed as a combination of two circularly polarized beams of light. Assume the angle Ф between the polarization plane and the y-axis, the phase difference between these two composite beams of the light is 2Ф. A detailed calculation [30] for a linearly polarized light gives the spin current J xy =J 0 +J 1 cos2ф. Either left or right circularly polarized light may pump electrons from the valence to conduction band, and generate a spin current. The polarization dependence of the spin current originates from the interference of two composite circularly polarized lights. The spin current generated in this way has been observed experimentally. Cui and his colleagues in the University of Hong Kong [31] measured the electric currents in a cross-bar shaped sample of InGaAs/AlGaAs heterostrucures. Owing to the scattering of spin-orbit coupling, the spin current will be converted into transverse electric currents. The flow pattern of the induced currents are flowing inward in one direction, and flowing outward in another direction. One of the characteristics is that the traditional Hall voltage is zero, but the adjunct electrodes do have currents. The experimental observation is in good agreement with theoretical prediction [15]. This effect combining with the spin Hall effect demonstrates that the spin polarization of spin current can manipulate the flow direction and pattern of induced current. Ganichev s group [32] from Regensburg University, Germany utilized free-carrier absorption of terahertz (THz) radiation to generate spin current in wide range of temperatures. To measure the spin current, a magnetic field is applied in the plain of the sample along the direction of polarization of the incident light to break the spin up-down symmetry, and to convert the spin current into a spin polarized current, which was measured directly. In contrast to the spin Hall effect, it does not require an electric current to flow: without bias the spin separation is achieved by spin-dependent scattering of electrons in media with suitable symmetry. Moreover, the experimental results provide evidence that simple electron gas heating by any means is already sufficient to yield spin separation due to spin dependent energyrelaxation processes. Recently, Wang, Zhu, and Liu [33] put forward an intrinsic interaction between a polarized light beam as a photon spin current and a pure spin current in a semiconductors, which arises from the spin-orbit coupling in the valence bands as a pure relativity effect. The interaction leads to linear and circular optical birefringence. This provides a direct and nondemolition measurement of pure spin current. 5. CONCLUSIONS In the past few years studies of spin current has emerged into a hot topic in condensed matter physics. It is out of question that the pure spin current is physically measurable from the experimental data of different groups by different means. General speaking, it is just a start for studies of spin current. It is believed that it will be active and meaningful topic in the field to efficiently generate, manipulate and detect spin current. It determines whether it can be utilized effectively in spintronic devices. From the aspect of material science, metallic spintronic device has made significant progresses over last decade. Successful measurement of spin current in metallic aluminum (Al) and platinum (Pt) indicates that it is highly possible that the spin current can be applied in metallic spintronic devices. Spin injection in diluted magnetic semiconductor also made important progresses. The efficiency of spin injection has been enhanced significantly. In most cases the spin injection means spin polarized current injection. 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