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alized as the balance between spins added by the mag-netization current and spins removed by spin relaxation.22
Generation of nonequilibrium spin polarization and spin accumulation is also possible by optical methods known as optical orientation or optical pumping.In op-tical orientation,the angular momentum of absorbed circularly polarized light is transferred to the medium. Electron orbital momenta are directly oriented by light and through spin-orbit interaction electron spins be-come polarized.In Sec.II.B we focus on optical orien-tation in semiconductors,a well-established technique (Meier and Zakharchenya,1984).In a pioneering work Lampel(1968)demonstrated that spins in silicon can be optically oriented(polarized).This technique is derived from the optical pumping proposed by Kastler(1950)in which optical irradiation changes the relative popula-tions within the Zeeman and hyper?ne levels of the ground states of atoms.While there are similarities with previous studies of free atoms(Cohen-Tannoudji and Kostler,1966;Happer,1972),optical orientation in semi-conductors has important differences related to the strong coupling between the electron and nuclear spin and the macroscopic number of particles(Paget et al., 1977;Meier and Zakharchenya,1984;Hermann et al., 1985).Polarized nuclei can exert large magnetic?elds (?5T)on electrons.In bulk III-V semiconductors,such as GaAs,optical orientation can lead to50%polariza-tion of electron density,which could be further en-hanced in quantum structures of reduced dimensionality or by applying a strain.A simple reversal in the polar-ization of the illuminating light(from positive to nega-tive helicity)also reverses the sign of the electron den-sity d72efe37f111f18583d05a9dbining these properties of optical orientation with semiconductors tailored to have a nega-tive electron af?nity allows photoemission of spin-polarized electrons to be used as a powerful detection technique in high-energy physics and for investigating surface magnetism(Pierce and Celotta,1984).
II.GENERATION OF SPIN POLARIZATION
A.Introduction
Transport,optical,and resonance methods(as well as their combination)have all been used to create nonequi-librium spin.After introducing the concept of spin po-larization in solid-state systems we give a pedagogical picture of electrical spin injection and detection of po-larized carriers.While electrical spin injection and opti-cal orientation will be discussed in more detail later in this section,we also survey here several other tech-niques for polarizing carriers.
Spin polarization not only of electrons,but also of holes,nuclei,and excitations can be de?ned as P X?X s/X,(3) the ratio of the difference X s?X??X??,and the sum X?X??X??of the spin-resolved?components for a particular quantity X.To avoid ambiguity as to what precisely is meant by spin polarization,both the choice of the spin-resolved components and the relevant physi-cal quantity X need to be speci?ed.Conventionally,?is taken to be↑or?(numerical value?1)for spin up, and↓or?(numerical value?1)for spin down,with respect to the chosen axis of quantization.23In ferro-magnetic metals it is customary to refer to↑(↓)as car-riers with magnetic moment parallel(antiparallel)to the magnetization or,equivalently,as carriers with majority or minority spin(Tedrow and Meservey,1973).In semi-conductors the terms majority and minority usually refer to relative populations of the carriers while↑or?and↓or?correspond to the quantum numbers m j with re-spect to the z axis taken along the direction of the light propagation or along the applied magnetic?eld(Meier and Zakharchenya,1984;Jonker et al.,2003).It is im-portant to emphasize that both the magnitude and the sign of the spin polarization in Eq.(3)depend on the choice of X,relevant to the detection technique em-ployed,say optical vs transport and bulk vs surface mea-surements(Mazin,1999;Jonker et al.,2003).Even in the same homogeneous material the measured P X can vary for different X,and it is crucial to identify which physi-cal quantity—charge current,carrier density,conductiv-ity,or the density of states—is being measured experi-mentally.
The spin polarization of electrical current or carrier density,generated in a nonmagnetic region,is typically used to describe the ef?ciency of electrical spin injec-tion.Silsbee(1980)suggested that the nonequilibrium density polarization in the N region,or equivalently the nonequilibrium magnetization,acts as the source of spin electromotive force(emf)and produces a measurable ‘‘spin-coupled’’voltage V s??d72efe37f111f18583d05a9ding this concept,also referred to as spin-charge coupling,Silsbee(1980)pro-posed a detection technique consisting of two ferromag-nets F1and F2(see Fig.5)separated by a nonmagnetic region.24F1serves as the spin injector(spin aligner)and F2as the spin detector.This could be called the polarizer-analyzer method,the optical counterpart of the transmission of light through two optical linear po-larizers.From Fig.5it follows that the reversal of the magnetization direction in one of the ferromagnets
22The spin diffusion length is an important quantity for CPP giant magnetoresonance.The thickness of the N region in Fig. 3should not exceed the spin diffusion length,otherwise the information on the orientation of the magnetization in F1will not be transferred to the F2region.
23For example,along the spin angular momentum,applied magnetic?eld,magnetization,or direction of light propaga-tion.
24A similar geometry was also proposed independently by de Groot,Janner,and Mueller(1983),where F1and F2were two half-metallic ferromagnets,with the goal of implementing spin-based devices to amplify and/or switch current.
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would lead either to V s →?V s ,in an open circuit (in the limit of large impedance Z ),or to the reversal of charge current j →?j ,in a short circuit (at small Z ),a conse-quence of Silsbee-Johnson spin-charge coupling (Sils-bee,1980;Johnson and Silsbee,1987,1988a).Corre-spondingly,as discussed in the following sections,spin injection could be detected through the spin accumula-tion signal as either a voltage or a resistance change when the magnetizations in F1and F2are changed from parallel to antiparallel alignment.
Since the experiments demonstrating the spin accu-mulation of conduction electrons in metals (Johnson and Silsbee,1985),spin injection has been realized in a wide range of materials.While in Sec.II.C we focus on re-lated theoretical work motivated by potential applica-tions,experiments on spin injection have also stimulated proposals for examining the fundamental properties of electronic systems.25
The generation of nonequilibrium spin polarization has a long tradition in magnetic resonance methods (Abragam,1961;Slichter,1989).However,transport
methods to generate carrier spin polarization are not limited to electrical spin injection.For example,they also include scattering of unpolarized electrons in the presence of spin-orbit coupling (Mott and Massey,1965;Kessler,1976)and in materials that lack inversion sym-metry (Levitov et al.,1984),adiabatic (Mucciolo et al.,2002;Sharma and Chamon,2003;Watson et al.,2003)and nonadiabatic quantum spin pumping (Zheng et al.,2003;for an instructive description of parametric pump-ing see Brouwer,1998),and proximity effects (Ciuti et al.,2002a).
It would be interesting to know what the limits are on the magnitude of various spin polarizations.Could we have a completely polarized current ?P j →?;see Eq.(3)],with only a spin current (j ↑?j ↓)and no charge cur-rent (j ↑?j ↓?0)?While it is tempting to recall the Stern-Gerlach experiment and try to set up magnetic drift through inhomogeneous magnets (Kessler,1976),this would most likely work only as a transient effect (Fabian and Das Sarma,2002).It was proposed by D’yakonov and Perel’(1971a,1971c)that a transverse spin current (and transverse spin polarization in a closed sample)would form as a result of spin-orbit coupling-induced skew scattering in the presence of a longitudinal electric ?eld.This interesting effect,also called the spin Hall effect (Hirsch,1999;Zhang,2000),has yet to be demon-strated.An alternative scheme for producing pure spin currents was proposed by Bhat and Sipe (2000),moti-vated by the experimental demonstration of phase-coherent control of charge currents (Atanasov et al.,
1996;Hache
′et al.,1997)and carrier population (Fraser et al.,1999).A quantum-mechanical interference be-tween one-and two-photon absorptions of orthogonal linear polarizations creates an opposite ballistic ?ow of spin-up and spin-down electrons in a semiconductor.Only a spin current can ?ow without a charge current,as
demonstrated by Stevens et al.(2003)and Hu
¨bner et al.(2003),who were able to achieve coherent control of the spin current direction and magnitude by the polarization and relative phase of two exciting laser light ?elds.
Charge current also can be driven by circularly polar-ized light (Ivchenko and Pikus,1997).Using the prin-ciples of optical orientation (see Sec.I.B.2and further discussion in Sec.II.B)in semiconductors of reduced dimensionality or lower symmetry,both the direction and the magnitude of a generated charge current can be controlled by circular polarization of the light.This is called the circular photovoltaic effect (Ganichev and Prettl,2003),which can be viewed as a transfer of the angular momentum of photons to directed motion of electrons.This could also be called a spin corkscrew ef-fect,since a nice mechanical analog is a corkscrew whose rotation generates linear directed motion.A re-lated effect,in which spin photocurrent is driven,is called the spin-galvanic effect (Ganichev and Prettl,2003).The current here is caused by the difference in spin-?ip scattering rates for electrons with different spin states in some systems with broken inversion symmetry.A comprehensive survey of the related effects,from the circular photogalvanic effect (Asnin et al.,1979)to re-cent demonstrations in semiconductor quantum wells
