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For example,studies probing the spin-charge separation in the non-Fermi liquids have been proposed by Kivelson and Rokhsar (1990);Zhao and Hersh?eld (1995);Si (1997,1998);Balents and Egger (2000,2001).Spin and charge are carried by separate excitations and can lead to spatially separated spin and charge currents (Kivelson and Rokhsar,
1990).
FIG.5.(Color in online edition)Spin injection,spin accumu-lation,and spin detection:(a)two idealized completely polar-ized ferromagnets F1and F2(the spin-down density of states
N ↓is zero at the electrochemical potential energy E ??0)with parallel magnetizations are separated by the nonmagnetic re-gion N;(b)density-of-states diagrams for spin injection from F1into N,accompanied by the spin accumulation-generation of nonequilibrium magnetization ?M .At F2in the limit of low impedance (Z ?0)electrical spin is detected by measuring the spin-polarized current across the N/F2interface.In the limit of high impedance (Z ??)spin is detected by measuring the voltage V s ??M developed across the N/F2interface;(c)spin accumulation in a device in which a superconductor (with the superconducting gap ?)is occupying the region between F1and F2.
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(Ganichev et al.,2001;Ganichev,Danilov,et al.,2002; Ganichev,Ivchenko,et al.,2002;Ganichev et al.,2003), is given by Ganichev and Prettl(2003).
There is a wide range of recent theoretical proposals for devices that would give rise to a spin electromotive force(Zˇutic′et al.,2001a,2001b;Brataas et al.,2002; Governale et al.,2003;Long et al.,2003;Mal’shukov et al.,2003;Ting and Cartoixa`,2003),often referred to as spin(-polarized)pumps,cells,or batteries.However, even when it is feasible to generate pure spin current, this does not directly imply that it would be dissipation-less.In the context of superconductors,it has been shown that Joule heating can arise from pure spin cur-rent?owing through a Josephson junction(Takahashi et al.,2001).
B.Optical spin orientation
In a semiconductor the photoexcited spin-polarized electrons and holes exist for a time?before they recom-bine.If a fraction of the carriers’initial orientation sur-vives longer than the recombination time,that is,if???s,26where?s is the spin relaxation time(see Sec.III),
the luminescence(recombination radiation)will be par-tially polarized.By measuring the circular polarization of the luminescence it is possible to study the spin dy-namics of the nonequilibrium carriers in semiconductors (Oestreich et al.,2002)and to extract such useful quan-tities as the spin orientation,the recombination time,or the spin relaxation time of the carriers(Parsons,1969; Ekimov and Safarov,1970;Garbuzov et al.,1971;Meier and Zakharchenya,1984).
We illustrate the basic principles of optical orientation by the example of GaAs,which is representative of a large class of III-V and II-VI zinc-blende semiconduc-tors.The band structure is depicted in Fig.6(a).The
band gap is E g?1.52eV at T?0K,while the spin split-off band is separated from the light and heavy hole
bands by?so?0.34eV.We denote the Bloch states ac-cording to the total angular momentum J and its projec-tion onto the positive z axis m j:?J,m j?.Expressing the wave functions with the symmetry of s,p x,p y,and p z orbitals as?S?,?X?,?Y?,and?Z?,respectively,the band wave functions can be written as listed in Table I(Pierce and Meier,1976,with minor typos removed;see also Kittel,1963).
To obtain the excitation(or recombination)probabili-
ties,consider photons arriving in the z direction.Let??represent the helicity of the exciting light.When we rep-resent the dipole operator corresponding to the??op-tical transitions as27?(X?iY)?Y1?1,where Y l m is the spherical harmonic,it follows from Table I that
??1/2,?1/2?Y11?3/2,?3/2??2
??1/2,1/2?Y11?3/2,?1/2??2?3(4) for the relative intensity of the??transition between the heavy(?m j?3/2?)and the light(?m j?1/2?)hole sub-bands and the conduction band.Other transitions are
analogous.The relative transition rates are indicated in
Fig.6(b).The same selection rules apply to the optical
orientation of shallow impurities(Parsons,1969;Eki-
mov and Safarov,1970).
The spin polarization of the excited electrons28de-pends on the photon energy??.For??between E g and E g??so,only the light and heavy hole subbands contribute.Denoting by n?and n?the density of elec-trons polarized parallel(m j?1/2)and antiparallel(m j ??1/2)to the direction of light propagation,we de?ne the spin polarization as(see Sec.II.A)
P n??n??n??/?n??n??.(5) For our example of the zinc-blende structure,
P n??1?3?/?3?1???1/2(6) is the spin polarization at the moment of photoexcita-tion.The spin is oriented against the direction of light propagation,since there are more transitions from the heavy hole than from the light hole subbands.The cir-cular polarization of the luminescence is de?ned as
26In Si this condition is not ful?lled.Instead of measuring the luminescence polarization,Lampel(1968)has used NMR to detect optical spin orientation.
27For an outgoing light in the?z direction the helicities are reversed.
28Although holes are initially polarized too,they lose spin orientation very fast,on the time scale of the momentum re-laxation time(see Sec.III.D.1).However,it was suggested that manipulating hole spin by short electric?eld pulses,between momentum scattering events,could be useful for ultrafast spin-tronic applications(Dargys,
2002).
FIG.6.Interband transitions in GaAs:(a)schematic band structure of GaAs near the center of the Brillouin zone(?point),where E g is the band gap and?so the spin-orbit split-ting;CB,conduction band;HH,valence heavy hole;LH,light hole;SO,spin-orbit split-off subbands;?6,7,8are the corre-sponding symmetries at the k?0point,or,more precisely,the irreducible representations of the tetrahedron group T d (Ivchenko and Pikus,1997);(b)selection rules for interband transitions between the m j sublevels for circularly polarized light??and??(positive and negative helicity).The circled numbers denote the relative transition intensities that apply for both excitations(depicted by the arrows)and radiative re-combinations.
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P circ??I??I??/?I??I??,(7) where I?is the radiation intensity for the helicity??. The polarization of the??photoluminescence is then
P circ??n??3n????3n??n??
?n??3n????3n??n??
??
P n
2
?
1
4
.(8)
If the excitation involves transitions from the spin split-off band,that is,if???E g??so,the electrons will not be spin polarized(P n?P circ?0),underlining the vi-tal role of spin-orbit coupling for spin orientation.On the other hand,Fig.6suggests that a removal of the heavy/light hole degeneracy can substantially increase P n(D’yakonov and Perel’,1984),up to the limit of com-plete spin polarization.An increase in P n and P circ in GaAs strained due to a lattice mismatch with a sub-strate,or due to con?nement in quantum well hetero-structures,has indeed been demonstrated(Vasilev et al., 1993;Oskotskij et al.,1997),detecting P n greater than 0.9.
While photoexcitation with circularly polarized light creates spin-polarized electrons,the nonequilibrium spin decays due to both carrier recombination and spin relax-ation.The steady-state degree of spin polarization de-pends on the balance between the spin excitation and decay.Sometimes a distinction is made(Pierce and Meier,1976;Meier and Zakharchenya,1984)between the terms optical spin orientation and optical spin pump-ing.The former term is used in relation to the minority carriers(such as electrons in p-doped samples)and rep-resents the orientation of the excited carriers.The latter term is reserved for the majority carriers(electrons in n-doped samples),representing spin polarization of the ‘‘ground’’state.Both spin orientation and spin pumping were demonstrated in the early investigations on p-GaSb(Parsons,1969)and p-and n-Ga0.7Al0.3As(Eki-mov and Safarov,1970,1971;Zakharchenya et al.,1971). Unless speci?ed otherwise,we shall use the term optical orientation to describe both spin orientation and spin pumping.
To derive the steady-state expressions for the spin po-larization due to optical orientation,consider the simple model of carrier recombination and spin relaxation(see Sec.IV.A.4)in a homogeneously doped semiconductor. The balance between direct electron-hole recombination and optical pair creation can be written as
r?np?n0p0??G,(9) where r measures the recombination rate,the electron and hole densities are n and p,with index zero denoting the equilibrium values,and G is the electron-hole pho-toexcitation rate.Similarly,the balance between spin re-laxation and spin generation is expressed by
rsp?s/?s?P n?t?0?G,(10) where s?n??n?is the electron spin density and P n(t
?0)is the spin polarization at the moment of photoex-citation,given by Eq.(5).Holes are assumed to lose their spin orientation very fast,so they are treated as unpolarized.The?rst term in Eq.(10)describes the dis-appearance of the spin density due to carrier recombi-nation,while the second term describes the intrinsic spin relaxation.From Eqs.(9)and(10)we obtain the steady-state electron polarization as(Zˇutic′et al.,2001b)
P n?P n?t?0?
1?n0p0/np
1?1/?s rp
.(11) In a p-doped sample p?p0,n?n0,and Eq.(11)gives P n?P n?t?0?/?1??/?s?,(12) where??1/rp0is the electron lifetime.29The steady-state polarization is independent of the illumination in-tensity,being reduced from the initial spin polarization P n(t?0).30The polarization of the photoluminescence is P circ?P n(t?0)P n(Parsons,1969).Early measure-ments of P n?0.42?0.08in GaSb(Parsons,1969)and P n?0.46?0.06in Ga0.7Al0.3As(Ekimov and Safarov, 1970)showed an effective spin orientation close to the maximum value of P n(t?0)?1/2for a bulk unstrained zinc-blende structure,indicating that?/?s?1.
