曾经的曾经of the contact resistance obtained on different samples,63for a conclusive understanding it will be crucial to have in situ measurements.
In analyzing data for the van der Pauw cross,a two-dimensional geometry has an important effect—while the electric current is following the paths depicted in Fig.11,the spin current,through the diffusion of non-equilibrium spin,would have similar ?ow in all four arms (Johnson,2002a).This is different from the usual (quasi-)one-dimensional analysis in which spin and charge currents ?ow along the same paths.For a full understanding of the van der Pauw cross geometry,two-dimensional modeling might be necessary (Johnson and Byers,2003;Takahashi and Maekawa,2003).
In the second type of experiment,tunneling contacts were fabricated by inserting Al 2O 3as an insulator into the regions where F1and F2overlapped with the cross.By applying a transverse ?eld B z (see Fig.11)the pre-cession of the injected nonequilibrium spin was con-trolled and the amplitude of the Hanle effect was mea-sured (Jedema,Costache,et al.,2002;Jedema,Heersche,et al.,2002a)as outlined in Sec.II.D.1.From Co/Al 2O 3/Al/Al 2O 3/Co structures L s ?0.5?m was ex-tracted at room temperature.The analysis of the Hanle signal was performed by averaging contributions of dif-ferent lifetimes (D’yakonov and Perel’,1984,p.40).This proved to be equivalent to Johnson and Silsbee’s (1988d)solution to the Bloch-Torrey equations.
3.All-semiconductor spin injection
If a magnetic semiconductor could be used as a robust spin injector (spin aligner)into a nonmagnetic semicon-ductor it would facilitate the integration of spintronics and semiconductor-based d72efe37f111f18583d05a9dparable resis-tivities of magnetic and nonmagnetic semiconductors could provide ef?cient spin injection [see Eq.(31),with r F ?r N ]even without using resistive contacts.Ulti-mately,for a wide range of applications and for compat-ibility with complementary metal-oxide semiconductors (CMOS;Wong et al.,1999),it would be desirable to be able to inject spin into silicon at room temperature.Early studies (Osipov et al.,1990,1998;Viglin et al.,1991,1997),which have since largely been ignored,used a Cr-and Eu-based chalcogenide ferromagnetic semi-conductor (FSm)(Nagaev,1983)as the spin injector.64The experiments were motivated by the theoretical
63
For example,the measured resistance of clean F/N contacts in CPP giant magnetoresistance (Bussmann et al.,1998)was used to infer that there is also a large contact resistance in all-metal spin injection experiments (Johnson,2002b).64
These materials,while more dif?cult to fabricate than the subsequent class of III-V ferromagnetic semiconductors,have the desirable properties of providing injection of spin-polarized electrons (with spin lifetimes typically much longer than for holes)and large spin splitting ??0.5eV at 4.2K for n -doped HgCr 2Se 4(Nagaev,1983)]with nearly complete spin polarization and a Curie temperature T C of up to 130K (HgCr 2Se 4)(Osipov et al.,
1998).
FIG.11.(Color in online edition)Schematic representation of
(a)local and (b)nonlocal geometry used to measure the ef-fects of spin injection and spin accumulation.
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work of Aronov(1976a;Aronov and Pikus,1976)pre-dicting that the electron spin resonance signal,propor-tional to the steady-state magnetization,would be changed by spin injection.The measurements of Osipov et al.(1990)and Viglin et al.(1991)prompted a related prediction(Margulis and Margulis,1994)that spin injec-tion could be detected through changes in electric dipole spin resonance(EDSR).EDSR is the spin-?ip reso-nance absorption for conduction electrons at Zeeman frequency,which is excited by the electric-?eld vector of an incident electromagnetic wave.The theory of EDSR, developed by Rashba and Sheka(1961),is extensively reviewed by Rashba and Sheka(1991). Ferromagnetic semiconductor spin injectors formed p-n and n-n heterostructures with a nonmagnetic semi-conductor InSb.The choice of InSb is very suitable,due to its large negative(??50)g factor(McCombe and Wagner,1971),for detecting the effects of spin injection through electron spin resonance.The observed absorp-tion and emission of microwave power(Osipov et al., 1998)was tuned by an applied magnetic?eld(from35 GHz at?400G up to1.4THz at20kG)and only seen when electrons?owed from FSm into an Sm region.The injection to the lower Zeeman level increased the ab-sorption of electron spin resonance,while injection to the higher Zeeman level,leading to population inver-sion,generated microwave emission.
The most recent experiments using semiconductor
spin injectors can be grouped into two different classes. In one approach(II,Mn)VI paramagnetic semiconduc-tors were employed as the spin aligners.These included CdMnTe(Oestreich et al.,1999),BeMnZnSe(Fiederling et al.,1999),and ZnMnSe(Jonker et al.,2000).In the second approach ferromagnetic semiconductors like (Ga,Mn)As(Ohno,Young,et al.,1999;Chun et al.,2002; Mattana et al.,2003)were used.Both approaches were also employed to inject spins into CdSe/ZnSe(Seufert et al.,2004)and InAs(Chye et al.,2002)quantum dots, respectively.
In(II,Mn)VI materials,at low Mn concentration and at low temperatures,there is a giant Zeeman splitting ?E?g*?B H(Furdyna,1988;Gaj,1988)of the conduc-
tion band,in which g*is the effective electron g factor. Such splitting arises due to sp-d exchange between the spins of conduction electrons and the S?5/2spins of the localized Mn2?ions.The g*factor for H 0can exceed65100and is given by(Brandt and Moshchalkov, 1984;Furdyna,1988)
g*?g??M/?g Mn?B2H?,(50) where g is the H?0II-VI‘‘band’’value g,generally different from the free-electron value,magnetization M??S z??B s?(g Mn?B SH)/(k B T)?,B s is the Brillouin function(Ashcroft and Mermin,1976),and?is the ex-change integral for s-like?6electrons(see Table I in Sec.II.B),given by(Furdyna,1988)
???S?J sp?d?S?/V0,(51) where J sp?d is the electron-ion exchange coupling,and V0is the volume of an elementary cell.From Eqs.(50) and(51)it follows that g*?g*(H)can even change its sign.Similar analysis also applies to g factors of holes, with the Zeeman splitting of a valence band being typi-cally several times larger than that of a conduction band (Brandt and Moshchalkov,1984).
(II,Mn)VI materials can be incorporated in high-quality heterostructures with different optically active III-V nonmagnetic semiconductors which,by providing circularly polarized luminescence,can also serve as spin detectors.In this case carriers are excited by electrical means and we speak of electroluminescence rather than photoluminescence.The selection rules for the recombi-nation light are the same as discussed in Sec.II.B. Figure12depicts a scheme for realization of all-semiconductor electrical spin injection and optical de-tection(Fiederling et al.,1999;Jonker et al.,2000).Dis-played is a spin light-emitting diode(LED;Jonker et al., 1999)in a Faraday geometry where both the applied B ?eld and the direction of propagation of the emitted light lie along the growth direction.Similar to an ordi-nary LED(Sze,1981),electrons and holes recombine in a quantum well or a p-n junction and produce electrolu-minescence.However,in a spin LED,as a consequence of radiative recombination of spin-polarized carriers,the emitted light is circularly polarized.In experiments of
65At low temperatures(?1K)Cd
0.95Mn0.05Se has?g*??500
(Dietl,1994),while in n-doped(In,Mn)As?g*??100at30K (Zudov et al.,2002).Such large g factors,in the presence of a highly inhomogeneous magnetic?eld could lead to the charge carrier localization(Berciu and Janko′,
2003).FIG.12.(Color in online edition)Schematic device geometry and band diagram of a spin LED:(a)Recombination of spin-polarized electrons injected from the(II,Mn)VI spin aligner and unpolarized holes injected from the p-doped GaAs,in the intrinsic GaAs quantum well,producing circularly polarized light;(b)conduction and valence bands of a spin aligner in an external magnetic?eld;(c)sketch of the corresponding band edges and band offsets in the device geometry.In the quantum well,spin-down electrons and unpolarized holes are depicted by solid and empty circles,respectively.Adapted from Fieder-ling et al.,1999.
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