曾经的曾经A more effective detection of the spin injection is re-alized through measurements of the Hanle effect,also discussed in Secs.II.
B and III.A.2,and described by Bloch-Torrey equations [Bloch,1946;Torrey,1956;see Eqs.(52)–(54)].The inset of Fig.10summarizes results from a series of Hanle experiments on a single sample.For the Hanle effect B must have a component perpen-dicular to the orientation axes of the injected spins.Only projection of B perpendicular to the spin axis applies a torque and dephases spins.The magnitude of B ,applied at an angle ?to the z axis in the y -z plane,is small enough that the magnetizations in ferromagnetic thin ?lms remain in the x -z plane (see Fig.9).If,at B ?0,
injected nonequilibrium magnetization is ?M (0)z
?then at ?nite ?eld ?M precesses about B with a cone of angle 2?.After averaging over several cycles,only ?M (0)cos ?,the component ?B ,will survive.The volt-age detector 58senses the remaining part of the magneti-zation projected on the axis of the detector ?M (0)cos ??cos ?(Johnson and Silsbee,1988a).The
56
The spin relaxation time in a ferromagnet is often assumed to be very short.Correspondingly,in the analysis of the experi-mental data,both the spin diffusion length and ?M are taken to vanish in the F region (Silsbee,1980;Johnson and Silsbee,1985,1988a,1988d).
57
This method for detecting the effects of spin injection is also referred to as a potentiometric method .58
Recall from the discussion leading to Eq.(39)that the spin-coupled signal is proportional to ?M
.
FIG.9.Schematic top view of nonlocal,quasi-one-dimensional
geometry used by Johnson and Silsbee (1985):F1and F2,the two metallic ferromagnets having magnetizations in the x -z plane;dotted lines,equipotentials characterizing electrical cur-rent ?ow;gray shading,diffusing population of nonequilibrium spin-polarized electrons injected at x ?0,with darker shades corresponding to higher density of polarized electrons.From Johnson,
2002a.
FIG.10.Spin injection data from bulk Al wire sample.Nega-tive magnetic ?eld is applied parallel to the magnetization (?z axis)in the two ferromagnetic regions.As the ?eld is increased,at B 0,1magnetization in one of the ferromagnetic regions is reversed,and at B 0,2the magnetization in the other region is also reversed (both are along ?z axis).Inset:ampli-tude of the observed Hanle signal as a function of orientation angle ?of magnetic ?eld.From Johnson and Silsbee,1985.
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ˇutic ′,Fabian,and Das Sarma:Spintronics:Fundamentals and applications Rev.Mod.Phys.,Vol.76,No.2,April 2004
predicted angular dependence for the amplitude of the
Hanle signal(proportional to the depolarization of?M in a?nite?eld)??M(0)??M(0)cos2??is plotted in the inset together with the measured data.59Results con?rm
the?rst application of the Hanle effect to dc spin injec-
tion.
The Hanle effect was also studied theoretically by
solving the Bloch-Torrey equations for an arbitrary ori-
entation,characterized by the angle?,between the mag-netization in F1and F2(Johnson and Silsbee,1988a). From the Hanle curve?V s(B?)?measured at T?4.3 (36.6)K,the parameters L s?450(180)?m and P??0.06(0.08)were extracted.60This spin injection tech-nique using the few-pV resolution of a superconducting quantum interference device(SQUID)and with an esti-mated P??0.07provided an accuracy able to detect P n?5?10?12,causing speculation that a single-spin sen-sitivity might be possible in smaller samples(Johnson and Silsbee,1985,1988d).While in a good conductor, such as Al,the observed resistance change?R was small (?n?),the relative change at low temperatures and for L x?L s was?R/R?5%,where?R is de?ned as in Eq.
(1),determined by the relative orientation of the mag-
netization in F1and F2,and R is the Ohmic resistance
(Johnson,2002a).Analysis from Sec.II.C.2shows that
measurement of?R could be used to determine the
product of injected current polarizations in the two F/N
junctions.
The studies of spin injection were extended to the
thin-?lm geometry,also known as the‘‘bipolar spin
switch’’or‘‘Johnson spin transistor’’(Johnson,1993a,
1993b)similar to the one depicted in Fig.5(a).The mea-
sured spin-coupled signals61in Au?lms were larger than
the values obtained in bulk Al wires(Johnson and Sils-
bee,1985,1988d).A similar trend,V s?1/d,potentially important for applications,was already anticipated by Silsbee(1980).The saturation of this increase can be inferred from Eqs.(43)and(44)for d?L sN and been discussed by Fert and Lee(1996)and Hersh?eld and Zhao(1997).
When polarizer-analyzer detection was used,one of
the?tting parameters from the measured data P?some-
times exceeded1—which corresponds to complete inter-
facial polarization.The origin of this discrepancy re-
mains to be fully resolved(Johnson,1993b,2002a;Fert
and Lee,1996;Hersh?eld and Zhao,1997;Geux et al.,
2000).Results obtained from the Hanle effect,on simi-lar samples,gave the expected P??1values(Johnson, 2002a).62
A modi?cation of the bipolar spin-switch structure was used to demonstrate spin injection into a niobium ?lm(Johnson,1994),realizing the theoretical assertion of Aronov(1976a)that nonequilibrium spin could be injected into a superconductor.Two insulating Al2O3?lms were inserted between F1and F2(both made of Py)and a Nb?lm[see Fig.5(b)].The measurements were performed near the superconducting transition temperature T c with the data qualitatively similar,above and below T c,to the spin-coupled voltage,as obtained in the magnetic-?eld sweep from Fig.10.The results were interpreted as support for enhanced depletion of the superconducting condensate(and correspondingly the reduction of the critical current I c)by spin-polarized quasiparticles,as compared to the usual spin-unpolarized quasiparticle injection.Related measure-ments were recently performed in a CPP geometry(Gu et al.,2002),and the penetration depth of the quasipar-ticle in the Nb?lms was measured to be?16nm,as compared to2nm in Johnson(1994).The corresponding temperature dependence of CPP giant magnetoresis-tance is well explained by the theory of Yamashita,Ima-mura,et al.(2003)and the modi?cation of Andreev re-?ection(see Sec.IV.A.3)by spin polarization.
The spin injection technique of Johnson and Silsbee was also applied to semiconductors.Initial experiments on using a metallic ferromagnet to inject spin into a two-dimensional electron gas(2DEG)showed only a very low(?1%)ef?ciency(Hammar et al.,1999)for which various explanations were offered(Hammar et al.,2000; Monzon et al.,2000;van Wees,2000).However,stimu-lated by the proposal of Rashba(2000)to employ spin-selective diffusive contacts(Sec.II.C.1),the subsequent measurements have showed substantially more ef?cient spin injection into a2DEG after an insulating layer was inserted(Hammar and Johnson,2001,2002).The geom-etry employed is depicted in Fig.9.In interpreting the results,the spin-orbit coupling and the energy-independent density of states at the Fermi level were taken into account(Silsbee,2001).This topic is reviewed by Tang et al.(2002).
2.Spin injection into metals
An important part of the operation of CPP giant mag-netoresistance structures is the presence of nonequilib-
59The range of the angle?,in the inset,is corrected from the one originally given in Fig.3of Johnson and Silsbee(1985).
60The?tting parameters are?
s ,P?,and?(Johnson and Sils-
bee,1988d),and since the diffusion coef?cient is obtained from Einstein’s relation L s is known.
61d?100nm was much smaller than the separation between F1and F2in bulk Al wires(Johnson and Silsbee,1985),and the amplitude of the Hanle effect was about104larger (Johnson,2002a).
62Theoretical estimates for V
s
from which P??1was inferred are modi?ed when one considers the Coulomb interaction and proximity effects—near the N/F interface the spin splitting of the carrier bands in the N region will be?nite even at equilib-rium.Model calculations(Chui,1995;Chui and Cullen,1995), which treat the F/N/F junction as a whole,show that the mag-netic susceptibility?in N can be much smaller than the free-electron value and can increase the predicted V s?1/?.These corrections to the free-electron picture of an F/N/F junction are smaller for larger d,as in the bulk-wire geometry of Johnson and Silsbee(1985),where theoretical estimates of V s did not lead to P??1.
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Zˇutic′,Fabian,and Das Sarma:Spintronics:Fundamentals and applications Rev.Mod.Phys.,Vol.76,No.2,April2004
rium spin polarization in nonmagnetic metallic regions.Studies of spin-injection parameters in such systems have been reviewed by Bass and Pratt (1999)and Gijs and Bauer (1997).However,until recently,except for the work of Johnson and Silsbee,there were few other experimental studies directly concerned with spin injec-tion into metals.A series of experiments (Jedema et al.,2001;Jedema,Costache,et al.,2002;Jedema,Heersche,et al.,2002a;Jedema,Nijboer,et al.,2002)at both low (4.2K)and room temperature,were performed using the van der Pauw geometry depicted in Fig.11.In vari-ous structures (Jedema,2002)the two ferromagnetic re-gions (made of Py,Co,or Ni)were chosen to be of dif-ferent sizes to provide different coercive ?elds,allowing an independent reversal of magnetization in F1and F2.The cross-shaped nonmagnetic region was made of Al or Cu (Jedema,2002).Nonlocal measurements,similar to the approach shown in Figs.5and 9(discussed by Johnson,1993b;Johnson and Silsbee,1988d),were shown to simplify the extraction of spurious effects (for example,anisotropic magnetoresistance and the Hall signal)from effects intrinsic to spin injection,as com-pared to the local or conventional spin-valve geometry.In the ?rst type of experiment the cross-shaped region was deposited directly over the F region (Fig.11),and the spin-coupled resistance ?R ,de?ned analogously to Eq.(1),was measured as a function of an in-plane mag-netic ?eld.A theoretical analysis (Jedema et al.,2001;Jedema,Nijboer,et al.,2002)was performed assuming no interfacial resistance (r c ?0)and the continuity of the electrochemical potentials at the F/N interface (see Sec.II.C.1).For a spin injection from Py into Cu,the maximum current polarization obtained was P j ?0.02at 4.2K.The results for ?R (Jedema et al.,2001)scaled to the size of the samples used by Johnson (1993a,1993b)were interpreted to be three to four orders of magnitude smaller.As discussed in Secs.II.C.1and II.C.2,the pres-ence of interfacial spin-selective resistance can substan-tially change the spin injection ef?ciency and in?uence the resistance mismatch between the F and N regions [see Eq.(19)].Estimates of how these considerations would affect the results of Jedema et al.(2001)were given by Jedema,Heersche,et al.(2002b)as well as by others (Johnson and Byers,2003;Takashi and Maekawa,2003),who analyzed the importance of multidimensional geometry.In addition to comparing characteristic values
