自旋轨道耦合的二维电子气中自旋输运相关性质的研究
|
摘要
自旋电子学是近年来凝聚态物理中飞速发展的前沿学科领域之一,它是以研究介观和微观尺度范围内自旋极化电子的输运特性(包括自旋极化、自旋相关的散射与自旋弛豫等)以及基于它的这些独特性质而设计、开发的在新的输运机理下工作的功能器件为主要内容的一门新的交叉学科。自旋轨道耦合是影响常见的半导体材料自旋调控和弛豫的重要物理机理,因此是半导体自旋电子学器件应用值得考虑的可能因素。近年来,国际上关于半导体中自旋轨道耦合引致的各种新奇的物理现象进行了研究并取得了许多重要的进展,如本征自旋霍尔效应等。这些研究为在半导体中产生自旋流提供了新的途径,并为未来的全电操纵的自旋电子学器件提供了物理基础。本文主要研究了二维电子气在自旋轨道耦合影响下一些相关性质的研究,主要包括:外磁场对螺旋自旋(SpinHelix)寿命的影响,各向异性的磁性杂质对反常霍尔电导率的影响以及各向异性的磁性杂质对自旋极化情况的影响。
第一章在概述自旋电子学发展趋势的基础上,首先简单介绍了二维电子气中自旋轨道耦合的主要模型:Rashba,Dresselhaus型自旋轨道耦合作用,接着介绍了自旋流以及自旋流产生的一些物理效应,然后概述了由于自旋轨道耦合所产生的自旋霍尔现象,以及对该现象的产生所作出的不同的解释,包括本征自旋霍尔效应和非本征自旋霍尔效应,并简单介绍了二维电子气中自旋霍尔效应的检测和应用。最后阐明了本论文的主要内容和意义。
第二章在简单介绍螺旋自旋(spin Helix)的基础上,主要探讨了存在螺旋自旋的两种不同的自旋轨道耦合的二维电子气中,即同时存在相等耦合强度的Rashba和Dresselhaus自旋轨道耦合体系和[110]型Dresselhaus自旋轨道耦合体系中,不同方向的外磁场对螺旋自旋寿命的影响情况。
第三章基于久保公式和格林函数的方法,采用梯形近似,计算了各向异性的磁性杂质对自旋极化的顶角修正项,从而讨论了各向异性的磁性杂质对Rashba型自旋轨道耦合的二维电子体系总的自旋极化的影响,除了讨论对极化强度的影响,还讨论了磁性杂质对极化方向的影响。结果发现,磁性杂质的各向异性系数对极化强度有削弱作用,但磁性杂质和非磁性杂质一样,他们的引入并不改变自旋极化方向。
第四章利用久保公式的线性响应理论,以Rashba型自旋轨道耦合的二维电子气为例,我们计算了自旋极化的该体系中的反常霍尔效应,分别讨论了非磁性杂质散射势和各向异性的磁性杂质散射势对反常霍尔电导率的影响。
Spintronics has become a fast developing area using the electron spin degrees of freedom,rather than the conventional electron charge in electronic devices.Spin-orbit Coupling(SOC) is the crucial physical mechanism,which influences the usual semiconductor materials in both spin control and relaxation.Thus SOC is the conceivable factor which is worthy to be taken into account in the applications of semiconductor spintronics devices.Recently,SOC in semiconductor has attracted many scientists attention in the world,and many important developments have been obtained,such as intrinsic Spin Hall Effect(ISHE).These researches provide new avenue for the generation of spin current in the semiconductors,and afford the physical basis for the spin electronics devices which are fully controlled by electric field in the future.
In Chapter one,based on the summarization of the spintronics development trend, we first introduce the two kinds of spin-orbit coupling in two-dimensional electron systems simply,including Rashba SOC and Dresselhaus SOC.In addition,we also introduce the spin Hall effect(SHE) which is induced by the spin-orbit coupling.According to the different explanation,SHE can be divided into intrinsic SHE(ISHE) and extrinsic SHE(ESHE).Subsequently,we continue to introduce the characters of transport electrons in two-dimensional electron gas,including spin current,spin polarization, spin accumulation,as well as the impact of impurity or defect to these characters.Besides, we also introduce the present experimental evolvement about the SHE.At last, the main content and meaning of this paper are illustrated.
In Chapter two,based on the simple introduction about the spin helix,for a two-dimensional electron gas with equal Rashba and Dresselhaus spin-orbit coupling strength(ReD model),and the Dresselhaus[110]model,the influence of an external magnetic field on the lifetime of the Spin Helix(SH) has been considered.
In Chapter three,in terms of Kubo's formula and Green's function method,we study the spin polarization due to the effect from magnetic impurities with anisotropic spin dependent delta type coupling to electrons when an external dc electric field in plane is applied.The vertex correction of impurities in ladder approximation is carried out.We find that the strength of spin polarization can be significantly modified by vertex correction and the spin polarization is relevant to the anisotropy coefficient,but the direction of spin polarization can not be changed.
In Chapter four,making use of the Kubo's linear response theory,we discuss the anomalous Hall Effect(AHE) in a two-dimensional electron gas(2DEG) with Rashba SOC subjected to a homogeneous out-of-plane magnetization,by taking into account the coupling between the nonmagnetic impurities,anisotropic magnetic impurities and the itinerant electrons,respectively.We found that the anomalous Hall conductivity is nonvanishing and is correlative to the anisotropy coefficient,which is different from the nonmagnetic impurities conditions.
第一章在概述自旋电子学发展趋势的基础上,首先简单介绍了二维电子气中自旋轨道耦合的主要模型:Rashba,Dresselhaus型自旋轨道耦合作用,接着介绍了自旋流以及自旋流产生的一些物理效应,然后概述了由于自旋轨道耦合所产生的自旋霍尔现象,以及对该现象的产生所作出的不同的解释,包括本征自旋霍尔效应和非本征自旋霍尔效应,并简单介绍了二维电子气中自旋霍尔效应的检测和应用。最后阐明了本论文的主要内容和意义。
第二章在简单介绍螺旋自旋(spin Helix)的基础上,主要探讨了存在螺旋自旋的两种不同的自旋轨道耦合的二维电子气中,即同时存在相等耦合强度的Rashba和Dresselhaus自旋轨道耦合体系和[110]型Dresselhaus自旋轨道耦合体系中,不同方向的外磁场对螺旋自旋寿命的影响情况。
第三章基于久保公式和格林函数的方法,采用梯形近似,计算了各向异性的磁性杂质对自旋极化的顶角修正项,从而讨论了各向异性的磁性杂质对Rashba型自旋轨道耦合的二维电子体系总的自旋极化的影响,除了讨论对极化强度的影响,还讨论了磁性杂质对极化方向的影响。结果发现,磁性杂质的各向异性系数对极化强度有削弱作用,但磁性杂质和非磁性杂质一样,他们的引入并不改变自旋极化方向。
第四章利用久保公式的线性响应理论,以Rashba型自旋轨道耦合的二维电子气为例,我们计算了自旋极化的该体系中的反常霍尔效应,分别讨论了非磁性杂质散射势和各向异性的磁性杂质散射势对反常霍尔电导率的影响。
Spintronics has become a fast developing area using the electron spin degrees of freedom,rather than the conventional electron charge in electronic devices.Spin-orbit Coupling(SOC) is the crucial physical mechanism,which influences the usual semiconductor materials in both spin control and relaxation.Thus SOC is the conceivable factor which is worthy to be taken into account in the applications of semiconductor spintronics devices.Recently,SOC in semiconductor has attracted many scientists attention in the world,and many important developments have been obtained,such as intrinsic Spin Hall Effect(ISHE).These researches provide new avenue for the generation of spin current in the semiconductors,and afford the physical basis for the spin electronics devices which are fully controlled by electric field in the future.
In Chapter one,based on the summarization of the spintronics development trend, we first introduce the two kinds of spin-orbit coupling in two-dimensional electron systems simply,including Rashba SOC and Dresselhaus SOC.In addition,we also introduce the spin Hall effect(SHE) which is induced by the spin-orbit coupling.According to the different explanation,SHE can be divided into intrinsic SHE(ISHE) and extrinsic SHE(ESHE).Subsequently,we continue to introduce the characters of transport electrons in two-dimensional electron gas,including spin current,spin polarization, spin accumulation,as well as the impact of impurity or defect to these characters.Besides, we also introduce the present experimental evolvement about the SHE.At last, the main content and meaning of this paper are illustrated.
In Chapter two,based on the simple introduction about the spin helix,for a two-dimensional electron gas with equal Rashba and Dresselhaus spin-orbit coupling strength(ReD model),and the Dresselhaus[110]model,the influence of an external magnetic field on the lifetime of the Spin Helix(SH) has been considered.
In Chapter three,in terms of Kubo's formula and Green's function method,we study the spin polarization due to the effect from magnetic impurities with anisotropic spin dependent delta type coupling to electrons when an external dc electric field in plane is applied.The vertex correction of impurities in ladder approximation is carried out.We find that the strength of spin polarization can be significantly modified by vertex correction and the spin polarization is relevant to the anisotropy coefficient,but the direction of spin polarization can not be changed.
In Chapter four,making use of the Kubo's linear response theory,we discuss the anomalous Hall Effect(AHE) in a two-dimensional electron gas(2DEG) with Rashba SOC subjected to a homogeneous out-of-plane magnetization,by taking into account the coupling between the nonmagnetic impurities,anisotropic magnetic impurities and the itinerant electrons,respectively.We found that the anomalous Hall conductivity is nonvanishing and is correlative to the anisotropy coefficient,which is different from the nonmagnetic impurities conditions.
引文
[1]詹文山,自旋电子学研究与进展[J],物理,2006,35(10):811
[2]Simmonds.J.L,Phys.Today,1995(4):24
[3]Ohno.H et al.,(Ga,Mn)As:A new diluted magnetic semiconductor based on GaAs[J].Appl.phys.Lett.,1996,69:363
[4]Awschalom.D et al.,Electron spin and optical coherence in semiconductors[J].Phys.Today,1999,52(6):33
[5]Black.W.C and Das.B,Programmable logic using giant-magnetoresistance and spin-dependent tunneling devices[J].J.Appl.Phys.,2000,87:6674
[6]Ney.A et al.,Programmable computing with a single magnetoresistive element [J].Nature,2003,425:485
[7]Grunberg.P,Schreiber.R,Pang.Yet al.,Phys.Rev.Lett.,Layered Magnetic Structures:Evidence for Antiferromagnetic Coupling of Fe Layers across Cr Interlayers [J].1986,57:2442
[8]Meservey.R,Tedrow.P.M and Flude.P,Magnetic Field Splitting of the Quasiparticle States in Superconducting Aluminum Films[J].Phys.Rev.Lett.,1970,25:1270
[9]Han.X.F et al.,High-magnetoresistance tunnel junctions using Co75Fe25 ferromagnetic electrodes[J].Jpn.Appl.Phys.,2000,39:L439
[10]刘林生等,半导体自旋电子学的研究与应用进展[J].电子器件,2007,30(3):1125
[11]Ohno.H,Making nonmagnetic semiconductors ferromagnetic[J].Science,1998,281:951
[12]Munekata.H,Ohno.H and Von.M.Set al.,Diluted Magnetic Ⅲ—V Semiconductors [J].Phys.Rev.Lett,1989,63(17):1849
[13] De. B. J, Oersterholt. R and Van. E. A et al., Nanometer-Scale Magnetic MnAs Particles in GaAs Grown by Molecular Beam Epitaxy [J], Appl. Phys. Lett., 1996, 68(19): 2744
[14] Xu. J. L, Schilfgaarde. M. V and Samolyuk. G. D, Role of Disorder in Mn: GaAs, Cr: GaAs, andCr: GaN [J]. Phys. Rev. Lett., 2005, 94: 097201
[15] Dietl. T, Ohno. H and Matsukura. F et al., Zener Model De-scrip—tion of Ferromagnetism in Zine-Blende Magnetic Semiconductors [J]. Science, 2000, 287: 1019
[16] Mi. W. B, Bai. H. L and Liu. H et al., Microstructure, Magnetic, and Optical Properties of Sputtered Mn-Doped ZnO Films with High-Temperature Ferromagnetism [J]. J. Appl. Phys., 2007, 101: 023904
[17] Hu. C. M, Nitta. J and Jensen. A et al., SPin Polarized Transport in a two-Dimension Electron Gas with Interdigital-Ferromagnetic Contacts [J]. Phys. Rev. B, 2001, 63: 125333
[18] Schmidit. G, Ferrand. D and Molenkamp. L. W et al., Fundamental Obstacle for Electrical Spin injection from a Ferromagnetic Metal into a Diffusive Semiconductor [J]. Phys. Rev. B, 2000, 62: R4790
[19] S. F. Alvarado, P. Renaud, Observation of Spin Polarized Electron Tunneling from a Ferromagnet into GaAs[J]. Phys. Rev. Lett., 1992, 68: 1387
[20] Rashba. E. I, Theory of Electrical Spin injection: Tunnel Contacts as a Solution of the Conductivity Mismatch Problem [J]. Phys. Rev. B, 2000, 62: R16267
[21] H. J. Zhu, Rom-Temperature Spin Injection from Fe into GaAs [J]. Phys. Rev. Lett., 2001, 87: 016601
[22] Hu. C. M and Matsuyanma. T, Spin Injection Across a Heterojunctions: a Ballistic Picture [J]. Phys. Rev. Lett., 2001, 87(6): 066803
[23] Jansen. R, The Spin-Valve Transistor: Fabrication, Characterization, and Physics [J]. J. Appl. Phys., 2001, 89: 7431
[24] Fiederling. R, Reuscher. G and Ossau. W et al., Injection and Detection of a Spin Polarized Current in a Light-Emitting Diode [J]. Nature, 1999, 402: 787
[25] Ohno. Y, Young, D. K and Beschoten. B et al., Electrical Spin Injection in a Ferromagnetic Semiconductor Heterostructure [J]. Nature, 2000, 402: 790
[26] Hagele. D, Oestreich. M and Ruhle. W. W et al., Spin Transport in GaAs [J]. Appl. Phys.Lett., 1998, 73: 1580
[27] Sogawa. T, Ando. H and Ando. S, Spin-Transport Dynamics of Optically Spin-Polarized Electrons in GaAs Quantum Wires [J]. Phys. Rev. B, 2000, 61: 5535
[28] Zutic. I, Fabian. J and Sarma. S. D, Spintronics: Fundamentals and Applications [J]. Rev. Mod. Phys, 2004, 76: 323
[29] Yafet. Y, Calculation of the g Factor of Metallic Sodium [J]. Phys. Rev., 1952, 85(3): 478
[30] Elliott. R. J, Theory of the Effect of Spin-Orbit Coupling on Magnetic Resonance in some Semiconductors [J]. Phys. Rev., 1954, 96(2): 266
[31] Fishman. G and Lampel. G, spin Relaxation of Photoelectrons in p- Type Gallium Arsenide [J]. Phys. Rev. B, 1977, 16(2): 820
[32] Sarma. S. D, J. Fabian and X. D. Hu et al., Spin Electronics and Spin Computation [J]. Solid State Communications, 2001, 119: 207
[33] Henini. M, Karimov. O. Z and John. G. H et al., Gated Spin Relaxation in(l 10)-Oriented Quantum Wells [J]. Physica E, 2004, 23: 309
[34] Kato. Y. K, Myers. R. C and Gossard. A. C et al., Observation of the Spin Hall Effect in Semiconductors [J]. Science, 2004, 306: 1910
[35] Silov. A. Y, Blajnov. P. A and Wolter. J. H et al., Current—Induced Spin Polarization at a Single Heterojunction [J]. Appl. Phys. Lett., 2004, 85(24): 5929
[36] Winkler R, Spin-orbit coupling effects in two-dimensional electron and hole systems [M]. Springer-Verlag, Berlin, 2003
[37]沈顺清,自旋电子学和自旋流[J],物理,2008,37(1):16
[38]Shi J R,Zhang P,Xiao D et al.,Proper Definition of Spin Current in Spin-Orbit Coupled Systems[J].Phys.Rev.Lett.,2006,96:076604
[39]Shen.S.Q,Spin Transverse Force on Spin Current in an Electric Field[J],Phys.Rev.Lett.,2005,95:187203
[40]Sun.Q.F,Guo.H and Wang.J,Spin-current-induced electric field[J].Phys.Rev.B,2004,69:054409
[41]Culcer.D,Sinova.J,Sinitsyn.N.A et al.,Semiclassical Spin Transport in Spin-Orbit-Coupled Bands[J].Phys.Rev.Lett.,2004,93:046602
[42]Zhang.S,Spin Hall Effect in the Presence of Spin Diffusion[J].Phys.Rev.Lett.,2000,85:393
[43]Ma.X.H,Hu.L.B,Tao.R.B and Shen.S.Q,Influences of spin accumulation on the intrinsic spin Hall effect in two-dimensional electron gases with Rashba spin-orbit coupling[J].Phys.Rev.B,2004,70:195343
[44]杨锡震,杨道生,田强,异常霍尔效应和自旋霍尔效应[J],物理实验,2005,25(10):3
[45]Chazalviel.J.N,Spin-dependent Hall effect in semiconductors[J].Phys.Rev.B,1975,11(16):3918.
[46]Kato.Yet al.,Current-induced spin polarization in strained semiconductors[J].Phys.Rev.Lett.,2004,93(17):176601.
[47]Hirsch.I.E,Spin Hall effect[J].Phys.Rev.Lett.,1999,83(9):1834.
[48]Zhang.S.F,Spin Hall effect in presence of spin diffusion[J].Phys.Rev.Lett.,2000,85(2):393.
[49]Silsbee.R.H,Spin-orbit induced coupling of charge current and spin polarization [J].J.Phys.CM,2004,16:R179.
[50]莫斯T S.半导体光学性质[M].鲍友恭等译.上海:上海科学技术出版社,1963.
[51] Kato. Y et al., Coherent spin manipulation without magnetic fields in strained semiconductors [ J ]. Nature , 2004,427 (6969): 50.
[52] Allen. W et al., Anomalous Hall effect in ferromagnetic semiconductors with hopping transport [ J ]. Phys. Rev. B , 2004 ,70 (12) .125320.
[53] Jungwirth. T et al., Anomalous Hall effect in ferromagnetic semiconductors [ J ]. Phys. Rev. Lett., 2002 ,88 (20): 207208.
[54] Smit. J, The spontaneous Hall effect in ferromagnetics II [J ]. Physica, 1958 ,24: 39.
[55] Berger. L, Side-jump mechanism for the Hall effect of ferromagnets [ J ] . Phys. Rev.B, 1970,2: 4559.
[1] Bernevig B A, Orenstein J and Zhang S C, Exact SU(2) Symmetry and Persistent Spin Helix in a Spin-Orbit Coupled System [J]. Phys. Rev. Lett., 2006,97: 233601
[2] Sinova J, Culcer D, Niu Q, Sinitsyn A, Jungwirth T and Macdonald A H, Universal Intrinsic Spin Hall Effect [J]. Phys. Rev. Lett., 2004, 92: 126603
[3] Murakami S, Nagaosa N and Zhang S C, Dissipationless quantum spin current at room temperature [J]. Science, 2003, 301: 1348
[4] Kato Y K, Myers R C, Gossard A C and Awschalom D D, Current-Induced Spin Polarization in Strained Semiconductors [J]. Phys. Rev. Lett., 2004, 93: 176601
[5] Kato Y K, Myers R C, Gossard A C and Awschalom D D, Observation of the spin hall effect in semiconductors [J]. Science, 2004, 306: 1910
[6] Kato Y K, Myers R C, Gossard A C and Awschalom D D, Coherent spin manipulation without magnetic fields in strained semiconductors [J]. Nature, 2004, 427: 50
[7] Wunderlich J, Kaestner B, Sinova J and Jungwirth T, Experimental Observation of the Spin-Hall Effect in a Two-Dimensional Spin-Orbit Coupled Semiconductor System [J]. Phys. Rev. Lett., 2005, 94: 047204
[8] Nitta J, Akazaki T, Takayanagi H and Enoki T, Gate Control of Spin-Orbit Interaction in an Inverted In0.53Ga0.47As/In0.52A10.48As Heterostructure [J]. Phys. Rev. Lett., 1997, 78: 1335
[9] Prinz G A, Magnetoelectronics [J]. Science, 1998, 282: 1660
[10] Wolf S A et al., Spintronics: A Spin-Based Electronics Vision for the Future [J]. Science, 2001, 294: 1488
[11] Awschalom D D, Loss D and Samarth N (eds.), Semiconductor Spintronics and Quantum Computation [M].(Springer-Verlag, Berlin, 2002)
[12] Zutic I, Fabian J and Das Sarma s, Spintronics: Fundamentals and applications [J]. Rev. Mod. Phys., 2004, 76: 323
[13] Murakami S, Nagaosa N and Zhang S C, SU(2) non-Abelian holonomy and dis-sipationless spin current in semiconductors [J]. Phys. Rev. B, 2004, 69: 235206
[14] Zhang S and Yang Z, Intrinsic Spin and Orbital Angular Momentum Hall Effect [J], Phys. Rev. Lett., 2005, 94: 066602
[15] Culcer D, Sinova J, Sinitsyn N A, Jungwirth T, Macdonald A H and Niu Q, Semi-classical Spin Transport in Spin-Orbit-Coupled Bands [J]. Phys. Rev. Lett., 2004, 93: 046602
[16] Sun Q F and Xie X C, Definition of the spin current: The angular spin current and its physical consequences [J]. Phys. Rev. B, 2005, 72: 245305
[17] Jin P Q, Li Y Q and Zhang F C, SU(2) X U(1) unified theory for charge, orbit and spin currents [J]. J. Phys. A: Math. Gen., 2006, 39: 7115
[18] Shi J R, Zhang P, Xiao D and Niu Q, Proper Definition of Spin Current in Spin-Orbit Coupled Systems [J]. Phys. Rev. Lett., 2006, 96: 076604
[19] Wang J, Wang B G, Ren W and Guo H, Conservation of spin current: Model including self-consistent spin-spin interaction [J]. Phys. Rev. B, 2006,74: 155307
[20] Wang Y, Xia K, Su Z B and Ma Z, Consistency in Formulation of Spin Current and Torque Associated with a Variance of Angular Momentum [J]. Phys. Rev. Lett., 2006, 96: 066601
[21] Shen R, Chen Y and Wang Z D, Conservation of spin currents in spin-orbit-coupled systems [J]. Phys. Rev. B, 2006, 74: 125313
[22] Mireles F and Kirczenow G, Ballistic spin-polarized transport and Rashba spin precession in semiconductor nanowires [J]. Phys. Rev. B, 2001, 64: 024426
[23] 李正中, 固体理论 (第二版) [M], 高等教育出版社, 2003
[24] Ren L, Spin helix in the presence of external magnetic field [J]. Modern Physics Letters B, 2007, 21(28): 1885
[1] Rashba E I, and Efros A L, Efficient electron spin manipulation in a quantum well by an in-plane electric field [J]. Appl. Phys. Lett., 2003, 83: 5295
[2] Murakami S, Nagaosa N, and Zhang S C, Dissipationless quantum spin current at room temperature [J]. Science, 2003, 301: 1348
[3] Sinova J, Culcer D, Niu Q, Sinitsyn N A, Jungwirth T, and MacDonald A H, Universal Intrinsic Spin Hall Effect [J]. Phys. Rev. Lett., 2004, 92: 126603
[4] Inoue J I, Bauer G E W, and Molenkamp L W, Diffuse transport and spin accumulation in a Rashba two-dimensional electron gas [J]. Phys. Rev. B, 2003, 67: 033104
[5] Mishchenko E G, Shytov A V, and Halperin B I, Spin Current and Polarization in Impure Two-Dimensional Electron Systems with Spin-Orbit Coupling [J]. Phys. Rev. Lett., 2004, 93: 226602
[6] Ma X H, Hu L B, Tao R B, and Shen S Q, Influences of spin accumulation on the intrinsic spin Hall effect in two-dimensional electron gases with Rashba spin-orbit coupling [J]. Phys. Rev. B, 2004, 70: 195343
[7] Bychkov Y A, and Rashba E I, Oscillatory effects and the Magnetic Susceptibility of carriers in inversion-layers [J]. J. Phys. C, 1984, 17: 6039
[8] Inoue J I, Bauer G E W, and Molenkamp L W, Suppression of the persistent spin Hall current by defect scattering [J]. Phys. Rev. B, 2004, 70: 041303(R)
[9] Luttinger J M, Quantum Theory of Cyclotron Resonance in Semiconductors: General Theory [J]. Phys. Rev., 1956, 102: 1030
[10] Murakami S, Absence of vertex correction for the spin Hall effect in p -type semiconductors [J]. Phys. Rev. B, 2004, 69: 241202(R)
[11] Bernevig B A, Zhang S C, Intrinsic Spin Hall Effect in the Two-Dimensional Hole Gas [J]. Phys. Rev. Lett., 2005, 95: 016801
[12] Nomura K, Sinova J, Sinisyn N A, and Macdonald A H, Dependence of the intrinsic spin-Hall effect on spin-orbit interaction character [J]. Phys. Rev. B, 2005, 72: 165316
[13] Liu S Y, and Lei X L, Disorder effects on the spin-Hall current in a diffusive Rashba two-dimensional heavy-hole system [J]. Phys. Rev. B, 2005, 72: 155314
[14] Wunderlich J, Kaestner B, Sinova J, and Jungwirth T, Experimental Observation of the Spin-Hall Effect in a Two-Dimensional Spin-Orbit Coupled Semiconductor System [J]. Phys. Rev. Lett., 2005, 94: 047204
[15] Inoue J I, Kato T, Ishikawa Y, Itoh H, Bauer G E W, and Molenkamp L W, Vertex Corrections to the Anomalous Hall Effect in Spin-Polarized Two-Dimensional Electron Gases with a Rashba Spin-Orbit Interaction [J]. Phys. Rev. Lett., 2006, 97: 046604
[16] Wang P, Li Y Q, and Zhao X A, Nonvanishing spin Hall currents in the presence of magnetic impurities [J]. Phys. Rev. B, 2007,75: 075326
[17] Ren L, Vertex correction of the anisotropic magnetic impurities to the spin polarization of 2D electron gas [J]. (to be published in Physics Letters A)
[18] Edelstein V M, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems [J]. Solid. State. Commun., 1990, 73: 233
[19] Dimitrova O V, Spin-Hall conductivity in a two-dimensional Rashba electron gas [J]. Phys. Rev. B, 2005, 71: 245327
[20] Rammer J, Quantum Transport Theory (Perseus Books, 1998)
[21] Duckheim M and Loss D, Electric-dipole-induced spin resonance in disordered semiconductors [J]. Nat. Phys., 2006, 2: 195
[22] Duckheim M and Loss D, Resonant spin polarization and spin current in a two-dimensional electron gas [J]. Phys. Rev. B, 2007, 75: 201305(R)
[1]梁拥成,张英,郭万林,姚裕贵,方忠,反常霍尔效应理论的研究进展[J],物理,2007,36(5):385
[2]杨锡震,杨道生,田强,异常霍尔效应和自旋霍尔效应[J],物理实验,2005,25(10):3
[3]Ohno H,Munekata H and Penney T et al.,Magnetotransport properties of p-type (In,Mn)As diluted magnetic Ⅲ-Ⅴ semiconductors[J].Phys.Rev.Lett.,1992,68:2664
[4]Ohno H,Making Nonmagnetic Semiconductors Ferromagnetic[J].Science,1998,281:951
[5]Hall E H,Philos.Mag.,1880,10:301
[6]Hall E H,Philos.Mag.,1881,12:157
[7]Chien C L and Westgate C R,The Hall Effect and Its Application[M],New York:Plenum,1980,55
[8]Kundt A,Wied.Ann.,1893,49:257
[9]Smith A W and Sears R W,The Hall Effect in Permalloy[J].Phys.Rev.,1929,34:1466
[10]Shchelushkin R V and Brataas A,Spin Hall effects in diffusive normal metals[J].Phys.Rev.B,2005,71:045123
[11]Karplus R and Luttinger J M,Hall Effect in Ferromagnetics[J].Phys.Rev.,1954,95:1154
[12]Sinova J,Jungwith T and Cerne J,Magneto-transport and magneto-optical properties of ferromagnetic(Ⅲ,Mn)Ⅴ semiconductors:A Review[J].Inter.J.of Mod.Phys.B,2004,18(8):1083
[13] Hurd C M, The Hall Effect in Metals and Alloys [M], New York: Plenum, 1972. 167
[14] Smit J, The spontaneous hall effect in ferromagnetics I [J]. Physica, 1955,21: 877
[15] Kohn W and Luttinger J, Quantum Theory of Electrical Transport Phenomena [J]. Phys. Rev., 1957,108: 590
[16] Luttinger J, Theory of the Hall Effect in Ferromagnetic Substances [J]. Phys. Rev., 1958,112:739
[17] Berger L, Side-Jump Mechanism for the Hall Effect of Ferromagnets [J]. Phys. Rev. B, 1970, 2: 4559
[18] Smit J, Side-Jump and Side-Slide Mechanisms for Ferromagnetic Hall Effect [J]. Phys. Rev. B, 1973, 8: 2349
[19] Berger L, Comment on Side-Jump and Side-Slide Mechanisms for Ferromagnetic Hall Effect: A Reply [J]. Phys. Rev. B, 1970, 8: 2351
[20] Smit J, Account of scattering-independent contributions to the Hall conductivity in ferromagnets [J]. Phys. Rev. B, 1978, 17: 1450
[21] Berger L, Account of scattering-independent contributions to the Hall conductivity in ferromagnets: A reply [J]. Phys. Rev. B, 1978, 17: 1453
[22] Ye J, Kim Y B and Millis A J et al., Berry Phase Theory of the Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites [J]. Phys. Rev. Lett., 1999, 83: 3737
[23] Onoda M and Nagaosa N J, Phys. Soc. Jpn., 2002, 71:19
[24] Taguchi Y, Ohara Y and Yoshizawa H et al., Science, 2001, 291: 2573
[25] Lyanda G Y, Chun S H and Salamon M B et al., Charge transport in manganites: Hopping conduction, the anomalous Hall effect, and universal scaling [J]. Phys. Rev. B, 2001, 63: 184426
[26] Jungwirth T, Niu Q and Macdonald A H, Anomalous Hall Effect in Ferromagnetic Semiconductors [J]. Phys. Rev. Lett., 2002, 88: 207208
[27] Fang Z, Nagaosa N and Takahashi K S et al., The Anomalous Hall Effect and Magnetic Monopoles in Momentum Space [J]. Science, 2003, 302: 92
[28] Fang Z, Terakura K and Nagaosa N, Orbital physics in ruthenates: first-principles studies [J]. New J. of Phys., 2005,7: 66
[29] Thouless D J, Kohmoto M and Nightingale M P et al., Quantized Hall Conductance in a Two-Dimensional Periodic Potential [J]. Phys. Rev. Lett., 1982, 49: 405
[30] Chang M C and Niu Q, Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands [J]. Phys. Rev. B, 1996, 53: 7010
[31] Sundaram G and Niu Q, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects [J]. Phys. Rev. B, 1999,59: 14915
[32] Crepieux A and Bruno P, Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation [J]. Phys. Rev. B, 2001, 64: 014416
[33] Jungwirth T, Sinova J and Wang K Y et al., Dc-transport properties of ferromagnetic (Ga,Mn)As semiconductors [J]. Apl. Phys. Lett., 2003, 83: 320
[34] Yao Y G, Kleinman L and MacDonld A H et al., First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe [J]. Phys. Rev. Lett., 2004, 92: 037204
[35] Inoue J I, Kato T and Ishikawa Y et al., Vertex Corrections to the Anomalous Hall Effect in Spin-Polarized Two-Dimensional Electron Gases with a Rashba Spin-Orbit Interaction [J]. Phys. Rev. Lett., 2006, 97: 046604
[36] Onoda S, Sugimoto N and Nagaosa N, Intrinsic Versus Extrinsic Anomalous Hall Effect in Ferromagnets [J]. Phys. Rev. Lett., 2006, 97: 126602
[37] Mathieu R, Asamitsu A and Yamada H et al., Scaling of the Anomalous Hall Effect in Srl-xCaxRuO3 [J]. Phys. Rev. Lett., 2004, 93: 016602
[38] Murakami S, Nagaosa N and Zhang S C, Dissipationless quantum spin current at room temperature [J]. Science, 2003, 301: 1348
[39] Sinova J, Culcer D, Niu Q, Sinitsyn A, Jungwirth T and Macdonald A H, Universal Intrinsic Spin Hall Effect [J]. Phys. Rev. Lett., 2004, 92: 126603
[40] Wunderlich J, Kaestner B, Sinova J and Jungwirth T, Experimental Observation of the Spin-Hall Effect in a Two-Dimensional Spin-Orbit Coupled Semiconductor System [J]. Phys. Rev. Lett., 2005, 94: 047204
[41] Kato Y K, Myers R C, Gossard A C and Awschalom D D, Observation of the spin hall effect in semiconductors [J]. Science, 2004, 306: 1910
[42] Shi J R, Zhang P, Xiao D and Niu Q, Proper Definition of Spin Current in Spin-Orbit Coupled Systems [J]. Phys. Rev. Lett., 2006, 96: 076604
[43] Yao Y G and Fang Z, Sign Changes of Intrinsic Spin Hall Effect in Semiconductors and Simple Metals: First-Principles Calculations [J]. Phys. Rev. Lett., 2005, 95: 156601
[44] Guo G Y, Yao Y G and Niu Q, Ab initio Calculation of the Intrinsic Spin Hall Effect in Semiconductors [J]. Phys. Rev. Lett., 2005,94: 226601
[45] Dugaev V K, Bruno P, Taillefumier M, Canals B, and Lacroix C, Anomalous Hall effect in a two-dimensional electron gas with spin-orbit interaction [J]. Phys. Rev. B, 2005, 71: 224423
[46] Sinitsyn N A, MacDonald A H, Jungwirth T, Dugaev V K, and Sinova J, Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach [J]. Phys. Rev. B, 2007, 75: 045315
[47] Nunner T S, Sinitsyn N A, Borunda M F, Kovalev A A, Abanov A, Timm C, Jungwirth T, Inoue J I, MacDonald A H, and Sinova J, Anomalous Hall effect in a two-dimensional electron gas [J], cond-mat/07060056
[48] Wang P, Li Y Q, and Zhao X A, Nonvanishing spin Hall currents in the presence of magnetic impurities [J]. Phys. Rev. B, 2007, 75: 075326
[49] Ren L, Nonvanishing anomalous Hall conductivity in spin-polarized two-dimensional electron gas with Rashba spin - orbit interaction [J]. J. Phys: Con-dens. Matter., 2008, 20: 075216
[50] Kato T, Ishikawa Y, Itoh H and Inoue J I, Anomalous Hall effect in spin-polarized two-dimensional electron gases with Rashba spin - orbit interaction [J]. New Journal of Physics, 2007, 9: 350
[51] Rammer J, Quantum Transport Theory [M].(Perseus Books, 1998) [52] Ren L (to be published in Phys. Lett. A).
[53] Edelstein V M, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems [J]. Solid. State. Commun., 1990, 73: 233
[54] Inoue J I, Bauer G E W, and Molenkamp L W, Suppression of the persistent spin Hall current by defect scattering [J]. Phys. Rev. B, 2004, 70: 041303(R)
[55] Inoue J I, Bauer G E W, and Molenkamp L W, Diffuse transport and spin accumulation in a Rashba two-dimensional electron gas [J]. Phys. Rev. B, 2003, 67: 033104
[2]Simmonds.J.L,Phys.Today,1995(4):24
[3]Ohno.H et al.,(Ga,Mn)As:A new diluted magnetic semiconductor based on GaAs[J].Appl.phys.Lett.,1996,69:363
[4]Awschalom.D et al.,Electron spin and optical coherence in semiconductors[J].Phys.Today,1999,52(6):33
[5]Black.W.C and Das.B,Programmable logic using giant-magnetoresistance and spin-dependent tunneling devices[J].J.Appl.Phys.,2000,87:6674
[6]Ney.A et al.,Programmable computing with a single magnetoresistive element [J].Nature,2003,425:485
[7]Grunberg.P,Schreiber.R,Pang.Yet al.,Phys.Rev.Lett.,Layered Magnetic Structures:Evidence for Antiferromagnetic Coupling of Fe Layers across Cr Interlayers [J].1986,57:2442
[8]Meservey.R,Tedrow.P.M and Flude.P,Magnetic Field Splitting of the Quasiparticle States in Superconducting Aluminum Films[J].Phys.Rev.Lett.,1970,25:1270
[9]Han.X.F et al.,High-magnetoresistance tunnel junctions using Co75Fe25 ferromagnetic electrodes[J].Jpn.Appl.Phys.,2000,39:L439
[10]刘林生等,半导体自旋电子学的研究与应用进展[J].电子器件,2007,30(3):1125
[11]Ohno.H,Making nonmagnetic semiconductors ferromagnetic[J].Science,1998,281:951
[12]Munekata.H,Ohno.H and Von.M.Set al.,Diluted Magnetic Ⅲ—V Semiconductors [J].Phys.Rev.Lett,1989,63(17):1849
[13] De. B. J, Oersterholt. R and Van. E. A et al., Nanometer-Scale Magnetic MnAs Particles in GaAs Grown by Molecular Beam Epitaxy [J], Appl. Phys. Lett., 1996, 68(19): 2744
[14] Xu. J. L, Schilfgaarde. M. V and Samolyuk. G. D, Role of Disorder in Mn: GaAs, Cr: GaAs, andCr: GaN [J]. Phys. Rev. Lett., 2005, 94: 097201
[15] Dietl. T, Ohno. H and Matsukura. F et al., Zener Model De-scrip—tion of Ferromagnetism in Zine-Blende Magnetic Semiconductors [J]. Science, 2000, 287: 1019
[16] Mi. W. B, Bai. H. L and Liu. H et al., Microstructure, Magnetic, and Optical Properties of Sputtered Mn-Doped ZnO Films with High-Temperature Ferromagnetism [J]. J. Appl. Phys., 2007, 101: 023904
[17] Hu. C. M, Nitta. J and Jensen. A et al., SPin Polarized Transport in a two-Dimension Electron Gas with Interdigital-Ferromagnetic Contacts [J]. Phys. Rev. B, 2001, 63: 125333
[18] Schmidit. G, Ferrand. D and Molenkamp. L. W et al., Fundamental Obstacle for Electrical Spin injection from a Ferromagnetic Metal into a Diffusive Semiconductor [J]. Phys. Rev. B, 2000, 62: R4790
[19] S. F. Alvarado, P. Renaud, Observation of Spin Polarized Electron Tunneling from a Ferromagnet into GaAs[J]. Phys. Rev. Lett., 1992, 68: 1387
[20] Rashba. E. I, Theory of Electrical Spin injection: Tunnel Contacts as a Solution of the Conductivity Mismatch Problem [J]. Phys. Rev. B, 2000, 62: R16267
[21] H. J. Zhu, Rom-Temperature Spin Injection from Fe into GaAs [J]. Phys. Rev. Lett., 2001, 87: 016601
[22] Hu. C. M and Matsuyanma. T, Spin Injection Across a Heterojunctions: a Ballistic Picture [J]. Phys. Rev. Lett., 2001, 87(6): 066803
[23] Jansen. R, The Spin-Valve Transistor: Fabrication, Characterization, and Physics [J]. J. Appl. Phys., 2001, 89: 7431
[24] Fiederling. R, Reuscher. G and Ossau. W et al., Injection and Detection of a Spin Polarized Current in a Light-Emitting Diode [J]. Nature, 1999, 402: 787
[25] Ohno. Y, Young, D. K and Beschoten. B et al., Electrical Spin Injection in a Ferromagnetic Semiconductor Heterostructure [J]. Nature, 2000, 402: 790
[26] Hagele. D, Oestreich. M and Ruhle. W. W et al., Spin Transport in GaAs [J]. Appl. Phys.Lett., 1998, 73: 1580
[27] Sogawa. T, Ando. H and Ando. S, Spin-Transport Dynamics of Optically Spin-Polarized Electrons in GaAs Quantum Wires [J]. Phys. Rev. B, 2000, 61: 5535
[28] Zutic. I, Fabian. J and Sarma. S. D, Spintronics: Fundamentals and Applications [J]. Rev. Mod. Phys, 2004, 76: 323
[29] Yafet. Y, Calculation of the g Factor of Metallic Sodium [J]. Phys. Rev., 1952, 85(3): 478
[30] Elliott. R. J, Theory of the Effect of Spin-Orbit Coupling on Magnetic Resonance in some Semiconductors [J]. Phys. Rev., 1954, 96(2): 266
[31] Fishman. G and Lampel. G, spin Relaxation of Photoelectrons in p- Type Gallium Arsenide [J]. Phys. Rev. B, 1977, 16(2): 820
[32] Sarma. S. D, J. Fabian and X. D. Hu et al., Spin Electronics and Spin Computation [J]. Solid State Communications, 2001, 119: 207
[33] Henini. M, Karimov. O. Z and John. G. H et al., Gated Spin Relaxation in(l 10)-Oriented Quantum Wells [J]. Physica E, 2004, 23: 309
[34] Kato. Y. K, Myers. R. C and Gossard. A. C et al., Observation of the Spin Hall Effect in Semiconductors [J]. Science, 2004, 306: 1910
[35] Silov. A. Y, Blajnov. P. A and Wolter. J. H et al., Current—Induced Spin Polarization at a Single Heterojunction [J]. Appl. Phys. Lett., 2004, 85(24): 5929
[36] Winkler R, Spin-orbit coupling effects in two-dimensional electron and hole systems [M]. Springer-Verlag, Berlin, 2003
[37]沈顺清,自旋电子学和自旋流[J],物理,2008,37(1):16
[38]Shi J R,Zhang P,Xiao D et al.,Proper Definition of Spin Current in Spin-Orbit Coupled Systems[J].Phys.Rev.Lett.,2006,96:076604
[39]Shen.S.Q,Spin Transverse Force on Spin Current in an Electric Field[J],Phys.Rev.Lett.,2005,95:187203
[40]Sun.Q.F,Guo.H and Wang.J,Spin-current-induced electric field[J].Phys.Rev.B,2004,69:054409
[41]Culcer.D,Sinova.J,Sinitsyn.N.A et al.,Semiclassical Spin Transport in Spin-Orbit-Coupled Bands[J].Phys.Rev.Lett.,2004,93:046602
[42]Zhang.S,Spin Hall Effect in the Presence of Spin Diffusion[J].Phys.Rev.Lett.,2000,85:393
[43]Ma.X.H,Hu.L.B,Tao.R.B and Shen.S.Q,Influences of spin accumulation on the intrinsic spin Hall effect in two-dimensional electron gases with Rashba spin-orbit coupling[J].Phys.Rev.B,2004,70:195343
[44]杨锡震,杨道生,田强,异常霍尔效应和自旋霍尔效应[J],物理实验,2005,25(10):3
[45]Chazalviel.J.N,Spin-dependent Hall effect in semiconductors[J].Phys.Rev.B,1975,11(16):3918.
[46]Kato.Yet al.,Current-induced spin polarization in strained semiconductors[J].Phys.Rev.Lett.,2004,93(17):176601.
[47]Hirsch.I.E,Spin Hall effect[J].Phys.Rev.Lett.,1999,83(9):1834.
[48]Zhang.S.F,Spin Hall effect in presence of spin diffusion[J].Phys.Rev.Lett.,2000,85(2):393.
[49]Silsbee.R.H,Spin-orbit induced coupling of charge current and spin polarization [J].J.Phys.CM,2004,16:R179.
[50]莫斯T S.半导体光学性质[M].鲍友恭等译.上海:上海科学技术出版社,1963.
[51] Kato. Y et al., Coherent spin manipulation without magnetic fields in strained semiconductors [ J ]. Nature , 2004,427 (6969): 50.
[52] Allen. W et al., Anomalous Hall effect in ferromagnetic semiconductors with hopping transport [ J ]. Phys. Rev. B , 2004 ,70 (12) .125320.
[53] Jungwirth. T et al., Anomalous Hall effect in ferromagnetic semiconductors [ J ]. Phys. Rev. Lett., 2002 ,88 (20): 207208.
[54] Smit. J, The spontaneous Hall effect in ferromagnetics II [J ]. Physica, 1958 ,24: 39.
[55] Berger. L, Side-jump mechanism for the Hall effect of ferromagnets [ J ] . Phys. Rev.B, 1970,2: 4559.
[1] Bernevig B A, Orenstein J and Zhang S C, Exact SU(2) Symmetry and Persistent Spin Helix in a Spin-Orbit Coupled System [J]. Phys. Rev. Lett., 2006,97: 233601
[2] Sinova J, Culcer D, Niu Q, Sinitsyn A, Jungwirth T and Macdonald A H, Universal Intrinsic Spin Hall Effect [J]. Phys. Rev. Lett., 2004, 92: 126603
[3] Murakami S, Nagaosa N and Zhang S C, Dissipationless quantum spin current at room temperature [J]. Science, 2003, 301: 1348
[4] Kato Y K, Myers R C, Gossard A C and Awschalom D D, Current-Induced Spin Polarization in Strained Semiconductors [J]. Phys. Rev. Lett., 2004, 93: 176601
[5] Kato Y K, Myers R C, Gossard A C and Awschalom D D, Observation of the spin hall effect in semiconductors [J]. Science, 2004, 306: 1910
[6] Kato Y K, Myers R C, Gossard A C and Awschalom D D, Coherent spin manipulation without magnetic fields in strained semiconductors [J]. Nature, 2004, 427: 50
[7] Wunderlich J, Kaestner B, Sinova J and Jungwirth T, Experimental Observation of the Spin-Hall Effect in a Two-Dimensional Spin-Orbit Coupled Semiconductor System [J]. Phys. Rev. Lett., 2005, 94: 047204
[8] Nitta J, Akazaki T, Takayanagi H and Enoki T, Gate Control of Spin-Orbit Interaction in an Inverted In0.53Ga0.47As/In0.52A10.48As Heterostructure [J]. Phys. Rev. Lett., 1997, 78: 1335
[9] Prinz G A, Magnetoelectronics [J]. Science, 1998, 282: 1660
[10] Wolf S A et al., Spintronics: A Spin-Based Electronics Vision for the Future [J]. Science, 2001, 294: 1488
[11] Awschalom D D, Loss D and Samarth N (eds.), Semiconductor Spintronics and Quantum Computation [M].(Springer-Verlag, Berlin, 2002)
[12] Zutic I, Fabian J and Das Sarma s, Spintronics: Fundamentals and applications [J]. Rev. Mod. Phys., 2004, 76: 323
[13] Murakami S, Nagaosa N and Zhang S C, SU(2) non-Abelian holonomy and dis-sipationless spin current in semiconductors [J]. Phys. Rev. B, 2004, 69: 235206
[14] Zhang S and Yang Z, Intrinsic Spin and Orbital Angular Momentum Hall Effect [J], Phys. Rev. Lett., 2005, 94: 066602
[15] Culcer D, Sinova J, Sinitsyn N A, Jungwirth T, Macdonald A H and Niu Q, Semi-classical Spin Transport in Spin-Orbit-Coupled Bands [J]. Phys. Rev. Lett., 2004, 93: 046602
[16] Sun Q F and Xie X C, Definition of the spin current: The angular spin current and its physical consequences [J]. Phys. Rev. B, 2005, 72: 245305
[17] Jin P Q, Li Y Q and Zhang F C, SU(2) X U(1) unified theory for charge, orbit and spin currents [J]. J. Phys. A: Math. Gen., 2006, 39: 7115
[18] Shi J R, Zhang P, Xiao D and Niu Q, Proper Definition of Spin Current in Spin-Orbit Coupled Systems [J]. Phys. Rev. Lett., 2006, 96: 076604
[19] Wang J, Wang B G, Ren W and Guo H, Conservation of spin current: Model including self-consistent spin-spin interaction [J]. Phys. Rev. B, 2006,74: 155307
[20] Wang Y, Xia K, Su Z B and Ma Z, Consistency in Formulation of Spin Current and Torque Associated with a Variance of Angular Momentum [J]. Phys. Rev. Lett., 2006, 96: 066601
[21] Shen R, Chen Y and Wang Z D, Conservation of spin currents in spin-orbit-coupled systems [J]. Phys. Rev. B, 2006, 74: 125313
[22] Mireles F and Kirczenow G, Ballistic spin-polarized transport and Rashba spin precession in semiconductor nanowires [J]. Phys. Rev. B, 2001, 64: 024426
[23] 李正中, 固体理论 (第二版) [M], 高等教育出版社, 2003
[24] Ren L, Spin helix in the presence of external magnetic field [J]. Modern Physics Letters B, 2007, 21(28): 1885
[1] Rashba E I, and Efros A L, Efficient electron spin manipulation in a quantum well by an in-plane electric field [J]. Appl. Phys. Lett., 2003, 83: 5295
[2] Murakami S, Nagaosa N, and Zhang S C, Dissipationless quantum spin current at room temperature [J]. Science, 2003, 301: 1348
[3] Sinova J, Culcer D, Niu Q, Sinitsyn N A, Jungwirth T, and MacDonald A H, Universal Intrinsic Spin Hall Effect [J]. Phys. Rev. Lett., 2004, 92: 126603
[4] Inoue J I, Bauer G E W, and Molenkamp L W, Diffuse transport and spin accumulation in a Rashba two-dimensional electron gas [J]. Phys. Rev. B, 2003, 67: 033104
[5] Mishchenko E G, Shytov A V, and Halperin B I, Spin Current and Polarization in Impure Two-Dimensional Electron Systems with Spin-Orbit Coupling [J]. Phys. Rev. Lett., 2004, 93: 226602
[6] Ma X H, Hu L B, Tao R B, and Shen S Q, Influences of spin accumulation on the intrinsic spin Hall effect in two-dimensional electron gases with Rashba spin-orbit coupling [J]. Phys. Rev. B, 2004, 70: 195343
[7] Bychkov Y A, and Rashba E I, Oscillatory effects and the Magnetic Susceptibility of carriers in inversion-layers [J]. J. Phys. C, 1984, 17: 6039
[8] Inoue J I, Bauer G E W, and Molenkamp L W, Suppression of the persistent spin Hall current by defect scattering [J]. Phys. Rev. B, 2004, 70: 041303(R)
[9] Luttinger J M, Quantum Theory of Cyclotron Resonance in Semiconductors: General Theory [J]. Phys. Rev., 1956, 102: 1030
[10] Murakami S, Absence of vertex correction for the spin Hall effect in p -type semiconductors [J]. Phys. Rev. B, 2004, 69: 241202(R)
[11] Bernevig B A, Zhang S C, Intrinsic Spin Hall Effect in the Two-Dimensional Hole Gas [J]. Phys. Rev. Lett., 2005, 95: 016801
[12] Nomura K, Sinova J, Sinisyn N A, and Macdonald A H, Dependence of the intrinsic spin-Hall effect on spin-orbit interaction character [J]. Phys. Rev. B, 2005, 72: 165316
[13] Liu S Y, and Lei X L, Disorder effects on the spin-Hall current in a diffusive Rashba two-dimensional heavy-hole system [J]. Phys. Rev. B, 2005, 72: 155314
[14] Wunderlich J, Kaestner B, Sinova J, and Jungwirth T, Experimental Observation of the Spin-Hall Effect in a Two-Dimensional Spin-Orbit Coupled Semiconductor System [J]. Phys. Rev. Lett., 2005, 94: 047204
[15] Inoue J I, Kato T, Ishikawa Y, Itoh H, Bauer G E W, and Molenkamp L W, Vertex Corrections to the Anomalous Hall Effect in Spin-Polarized Two-Dimensional Electron Gases with a Rashba Spin-Orbit Interaction [J]. Phys. Rev. Lett., 2006, 97: 046604
[16] Wang P, Li Y Q, and Zhao X A, Nonvanishing spin Hall currents in the presence of magnetic impurities [J]. Phys. Rev. B, 2007,75: 075326
[17] Ren L, Vertex correction of the anisotropic magnetic impurities to the spin polarization of 2D electron gas [J]. (to be published in Physics Letters A)
[18] Edelstein V M, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems [J]. Solid. State. Commun., 1990, 73: 233
[19] Dimitrova O V, Spin-Hall conductivity in a two-dimensional Rashba electron gas [J]. Phys. Rev. B, 2005, 71: 245327
[20] Rammer J, Quantum Transport Theory (Perseus Books, 1998)
[21] Duckheim M and Loss D, Electric-dipole-induced spin resonance in disordered semiconductors [J]. Nat. Phys., 2006, 2: 195
[22] Duckheim M and Loss D, Resonant spin polarization and spin current in a two-dimensional electron gas [J]. Phys. Rev. B, 2007, 75: 201305(R)
[1]梁拥成,张英,郭万林,姚裕贵,方忠,反常霍尔效应理论的研究进展[J],物理,2007,36(5):385
[2]杨锡震,杨道生,田强,异常霍尔效应和自旋霍尔效应[J],物理实验,2005,25(10):3
[3]Ohno H,Munekata H and Penney T et al.,Magnetotransport properties of p-type (In,Mn)As diluted magnetic Ⅲ-Ⅴ semiconductors[J].Phys.Rev.Lett.,1992,68:2664
[4]Ohno H,Making Nonmagnetic Semiconductors Ferromagnetic[J].Science,1998,281:951
[5]Hall E H,Philos.Mag.,1880,10:301
[6]Hall E H,Philos.Mag.,1881,12:157
[7]Chien C L and Westgate C R,The Hall Effect and Its Application[M],New York:Plenum,1980,55
[8]Kundt A,Wied.Ann.,1893,49:257
[9]Smith A W and Sears R W,The Hall Effect in Permalloy[J].Phys.Rev.,1929,34:1466
[10]Shchelushkin R V and Brataas A,Spin Hall effects in diffusive normal metals[J].Phys.Rev.B,2005,71:045123
[11]Karplus R and Luttinger J M,Hall Effect in Ferromagnetics[J].Phys.Rev.,1954,95:1154
[12]Sinova J,Jungwith T and Cerne J,Magneto-transport and magneto-optical properties of ferromagnetic(Ⅲ,Mn)Ⅴ semiconductors:A Review[J].Inter.J.of Mod.Phys.B,2004,18(8):1083
[13] Hurd C M, The Hall Effect in Metals and Alloys [M], New York: Plenum, 1972. 167
[14] Smit J, The spontaneous hall effect in ferromagnetics I [J]. Physica, 1955,21: 877
[15] Kohn W and Luttinger J, Quantum Theory of Electrical Transport Phenomena [J]. Phys. Rev., 1957,108: 590
[16] Luttinger J, Theory of the Hall Effect in Ferromagnetic Substances [J]. Phys. Rev., 1958,112:739
[17] Berger L, Side-Jump Mechanism for the Hall Effect of Ferromagnets [J]. Phys. Rev. B, 1970, 2: 4559
[18] Smit J, Side-Jump and Side-Slide Mechanisms for Ferromagnetic Hall Effect [J]. Phys. Rev. B, 1973, 8: 2349
[19] Berger L, Comment on Side-Jump and Side-Slide Mechanisms for Ferromagnetic Hall Effect: A Reply [J]. Phys. Rev. B, 1970, 8: 2351
[20] Smit J, Account of scattering-independent contributions to the Hall conductivity in ferromagnets [J]. Phys. Rev. B, 1978, 17: 1450
[21] Berger L, Account of scattering-independent contributions to the Hall conductivity in ferromagnets: A reply [J]. Phys. Rev. B, 1978, 17: 1453
[22] Ye J, Kim Y B and Millis A J et al., Berry Phase Theory of the Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites [J]. Phys. Rev. Lett., 1999, 83: 3737
[23] Onoda M and Nagaosa N J, Phys. Soc. Jpn., 2002, 71:19
[24] Taguchi Y, Ohara Y and Yoshizawa H et al., Science, 2001, 291: 2573
[25] Lyanda G Y, Chun S H and Salamon M B et al., Charge transport in manganites: Hopping conduction, the anomalous Hall effect, and universal scaling [J]. Phys. Rev. B, 2001, 63: 184426
[26] Jungwirth T, Niu Q and Macdonald A H, Anomalous Hall Effect in Ferromagnetic Semiconductors [J]. Phys. Rev. Lett., 2002, 88: 207208
[27] Fang Z, Nagaosa N and Takahashi K S et al., The Anomalous Hall Effect and Magnetic Monopoles in Momentum Space [J]. Science, 2003, 302: 92
[28] Fang Z, Terakura K and Nagaosa N, Orbital physics in ruthenates: first-principles studies [J]. New J. of Phys., 2005,7: 66
[29] Thouless D J, Kohmoto M and Nightingale M P et al., Quantized Hall Conductance in a Two-Dimensional Periodic Potential [J]. Phys. Rev. Lett., 1982, 49: 405
[30] Chang M C and Niu Q, Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands [J]. Phys. Rev. B, 1996, 53: 7010
[31] Sundaram G and Niu Q, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects [J]. Phys. Rev. B, 1999,59: 14915
[32] Crepieux A and Bruno P, Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation [J]. Phys. Rev. B, 2001, 64: 014416
[33] Jungwirth T, Sinova J and Wang K Y et al., Dc-transport properties of ferromagnetic (Ga,Mn)As semiconductors [J]. Apl. Phys. Lett., 2003, 83: 320
[34] Yao Y G, Kleinman L and MacDonld A H et al., First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe [J]. Phys. Rev. Lett., 2004, 92: 037204
[35] Inoue J I, Kato T and Ishikawa Y et al., Vertex Corrections to the Anomalous Hall Effect in Spin-Polarized Two-Dimensional Electron Gases with a Rashba Spin-Orbit Interaction [J]. Phys. Rev. Lett., 2006, 97: 046604
[36] Onoda S, Sugimoto N and Nagaosa N, Intrinsic Versus Extrinsic Anomalous Hall Effect in Ferromagnets [J]. Phys. Rev. Lett., 2006, 97: 126602
[37] Mathieu R, Asamitsu A and Yamada H et al., Scaling of the Anomalous Hall Effect in Srl-xCaxRuO3 [J]. Phys. Rev. Lett., 2004, 93: 016602
[38] Murakami S, Nagaosa N and Zhang S C, Dissipationless quantum spin current at room temperature [J]. Science, 2003, 301: 1348
[39] Sinova J, Culcer D, Niu Q, Sinitsyn A, Jungwirth T and Macdonald A H, Universal Intrinsic Spin Hall Effect [J]. Phys. Rev. Lett., 2004, 92: 126603
[40] Wunderlich J, Kaestner B, Sinova J and Jungwirth T, Experimental Observation of the Spin-Hall Effect in a Two-Dimensional Spin-Orbit Coupled Semiconductor System [J]. Phys. Rev. Lett., 2005, 94: 047204
[41] Kato Y K, Myers R C, Gossard A C and Awschalom D D, Observation of the spin hall effect in semiconductors [J]. Science, 2004, 306: 1910
[42] Shi J R, Zhang P, Xiao D and Niu Q, Proper Definition of Spin Current in Spin-Orbit Coupled Systems [J]. Phys. Rev. Lett., 2006, 96: 076604
[43] Yao Y G and Fang Z, Sign Changes of Intrinsic Spin Hall Effect in Semiconductors and Simple Metals: First-Principles Calculations [J]. Phys. Rev. Lett., 2005, 95: 156601
[44] Guo G Y, Yao Y G and Niu Q, Ab initio Calculation of the Intrinsic Spin Hall Effect in Semiconductors [J]. Phys. Rev. Lett., 2005,94: 226601
[45] Dugaev V K, Bruno P, Taillefumier M, Canals B, and Lacroix C, Anomalous Hall effect in a two-dimensional electron gas with spin-orbit interaction [J]. Phys. Rev. B, 2005, 71: 224423
[46] Sinitsyn N A, MacDonald A H, Jungwirth T, Dugaev V K, and Sinova J, Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach [J]. Phys. Rev. B, 2007, 75: 045315
[47] Nunner T S, Sinitsyn N A, Borunda M F, Kovalev A A, Abanov A, Timm C, Jungwirth T, Inoue J I, MacDonald A H, and Sinova J, Anomalous Hall effect in a two-dimensional electron gas [J], cond-mat/07060056
[48] Wang P, Li Y Q, and Zhao X A, Nonvanishing spin Hall currents in the presence of magnetic impurities [J]. Phys. Rev. B, 2007, 75: 075326
[49] Ren L, Nonvanishing anomalous Hall conductivity in spin-polarized two-dimensional electron gas with Rashba spin - orbit interaction [J]. J. Phys: Con-dens. Matter., 2008, 20: 075216
[50] Kato T, Ishikawa Y, Itoh H and Inoue J I, Anomalous Hall effect in spin-polarized two-dimensional electron gases with Rashba spin - orbit interaction [J]. New Journal of Physics, 2007, 9: 350
[51] Rammer J, Quantum Transport Theory [M].(Perseus Books, 1998) [52] Ren L (to be published in Phys. Lett. A).
[53] Edelstein V M, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems [J]. Solid. State. Commun., 1990, 73: 233
[54] Inoue J I, Bauer G E W, and Molenkamp L W, Suppression of the persistent spin Hall current by defect scattering [J]. Phys. Rev. B, 2004, 70: 041303(R)
[55] Inoue J I, Bauer G E W, and Molenkamp L W, Diffuse transport and spin accumulation in a Rashba two-dimensional electron gas [J]. Phys. Rev. B, 2003, 67: 033104