Theory of Spin Hall Effects in Semiconductors

Engel, Hans–Andreas; Rashba, Emmanuel I.; Halperin, Bertrand I.

doi:10.1002/9780470022184.hmm508

Cited by 95 publications

(176 citation statements)

References 124 publications

(183 reference statements)

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“…in the ballistic regime, the corresponding contribution being called intrinsic. Later several papers appeared where the effect of scattering by impurities was taken into account for the Rashba model 5,6,7,8,9,10 , besides, the extrinsic contribution was described 11,12 to explain the recent experiment done by Awschalom's group 13 , see also experiment 14 .…”

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confidence: 99%

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Intrinsic spin current for an arbitrary Hamiltonian and scattering potential

Khaetskii

2006

Phys. Rev. B

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We have described electron spin dynamics in the presence of the spin-orbit interaction and disorder using the spin-density matrix method. Exact solution is obtained for an arbitrary 2D spin-orbit Hamiltonian and arbitrary smoothness of the disorder potential. Spin current depends explicitely on the disorder properties, namely the smoothness of the disorder potential, even in the ballistic limit when broadening by scattering is much smaller than the spin-orbit related splitting of the energy spectrum. In this sense universal intrinsic spin current does not exist. 73.50.Bk Spin-orbit coupling brings about a number of interesting effects, one of which is generation of a spin flux in the plane perpendicular to the charge current direction. This phenomenon occurs in the paramagnetic system and has been very well known for quite a long time, see Ref. 1 . It results from the fact that in the presense of spin-orbit coupling the scattering by impurities has an asymmetric character 2 . Extrinsic contribution exists only beyond the Born approximation in the scattering amplitude and leads to an accumulation of the spin density near the sample surface 1 .It has been recently claimed 3,4 that an analogous phenomenon can exist even without scattering by impurities, i.e. in the ballistic regime, the corresponding contribution being called intrinsic. Later several papers appeared where the effect of scattering by impurities was taken into account for the Rashba model 5,6,7,8,9,10 , besides, the extrinsic contribution was described 11,12 to explain the recent experiment done by Awschalom's group 13 , see also experiment 14 .Here we study the dependence of the intrinsic contribution to the spin current on the form of the Hamiltonian and properties of the disorder potential using the spin-density matrix method 15 . We have considered an arbitrary Hamiltonian, for example, the generalized 2D Rashba Hamiltonian with an arbitrary momentum dependence of the spin-orbit term or the 3D Luttinger Hamiltonian, and the arbitrary smoothness of the disorder potential. In the case of the generalized 2D Rashba model and the arbitrary smoothness of the disorder potential an exact solution for spin current in the ballistic limit ∆τ ≫ 1 is obtained, where ∆ is the spin splitting of the electron spectrum and τ is the transport scattering time. Spin current depends explicitely on the disorder properties, namely, the smoothness of the disorder potential, even in the ballistic limit. In this sense universal intrinsic spin current does not exist. The problem of 2D holes with the p 3 spin-orbit term has been numerically considered recently by several groups 16,17 . Analytically it was studied in Ref.18 for the δ-scattering, where the incorrect answer was obtained due to the wrong calculation method. The case of the arbitrary smoothness of the disorder potential has been analytically considered very recently in Refs. 19,20,21 , some results were also reported in Ref. 22 . Below we will compare the results obtained here with those from Ref.20. I also ...

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“…We can see that the scattering transitions within the band (+ or −) and between the bands correspond to different values of the p 1 momentum entering the kernel of the collision term, see Eq. (11). In the case of the intraband transitions p 1 = p, while for the interband transitions its value is either p + or p − .…”

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confidence: 99%

Intrinsic spin current for an arbitrary Hamiltonian and scattering potential

Khaetskii

2006

Phys. Rev. B

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“…During the last decade, semiconductor spintronics developed into a wide and diversified field. Early review papers [1, 2] were followed by more recent surveys covering specific scientific problems and technological perspectives of this rapidly developing field [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. There exists close connection between the recent work on electric spin manipulation in low-dimensional systems and the previous work on anomalous Hall effect [18], electric dipole spin resonance [19], optical orientation [20] and photogalvanic effect [21,22] in three-dimensional systems.…”

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confidence: 99%

Restrictions on modeling spin injection by resistor networks

Rashba¹

2008

Semicond. Sci. Technol.

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Because of the technical difficulties of solving spin transport equations in inhomogeneous systems, different resistor networks are widely applied for modeling spin transport. By comparing an analytical solution for spin injection across a ferromagnet -paramagnet junction with a resistor model approach, its essential limitations stemming from inhomogeneous spin populations are clarified. PACS numbers:Conventional electronics is based on a single parameter of electron, its charge. Therefore, electronics deals only with electron trajectories. It does not involve electron spin, its internal degree of freedom. The new paradigm of spin-based electronics, or spintronics, is based on active involvement of electron spin in transport and optical phenomena, and on employing electron spin for both information processing and information storage. During the last decade, semiconductor spintronics developed into a wide and diversified field. Early review papers [1, 2] were followed by more recent surveys covering specific scientific problems and technological perspectives of this rapidly developing field [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. There exists close connection between the recent work on electric spin manipulation in low-dimensional systems and the previous work on anomalous Hall effect [18], electric dipole spin resonance [19], optical orientation [20] and photogalvanic effect [21,22] in three-dimensional systems. Strong impetus for semiconductor spintronics was given by the discovery of giant magnetoresistance in metallic systems [23,24] and by its impressing practical applications.Spin injection from ferromagnetic sources into paramagnetic media is believed to be an important part of the new phenomena and applications in the field of the spin-polarized electron transport. The concept of a field effect spin transistor [25] served as one of the stimuli. Successful experiments on spin injection into superconductors [26] and normal metals [27] were very promising, and theoretical work supported reliability of the idea [28,29,30,31,32,33]. Successful detection of the floating potential (spin-e.m.f., electromotive force [34]) at a ferromagnetic probe became an independent confirmation of efficient spin injection. Meantime, the methods that resulted in a remarkable success in spin injection from ferromagnetic metals into paramagnetic metals turned inefficient as applied to the spin injection from ferromagnetic metals into semiconductors. Spin injection at the level of only about 1% was reported [35,36], and persuasiveness of the results was disputed [37,38]. Absence of any measurable spin-e.m.f. also indicated that the concentration of the electrically injected nonequilibrium spins was vanishingly small [39].Inefficiency of a "perfect" contact between a ferromagnetic metal and a semiconductor as a spin emitter, that seemed puzzling, found its natural explanation in the framework of the conductivity mismatch concept [40]. The next step was proposing resistive spin selective contacts, like tunnel or Schottky barriers, a...

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“…This effect, known now as the spin Hall effect (SHE) 3 , was studied extensively in the last few years [3][4][5][6][7][8][9] , and is still of current interest -mainly because it offers a new possibility of spin manipulation with electric field only. The possibility of pure electrical manipulation of spin degrees of freedom is interesting not only from fundamental reasons, but also from the point of view of possible applications in future spintronics devices and information processing technologies [10][11][12][13] .…”

Section: Introductionmentioning

confidence: 99%

Intrinsic contribution to spin Hall and spin Nernst effects in a bilayer graphene

Dyrdał¹,

Barnaś²

2012

J. Phys.: Condens. Matter

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We consider intrinsic contributions to the spin Hall and spin Nernst effects in a bilayer graphene. The relevant electronic spectrum is obtained from the tight binding Hamiltonian, which also includes the intrinsic spin-orbit interaction. The corresponding spin Hall and spin Nernst conductivities are compared with those obtained from effective Hamiltonians appropriate for states in the vicinity of the Fermi level of a neutral bilayer graphene. Both conductivities are determined within the linear response theory and Green function formalism. The influence of an external voltage between the two atomic sheets is also included. We found transition from the topological spin Hall insulator phase at low voltages to conventional insulator phase at larger voltages.

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Theory of Spin Hall Effects in Semiconductors

Cited by 95 publications

References 124 publications

Intrinsic spin current for an arbitrary Hamiltonian and scattering potential

Intrinsic spin current for an arbitrary Hamiltonian and scattering potential

Restrictions on modeling spin injection by resistor networks

Intrinsic contribution to spin Hall and spin Nernst effects in a bilayer graphene

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