Boundary conditions for spin diffusion in disordered systems

Galitski, Victor; Burkov, A. A.; Sarma, S. Das

doi:10.1103/physrevb.74.115331

Cited by 58 publications

(76 citation statements)

References 26 publications

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“…And even if we have the one, there still remains a problem whether the spin current actually corresponds to the observable physical quantity or not. 146,152,153) The most concrete and reliable way is to capture the experimental situation appropriately, and then calculate the corresponding observable physical quantities, such as the magnetization or the electric voltage. Nevertheless, the natural and simple definition as j µ ν ≡ 1 2 v ν , s µ will give a first brief idea for the SHE.…”

Section: Discussionmentioning

confidence: 99%

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

2015

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Bismuth crystal is known for its remarkable properties resulting from particular electronic states, e. g., the Shubnikovde Haas effect and the de Haas-van Alphen effect. Above all, the large diamagnetism of bismuth had been a long-standing puzzle soon after the establishment of quantum mechanics, which had been resolved eventually in 1970 based on the effective Hamiltonian derived by Wolff as due to the interband effects of a magnetic field in the presence of a large spin-orbit interaction. This Hamiltonian is essentially the same as the Dirac Hamiltonian, but with spatial anisotropy and an effective velocity much smaller than the light velocity. This paper reviews recent progress in the theoretical understanding of transport and optical properties, such as the weak-field Hall effect together with the spin Hall effect, and ac conductivity, of a system described by the Wolff Hamiltonian and its isotropic version with a special interest of exploring possible relationship with orbital magnetism. It is shown that there exist a fundamental relationship between spin Hall conductivity and orbital susceptibility in the insulating state on one hand, and the possibility of fully spinpolarized electric current in magneto-optics. Experimental tests of these interesting features have been proposed.

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Section: Discussionmentioning

confidence: 99%

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

2015

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“…Physical phenomena in which an electric current is converted into a spin polarization and/or a spin current, are receiving a great deal of attention in the context of orbital spintronics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] -an appealing alternative to "classical" spintronics [18][19][20][21][22] . While in classical spintronics the spin dynamics is mainly controlled by exchange interactions, in orbital spintronics the central role is played by the spin-orbit (SO) interaction, which allows direct manipulation of the spins by electric fields.…”

Section: Introductionmentioning

confidence: 99%

Current-induced spin polarization at the surface of metallic films: A theorem and anab initiocalculation

2015

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The broken inversion symmetry at the surface of a metallic film (or, more generally, at the interface between a metallic film and a different metallic or insulating material) greatly amplifies the influence of the spin-orbit interaction on the surface properties. The best known manifestation of this effect is the momentum-dependent splitting of the surface state energies (Rashba effect). Here we show that the same interaction also generates a spin-polarization of the bulk states when an electric current is driven through the bulk of the film. For a semi-infinite jellium model, which is representative of metals with a closed Fermi surface, we prove as a theorem that, regardless of the shape of the confinement potential, the induced surface spin density at each surface is given by S = −γ ẑ × j, where j is the particle current density in the bulk,ẑ the unit vector normal to the surface, and γ = 4mc 2 contains only fundamental constants. For a general metallic solid γ becomes a material-specific parameter that controls the strength of the interfacial spin-orbit coupling. Our theorem, combined with an ab initio calculation of the spin polarization of the current-carrying film, enables a determination of γ, which should be useful in modeling the spin-dependent scattering of quasiparticles at the interface.

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“…The second one requires that the perpendicular SC is dephased in the FM on a length scale that is much smaller than the mean free path. The third condition, i.e., continuity of the SA in the magnetization direction, has been useful for purposes of illustration before [28,29], but does not hold for general interfaces [30].…”

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confidence: 99%

Detection of Current-Induced Spins by Ferromagnetic Contacts

2006

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Detection of current-induced spin accumulation via ferromagnetic contacts is discussed. Onsager's relations forbid that in a two-probe configuration, spins excited by currents in time-reversal symmetric systems can be detected by switching the magnetization of a ferromangetic detector contact. Nevertheless, current-induced spins can be transferred as a torque to a contact magnetization and can affect the charge currents in many-terminal configurations. We demonstrate the general concepts by solving the microscopic transport equations for the diffuse Rashba system with magnetic contacts. DOI: 10.1103/PhysRevLett.97.256601 PACS numbers: 72.25.Dc, 72.20.Dp, 72.25.Mk The notion that netto spin distributions can be generated by electric currents in the bulk of nonmagnetic semiconductors with intrinsic spin-orbit (SO) interaction has been predicted [1,2] and experimentally confirmed [3]. The related spin-Hall effect, causing accumulations of spins at the edges, has also been observed [4]. It can be extrinsic, i.e., caused by impurities with SO scattering [5,6] or intrinsic due to an SO split band structure [7,8]. However, all experiments to date detected the current-induced spins optically [16]. An important remaining challenge for theory and experiment is to find ways to transform the novel spin accumulation (SA) and spin currents (SCs) into voltage differences and charge currents in micro-or nanoelectronic circuits in order to fulfill the promises of spintronics.In this Letter, we address the possibility to generate a spin-related signal to be picked up by ferromagnetic contacts. This signal can be in the form of a voltage change or a torque acting on the magnetization of the ferromagnet (FM). In practice, this raises technical difficulties due the conductance mismatch [17] that can be solved [18] and are not addressed here. We rather focus on conceptual problems that are related to the voltage and torque signals generated by current-induced spins [19]. The Onsager relations for the conductance [20] forbid voltage based detection of current-induced spins by a ferromagnetic lead in a two-probe setup within linear response. We sketch a microscopic picture of the physics and formulate a semiclassical scheme in the diffuse limit. We address spin detection in a multiprobe geometry, calculate the Hall conductivity, and compare it to the anomalous Hall effect. We also discuss the possibility to construct spin filters not based on FMs, but on conductors with spatially modulated SO interactions.We first address the symmetry properties in terms of the Onsager relations for the (linear) conductance [20 -23]. A generic SO-Hamiltonian H involves products of velocity and spin operators that are invariant under time reversal. Even when spin-degenerate bands are split due to a broken inversion symmetry, the Kramers degeneracy remains intact. The Hamiltonian of the combined SOjF system has the symmetry TH m T ÿ1 H ÿm , where m is a unit vector in the direction of the magnetization of the FM and T the time-reversal operator. We n...

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Boundary conditions for spin diffusion in disordered systems

Cited by 58 publications

References 26 publications

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

Transport Properties and Diamagnetism of Dirac Electrons in Bismuth

Current-induced spin polarization at the surface of metallic films: A theorem and anab initiocalculation

Detection of Current-Induced Spins by Ferromagnetic Contacts

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