Spin currents, spin-transfer torque, and spin-Hall effects in relativistic quantum mechanics

Vernes, A.; Györffy, B. L.; Weinberger, P.

doi:10.1103/physrevb.76.012408

Cited by 59 publications

(80 citation statements)

References 15 publications

(11 reference statements)

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“…The operatorÂ ν representing in all three cases the perturbation is the electric current density operatorĵ ν = −|e|cα ν . For the calculations of the anomalous Hall conductivity one has for the responseB =Â, for the spin Hall conductivityB =PÂ with the relativistic spin-polarization operatorP [25,26], while for the calculations of the spin-orbit torkances t µν the torque operatorB µ =T µ has to be used. Additional calculations for the Fermi sea torkance have been performed following the relationship between this quantity and the DMI parameters as suggested by Freimuth et al [14].…”

Section: Theoretical Detailsmentioning

confidence: 99%

Composition-dependent magnetic response properties of Mn1−xFexGe alloys

et al. 2018

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The composition-dependent behavior of the Dzyaloshinskii-Moriya interaction (DMI), the spinorbit torque (SOT), as well as anomalous and spin Hall conductivities of Mn1−xFexGe alloys have been investigated by first-principles calculations using the relativistic multiple scattering KorringaKohn-Rostoker (KKR) formalism. The Dxx component of the DMI exhibits a strong dependence on the Fe concentration, changing sign at x ≈ 0.85 in line with previous theoretical calculations as well as with experimental results demonstrating the change of spin helicity at x ≈ 0.8. A corresponding behavior with a sign change at x ≈ 0.5 is predicted also for the Fermi sea contribution to the SOT, as this is closely related to the DMI. In the case of anomalous and spin Hall effects it is shown that the calculated Fermi sea contributions are rather small and the composition-dependent behavior of these effects are determined mainly by the electronic states at the Fermi level. The spin-orbitinduced scattering mechanisms responsible for both these effects suggest a common origin of the minimum of the AHE and the sign change of the SHE conductivities.

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Section: Theoretical Detailsmentioning

confidence: 99%

Composition-dependent magnetic response properties of Mn1−xFexGe alloys

et al. 2018

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“…As pointed out by several authors [16,17], a central issue for such an approach is an adequate definition for the spin-current density operator that accounts for SOC. This was supplied recently by Vernes et al [18] by starting from the Bargmann-Wigner four-vector spin polarization operator T [19]. Demanding that the spin polarization is connected with the spin-current density via a corresponding continuity equation an explicit expression for the spin-current operator was given.…”

mentioning

confidence: 99%

“…The response function to be considered for the SHE is the spin-current density. Considering for the z component of the spin polarization vector the current density along the x direction the corresponding operator is given by [18,21,22]…”

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confidence: 99%

Extrinsic and Intrinsic Contributions to the Spin Hall Effect of Alloys

Lowitzer¹,

et al. 2011

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A fully relativistic description of the spin-orbit induced spin Hall effect is presented that is based on Kubo's linear response formalism. Using an appropriate operator for the spin-current density a KuboStředa-like equation for the spin Hall conductivity (SHC) is obtained. An implementation using the Korringa-Kohn-Rostoker band structure method in combination with the coherent potential approximation allow detailed investigations on various alloy systems. A decomposition of the SHC into intrinsic and extrinsic contributions is suggested. Accompanying calculations for the skew-scattering contribution of the SHC using the Boltzmann equation demonstrate the equivalence to the Kubo formalism in the dilute alloy regime and support the suggested decomposition scheme. DOI: 10.1103/PhysRevLett.106.056601 PACS numbers: 72.25.Ba, 71.15.Rf, 75.76.+j, 85.75.Àd The emerging research field of spintronics has developed very rapidly during recent years. The reason for the broad interest in this field is based on the close connection to fundamental scientific questions as well as its impact on technology [1,2]. In this context, the spin Hall effect (SHE) is one of the most promising phenomena. It denotes the observation that a charge current flowing through a solid is accompanied by a transversal spin current. This occurs even for nonmagnetic solids as was demonstrated by experiments on pure Pt [3].Both the anomalous Hall effect (AHE) in ferromagnets and the SHE are caused by the influence of spin-orbit coupling (SOC). Accordingly, their theoretical description is quite similar [4][5][6][7][8][9][10][11][12][13][14][15]. For ideal systems an intrinsic mechanism was identified which allows the expression of the corresponding response function in terms of the Berry curvature [5,7]. On this basis, ab initio calculations for the intrinsic spin Hall conductivity (SHC) were performed [8][9][10][11]. As for the AHE, the additional extrinsic SHC in dilute and concentrated alloys is ascribed to skew and sidejump scattering caused by SOC. The role of these mechanisms for the SHE has been studied so far primarily by model calculations [12,13]. First principle calculations for the extrinsic SHC of dilute alloys on the basis of the Boltzmann formalism that account for the skew-scattering mechanism have been performed only very recently [14,15]. However, a complete description of intrinsic and extrinsic mechanisms giving rise to the SHE applicable to ideal as well as alloy systems, as it is presented below, was missing so far. As pointed out by several authors [16,17], a central issue for such an approach is an adequate definition for the spin-current density operator that accounts for SOC. This was supplied recently by Vernes et al. [18] by starting from the Bargmann-Wigner four-vector spin polarization operator T [19]. Demanding that the spin polarization is connected with the spin-current density via a corresponding continuity equation an explicit expression for the spin-current operator was given.An adequate formal basis for the di...

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“…An interesting area arised from some aspects due to the spin, called spintronic, is showing the important role played by the spin of charged particles [1]. As accelerators get improved, we became able to investigate more and more properties of elementary particles.…”

Section: Introductionmentioning

confidence: 99%

The Gyromagnetic Factor of Elementary Particles and Non-Minimal Coupling

Morais¹,

Accioly²,

Helayël-Neto³

et al. 2009

Proceedings of 5th International School on Field Theory and Gravitation — PoS(ISFTG)

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In this work we investigate a possible magnetic moment generation for massive neutral particles with spins-1 and -2 coupled non-minimally, in a specific way, to an external electromagnetic field. It is found that, in the nonrelativistic limit, these particles present g = 1. This result, worked out in the framework of Relativistic Quantum Mechanics, seems to suggest that g = 1 for all massive and neutral particles of any spin ≤ 2. We also compare with the results obtained for massive charged particles of spins-1 and -2, in the same regime (nonrelativistic), in order to investigate the role played by the spin separetely from the charge.

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Spin currents, spin-transfer torque, and spin-Hall effects in relativistic quantum mechanics

Cited by 59 publications

References 15 publications

Composition-dependent magnetic response properties of Mn1−xFexGe alloys

Composition-dependent magnetic response properties of Mn1−xFexGe alloys

Extrinsic and Intrinsic Contributions to the Spin Hall Effect of Alloys

The Gyromagnetic Factor of Elementary Particles and Non-Minimal Coupling

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