Predicted Signatures of the Intrinsic Spin Hall Effect in Closed Systems

Valín-Rodríguez, Manuel

doi:10.1103/physrevlett.107.266801

Cited by 3 publications

(4 citation statements)

References 43 publications

(73 reference statements)

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“…It has been shown that, in the generic k-linear system, the effective coupling between spin z component s z and orbital angular momentum L z is given by (−2m/ 4 )det( β)s z L z [26,27]. When det( β) = 0, the effective coupling between spin and orbital angular momentums in the z component vanishes; thus, both conventional and spin torque currents must be zero.…”

Section: Berry Phase Inmentioning

confidence: 99%

“…The physical meaning of the topological number det( β)/|det( β)| = ±1 is as follows. It has been shown that det( β) governs the effective coupling 2 of s z and L z via det( β)s z L z [26,27] and, thus, represents the orbital chirality of the spin s z . When det( β)/|det( β)| changes from +1 to −1, the current carrying +s z changes orbital chirality from L z to −L z , and −s z changes orbital chirality from −L z to +L z .…”

Section: Berry Phase Inmentioning

confidence: 99%

“…However, it is interesting to evaluate each integral in Eq. (26). The integral can be performed by using the residue method to the two poles λ 1 = (β xx + β yy ) + i(β yx − β xy ) and λ 2 = (β xx − β yy ) + i(β yx + β xy ), and the result is given by …”

Section: Berry Phase and Spin Currentmentioning

confidence: 99%

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Spin-torque current induced by topological Berry phase in a two-dimensional system with generick-linear spin-orbit interaction

Chen

2014

Phys. Rev. B

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The Berry phase on the Fermi surface and its influence on the conserved spin current in a twodimensional system with generic k-linear spin-orbit interaction are investigated. We calculate the response of the effective conserved spin current to the applied electric field, which is composed of conventional and spin torque currents, by using the Kubo formula. We find that the conventional spin current is not determined by the Berry phase effect. Remarkably, the spin torque Hall current is found to be proportional to the Berry phase, and the longitudinal spin torque current vanishes because of the Berry phase effect. When the k-linear spin-orbit interaction dominates the system, the Berry phase on the Fermi surface maintains two invariant properties. One is that the magnitude of the spin torque current protected by the Berry phase is unchanged by a small fluctuation of energy dispersion. The other one is that the change in the direction of the applied electric field does not change the magnitude of the spin torque current even if the energy dispersion is not spherically symmetric; i.e., the Berry phase effect has no dependence on the two-dimensional material orientation. The spin torque current is a universal value for all k-linear systems, such as Rashba, Dresselhaus, and Rashba-Dresselhaus systems. The topological number attributed to the Berry phase on the Fermi surface represents the phase of the orbital chirality of spin in the k-linear system. The change in the topological number results in a phase transition in which the orbital chirality of spin sz and −sz is exchanged. We found that the spin torque current can be experimentally measured.

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Section: Berry Phase Inmentioning

confidence: 99%

Section: Berry Phase Inmentioning

confidence: 99%

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Spin-torque current induced by topological Berry phase in a two-dimensional system with generick-linear spin-orbit interaction

Chen

2014

Phys. Rev. B

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“…We neglect effects of order α 2 R such as interfaceinduced magnetic anisotropy, contributions to Gilbert damping [25,26], and to the nonadiabaticity parameter [27]. We introduce the unitary transformation [28,29]…”

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confidence: 99%

Chirality from Interfacial Spin-Orbit Coupling Effects in Magnetic Bilayers

et al. 2013

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As nanomagnetic devices scale to smaller sizes, spin-orbit coupling due to the broken structural inversion symmetry at interfaces becomes increasingly important. Here, we study interfacial spin-orbit coupling effects in magnetic bilayers using a simple Rashba model. The spin-orbit coupling introduces chirality into the behavior of the electrons and through them into the energetics of the magnetization. In the derived form of the magnetization dynamics, all of the contributions that are linear in the spin-orbit coupling follow from this chirality, considerably simplifying the analysis. For these systems, an important consequence is a correlation between the Dzyaloshinskii-Moriya interaction and the spin-orbit torque. We use this correlation to analyze recent experiments.

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Maximum intrinsic spin-Hall conductivity in two-dimensional systems withk-linear spin–orbit interaction

Chen¹

2013

J. Phys.: Condens. Matter

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We analytically calculate the intrinsic spin-Hall conductivity (ISHC) (σ z xy and σ z yx ) in a clean, two-dimensional system with generic k-linear spin-orbit interaction. The coefficients of the product of the momentum and spin components form a spin-orbit matrix β. We find that the determinant of the spin-orbit matrix det β describes the effective coupling of the spin sz and orbital motion Lz. The decoupling of spin and orbital motion results in a sign change of the ISHC and the band-overlapping phenomenon. Furthermore, we show that the ISHC is in general unsymmetrical (σ z xy = −σ z yx ), and it is governed by the asymmetric response function ∆ β, which is the difference in band-splitting along two directions: those of the applied electric field and the spin-Hall current. The obtained non-vanishing asymmetric response function also implies that the ISHC can be larger than e/8π, but has an upper bound value of e/4π. We will that the unsymmetrical properties of the ISHC can also be deduced from the manifestation of the Berry curvature at the nearly degenerate area. On the other hand, by investigating the equilibrium spin current, we find that det β determines the field strength of the SU(2) non-Abelian gauge field.

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Predicted Signatures of the Intrinsic Spin Hall Effect in Closed Systems

Cited by 3 publications

References 43 publications

Spin-torque current induced by topological Berry phase in a two-dimensional system with generick-linear spin-orbit interaction

Spin-torque current induced by topological Berry phase in a two-dimensional system with generick-linear spin-orbit interaction

Chirality from Interfacial Spin-Orbit Coupling Effects in Magnetic Bilayers

Maximum intrinsic spin-Hall conductivity in two-dimensional systems withk-linear spin–orbit interaction

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