Erratum: Spin Hall and Edelstein effects in metallic films: From two to three dimensions [Phys. Rev. B<b>89</b>, 245443 (2014)]

Borge, Juan; Gorini, Cosimo; Vignale, Giovanni; Raimondi, Roberto

doi:10.1103/physrevb.91.239904

Cited by 18 publications

(26 citation statements)

References 2 publications

(6 reference statements)

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“…[17,39]. The opposite limit of a bulk metal with a sharp δ-like Rashba spin-orbit coupling at the interface has also been considered [21,[40][41][42] and recently discussed in great detail [43,44].…”

Section: Introductionmentioning

confidence: 99%

“…The same class of setups is also used to study the reciprocal effect, when spin currents generated in the normal layer enter the magnetic material and exert a torque on its magnetization [13,[15][16][17]. The spin-galvanic effect (SGE) [18,19], which can be related to the ISHE [20,21], represents another channel for spin-to-charge conversion. It is also referred to as the inverse Edelstein effect [22,23] and consists of the generation of a charge current perpendicular to the polarization of a nonequilibrium spin density.…”

Section: Introductionmentioning

confidence: 99%

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Spin-charge coupled dynamics driven by a time-dependent magnetization

2017

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The spin-charge coupled dynamics in a thin, magnetized metallic system are investigated. The effective driving force acting on the charge carriers is generated by a dynamical magnetic texture, which can be induced, e.g., by a magnetic material in contact with a normal-metal system. We consider a general inversion-asymmetric substrate/normal-metal/magnet structure, which, by specifying the precise nature of each layer, can mimic various experimentally employed setups. Inversion symmetry breaking gives rise to an effective Rashba spinorbit interaction. We derive general spin-charge kinetic equations which show that such spin-orbit interaction, together with anisotropic Elliott-Yafet spin relaxation, yields significant corrections to the magnetization-induced dynamics. In particular, we present a consistent treatment of the spin density and spin current contributions to the equations of motion, inter alia, identifying a term in the effective force which appears due to a spin current polarized parallel to the magnetization. This "inverse-spin-filter" contribution depends markedly on the parameter which describes the anisotropy in spin relaxation. To further highlight the physical meaning of the different contributions, the spin-pumping configuration of typical experimental setups is analyzed in detail. In the two-dimensional limit the buildup of dc voltage is dominated by the spin-galvanic (inverse Edelstein) effect. A measuring scheme that could isolate this contribution is discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spin-charge coupled dynamics driven by a time-dependent magnetization

2017

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“…43 The Rashba splitting of surface states is by no means the only important manifestation of SO at a surface. Recently, it has been pointed out that the surface-induced SO coupling can have large effects also on the bulk states of a thin metallic film that is sandwiched between two insulating barriers [44][45][46][47] . The bulk of such a metal is typically inversion-symmetric and its electronic states remain therefore doubly degenerate -at variance with the spin-split bands of the Rashba model.…”

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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“…Moreover, we wish to identify the possible connections between the four phenomena. It is known, for example, that in a 2DEG at low T , the spin Hall and Edelstein effects may be related [22][23][24][25], and that such a relation can be extended to thin (quasi-2D) films as well [26]. Whether a connection exists, possibly in a modified form, also at high T or in 3D is an open question.…”

Section: Introductionmentioning

confidence: 99%

“…Notice that this is complementary to what is done in Refs. [26,40,41], where the Rashba interaction is a δ function different from zero only exactly at the film edges.…”

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confidence: 99%

Room-temperature spin thermoelectrics in metallic films

2014

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Considering metallic films at room temperature, we present the first theoretical study of the spin Nernst and thermal Edelstein effects that takes into account dynamical spin-orbit coupling, i.e., direct spin-orbit coupling with the vibrating lattice (phonons) and impurities. This gives rise to a novel process, namely, a dynamical side-jump mechanism, and to dynamical Elliott-Yafet spin relaxation, never before considered in this context. Both are the high-temperature counterparts of the well-known T = 0 side-jump and Elliott-Yafet, central to the current understanding of the spin Hall, spin Nernst and Edelstein (current-induced spin polarization) effects at low T . We consider the experimentally relevant regime T > T D , with T D the Debye temperature, as the latter is lower than room temperature in transition metals such as Pt, Au and Ta typically employed in spin injection/extraction experiments. We show that the interplay between intrinsic (Bychkov-Rashba type) and extrinsic (dynamical) spin-orbit coupling yields a nonlinear T dependence of the spin Nernst and spin Hall conductivities.

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Erratum: Spin Hall and Edelstein effects in metallic films: From two to three dimensions [Phys. Rev. B89, 245443 (2014)]

Cited by 18 publications

References 2 publications

Spin-charge coupled dynamics driven by a time-dependent magnetization

Spin-charge coupled dynamics driven by a time-dependent magnetization

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

Room-temperature spin thermoelectrics in metallic films

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