Extrinsic spin-charge coupling in diffusive superconducting systems

Abstract

We present a theoretical study of diffusive superconducting systems with extrinsic spin-orbit coupling and arbitrarily strong impurity potential. We derive from a microscopic Hamiltonian a diffusion equation for the quasi-classical Green function, and demonstrate that all mechanisms related to the spin-orbit coupling are expressed in terms of three kinetic coefficients: the spin Hall angle, the spin current swapping coefficient, and the spin relaxation rate due to Elliott-Yafet mechanism. The derived diffusion equation contains a hitherto unknown term describing a spinorbit torque that appears exclusively in the superconducting state. As an example, we provide a qualitative description of a magnetic vortex in a superconductor with triplet correlations, and show that the novel term describes a spin torque proportional to the vector product between the spectral angular momentum of the condensate and the triplet vector. Our equation opens up the possibility to explore spintronic effects in superconductors with no counterparts in the normal metallic state. arXiv:1807.07029v2 [cond-mat.supr-con]

Thermal, electric and spin transport in superconductor/ferromagnetic-insulator structures

“…The extension of the formalism to include additional types of interactions and couplings is in principle rather straightforward. For example, one can include magneto-electric effects associated with the charge-spin coupling in systems with linear-in-momentum spin-orbit coupling, by introducing an effective SU(2) gauge potential in the quasiclassical equations [291,292,112], or, in the case of an extrinsic spin-orbit coupling, by taking into account higher-order terms in the impurity potential [113]. Inclusion of such effects in a non-equilibrium situation and with time-dependent fields, is an interesting further development of the field [293].…”

“…One further perspective of the present work is the extension of the Keldysh quasiclassical formalism used in this review to include magneto-electric effects associated with the spin-orbit coupling (SOC) [291,292,112,113,111,293], and the coupling magnetization dynamics to the electronic degrees of freedom via the reciprocal effects of spin transfer torque and spin pumping [227].…”

“…Such effects enter the kinetic equations in a higher order of the gradient expansion and can be neglected in the leading order. The spin-charge coupling in diffusive superconductors leads to non-dissipative magnetoelectric effects and the appearance of an anomalous phase in Josephson junctions, [111,112,113]. The parameters τ sf , β of the spin-dependent scattering are material specific.…”

Giant enhancement to spin battery effect in superconductor/ferromagnetic insulator systems

“…We expect this effect also to explain the giant spin-Hall signal measured in Ref. [34], but its precise description would require appending the theory with the description of the spin-Hall angle [75][76][77].…”

Magnetoelectric effects in superconductors due to spin-orbit scattering: Nonlinear σ -model description

“…The magnetoelectric effects associated with SOC due to extrinsic impurity scattering have been extensively discussed in the normal state [1][2][3], but in the superconducting state have received somewhat less attention [4][5][6] compared to the intrinsic effects [7]. In contrast, the effect of the spinorbit scattering on spin relaxation in superconductors is well-known [8].…”