Spin torques due to diffusive spin current in magnetic texture

Abstract

We present a microscopic theory of spin torque due to diffusive spin currents induced by spin accumulation. The obtained expression is a natural extension of the existing one due to 'local' spin currents associated with ordinary electric currents, and is the reciprocal of the spin motive force which induces charge accumulation as studied recently [J. Shibata and H. Kohno, Phys. Rev. B84, 184408 (2011)]. The result is applied to a domain wall motion in a nonlocal spin injection system, and the torque and force due to diffusive spin current are evaluated.

Domain wall motion in a diffusive weak ferromagnet

“…In particular, due to the spin relaxation both the force and torque are exponentially decaying as functions of the distance of the domain wall from the injector, similar to the case in Ref. 18. We also study the resulting domain wall dynamics, and show that the domain wall motion with decaying force and torque has its characteristic features.…”

“…It was shown that the domain wall motion in this case is also very efficient, in terms of the change of the magnetization at the interface of the ferromagnet where the spin current is absorbed. The force and torque in this structure have also been calculated for a case of weak impurity scattering, 18 but the ensuing domain wall dynamics have not yet been studied theoretically.…”

“…Here we consider a similar structure with the one in Ref. 18, except that the nonmagnetic metal is replaced by a weak ferromagnet containing a domain wall, and a spin polarized current is injected from a strong ferromagnetic electrode. We define the concepts of the "weak" and "strong" ferromagnets based on the size of the spin polarization and the possibility of using the spin diffusion equation to describe the two systems.…”

Microscopic calculation of thermally induced spin-transfer torques

“…Each factor (−iω) −1 in Eqs. (E4) and (E6) reflects conservation of electron number and energy, respectively, and comes from ladder-type vertex correction [45,46]. Therefore, even in the static limit, ω → 0, the B φ and B ψ terms survive in Eqs.…”