Role of spin diffusion in current-induced domain wall motion for disordered ferromagnets

Abstract

Current-induced spin transfer torque and magnetization dynamics in the presence of spin diffusion in disordered magnetic textures is studied theoretically. We demonstrate using tight-binding calculations that weak, spin-conserving impurity scattering dramatically enhances the nonadiabaticity. To further explore this mechanism, a phenomenological drift-diffusion model for incoherent spin transport is investigated. We show that incoherent spin diffusion indeed produces an additional spatially dependent torque of the form $\ensuremath{\sim}{\ensuremath{\nabla}}^{2}[\mathbf{m}\ifmmode\times\else\texttimes\fi{}(\mathbf{u}\ifmmode\cdot\else\textperiodcentered\fi{}\ensuremath{\nabla})\mathbf{m}]+\ensuremath{\xi}{\ensuremath{\nabla}}^{2}[(\mathbf{u}\ifmmode\cdot\else\textperiodcentered\fi{}\ensuremath{\nabla})\mathbf{m}]$, where $\mathbf{m}$ is the local magnetization direction, $\mathbf{u}$ is the direction of injected current, and $\ensuremath{\xi}$ is a parameter characterizing the spin dynamics (precession, dephasing, and spin-flip). This torque, which scales as the inverse square of the domain wall width, only weakly enhances the longitudinal velocity of a transverse domain wall but significantly enhances the transverse velocity of vortex walls. The spatial-dependent spin transfer torque uncovered in this study is expected to have significant impact on the current-driven motion of abrupt two-dimensional textures such as vortices, skyrmions, and merons.