Extended s-d model for magnetization dynamics of strongly noncollinear configurations

In the conventional s-d model of magnetization dynamics, it is assumed that for an adiabatic situation the s magnetization is ferromagnetically aligned to the d magnetization. For configurations with strong noncollinearity in the d magnetization, this no longer holds true for all cases. In the present paper it is shown that, as a consequence of this noncollinearity between the adiabatic s and d magnetizations, there arise several additional torques in the micromagnetic equation of motion for the d magnetization. The equation is solved for a Neel wall driven by an external field and/or a spin-polarized current, yielding a correction term to the result of the conventional theory. By calculations with the ab initio density-functional electron theory, the magnitude of the correction term is estimated. It is concluded that for 3d metals the effects of the additional torques are very small except possibly for atomic-scale noncollinearities or for the long-term trajectories of complicated magnetization configurations.