Electron transport driven by nonequilibrium magnetic textures

Spin-polarized electron transport driven by inhomogeneous magnetic dynamics is discussed in the limit of a large exchange coupling. Electron spins rigidly following the time-dependent magnetic profile experience spin-dependent fictitious electric and magnetic fields. We show that the electric field acquires important corrections due to spin dephasing, when one relaxes the spin-projection approximation. Furthermore, spin-flip scattering between the spin bands needs to be taken into account in order to calculate voltages and spin accumulations induced by the magnetic dynamics. A phenomenological approach based on the Onsager reciprocity principle is developed, which allows us to capture the effect of spin dephasing and make a connection to the well studied problem of current-driven magnetic dynamics. A number of results that recently appeared in the literature are related and generalized.

Figure 1

(Color online) Two simple scenarios for voltage generation by the magnetic dynamics: (1) Magnetic texture $\mathbf{m}\left(x,t\right)$, such as a domain wall along the $x$ axis, is steadily rotating around the $x$ axis and (2) the same texture rigidly sliding along the $x$ axis. In the former case, the force $F_x$ acting on electrons is proportional to the frequency of rotation $\omega$, with the dominant term having a purely geometric meaning in terms of the position-dependent Berry-phase accumulation rate. (An alternative physical explanation can also be provided by transforming to the rotating frame of reference and applying the Larmor theorem.) In the case of the sliding dynamics, the leading contribution to the magnetically induced force is proportional to the spin-dephasing rate (parametrized by $\beta$) and the “curvature” of the texture profile ${\left({\partial }_x\mathbf{m}\right)}^2$.