Spin torque and charge resistance of ferromagnetic semiconductor $2\pi$ and $\pi$ domain walls

Charge resistance and spin torque are generated by coherent carrier transport through ferromagnetic $2\pi$ domain walls, but with qualitatively different trends than for $\pi$ walls. We calculate charge and spin transport and torque for $\pi$ and $2\pi$ domain walls in a ferromagnetic semiconductor. Under coherent transport conditions, analytic solutions for spin-dependent transmission and reflection coefficients are possible [1,2]. The $2\pi$ wall resistance has a maximum at an intermediate wall width; the $\pi$ wall resistance monotonically decreases with width. The spin torque on a $\pi$ wall is highly nonlinear and insensitive to width, except for very thin walls. In $2\pi$ walls, large nonlinear spin torque is generated over a range of intermediate wall widths, but vanishes for very thin and very thick walls. We find the peak domain wall velocity is larger for a $2\pi$ wall than a $\pi$ wall, suggesting unexpected nonlinearities in magnetoelectronic devices incorporating domain wall motion.\\[4pt] [1] P. Levy and S. Zhang, PRL 79, 5110 (1997)\\[0pt] [2] G. Vignale and M. E. Flatt\'e, PRL 89, 098302 (2002)