Voltage drop due to longitudinal spin accumulation across the ballistic domain wall

The ballistic magnetoresistance (MR) of a domain wall constricted in a nanocontact between two $p$-type semiconducting magnetic nanowires is studied theoretically using the Landauer-B\"uttiker approach. Our analysis is based on coherent scattering of the carriers by the spin-dependent potential associated with the wall structure. The transmission properties of coherent states are obtained by introducing an algorithm to solve the coupled spin channels Schr\"odinger equation with mixed Dirichlet-Neumann boundary conditions applied far from the domain wall. Then, the local accumulated spin densities along the nanowire produced by electrical spin injection at the nanocontact are numerically calculated. It is demonstrated that the induced voltage drop due to the longitudinal spin accumulation considerably increases in the case of the narrow domain walls. Furthermore, it is shown that two spin accumulation and mistracking effects give approximately equal contributions to the wall MR ratio in the limit of the sharp domain walls. However, the MR ratio is dominantly determined by the spin accumulation effect as the domain wall width increases.