The ballistic magnetoresistance of a geometrically confined 180◦ head-to-head domain wall at a magnetic point contact in a two-dimensional (2D) metallic nanowire is studied theoretically using the multichannel LandauerButtiker formalism. The 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 a new algorithm to solve the coupled spin channels Schrodinger ¨ equations with mixed Dirichlet-Neumann boundary conditions applied far from the domain wall. The conductance and thermally averaged magnetoresistance of the domain wall are computed to evaluate the performance of the proposed algorithm. As expected, an oscillatory behavior with successively decreasing extrema is achieved in the magnetoresistance by increasing the domain wall width.
