Electrons in ferromagnets with domain walls

Domain walls can significantly modify electronic properties of ferromagnetic metals. In this paper we consider theoretically the influence of domain walls on transport properties of ferromagnetic materials and the results are compared with recent experiments. In the case of diffusive transport through a thick domain wall, the semiclassical approximation is applied and a local spin transformation is performed, which replaces the system with a domain wall by the corresponding system without a domain wall but with an additional gauge field. Due to a redistribution of single-particle electron states at the wall, one obtains then either negative or positive contributions to resistivity. The situation is different for very narrow and/or constrained domain walls. In such a case, the semiclassical approximation is not valid. Instead of this the approach based on scattering matrix is applied. The domain wall then gives rise to a large positive contribution to electrical resistivity. The corresponding magnetoresistance can be therefore very large, which is in agreement with recent experiments. The limiting case of narrow domain walls in systems with a single conduction channel is analysed in detail, with the effects due to electron-electron interaction taken into account. In this particular case the magnetoresistance due to a domain wall can be extremely large