Role of exchange interaction and spin-orbit coupling in magnetic domain walls in bulk and thin film Fe

We investigate magnetic domain wall structures in bulk Fe and a thin film Fe(110) monolayer with the first principles full-potential linearized augmented plane-wave method including intra-atomic noncollinear magnetism. In the bulk case, the exchange interaction favors the slower variation of the magnetization and the wall width is determined by a competition between the exchange interaction and the magnetic anisotropy arising from the spin-orbit coupling (SOC)-as expected from phenomenological theory. In the thin film, however, the magnetization in the domain wall changes rapidly within a width of 8 Å. This narrow domain wall arises from the exchange interaction while the SOC favors the ferromagnetic state. Importantly, we find that the SOC effects give rise to not only the magnetic anisotropy but also to a breaking of the degeneracy of the Bloch and Ńel walls, which plays a minor role in the bulk but a major role in the thin film.