The bound dynamics of the same polarity 180-degree domain walls in biaxial ferromagnets

The bound dynamics of two same polarity 180° domain walls with the opposite topological charges in a biaxial ferromagnet with a large quality factor is theoretically investigated. The domain walls moving towards each other under the influence of an external magnetic field with regard to dissipation are considered. The case of a large size ferromagnet with small external magnetic fields and attenuations has been studied. An inhomogeneous exchange interaction, uniaxial and rhombic anisotropy are taken into account in the magnetic energy density. A one-dimensional in coordinates soliton model in which the interacting domain walls are regarded as a two-soliton solution is used. A system of ordinary differential equations describing the evolution of the soliton solution parameters under the influence of the magnetic field and attenuation is obtained. The numerical study of differential equations shows a strong dependence of walls interaction in the magnetic field on the attenuation. It was found that on the interaction of two 180-degree walls of the same polarity at a low attenuation and specific direction of the external magnetic field there occurs an annihilation of the walls, accompanied by multiple scattering process and the walls polarity change. With the increase of the attenuation parameter the annihilation of soliton-antisoliton pair happens as a result of a single scattering process. In the case of the field opposite direction same polarity 180-degree domain walls while moving come close at the minimum distance, and then the repulsion and subsequent divergence from each other occur.