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

The bound dynamics of two 180 degrees domain walls with the same polarity and opposite topological charges is investigated theoretically in a biaxial ferromagnet with a large quality factor. The domain walls moving towards each other under the influence of an external magnetic field are considered taking dissipation into account. The case of a large size ferromagnet under small external magnetic field and attenuation has been studied. An inhomogeneous exchange interaction, uniaxial and rhombic anisotropy are taken into account in the magnetic energy density. A soliton model with one spatial coordinate, 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 the differential equations shows a strong dependence of the interaction of walls in the magnetic field on the attenuation. It was found that during 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 of the opposite direction, same polarity 180-degree domain walls, while moving, come at the minimum distance and then repel each other and move away from each other.