Walker breakdown of Brownian domain wall dynamics

The Brownian motion of domain walls in uniaxial and biaxial ferromagnetic nanowires is studied, comparing spin dynamics simulations with analytical calculations within the framework of a collective coordinate approach. Our results demonstrate that the interplay between spatial and angular dynamics gives rise to a complex time dependence of the MSD in biaxial nanowires and to a drastically reduced diffusion coefficient in uniaxial nanowires, analogous to magnetic skyrmions. This diffusion suppression is also responsible for the peculiar temperature dependence of the diffusion coefficient in biaxial systems: while it is found to scale linearly with temperature up to a certain threshold, the emergence of a Walker breakdown of Brownian motion is responsible for a reduction of the diffusion coefficient with increasing temperature above this threshold.publishe