Relaxation process of magnetic friction under sudden changes in velocity

Although there have been many studies of statistical mechanical models of magnetic friction, most of these have focused on the behavior in the steady state. In this study, we prepare a system composed of a chain and a lattice of Ising spins that interact with each other, and investigate the relaxation of the system when the relative velocity $v$ changes suddenly. The situation where $v$ is given is realized by attaching the chain to a spring, the other end of which moves with a constant velocity $v$. Numerical simulation finds that, when the spring constant has a moderate value, the relaxation of the frictional force is divided into two processes, which are a sudden change and a slow relaxation. This behavior is also observed on regular solid surfaces, although caused by different factors than our model. More specifically, the slow relaxation process is caused by relaxation of the magnetic structure in our model, but is caused by creep deformation in regular solid surfaces.