Spin waves cause non-linear friction
  Energy dissipation is studied for a hard magnetic tip that scans a soft magnetic substrate. The dynamics of the atomic moments are simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation numerically. The local energy currents are analysed for the case of a Heisenberg spin chain taken as substrate. This leads to an explanation for the velocity dependence of the friction force: The non-linear contribution for high velocities can be attributed to a spin wave front pushed by the tip along the substrate. 
Martin P. Magiera, Lothar Brendel, Dietrich E. Wolf, Ulrich Nowak
cond-mat.other