Micromagnetic simulations of domain wall depinning forced by oscillating fields

Notches in thin ferromagnetic strips act as pinning centers for the domain walls (DWs) existing in them, due to the locally lowering of the DW magnetostatic energy, that is, the formation of a pinning potential well. The work presents the study of the DW dynamics under the application of an in-plane magnetic field directed along the largest dimension of the strip. The strip has one constriction which consists of a couple of rectangular notches symmetrically placed on it, where a head-to-head DW has been pinned. The applied field is composed of two terms: a constant value plus a harmonically oscillating one. The constant part is fixed to different values lower than the required constant field to force the DW depinning while the amplitude of the harmonic part is investigated in order to produce the DW depinning at different frequencies. A resonant-like behavior can be observed if the frequency of the harmonic field is of the order of magnitude of the DW natural oscillation frequency. However, the resulting DW energy absorption peak is not centered at this natural oscillation frequency. On the contrary, it noticeably shifts to lower frequencies. This behavior is then explained by the increase of the DW exchange energy as it oscillates, and the nonlinearities which are present for large applied fields in the restoring force associated to the presence of the notch.