Spin configuration of magnetic multi-layers: effect of exchange, dipolar and Dzyalozhinski-Moriya interactions

We investigate the effect of coupling (intensity and nature), applied field, and anisotropy on the spin dynamics of a multi-layer system composed of a hard magnetic layer coupled to a soft magnetic layer through a nonmagnetic spacer. The soft layer is modeled as a stack of several atomic planes while the hard layer, of a different material, is either considered as a pinned macroscopic magnetic moment or again as a stack of atomic planes. We compute the magnetization profile and hysteresis loop of the whole multi-layer system by solving the Landau-Lifshitz equations for the net magnetic moment of each (atomic) plane. We study the competition between the intra-layer anisotropy and exchange interaction, applied magnetic field, and the interface exchange, dipolar or Dzyalozhinski-Moriya interaction. Compared with the exchange coupling, the latter two couplings present peculiar features in the magnetization profile and hysteresis loop that may help identify the nature of the interface coupling in multi-layer magnetic systems.