Inclusion of surface anisotropy in the micromagnetic analysis of exchange-coupled hard/soft bilayers

The effects of surface anisotropy and interface anisotropy in soft and hard layers have been considered in the frame of a previously developed micromagnetic continuum model for the study of demagnetization processes in exchange-coupled bi- and multi-layers of soft/hard-type with planar and perpendicular anisotropy, in order to extend and generalize it. In particular, fields applied along the easy direction and strong interface ferromagnetic coupling have been considered. The theoretical results have been applied to a bilayer with perpendicular anisotropy in the hard layer and positive perpendicular surface anisotropy in the soft layer, in order to compare them with those obtained by considering the equivalent volume anisotropy in the soft layer. Moreover, the separate effects of positive perpendicular surface and interface anisotropies in the bilayer have been compared. We have deduced the nucleation field equation and obtained plots of the nucleation field as a function of the soft layer thickness and of the surface and interface anisotropies. Demagnetization curves have been also calculated. The nucleation process can be reversible (exchange-spring (ES) regime) or irreversible (rigid magnet (RM) regime) depending on magnetic and geometrical parameters. The critical equation, which allows determining the boundary between RM and ES regions, has been deduced. Corresponding phase diagrams in the plane of soft and hard layer thickness have been obtained as a function of surface and interface anisotropies.