Flux reversal in hard-soft composite magnets

We analyze the reversal process and calculate the critical fields in the relevant case of a hard bulk enclosing a soft layer of varying thickness. The system behaves like a rigid magnet, an exchange spring magnet or a decoupled magnet in well-defined intervals of the layer thickness. The analysis is performed by considering a one-dimensional micromagnetic model of the hard-soft multilayer magnet. In particular, an analytical expression of the domain wall depinning field is obtained. In the case of the NdFeB/Fe system, the depinning field is about 10% of the hard-phase anisotropy field