Domain wall depinning in hard-soft composites

We study the optimization of the energy product of nanocomposites of hard magnetic material with soft magnetic material. In bulk magnets, nucleation centers exist on surfaces and along grain boundaries. The coercive field of the composite may not be the intrinsic coherent rotation nucleation field Hₙ but may be the depinning field Hd of domain walls. We study Hd as well as Hₙ by finite-temperature Monte Carlo simulation for a model of the composites. The dependence of Hd on the amount of the soft phase is different from that of Hₙ. As the amount of the soft material is increased, the depinning field increases, exhibits a maximum, and then decreases whereas Hₙ always decreases. Hd is much smaller than Hₙ. The optimum design parameters and the optimum energy product are different in the two cases.