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 H_n but may be the depinning field H_d of domain walls. We study H_d as well as H_n by finite-temperature Monte Carlo simulation for a model of the composites. The dependence of H_d on the amount of the soft phase is different from that of H_n. As the amount of the soft material is increased, the depinning field increases, exhibits a maximum, and then decreases whereas H_n always decreases. H_d is much smaller than H_n. The optimum design parameters and the optimum energy product are different in the two cases.