Switching of composite media by wall propagation

Using simple scaling arguments, we calculate the external field required to propagate a domain wall from the soft to the hard phase in a composite media. In the absence of the external field the domain-wall energy is lower in the soft phase, resulting in an energy barrier between the hard and soft phases. It is shown that as the external field increases the domain-wall energy in the soft phase also increases, and there is a corresponding wall energy reduction in the hard phase, resulting in the lowering of the energy barrier. The switching field is obtained as the field, which equalizes the domain-wall energies in both phases, reduces the wall barrier to zero, and leads to wall propagation and reversal. The calculation allows identification of field dependent anisotropies and wall widths of the two phases, which become equal at the reversal field. The reversal field is found to linearly depend upon the intrinsic anisotropy difference and inversely on the sum of magnetization of the two phases. Moreover, the reversal field is found to be independent of the volume of the two phases. An attempt at exhaustive comparison with experiments is made.