Landau theory of domain wall magnetoelectricity

We calculate the exact analytical solution to the domain wall properties in a generic multiferroic system with two order parameters that are coupled biquadratically. This is then adapted to the case of a magnetoelectric multiferroic material such as BiFeO₃, with a view to examine critically whether the domain walls can account for the enhancement of magnetization reported for thin films of this material, in view of the correlation between increasing magnetization and increasing volume fraction of domain walls as films become thinner. The present analysis can be generalized to describe a class of magnetoelectric devices based on domain walls rather than bulk properties.