Landau Theory of Ferroelectric Domain Walls in Magnetoelectrics

V. Janovec and J. Privratska developed [Ferroelectrics 204, 321 (1997)] a group theoretical model for the existence of pyromagnetism (or pyroelectricity) within the domain walls of an antiferromagnet (or antiferroelectric). However, their approach did not permit any estimate of magnitudes, or even whether it would be observable. In the present work we extend the Janovec-Privratska theory to an analytic model of magnitudes (local magnetization and polarization) within the domain-walls and discuss the wall thickness and domain widths as a function of those magnitudes. Specifically, it is shown that both the wall thickness and the domain width of magnetoelectric multiferroics are bigger than for pure ferroelectrics and smaller than for pure ferromagnets. It is also shown how ferroelectric domain walls in magnetoelectric materials may have net magnetization even when the domains themselves are still paramagnetic. Possible implications for magnetoelectric BiFeO3 are indicated.