Vector potential and surface magnetic field in magnetoelectric antiferromagnetic materials
A general formula for the average vector potential of bulk periodic systems is proposed and shown to set the boundary conditions at magnetic interfaces. Here, for antiferromagnetic materials, the study reveals a unique relation between the macroscopic potential and the orientation-dependent magnetic quadrupole as a result of the different crystalline and magnetic symmetries. In particular, at surfaces and interfaces of a truncated bulk without inversion and time-reversal symmetries, the average vector potential exhibits a discontinuity which results in an interfacial magnetic field. In general, however, due to the surface and interface electronic and atomic relaxations, additional magnetization may result. For the experimentally observed magnetoelectric antiferromagnets, in particular, our symmetry analysis suggests that the relaxation effects could well be a system response to the presence of such a potential discontinuity.