  A general formula for the average vector potential of bulk periodic systems
is proposed and shown to set the boundary conditions at magnetic interfaces.
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 suggest
that the relaxation effects could well be a system response to the presence of
such a potential discontinuity.

Materials Science;Mesoscale and Nanoscale Physics