Extensions to the Maxwell boundary conditions: Reflection from uniaxial and cubic antiferromagnets

Standard Maxwell boundary conditions do not always apply at the surface of an anisotropic magnetic medium in a vacuum, even when the $\mathbf{D}$ and $\mathbf{H}$ fields that describe the properties of the medium are taken in covariant form. It is shown that discontinuities may arise in these fields due to bound surface current and electric-dipole moment, and the leading multipole forms of these discontinuities are identified. Reflection matrices for normal incidence are derived for all uniaxial and cubic antiferromagnetic crystals. These matrices satisfy reciprocity (time-reversal symmetry) only when the extended boundary conditions are used. Various magnetic point groups are identified that exhibit nonreciprocal effects in reflection, but not in transmission. It is also shown that when nonreciprocal birefringence exists in transmission, nonreciprocal effects are absent in reflection at normal incidence. The magnetic point-group symmetry assigned to ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$ is questioned on the basis of the theory.