Magnetic effects in antiferromagnetic crystals in the electric quadrupole-magnetic dipole approximation

A multipole theory of light propagation in matter is used to describe magnetic effects due to electric quadrupoles and magnetic dipoles induced by light wave fields in non-absorbing antiferromagnetic crystals of the uniaxial and cubic systems. A new effect predicted by the theory is linear birefringence, of electric quadrupole origin, for light travelling along the edge directions in certain cubic crystals. Also predicted in many classes of uniaxial crystal, when propagation is along a crystallographic axis perpendicular to the axis of highest symmetry, is the existence of skew or S-rays. These are characterized by a divergence of the Poynting vector from the wave normal. A previously known effect, non-reciprocal or gyrotropic birefringence, is reconsidered and shown to be a property of media which exhibit Jones birefringence. Furthermore, the theory shows that non-reciprocal birefringence is not in general gyrotropic and that, where effects have previously been described, the results obtained by earlier workers are incomplete owing to the omission of electric quadrupole terms. As a consequence their expressions for physical observables are origin dependent and, in some cases, have led to erroneous conclusions regarding the nature of a physical effect.