Nonreciprocity in magnetoelectric crystals

We show here that antiferromagnetic crystals, and crystals with expected simultaneous ferroelectric and antiferromagnetic or antiferroelectric and antiferromagnetic properties, which display the magnetoelectric effect, will possess the fundamental property of nonreciprocity based solely upon this effect when exposed to electromagnetic waves. Proof is presented of this phenomenon by enlisting the anisotropic reaction theorem. Defining measures of reciprocity from this theorem, it is demonstrated which crystals have nonreciprocal behavior based upon the magnetoelectric effect and which crystals may be expected to show nonreciprocal behavior based upon the magnetoelectric effect