We show here that antiferromagnetic crystals, and crystals with expect
ed simultaneous ferroelectric and antiferromagnetic or antiferroelectr
ic 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 nonreciprocity from this theorem, it is
demonstrated which crystals have nonreciprocal behavior based upon the
magnetoelectric effect and which crystals may be expected to show non
reciprocal behavior based upon the magnetoelectric effect.