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Magnetoelectric phenomena are intimately linked to relativistic effects and also require the material to break spatial inversion symmetry and time-reversal invariance. Magnetoelectric coupling can substantially affect light–matter interaction and lead to non-reciprocal light propagation. Here, we confirm on a fully experimental basis, without invoking either symmetry-based or material-specific assumptions, that the optical magnetoelectric effect in materials with non-parallel magnetization ( M ) and electric polarization ( P ) generates a trilinear term in the refractive index,  δ  n  ∝  k  ⋅ ( P  ×  M ), where  k  is the propagation vector of light. Its sharp magnetoelectric resonances in the terahertz regime, which are simultaneously electric and magnetic dipole active excitations, make Co 2 Mo 3 O 8  an ideal compound to demonstrate this fundamental relation via independent variation of  M ,  P , and  k . Remarkably, the material shows almost perfect one-way transparency in moderate magnetic fields for one of these magnetoelectric resonances.

Confirming the trilinear form of the optical magnetoelectric effect in the polar honeycomb antiferromagnet Co2Mo3O8