Confirming the trilinear form of the optical magnetoelectric effect in the polar honeycomb antiferromagnet Co$_{2}$Mo$_3$O$_8$

TL;DR

This study experimentally confirms that the optical magnetoelectric effect in Co$_{2}$Mo$_3$O$_8$ produces a trilinear term in the refractive index, demonstrating fundamental relations and potential for one-way light transparency.

Contribution

It provides the first direct experimental verification of the trilinear form of the optical magnetoelectric effect in a polar honeycomb antiferromagnet without relying on symmetry or material assumptions.

Findings

Confirmed the trilinear form of the optical magnetoelectric effect.

Observed almost perfect one-way transparency at certain resonances.

Demonstrated independent control of magnetization, polarization, and light propagation vector.

Abstract

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 ($\boldsymbol{M}$) and electric polarization ($\boldsymbol{P}$) generates a trilinear term in the refractive index, $\delta n\propto\boldsymbol{k}\cdot(\boldsymbol{P}\times\boldsymbol{M})$, where $\boldsymbol{k}$ is the propagation vector of light. Its sharp magnetoelectric resonances, that 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 $\boldsymbol{M}$, $\boldsymbol{P}$ and $\boldsymbol{k}$. Remarkably, the material shows almost perfect one-way transparency in moderate magnetic fields at some of the magnetoelectric resonances.