Theory of Finite Frequency Magnetoelectric Coupling and Its Applications in Compensating Antiferromagnetic Materials.

Magnetoelectric coupling is a fundamental property of materials without inversion symmetry. Many research works have traditionally focused on the limits of static external fields. In contrast, in this work, we present the quantum-mechanical expression for the finite-frequency magnetoelectric coefficient. The finite frequency magnetoelectric coupling contains two gauge-independent but frequency-dependent terms and a gauge-dependent but frequency-independent Chern-Simons term. By symmetry consideration, we find in finite frequency, the magnetoelectric coupling in principle doesn't require time reversal symmetry breaking, unlike the static condition. We then focus on compensate antiferromagnetic (AFM) materials and reveal that light with certain helicity would split the degeneracy of magnetic ground states related by time reversal, and what's more would induce linear magneto-optical effects, such as reflective magnetic circular dichroism effect, which are prohibited in conventional theory. We implement the calculation with density functional theory (DFT) and demonstrate the effect in inversion-time symmetric AFM bulk material Cr₂O₃.