Both, linear magneto-optical effecfts [1-3], as introduced in Sect. 3.2.2, and the anomalous Hall effect [4] are based on the violation of time-reversal symmetry that manifests in a coupling to electromagnetic fields by energy-state shifts due to spin-orbit interaction. As a consequence, the material under consideration exhibits an anisotropic response to electromagnetic fields that relates to the direction of magnetic-field-induced or spontaneously-aligned magnetic moments, see Sect. 3.2.2. In contrast, the absence of point symmetries may allow for apparently similar macroscopic effects such as an optical birefringence or an optical activity. However, those effects are based on electric-field-induced or inherent crystal-field anisotropies with respect to atom-or ion-side symmetries in, e.g., a polar or chiral material. A combination of these two symmetry constraints with different microscopic origin results in a variety of optical effects, namely the magnetochiral effect (MChE) that arises in a chiral medium with broken time-reversal symmetry and an optical magnetoelectric effect (OME) in a polar medium with broken time reversal symmetry. More precisely, the OME can be understood as a combined Pockels and Voigt effect, both inducing linear birefringence. As a consequence, the origin of the effect does not have to be an intrinsic material property such as in a polar magnetic matter, but can be induced by applied electric and magnetic fields [5]. Both OME and MChE have in common that they manifest themselves in non-reciprocal directional-dependent material responses, associated for example with the sign of the light's propagation vector in optical experiments [6][7][8][9][10][11]. The OME is typically probed as a change of optical absorption (α) upon a sign change of the light's wave-vector component k i . In a polar magnetic material, for example, the sign of the effect depends on the sign of the triple product of the light's wave vector ( k) and the sample's polarisation ( P) and magnetisation ( M) as α α ∝ k • ( P × M). This difference is typically very small ( 1 %), because of the small magnitude of the microscopic source for the effect. The origin can be an optical interference between electric-and magnetic-dipole transitions, which usually have different resonance frequencies and oscillator strengths. Yet, if the two amplitudes corresponding to the resonances can be matched by the