Electric toroidal invariance generates distinct transverse electromagnetic responses

Breaking spatial-inversion or time-reversal symmetry in solids leads to transverse electromagnetic effects such as the anomalous Hall effect, Faraday rotation, non-reciprocal directional dichroism and off-diagonal linear magnetoelectricity. These are all tied to the framework of magnetic toroidal invariance. Here we introduce a distinct class of transverse electromagnetic responses that arise from electric toroidal invariance in ferro-rotational systems that preserve both inversion and time-reversal symmetries. It is different from that governed by magnetic toroidal invariance. We demonstrate a high-order off-diagonal magnetic susceptibility of ferro-rotational domains and a reduced linear diagonal magnetic susceptibility at these domain walls in doped ilmenite FeTiO3. Our results reveal the presence of anomalous transverse susceptibilities in ferro-rotational materials with spontaneous electric toroidal moments. Therefore, our findings illustrate emergent functionalities of ferro-rotational materials. Magnetic toroidal invariance generates transverse electromagnetic effects in materials with broken symmetries. Now a distinct magnetic response is shown to emerge in ferro-rotational systems in which both inversion and time-reversal symmetries are preserved.