Electrotoroidicity: New Paradigm for Transverse Electromagnetic Responses

Abstract: The exploration of transverse electromagnetic responses in solids with broken spatial-inversion (I) and/or time-reversal (T) symmetries has unveiled numerous captivating phenomena, including the (anomalous) Hall effect, Faraday rotations, non-reciprocal directional dichroism, and off-diagonal linear magnetoelectricity, all within the framework of magnetotoroidicity. Here, we introduce a novel class of transverse electromagnetic responses originating from electrotoroidicity in ferro-rotational (FR) systems with preserved I and T symmetries, distinct from magnetotoroidicity. We discover a high-order off-diagonal magnetic susceptibility of FR domains and a reduced linear diagonal magnetic susceptibility at FR domain walls in doped ilmenite FeTiO3. The non-trivial "Hall-like" effect of the former corresponds to an anomalous transverse susceptibility in the presence of spontaneous electrotoroidal moments in FR materials. Our findings unveil an emergent type of transverse electromagnetic responses even in I and T symmetry-conserved conditions and illustrate new functionalities of abundant FR materials.