Symmetry of Multiferroicity in a Frustrated Magnet TbMn${}_2$O${}_5$

Abstract

Based on measurements of soft x-ray magnetic scattering and symmetry considerations, we demonstrate that the magnetoelectric effect in TbMn${}_2$O${}_5$ arises from an internal field determined by ${\vec{S}}_{\vec{q}}\times {\vec{S}}_{-\vec{q}}$ with ${\vec{S}}_{\vec{q}}$ being the magnetization at modulation vector $\vec{q}$, whereas the magneto-elastic effect in the exchange energy governs the response to external electric fields. Our results set fundamental symmetry constraints on the microscopic mechanism of multiferroicity in frustrated magnets.