  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.
