Resonant magnetoelectric X-ray scattering in GaFeO3:: Observation of ordering of toroidal moments

We report on the first observation of magnetoelectric X-ray scattering (MEXS), i.e., incident-k-direction-dependent scattering, for a polar ferrimagnet GaFeO3. Near the K edge of Fe, the magnetic component of the (040) X-ray reflection shows a larger enhancement than that of the (020) X-ray reflection, which cannot be attributed to the genuine magnetic scattering, but to the MEXS of Fe3+ ions. Toroidal moments as defined by the Outer product of the Fe off-center displacement and the magnetic moment show ferroic ordering, which causes the resonant MEXS at the Fe 1s-3d excitation energy.