Polar and magnetoelectric multipoles in gallium ferrate inferred from optical and x-ray measurements

Observations utilizing optical and x-ray techniques of coexisting magnetoelectric, piezoelectric and magnetic modifications in gallium ferrate (GaFeO3) are successfully analysed with an atomic model that complies with the established chemical structure and the motifs of spontaneous polar and ferrimagnetic order. Electron variables in the corresponding scattering length, which is common to an analysis of dichroism and diffraction, are expressed as multipoles for charge, magnetic, magnetoelectric and polar electron degrees of freedom. Polar and magnetoelectric multipoles are parity-odd and cannot exist in a compound with a centrosymmetric structure. Magnetoelectric multipoles are time-odd and vanish with loss of long-range magnetic order. Dichroic signals measured in the energy region 1.0-2.5 eV and near the Fe K edge are consistent with a sum of magnetochiral and non-reciprocal linear signals caused by magnetoelectric multipoles in E1-M1 and E1-E2 absorption events. Resonant x-ray Bragg diffraction near the Fe K edge shows interference not previously reported between Thomson scattering and resonant E1, M1 and E2 processes.