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

Abstract

Observations utilizing optical and x-ray techniques of coexistingmagnetoelectric, piezoelectric and magnetic modifications in gallium ferrate(GaFeO3) are successfully analysed with an atomic model that complies with the establishedchemical structure and the motifs of spontaneous polar and ferrimagnetic order. Electronvariables in the corresponding scattering length, which is common to an analysis ofdichroism and diffraction, are expressed as multipoles for charge, magnetic, magnetoelectricand polar electron degrees of freedom. Polar and magnetoelectric multipoles are parity-oddand cannot exist in a compound with a centrosymmetric structure. Magnetoelectricmultipoles are time-odd and vanish with loss of long-range magnetic order. Dichroic signalsmeasured in the energy region 1.0–2.5 eV and near the Fe K edge are consistent with a sumof magnetochiral and non-reciprocal linear signals caused by magnetoelectric multipoles inE1–M1 and E1–E2 absorption events. Resonant x-ray Bragg diffraction near the Fe K edge showsinterference not previously reported between Thomson scattering and resonantE1,M1 and E2 processes.