Parity- and time-odd atomic multipoles in magnetoelectricGaFeO3as seen via soft x-ray Bragg diffraction

Abstract

We present resonant soft x-ray Bragg diffraction data on the space-group forbidden (010) reflection at the $\text{Fe}\text{ }{L}_{2,3}$ edges of magnetoelectric ${\text{GaFeO}}_{3}$. Observed intensities give direct evidence for strange atomic multipoles that violate both time and space inversion, in particular a magnetoelectric quadrupole. The discovery of magnetoelectric multipoles in the open $3d$ shell is a direct measure of coupling between magnetic and electric properties and a basis to a microscopic understanding of magnetically induced multiferroics.