Ferromagnetic-type order of atomic multipoles in the polar ferrimagnetic GaFeO3

Resonant x-ray Bragg diffraction by gallium ferrate (GaFeO3) at Friedel pairs of charge allowed reflections in the vicinity of the Fe K edge are presented. By use of the magnetization difference, the interference of charge diffraction with the magnetic diffraction is extracted. The study of Friedel pairs and concentrating at the pre-edge allows us to extract the effect of inversion symmetry breaking on the magnetic Fe 3d shell. The data are analyzed using a model based on atomic multipole moments which are magnetic and have no space inversion symmetry (magnetoelectric) interfering with the charge scattering. This model successfully describes data as a function of azimuthal angle and for different incident polarization and it shows that data can be directly related to the magnetoelectric dipole (toroidal) and quadrupole moments. Though the model describes most of the observations successfully, how to correctly describe the observed magnetic nonresonant intensity below the edge remains an open question.