Magnetoelectric effects studied by resonant x-ray diffraction in ferrimagnetic GaFeO3

Resonant x-ray Bragg diffraction experiments on space group forbidden reflections of type (0k0) with k odd taken in the vicinity of the Fe K edge are used to study magnetoelectric effects in GaFeO3. The main intensity of the various spectral features is caused by the E1-E1 transition and can be ascribed to the observation of an electric quadrupole moment, giving different intensities within a Friedel pair. Collecting the magnetic field difference intensity by having the magnetization parallel or antiparallel to the c axis in the ferrimagnetic phase is discussed in the framework of magnetoelectric multipole moments, which are both parity and time odd. The azimuthal angle dependence and the sign change in the magnetic signal when going from (0k0) to (0 (k) over bar0) reflections can be understood by the interference of the electric quadrupole with that of magnetoelectric quadrupole and octupole moments.