Optical Magnetoelectric Effects in Multiferroics

Multiferroics show peculiar magneto-optical properties: Optical refractive index and absorption change with the reversal of the propagation vector \textbf{k} of the electromagnetic wave. This magneto-optic effect is clearly distinct from the conventional magneto-optics like Faraday effect and named optical magneto-electric effect, because it can be considered as the high-frequency extension of the linear magneto-electric effect in multiferroics. We have recently succeeded in detecting the optical/x-ray magneto-electric effect in a polar ferrimagnet GaFeO$_{3}$, where spontaneous polarization \textbf{P}$_{0}$ and magnetization \textbf{M}$_{0}$ are parallel to the $b$ and $c$ axes, respectively. Optical magneto-electric effects are expected to show up for the electromagnetic wave with \textbf{k}//$a$, as the difference in absorption and refractive index with the sign reversal of the triple product of \textbf{P}$_{0}$, \textbf{M}$_{0}$, and \textbf{k}. X-ray magneto-electric absorption shows large enhancement at Fe 1$s$-3$d$ transition.$^{1}$ The obtained spectra are well explained by the interference between electric dipole and electric quadrupole transitions of Fe 1$s$ electrons in an FeO$_{6}$ cluster. Optical magneto-electric absorption of the order of 10$^{-3}$ was observed at around Fe intra-atomic d-d transition.$^{2}$ *Measurements of x-ray spectroscopy were performed at BL-1A, KEK-PF, Japan. $^{1}$M. Kubota et al., Phys. Rev. Lett. \textbf{92} (2004) 137401. $^{2}$J. H. Jung et al., Phys. Rev. Lett. \textbf{93} (2004) 037403.