Comprehensive study of the ferroelectricity induced by the spin-dependent d-p hybridization mechanism in Ba ₂XGe ₂O ₇ (X = Mn, Co, and Cu)

We have investigated the magnetoelectric properties originating from the spin-dependent hybridization between transition metal (X) d orbital and ligand ion p orbitals in the noncentrosymmetric crystals Ba ₂XGe ₂O ₇ (X=Mn, Co, Cu). The novel magnetic-field responses of the electric polarization observed in the staggered antiferromagnets Ba ₂MnGe ₂O ₇ (S=5/2) and Ba ₂CoGe ₂O ₇ (S=3/2) can be accounted for by the mean-field approximation based on the d-p hybridization mechanism. In the case of the S=1/2 helimagnet Ba ₂CuGe ₂O ₇, we have found the metamagnetic transition to the staggered spin state in the high magnetic field region and observed an electric polarization originating from the d-p hybridization mechanism. Especially, the observation of electric polarization not only in the fully spin-polarized state at high magnetic field in Ba ₂MnGe ₂O ₇ but also in all the compounds, under applied external magnetic field, strongly supports the single-spin mechanism of the d-p hybridization as the origin of ferroelectricity in this class of materials. We have examined the transition-metal dependence of the polarization magnitude in Ba ₂XGe ₂O ₇ in terms of the electronic configuration in d levels and found that the unquenched orbital angular momentum determines the magnitude of the electric polarization.