Interplay of 4f-3d interactions and spin-induced ferroelectricity in the green phase Gd_{2}BaCuO_{5}

In most of the spin-induced multiferroics, the ferroelectricity is caused by inversion symmetry breaking by complex spin structures of the transition-metal ions. Here, we report the importance of interplay of 4f-3d magnetic interactions in inducing ferroelectricity in the centrosymmetric (Pnma) green phase compound Gd_{2}BaCuO_{5}. With decreasing temperature, a long-range incommensurate ordering of both Gd^{3+} and Cu^{2+} spins at T_{N}=11.8K occurs with the modulation vector k=(0,0,g) and a lock-in transition to a strongly noncollinear structure with k_{c}=(0,0,½) at T_{loc}∼6K. Both spin structures induce electric polarization consistent with the polar magnetic space groups Pm1^{′}(α,0,g)ss and P_{a}ca2_{1}, respectively. Based on the symmetry analysis of magnetoelectric interactions, we suggest that the ferroelectricity in both commensurate and incommensurate phases is driven by a complex interplay of two-spins and single-spin contributions from magnetic ions located in noncentrosymmetric environments. Our study demonstrates that the green phase family of compounds may serve as a playground for studying the multiferroic phenomena, where the interplay of 4f-3d interactions demonstrates an alternative route to find magnetoelectric materials.