Interplay of 4f−3d interactions and spin-induced ferroelectricity in the green phase Gd2BaCuO5

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 $4f\text{−}3d$ magnetic interactions in inducing ferroelectricity in the centrosymmetric (Pnma) green phase compound $\mathrm{G}{\mathrm{d}}_2\mathrm{BaCu}{\mathrm{O}}_5$. With decreasing temperature, a long-range incommensurate ordering of both $\mathrm{G}{\mathrm{d}}^{3+}$ and $\mathrm{C}{\mathrm{u}}^{2+}$ spins at $T_N=11.8\mathrm{K}$ occurs with the modulation vector $\mathbf{k}=(0,0,g)$ and a lock-in transition to a strongly noncollinear structure with ${\mathbf{k}}_{\mathrm{c}}=(0,0,\mathrm{½})$ at $T_{\mathrm{loc}}\sim 6\mathrm{K}$. Both spin structures induce electric polarization consistent with the polar magnetic space groups $Pm{1}^{\prime }(\alpha ,0,g)ss$ and $P_{a}ca{2}_1$, 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 $4f\text{−}3d$ interactions demonstrates an alternative route to find magnetoelectric materials.