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

4 f − 3 d

magnetic interactions in inducing ferroelectricity in the centrosymmetric (Pnma) green phase compound

G d_{2} BaCu O_{5}

. With decreasing temperature, a long-range incommensurate ordering of both

G d^{3 +}

and

C u^{2 +}

spins at

T_{N} = 11.8 K

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)

T_{loc} \sim 6 K

. Both spin structures induce electric polarization consistent with the polar magnetic space groups

P m 1^{'} (α, 0, g) s s

and

P_{a} c a 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

4 f − 3 d

interactions demonstrates an alternative route to find magnetoelectric materials.

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