Interplay of $4f\text{−}3d$ interactions and spin-induced ferroelectricity in the green phase $\mathrm{G}{\mathrm{d}}_2\mathrm{BaCu}{\mathrm{O}}_5$

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 $4f\text{−}3d$ 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.

Figure 1

(a) Schematics of the crystal structure of $\mathrm{G}{\mathrm{d}}_2\mathrm{BaCu}{\mathrm{O}}_5$. (b) Temperature-dependent dc magnetization measured under various magnetic fields in field-cooled sequence (left axis) and specific heat data measured under zero magnetic field.

Figure 2

(a) Dielectric constant $\left({\varepsilon }_r\right)$ as a function of temperature measured under various magnetic fields at the frequency 50 kHz. (b) Pyrocurrent as function of temperature and magnetic field. Inset shows pyrocurrent under zero magnetic field (c) Polarization obtained by integrating the pyrocurrent with respect to time. (d) Polarization measured with positive and negative poling electric fields.

Figure 3

Refined neutron-diffraction data recorded at 1.3 K. Inset shows the noncollinear commensurate magnetic structure of $\mathrm{G}{\mathrm{d}}_2\mathrm{BaCu}{\mathrm{O}}_5$ at 1.3 K in the magnetic unit cell. ($\mathrm{G}{\mathrm{d}}_1$, purple; $\mathrm{G}{\mathrm{d}}_2$, orange; Cu, blue).

Figure 4

Magnetic structure of $\mathrm{G}{\mathrm{d}}_2\mathrm{BaCu}{\mathrm{O}}_5$ at 9.8 K viewed along the b axis (bottom) and a general orientation (upper part) described in $Pm{1}^{\prime }(a,0,g)ss$. The magnetic structure shown here is constituted by $1\times 1\times 10$ unit cells of the paramagnetic structure. The nonmagnetic atoms as well as the Cu atoms have been removed for the sake of clarity. ($\mathrm{G}{\mathrm{d}}_1$, purple; $\mathrm{G}{\mathrm{d}}_2$, orange).