Orbital-Ordering-Driven Multiferroicity and Magnetoelectric Coupling in ${\mathrm{GeV}}_4{\mathrm{S}}_8$

We report here the discovery of multiferroicity and large magnetoelectric coupling in the type I orbital order system ${\mathrm{GeV}}_4{\mathrm{S}}_8$. Our study demonstrates that this clustered compound displays a para-ferroelectric transition at 32 K. This transition originates from an orbital ordering which reorganizes the charge within the transition metal clusters. Below the antiferromagnetic transition at 17 K, the application of a magnetic field significantly affects the ferroelectric polarization, revealing thus a large magnetoelectric coupling. Our study suggests that the application of a magnetic field induces a metamagnetic transition which significantly affects the ferroelectric polarization thanks to an exchange striction phenomenon.

Figure 1

Temperature dependent dielectric permittivity: (a) at zero magnetic field during cooling and warming ($1\mathrm{K}/\min$) at four different frequencies (5–100 kHz) and (b) under different magnetic fields during cooling and warming ($1\mathrm{K}/\min$) at 100 kHz. Inset: picture of the crystal contacted with two electrodes used for dielectric measurements.

Figure 2

(a) Comparison of the V-V distances within the tetrahedral V clusters at 4, 25, and 300 K. (b) Temperature dependent residual polarization after poling along the [111] direction with different electric fields. (c) Polarization vs field at 10 and 20 K after extracting the residual polarization from pyroelectric measurements. Each point $P$ is obtained by calculating $P(E)=[P(+E)-P(-E)]/2$. The $PE$ loops were drawn from the polarization at the same positive and negative fields.

Figure 3

(a) Temperature dependent remnant polarization under different magnetic fields after poling the same static electric field ($E=43\mathrm{kV}/\mathrm{cm}$). The magnetic field is applied along the (111) axis of magnetization. (b) Temperature dependent field cooled warming magnetic susceptibility (polycrystalline sample) under different magnetic fields in the same range of temperature. (c) Nonlinear magnetization $M-{\chi }_{0}H$ vs magnetic field (${\chi }_0=\text{low}\text{−}\text{field}$ susceptibility) above and below $T_N$ (20 and 5 K, respectively). Below $T_N$, the upward curvature above 5 T points to the appearance of a metamagnetic transition. (d) Polarization increase induced by the magnetic field at 8 K.

Figure 4

(a) Differential charge density [dark grey (or purple): negative, light grey (or red): positive] calculated at 300 K between the non polar structure and the density obtained as the sum of individual atomic densities (b) idem for the orthorhombic structure at 25 K; paramagnetic insulator (PI).