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FeCr$_2$S$_4$ in magnetic fields: possible evidence for a multiferroic ground state

We report on neutron diffraction, thermal expansion, magnetostriction, dielectric, and specific heat measurements on polycrystalline FeCr2S4 in external magnetic fields. The ferrimagnetic ordering temperatures $T_{\mathrm{C}}\approx 170$ K and the transition at $T_{\mathrm{OO}}\approx 10$ K, which has been associated with orbital ordering, are only weakly shifted in magnetic fields up to 9 T. The cubic lattice parameter is found to decrease when entering the state below $T_{\mathrm{OO}}$. The magnetic moments of the Cr- and Fe-ions are reduced from the spin-only values throughout the magnetically ordered regime, but approach the spin-only values for fields $>$5.5 T. Thermal expansion in magnetic fields and magnetostriction experiments indicate a contraction of the sample below about 60 K. Below $T_{\mathrm{OO}}$ this contraction is followed by a moderate expansion of the sample for fields larger than $\sim$4.5 T. The transition at $T_{\mathrm{OO}}$ is accompanied by an anomaly in the dielectric constant. The dielectric constant depends on both the strength and orientation of the external magnetic field with respect to the applied electric field for $T<T_{\mathrm{OO}}$. A linear correlation of the magnetic-field-induced change of the dielectric constant and the magnetic-field dependent magnetization is observed. This behaviour is consistent with the existence of a ferroelectric polarization and a multiferroic ground state below 10 K.