Resolving structural changes and symmetry lowering in spinel ${\mathrm{FeCr}}_2{\mathrm{S}}_4$

The cubic spinel ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ has been receiving immense research interest because of its emergent phases and the interplay of spin, orbital, and lattice degrees of freedom. Despite the intense research, several fundamental questions are yet to be answered, such as the refinement of the crystal structure in the different magnetic and orbital ordered phases. Here, using high-resolution synchrotron powder diffraction on stoichiometric crystals of ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ we resolved the long sought-after cubic to tetragonal transition at $\sim 65\mathrm{K}$, reducing the lattice symmetry to $I{4}_1/amd$. With further lowering the temperature, at $\sim 9\mathrm{K}$, the crystal structure becomes polar, hence the compound becomes multiferroic—likely reducing the space group to $I{4}_{1}md$. The elucidation of the lattice symmetry throughout different phases of ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ provides a basis for the understanding this enigmatic system and also highlights the importance of structural deformation in correlated materials.

Figure 1

(a) Room temperature and (b) 4 K synchrotron high-resolution x-ray powder diffraction spectra of ${\mathrm{FeCr}}_2{\mathrm{S}}_4$. Rietveld refinement of spectra at 4 K with $I{4}_1/amd$ space group. $R{}_{wp}$ = 12.62%, $R{}_{\exp }$ = 8.27%, GOF = 1.53.

Figure 2

(a) Temperature dependence of the lattice parameters. Vertical grey dotted line shows separation between the use of the cubic and tetragonal space group for the Rietveld refinements. PM, C-FiM, NC-FiM, and OO mark respectively, cubic paramagnetic, pseudocubic collinear ferrimagnetic, tetragonal noncollinear ferrimagnetic, and tetragonal orbitally ordered multiferroic phases. (b) Temperature dependence of the cubic (8 0 0) peak. (c) Temperature dependence of the (12 4 0) peak. Both (b) and (c) show a clear splitting at 15 K and below, and a broadening already below 60 K.

Figure 3

Temperature dependence of the thermal expansion coefficient $\alpha$ of single crystalline ${\mathrm{FeCr}}_2{\mathrm{S}}_4$. Inset: Temperature dependence of the normalized sample length $\mathrm{\Delta }L/L$. Arrows mark the phase transition temperatures.

Figure 4

(a) Temperature-dependent resistivity measurements. (b) Polarization $P$ vs $T$. The different colors show the different applied fields with the direction of the polarization depending on the sign of the applied electric field, consistent with ferroelectricity. Inset: Pyrocurrent $I$ vs $T$ taken on cooling with the fields labeled in (b).

Figure 5

ZFC and FC magnetizations measured in a field of 0.01 T (left axis) and specific heat in representation $C_p/T$ in zero field (right axis) collected on the same sample. Both data sets show a step like anomaly at the onset of the magnetic ordering at $T{}_C\sim$ 165 K. The magnetic data have an additional peak at $T{}_m\sim$ 65 K, while a clear peak at $T{}_{OO}\sim$ 9 K in the specific heat is only slightly pronounced in the magnetization.

Figure 6

High-temperature cubic Fd3m unit cell. (b) Low-temperature tetragonal $I{4}_1/amd$ unit cell. In both (a) and (b) the blue atoms are Fe, the green atoms are Cr, and the gold atoms are S. (c) Schematic of the redefined unit cell across the structural transformation. Panels (a) and (b) are made using VESTA [43].