Infrared-active phonons in the ferrimagnetic and multiferroic phases of ${\mathrm{FeCr}}_2{\mathrm{S}}_4$: Evidence for structural distortions

We report on the temperature evolution of the infrared-active optical phonons in ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ investigated by Fourier-transform infrared spectroscopy. The eigenfrequencies of the four triply degenerate infrared-active $T_{1u}$ phonons of the room-temperature cubic spinel structure shift when entering into the ferrimagnetically ordered state below $T_C=165\mathrm{K}$ indicating strong spin-phonon coupling as reported earlier. A new mode at 200 ${\mathrm{cm}}^{-1}$ emerges below a temperature $T^{*}\simeq 115\mathrm{K}$ and a splitting of the lowest-lying cubic phonon mode at about 120 ${\mathrm{cm}}^{-1}$ appears below the temperature $T_M\approx 60\mathrm{K}$ associated with the onset of an incommensurate modulation of the magnetic structure. At the transition to the orbitally ordered and ferroelectric ground state at $T_{\text{OO}}=9\mathrm{K}$ two more modes emerge at 146 and 253 ${\mathrm{cm}}^{-1}$ in very good agreement with the eigenfrequencies of two of the cubic Raman-active phonon modes reported by Choi et al. [J. Phys. Condens. Matter 19, 145260 (2007)]. These new modes are interpreted as signatures of a symmetry lowering with a loss of inversion symmetry to induce the multiferroic orbitally ordered ground state.

Figure 1

(a) Reflectivity spectra of ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ for selected temperatures above and below the transition temperatures. Arrows mark the appearance of a splitting of the lowest cubic phonon into three modes $S_{1,2,3}$ and the new modes $M$ and $R_{1,2}$. The spectra are shifted by a positive offset with respect to the curve at 5 K. (b) Dielectric loss spectrum at 5 K as an example for the determination of the eigenfrequencies by the peak maxima.

Figure 2

Enlarged views of (a) the dielectric loss spectra of of lowest cubic $T_{1u}\left(1\right)$ phonon in ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ for 5 and 12 K to reveal changes at $T_{\text{OO}}=9\mathrm{K}$ and (b) the new modes $M$ and $R_{1,2}$ appearing below $T^{*}$ and $T_{\text{OO}}$, respectively. Arrows mark the determined positions of the split modes and the new modes.

Figure 3

Temperature dependence of the eigenfrequencies of the IR active modes (closed symbols) together with the eigenfrequencies of two Raman-active modes of the cubic structure at 5 K (open stars) taken from Ref. [24].