Unusual field-induced spin reorientation in ${\mathrm{FeCr}}_2{\mathrm{S}}_4$: Field tuning of the Jahn-Teller state

The multiferroic spinel ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ is a benchmark material for exploring the competition of spin-orbit (SO) and Jahn-Teller (JT) coupling. Our magnetic and thermodynamic studies of stoichiometric single-crystalline samples evidence a magnetic-field-induced spin-reorientation transition in the cooperative JT state below 10 K. At 2 K, at a critical magnetic field of 4.5 T, the magnetization measured along the hard magnetization axis $\langle 111\rangle$ manifests a jump to the fully saturated state accompanied by a steplike decrease of the sound velocity and an abrupt increase of the magnetostriction. All these quantities reveal a hysteretic behavior pointing towards a first-order magnetostructural transformation. Below the JT transition, the specific heat shows a complex behavior upon the application of magnetic fields depending on the crystallographic directions. The observed reduction by 20% of the magnetic anisotropy below the JT transition is attributed to the competition of the SO and JT interactions tuned by external magnetic fields. The concomitant change of the structural symmetry results in a change of the splitting of the lowest levels of the ${}^{5}E$ doublet of the tetrahedrally coordinated ${\mathrm{Fe}}^{2+}$ ions.

Figure 1

(a) Temperature-dependent magnetization $M$ (left scale) measured in an external magnetic field of 10 mT and zero-field specific heat plotted as $C/T$ vs $T$ (right scale) for single-crystalline ${\mathrm{FeCr}}_2{\mathrm{S}}_4$. Vertical arrows mark the Curie temperature $T_C=165.5$ K, the Jahn-Teller transition at $T_{OO}=8.9$ K, and the temperature $T_m=67$ K indicating deviations from collinear spin order via the appearance of irreversibility between the zero-field-cooled (ZFC) and field-cooled (FC) magnetization. The green dashed line shows the specific heat of the spinel ${\mathrm{ZnSc}}_2{\mathrm{S}}_4$. (b) Temperature-dependent specific heat $C/T$ vs $T$ measured in various external magnetic fields up to 9 T applied along the $\langle 111\rangle$ axis in the temperature range relevant for orbital ordering.

Figure 2

(a) Magnetization curves in ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ at 2 K measured along the crystallographic directions $\langle 100\rangle , \langle 110\rangle$, and $\langle 111\rangle$. The inset shows the temperature evolution of the FISR transition along the $\langle 111\rangle$ axis. (b) Magnetic-field dependence of the relative change of the sound velocity, $\mathrm{\Delta }v/v$, of the longitudinal waves propagating along the $\langle 111\rangle$ axis at 1.4 K. (c) Magnetic-field dependence of the normalized change of the sample length $\mathrm{\Delta }L/L$ measured along the $\langle 111\rangle$ axis at 1.5 K. Arrows mark the FISR transition field, $H{}_t$, and directions of the field sweeps. Note different scales for the horizontal axes in panels (a), (b), and (c).

Figure 3

(a) Temperature dependence of the anisotropy constant $K{}_1$ for ${\mathrm{FeCr}}_2{\mathrm{S}}_4$: the experimental data are shown by open circles. Last eight points at high temperature are derived from the ESR measurements. Inset shows the splittings of the levels of the tetrahedrally coordinated ${\mathrm{Fe}}^{2+}$ ion due to crystal-field (CF), exchange (EX), and SO interactions. (b) Temperature dependence of the anisotropy field $H_A=2K_1/M{}_s$ and of the saturation field $H{}_s$ extracted from the magnetization and ESR data. Dashed green lines in both frames show the fits to the experimental data within the single-ion model.

Figure 4

Temperature dependence of the orbital contribution to specific heat $C_{\mathrm{orb}}$ for ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ measured in zero field. Inset shows the temperature dependence of the JT splitting $\mathrm{\Delta }$. Solid lines in the main frame and in the inset show the fits to the experimental specific heat $C_{\mathrm{orb}}$ and splitting parameter ${\mathrm{\Delta }}_{\mathrm{orb}}$.