Structural anomalies and the orbital ground state in ${\text{FeCr}}_2{\text{S}}_4$

We report on high-resolution x-ray synchrotron powder-diffraction, magnetic-susceptibility, sound-velocity, thermal-expansion, and heat-capacity studies of the stoichiometric spinel ${\text{FeCr}}_2{\text{S}}_4$. We provide clear experimental evidence of a structural anomaly which accompanies an orbital-order transition at low temperatures due to a static cooperative Jahn-Teller effect. At 9 K, magnetic susceptibility, ultrasound velocity, and specific heat reveal pronounced anomalies that correlate with a volume contraction as evidenced by thermal-expansion data. The analysis of the low-temperature heat capacity using a mean-field model with a temperature-dependent gap yields a gap value of about 18 K and is interpreted as the splitting of the electronic ground state of ${\text{Fe}}^{2+}$ by a cooperative Jahn-Teller effect. This value is close to the splitting of the ground state due to spin-orbit coupling for isolated ${\text{Fe}}^{2+}$ ions in an insulating matrix, indicating that Jahn-Teller and spin-orbit coupling are competing energy scales in this system. We argue that due to this competition, the spin-reorientation transition at around 60 K marks the onset of short-range orbital ordering accompanied by a clear broadening of Bragg reflections, an enhanced volume contraction compared to usual anharmonic behavior, and a softening of the lattice observed in the ultrasound measurements.

Figure 1

(Color online) Temperature dependence of the linewidth of the Gaussian contribution to the [800] and [840] Bragg peaks. Inset: temperature dependence of the displacement parameters ${\beta }_{\text{ii}}$ of Fe (red triangles), Cr (green rhombs), and S (blue circles) from the high-resolution diffraction data. Lines through the data points are guide to the eyes.

Figure 2

(Color online) Normalized thermal expansion $\left(\Delta L/L_{\text{o}}\right)$ vs temperature in ${\text{FeCr}}_2{\text{S}}_4$ (closed blue circles). The dashed line corresponds to a fit with a behavior of a normal anharmonic solid as described in the text. The inset shows an enlarged region of the thermal expansion around the orbital-ordering temperature.

Figure 3

(Color online) Left scale: temperature dependence of zero-field-cooled (open red circles) and field-cooled (closed blue circles) susceptibility $\chi =M/H$ of ${\text{FeCr}}_2{\text{S}}_4$ in an external magnetic field $H=100\text{Oe}$. Right scale: temperature dependence of the relative change in the longitudinal sound velocity (solid green line). This line corresponds to an averaged change in the sound velocity as measured in heating and cooling cycles. The characteristic temperatures are indicated by vertical arrows.

Figure 4

(Color online) Heat capacity of ${\text{FeCr}}_2{\text{S}}_4$ in representation $C/T$ vs $T$ (red open circles). The characteristic temperatures of the orbital-ordering transition at $T_{\text{oo}}$, of the anomaly at $T_{\text{m}}$, and of the long-range ferrimagnetic order at $T_{\text{C}}$ are indicated by arrows. The simulated lattice contribution is shown by a blue dashed line. Inset: magnetic entropy determined after subtraction of the lattice contribution.

Figure 5

(Color online) Heat capacity of ${\text{FeCr}}_2{\text{S}}_4$ at low temperatures (open circles). The green triangles show the heat capacity of ${\text{Fe}}_{0.5}{\text{Cu}}_{0.5}{\text{Cr}}_2{\text{S}}_4$. The blue solid line is a fit describing the lattice contribution (see text). The inset shows the heat capacity solely derived from the orbital degrees of freedom. Here the phonon contribution as indicated in the main frame has been subtracted. The red solid line is a mean-field fit as described in the text utilizing a mean-field gap of 14.8 K.