Jahn-Teller induced nematic orbital order in tetragonal ${\mathrm{Sr}}_2{\mathrm{VO}}_4$

Using high resolution x-ray diffraction (XRD) on high purity powders, we resolved the structure and $ab$ symmetry of the intriguing compound ${\mathrm{Sr}}_2{\mathrm{VO}}_4$ from room temperature down to 20 K to an unprecedented level of accuracy. Upon cooling, this set of data unambiguously reveals a second-order phase transition lowering the symmetry from tetragonal to orthorhombic at a temperature $T_{c2}=136$ K. The observation of an orthorhombic distortion of the $ab$ plane is attributed to nematic phase formation supported by local Jahn-Teller (JT) dynamical instability. At $T_N=105$ K, spins order and at $T_{c1}=100$ K the tetragonal structure is recovered with an elongated $c$ axis.

Figure 1

(a) Temperature evolution of selected Bragg reflections. The two transition temperatures $T_{c1}$ and $T_{c2}$ are highlighted with blue lines. Temperature intervals are 1 K from 20 to 40 K, 5 K from 45 to 85 K, 1 K from 90 to 139 K, 10 K from 140 to 190 K, and 20 K from 200 to 280 K.

Figure 2

Temperature evolution of (a) $c/a,b$ ratio and volume of the cell, (b) lattice parameters, and (c) full width at half maximum (FWHM) of selected diffraction peaks in the high temperature and low temperature tetragonal phases (blue symbols) and in the orthorhombic phase (red and green symbols). The two transition temperatures $T_{c1}$ and $T_{c2}$ are highlighted with dotted lines. Note that error bars in (a) and (b) are smaller than the symbols. (d) Entropy corrected for the phonon and thermal expansion (see methods in the Appendix).

Figure 3

(a) Representation of ionic displacement corresponding to the $Q_2$, $Q_3$, and $Q_6$ Jahn-Teller distortion modes. (b) Scheme of the adiabatic potential profile due to electron lattice interaction. $Q$ is the distortion strength and $U_{\text{min}}=k_B{T}_{OO}$ the potential barrier. Scheme of (c) antiferro and (d) ferro distortions associated with coupling with each mode.

Figure 4

(a) Experimental data of the Jahn-Teller order parameter $(b-a)/(b+a)$, (b) calculation of the coupled Jahn-Teller order parameter $q$, and (c) the antiferromagnetic order parameter $m$ using Eq. (A6). The parameters are indicated in the figure and characteristic temperatures $T_{c1}$, $T_N$, and $T_{c2}$ are marked as vertical dashed lines.

Figure 5

Rietveld refinement of the orthorhombic phase at 110 K. Diffraction peaks for aluminum are marked with green stars.