Classical Spin Nematic Transition in ${\mathrm{LiGa}}_{0.95}{\mathrm{In}}_{0.05}{\mathrm{Cr}}_4{\mathrm{O}}_8$

We present the results of a combined ${}^7\mathrm{Li}$-NMR and diffraction study on ${\mathrm{LiGa}}_{0.95}{\mathrm{In}}_{0.05}{\mathrm{Cr}}_4{\mathrm{O}}_8$, a member of the ${\mathrm{LiGa}}_{1-x}{\mathrm{In}}_x{\mathrm{Cr}}_4{\mathrm{O}}_8$ “breathing” pyrochlore family. Via specific heat and NMR measurements, we find that the complex sequence of first-order transitions observed for ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ is replaced by a single second-order transition at $T_f=11\mathrm{K}$. Neutron and x-ray diffraction rule out both structural symmetry lowering and magnetic long-range order as the origin of this transition. Instead, reverse Monte Carlo fitting of the magnetic diffuse scattering indicates that the low-temperature phase may be described as a collinear spin nematic state, characterized by a quadrupolar order parameter. This state also shows signs of short-range order between collinear spin arrangements on tetrahedra, revealed by mapping the reverse Monte Carlo spin configurations onto a three-state color model.

Figure 1

(a) ${}^7\mathrm{Li}$-NMR spectra, normalized by the peak intensity. Here, $\mathrm{\Delta }f=0$ corresponds to the center of gravity. The inset shows the temperature dependence of the averaged full-spectral line width (red crosses) and the FWHM of the narrow (closed circles) and broad (open circles) components. (b) The temperature dependence of $1/T_1$ for $x=0.05$ (solid circles), compared with the paramagnetic (open triangles) and AF (solid triangles) components of $x=0$, respectively. The inset shows the temperature dependence of the specific heat divided by temperature $C_p/T$ of $x=0.05$.

Figure 2

(a)  Synchrotron x-ray pattern at low and high $T$ with its Rietveld refinement ($R_p=12.2$ $R_{wp}=15.6$ $R_e=4.05$) and the $T$-dependence of (008) peak (inset). Peaks visible in the measured pattern and not signed with green markers come from a $\sim 1\%{\mathrm{Cr}}_2{\mathrm{O}}_3$ impurity. Parameters resulting from the structure refinement: temperature dependence of (b) strain parameters $S_{400}$ and $S_{220}$, extracted from SXRD, and (c) $B_{\mathrm{i}\mathrm{s}\mathrm{o}}$ and Cr fractional position parameter $x$ obtained from ND.

Figure 3

(a) Diffuse scattering at 1.5 K and 30 K with RMC fits using free (Heisenberg) and collinear spins parallel to (001). (b) Normalized real-space spin-spin correlation functions $⟨S_0·S_i⟩/S(S+1)$ versus radial distance $r$ for both temperatures. The dashed lines indicate the expected envelope for the Coulomb-like phase $\propto 1/r^3$, and the green square is the expectation for $⟨S_0·S_1⟩/S(S+1)$ as $T\to 0$. (d) Reconstructed single crystal scattering from the 30-K Heisenberg fit compared with (c) bow-tie scattering (highlighted by the white dashed polygon) calculated for the breathing pyrochlore antiferromagnet within the self-consistent Gaussian approximation (SCGA) for $B_f=0.6$ and $T/J=0.5$ [30].

Figure 4

(a) Real-space plot of a color RMC configuration at 1.5 K ($2\times 2\times 2$ unit cells). The black spheres indicate $uuud$ tetrahedra (or vice versa), and the highlighted area shows a region with predominantly blue-green correlations. (b) Radial dependence of color-color correlations $⟨C_0{C}_i⟩$ at 1.5 K. The red lines correspond to the expected envelope for two-color correlations decaying exponentially with the correlation length ${\xi }_c=2\AA$.