We present the results of a combined $^7$Li NMR and diffraction study on LiGa$_{0.95}$In$_{0.05}$Cr$_4$O$_8$, a member of LiGa$_{1-x}$In$_{x}$Cr$_4$O$_8$ breathing pyrochlore family. Via specific heat and NMR measurements, we find that the complex sequence of first-order transitions observed for $x=0$ is replaced by a single, apparently second-order transition at $T_f=11$ 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 describing the manifold of nematic states.
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