  Spin nematics break spin-rotational symmetry while maintaining time-reversal
symmetry, analogous to liquid crystal nematics that break spatial rotational
symmetry while maintaining translational symmetry. Although several candidate
spin nematics have been proposed, the identification and characterization of
such a state remain challenging because the spin-nematic order parameter does
not couple directly to experimental probes. KFe$_{0.8}$Ag$_{1.2}$Te$_2$
(K$_5$Fe$_4$Ag$_6$Te$_{10}$, KFAT) is a local-moment magnet consisting of
well-separated 2$\times$2 Fe clusters, and in its ground state the clusters
order magnetically, breaking both spin-rotational and time-reversal symmetries.
Using uniform magnetic susceptibility and neutron scattering measurements we
find a small strain induces sizable spin anisotropy in the paramagnetic state
of KFAT, manifestly breaking spin-rotational symmetry while retaining
time-reversal symmetry, resulting in a strain-induced spin-nematic state in
which the $2\times2$ clusters act as the spin analogue of molecules in a liquid
crystal nematic. The strain-induced spin anisotropy in KFAT allows us to probe
its nematic susceptibility, revealing a divergent-like increase upon cooling,
indicating the ordered ground state is driven by a spin-orbital entangled
nematic order parameter.
