  Nematic fluctuations occur in a wide range of physical systems from liquid
crystals to biological molecules to solids such as exotic magnets, cuprates and
iron-based high-$T_c$ superconductors. Nematic fluctuations are thought to be
closely linked to the formation of Cooper-pairs in iron-based superconductors.
It is unclear whether the anisotropy inherent in this nematicity arises from
electronic spin or orbital degrees of freedom. We have studied the iron-based
Mott insulators La$_{2}$O$_{2}$Fe$_{2}$O$M$$_{2}$ $M$ = (S, Se) which are
structurally similar to the iron pnictide superconductors. They are also in
close electronic phase diagram proximity to the iron pnictides. Nuclear
magnetic resonance (NMR) revealed a critical slowing down of nematic
fluctuations as observed by the spin-lattice relaxation rate ($1/T_1$). This is
complemented by the observation of a change of electrical field gradient over a
similar temperature range using M\"ossbauer spectroscopy. The neutron pair
distribution function technique applied to the nuclear structure reveals the
presence of local nematic $C_2$ fluctuations over a wide temperature range
while neutron diffraction indicates that global $C_{4}$ symmetry is preserved.
Theoretical modeling of a geometrically frustrated spin-$1$ Heisenberg model
with biquadratic and single-ion anisotropic terms provides the interpretation
of magnetic fluctuations in terms of hidden quadrupolar spin fluctuations.
Nematicity is closely linked to geometrically frustrated magnetism, which
emerges from orbital selectivity. The results highlight orbital order and spin
fluctuations in the emergence of nematicity in Fe-based oxychalcogenides. The
detection of nematic fluctuation within these Mott insulator expands the group
of iron-based materials that show short-range symmetry-breaking.
