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 Mossbauer 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.
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