Unusual double-peak specific heat and spin freezing in a spin-2 triangular lattice antiferromagnet FeAl$_{2}$Se$_{4}$

We report the properties of a triangular lattice iron-chalcogenide antiferromagnet FeAl$_{2}$Se$_{4}$. The spin susceptibility reveals a significant antiferromagnetic interaction with a Curie-Weiss temperature {\Theta}$_{CW}$ ~ -200K and a spin-2 local moment. Despite a large spin and a large |{\Theta}$_{CW}$|, the low-temperature behaviors are incompatible with conventional classical magnets. No long-range order is detected down to 0.4K. Similar to the well-known spin-1 magnet NiGa$_{2}$S$_{4}$, the specific heat of FeAl$_{2}$Se$_{4}$ exhibits an unusual double-peak structure and a T$^{2}$ power law at low temperatures, which are attributed to the underlying quadrupolar spin correlations and the Halperin-Saslow modes, respectively. The spin freezing occurs at ~ 14K, below which the relaxation dynamics is probed by the ac susceptibility. Our results are consistent with the early theory for the spin-1 system with Heisenberg and biquadratic spin interactions. We argue that the early proposal of the quadrupolar correlation and gauge glass dynamics may be well extended to FeAl$_{2}$Se$_{4}$. Our results provide useful insights about the magnetic properties of frustrated quantum magnets with high spins.