Absence of nematic ordering transition in a diamond lattice: Application to $FeSc_2S_4$

TL;DR

This study demonstrates that $FeSc_2S_4$ on a diamond lattice does not exhibit a nematic transition due to the high susceptibility of its symmetries, explaining observed Fe environments without a distinct nematic phase.

Contribution

The paper provides a theoretical analysis showing the absence of a nematic ordering transition in $FeSc_2S_4$, linking symmetry breaking to experimental observations.

Findings

No distinct nematic transition temperature in $FeSc_2S_4$

High susceptibility of the diamond lattice to symmetry breaking

Presence of two Fe environments at high temperatures

Abstract

Recent neutron scattering observations by Plumb et al. [1] reveal that the ground state of $FeSc_2S_4$ is magnetic with two distinct Fe environments, instead of a quantum spin liquid as had been previously thought. Starting with the relevant O(N)-symmetric vector model of $FeSc_2S_4$, we study how the discrete ($Z_2$) and continuous rotational symmetries are successively broken, yielding nematic and ordered phases. At high temperatures, we find that the nematic order parameter falls as $T^{-\gamma}$ ($\gamma>0$), and therefore, $FeSc_2S_4$ lacks any distinct nematic ordering temperature. This feature indicates that the three-dimensional diamond lattice of $FeSc_2S_4$ is highly susceptible to the breaking of Ising symmetries, and explains the two distinct Fe environments that is present even at high temperatures, as seen by M\"ossbauer and far infrared optical spectroscopy.