Absence of nematic ordering transition in a diamond lattice: Application to FeSc2 S4

Recent neutron scattering observations by [Plumb, Phys. Rev. X 6, 041055 (2016)10.1103/PhysRevX.6.041055] reveal that the ground state of FeSc2S4 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 FeSc2S4, we study how the discrete (Z2) 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-γ (γ>0), and therefore, FeSc2S4 lacks any distinct nematic ordering temperature. This feature indicates that the three-dimensional diamond lattice of FeSc2S4 is highly susceptible to the breaking of Ising symmetries, and explains the two distinct Fe environments that are present even at high temperatures, as seen by Mössbauer and far-infrared optical spectroscopy.