Absence of nematic ordering transition in a diamond lattice: Application toFeSc2S4

Abstract

Recent neutron scattering observations by Plumb et al. [1] 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 is present even at high temperatures, as seen by Mössbauer and far infrared optical spectroscopy.Introduction: Frustrated magnetic systems, resisting ordering to the lowest temperatures, can arise from an intricate interplay between lattice geometry and the sign of the magnetic exchange interactions. While no single parameter can characterize the failure of a magnetic system to order, a commonly used measure of frustration is a large value of the ratio f = |Θ cw |/T c , where Θ cw (proportional to the exchange interaction) is the CurieWeiss temperature, and T c is the transition temperature; the system is considered frustrated in the regime T c < T < Θ cw . In the class of materials AB 2 X 4 [2-9], which are known as spinels, the exchange interactions are frustrated because the A-site atoms form a diamond lattice and are surrounded tetrahedrally by the X-site atoms. Consequently, numerous papers have proposed that the ground state of these materials is of the spin liquid type [6,[10][11][12][13]. In particular, because the frustration parameter in FeSc 2 S 4 is enormous (f ≈ 1000), this material has risen to the fore [5, 14-16] as a leading candidate for a spinel exhibiting quantum spin liquid behaviour.However, the recent neutron scattering measurements by Plumb et al. [1] are surprising, because they found that powdered samples of FeSc 2 S 4 exhibit a magnetic ordering transition at 11.8 K. With |Θ cw | ≈ 45 K [5], this observation drastically reduces the frustration parameter in this material from a thousand to about f ∼ 4. Their observations also uncovered a small and 'incipient' cubic to tetragonal structural transition (c/a = 0.998) that closely accompanies the formation of orbital order; both of these phases precede the magnetic transition and continue to prevail even at high temperatures. The structural transition distorts the sulfur atoms coordinating the Fe ions, and in the process leaves the two Fe sublattices surrounded by inequivalent atomic potentials. In this new lattice environment with a lower symmetry, the hole in the A sublattice occupies the d z 2 orbitals, while that in the B sublattice occupies the d x 2 −y 2 orbitals.In fact, the presence to two distinct Fe environments was present even in the original Mössbauer data [17,18] as noticed recently by B...

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