Singlet-Triplet Excitations and Long-Range Entanglement in the Spin-Orbital Liquid CandidateFeSc2S4

Abstract

Theoretical models of the spin-orbital liquid (SOL) FeSc2S4 have predicted it to be in close proximity to a quantum critical point separating a spin-orbital liquid phase from a long-range ordered magnetic phase. Here, we examine the magnetic excitations of FeSc2S4 through timedomain terahertz spectroscopy under an applied magnetic field. At low temperatures an excitation emerges that we attribute to a singlet-triplet excitation from the SOL ground state. A threefold splitting of this excitation is observed as a function of applied magnetic field. As singlet-triplet excitations are typically not allowed in pure spin systems, our results demonstrate the entangled spin and orbital character of singlet ground and triplet excited states. Using experimentally obtained parameters we compare to existing theoretical models to determine FeSc2S4's proximity to the quantum critical point. In the context of these models, we estimate that the characteristic length of the singlet correlations to be ξ/(a/2) ≈ 8.2 (where a/2 is the nearest neighbor lattice constant) which establishes FeSc2S4 as a SOL with long-range entanglement.The search for ground states without classical analogs, e.g. quantum ground states, is a central focus of modern condensed matter physics. A zero temperature spin liquid would be a prime realization of such a state [1]. Such systems possess local moments, but, due to quantum fluctuations, typically enhanced due to geometric frustration, do not order even at zero temperature. They are proposed to have quantum mechanically entangled wavefunctions, with exotic fractionalized excitations. Orbital degrees of freedom can also be disordered by quantum fluctuations [2]. Systems with both spin and orbital fluctuations as well as spin-orbit coupling (SOC) have been proposed to form a "spin-orbital liquid" (SOL) ground state, characterized by entangled spin and orbital degrees of freedom but no long range order [3][4][5][6][7].Recent experiments have shown a SOL phase may exist in the geometrically frustrated A site cubic spinel compound FeSc 2 S 4 . A tetrahedral S 4 crystal field splits a 3d shell into an upper t 2 orbital triplet and a lower e orbital doublet. With Hund's coupling, an Fe 2+ ion in a tetrahedral environment assumes a high spin S = 2 configuration with a lower 5 E orbital doublet ground state and an upper 5 T 2 orbital triplet excited state (Fig. 1). The ground state's two-fold orbital degeneracy is associated with the freedom to place a hole in either e orbital. Although orbital degeneracy is often relieved by Jahn-Teller distortions, heat capacity experiments show no sign of orbital ordering down to 50 mK and the magnetic susceptibility displays essentially perfect Curie-Weiss behavior with θ CW = -45.1 K in the range from 15 -400K [3]. The possible removal of the ground state orbital degeneracy FIG. 1: (a) Energy levels of Fe 2+ ion in an S=2 configuration after tetrahedral crystal field splitting and first and second order SOC, without including lattice effects. Numbers in parenthesis represen...

Antiferromagnetic and Orbital Ordering on a Diamond Lattice Near Quantum Criticality

“…Using the experimentally determined value for the SOC coupling constant λ = 1.57 (25) meV [20] and the unrenormalized magnetic exchange J 2 used in the spin wave model we find J2 /λ > 0.20 which falls well within the magnetic and orbitally ordered regime. We note that the Terahertz measurements also extract a value of J2 /λ > 1 /16, but based on the reported absence of magnetic order in previous neutron measurements conclude that quantum fluctuations renormalize x c [20]. The drastically reduced ordered moment of FeSc 2 S 4 and enhanced fluctuations we observe are a direct sign of the melting of the staggered magnetization in proximity to a critical point.…”

“…where ω 0 is the energy averaged over the fluctuation spectrum at Q=0. Time domain Terahertz spectroscopy has revealed a single well defined mode at ω = 4.5 meV which dominates the dynamic susceptibility at Q = 0 [20]; using this result we may apply a single mode approximation to obtain a lower bound on the anisotropy energy D = 4.5S(Q = 0). Fits to the static structure factor and first moment are shown in Fig.…”

“…While spin and orbital ordering is favoured by the exchange interactions, atomic spin orbit coupling favours local spin-orbital singlets and FeSc 2 S 4 is predicted to lie near the quantum critical point separating the spin-orbital singlet phase from a magnetically and orbitally ordered state. This hypothesis appears supported by terahertz and far infrared optical spectroscopy measurements which have revealed low energy (4.5 meV) excitations consistent with a so-called spin-orbiton [19][20][21], an excitation of entangled spin and orbital degrees of freedom. In this scenario, varying the magnetic exchange interactions relative to the spin orbit arXiv:1603.08033v1 [cond-mat.str-el] 25 Mar 2016 coupling through the application of hydrostatic pressure might drive FeSc 2 S 4 through the quantum critical point, stabilizing antiferromagnetism [17].…”

Frustrated spin one on a diamond lattice in NiRh2O4

“…The local hyperfine field measured by 61 Ni Mössbauer is very small, µ 0 H = 2.5 T, indicative of a lack of magnetic ordering [42]. These observations suggest that either only a small portion of the total moment is ordered, or that the entirety of the moment remains fluxional, similar to the behavior found for FeSc 2 S 4 [31,[43][44][45]. Though the NN interactions (J NN ) remain equivalent across the structural phase transition, the NNN interactions split into a set of four interactions within a plane (J NNN1 ) and a set of eight interactions out of that plane (J NNN2 ).…”

Reduction of effective terahertz focal spot size by means of nested concentric parabolic reflectors

“…[11][12][13] In particular time-domain terahertz spectroscopy has been proven very useful in studying different material systems at low temperatures including superconductors, 14,15 quantum magnets, [16][17][18][19] exciton states in TiO 2 nanotubes, 20 and topological insulators. 13,[21][22][23] With the photoconductive switches method of TDTS, one typically splits an infrared femtosecond laser pulse along two paths and sequentially excites a pair of photoconductive "Auston"-switch antennae.…”