Spin dynamics and spin freezing in the triangular lattice antiferromagnets FeGa2S4and NiGa2S

Abstract

Magnetic susceptibility and muon spin relaxation (µSR) experiments have been carried out on the quasi-2D triangular-lattice spin S = 2 antiferromagnet FeGa2S4. The µSR data indicate a sharp onset of a frozen or nearly-frozen spin state at T * = 31(2) K, twice the spin-glass-like freezing temperature T f = 16(1) K. The susceptibility becomes field dependent below T * , but no sharp anomaly is observed in any bulk property. A similar transition is observed in µSR data from the spin-1 isomorph NiGa2S4. In both compounds the dynamic muon spin relaxation rate λ d (T ) above T * agrees well with a calculation of spin-lattice relaxation by Chubukov, Sachdev, and Senthil in the renormalized classical regime of a 2D frustrated quantum antiferromagnet. There is no firm evidence for other mechanisms. At low temperatures λ d (T ) becomes temperature independent in both compounds, indicating persistence of spin dynamics. Scaling of λ d (T ) between the two compounds is observed from ∼T f to ∼1.5T* . Although the µSR data by themselves cannot exclude a truly static spin component below T * , together with the susceptibility data they are consistent with a slowly-fluctuating "spin gel" regime between T f and T * . Such a regime and the absence of a divergence in λ d (T ) at T * are features of two unconventional mechanisms: (1) binding/unbinding of Z2 vortex excitations, and (2) impurity spins in a nonmagnetic spin-nematic ground state. The absence of a sharp anomaly or history dependence at T * in the susceptibility of FeGa2S4, and the weakness of such phenomena in NiGa2S4, strongly suggest transitions to low-temperature phases with unconventional dynamics.

Spin Fluctuations from Hertz to Terahertz on a Triangular Lattice

“…While no significant frequency dependence is observed at the T * anomaly where the spin fluctuation rate is in the MHz range, frequency dependence is observed for T ≈ 3 K where the NQR signal is recovered [19]. Below 2.5(5) K, a quasi-static inhomogeneous internal field was inferred from the NQR experiments [19] while µSR is inhomogeneous at all temperatures [20,21]. These observations indicate a wide distribution of spin fluctuation rates, which is corroborated by the distinct time scales inferred from µSR, NQR and ac susceptibility data ( Fig.1(b)).…”

“…This is accompanied by a loss of the NQR signal between T * and 2.5(5) K indicating dynamic nuclear spin relaxation resulting from slow Ni spin fluctuations [20,21]. µSR provides information for T < T * where the NQR signal is absent, and shows the spin relaxation rate decreases slightly below T * but remains finite down to 25 mK [21]. These results demonstrate Ni spin dynamics persists to the lowest temperatures, with considerable spectral weight in the MHz frequency range.…”

“…Gallium nuclear quadrupole resonance (NQR) experiments [19] and µSR measurements [20,21] reveal critical slowing down of Ni-spin fluctuations between the Weiss temperature |θ W | = 80 K and a characteristic temperature T * = 8.5 K, where nominally elastic diffuse magnetic neutron scattering develops. This is accompanied by a loss of the NQR signal between T * and 2.5(5) K indicating dynamic nuclear spin relaxation resulting from slow Ni spin fluctuations [20,21]. µSR provides information for T < T * where the NQR signal is absent, and shows the spin relaxation rate decreases slightly below T * but remains finite down to 25 mK [21].…”

“…Extrapolation of the Vogel-Fulcher curve (Supplementary Information) for the AC susceptibility shows that microsecond spin dynamics is present at least down to T 0 . While neither the µSR or NSE data exclude a truly static component, the µSR data indicate significant MHz spin dynamics down to 25 mK [21]. At its freezing temperature, a canonical spin-glass is predicted to have diverging third and fifth-order nonlinear susceptibilities, χ 3 and χ 5 [23].…”

“…[19]. Above and below T * the muon spin relaxation rates are in the motionally-narrowed (∝ τ ) and adiabatic (∝ 1/τ ) limits, respectively [20,21] (see Supplementary Information for details). Vogel-Fulcher behavior from the AC susceptibility measurements is given by the dotted curve.…”