Fig. 4 | Nature Communications

Fig. 4

From: Coulomb spin liquid in anion-disordered pyrochlore Tb2Hf2O7

Fig. 4

Spin dynamics in Tb2Hf2O7 probed by ac-susceptibility and muon spin relaxation. a, b Ac-susceptibility (χ ac) as a function of temperature. The real (χac) and imaginary parts (χ′′ac) are shown for several frequencies f of the applied oscillating magnetic field. In a, the blue open symbols represent the zero-field cooled (ZFC) and field-cooled (FC) dc susceptibility (χ dc = M/H) evaluated from the magnetization (M) measured as a function of temperature in a low field (H = 0.01 T). The inset in a shows ln(τ) versus ln(t), where τ = 2π/f is the characteristic time and t = (T fT SG)/T SG is the reduced temperature of the peak temperature T f in χac at the frequency f, with T SG = 0.68 K the underlying spin-glass transition temperature. The black line is a fit to the dynamical scaling law of spin glasses τ = τ 0 × t , where τ 0 = 4.1 ± 0.4 × 10−8 s is the shortest relaxation time available to the system, z is the dynamic critical exponent, and ν is the critical exponent of the correlation length ( = 7.32 ± 0.06). c Results of zero-field muon spin relaxation experiments as a function of temperature. Spectra shown on Supplementary Fig. 3 were fitted to a stretched exponential function, A(t) = A 0 exp[-(t/T 1)β] + A bg. The parameters extracted from the fits are the relaxation rate λ = 1/T 1 and the exponent β. The error bars represent the standard deviation of the fit parameters

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