We first present a scaling argument for the relaxation times in spin glasses, as suggested by Binder and Young. We emphasize the relevance of our dynamic measurements near the magnetic field-temperature transition line to equilibrium properties such as the nonlinear susceptibility. We show how, in the insulating system Eu0.4Sr0.6S, the phase lag of the ac susceptibility with respect to the modulated field relates the measuring frequency ω to a characteristic response time τ. We are thus able to define the zero field freezing temperature, Tf(ω). Two scaling models are tested, appropriate to a finite critical temperature, Tc, and to a zero temperature transition. Respectively, this leads to two critical slowing down regimes: τ/τ0 ∼ (T - Tc)-zv and ln(τ/τ0) ∼ T -zv. Both are shown to be consistent with the data, and to lead to Tc = 1.50 K, zv = 8, τ0 = 3x10-12 s; or Tc = 0, zv = 9 and τ 0 = 10-8 s. The set of parameters derived for the former (finite Tc) case appears to be more consistent with previous data on Eu0.4Sr0.6S, and with recent computer simulations. We then generate, in the magnetic field-temperature plane, lines Tf (ω, H) associated with the response time τ. We include remanent magnetization measurements which refer to well defined experimental time scales (≤1 s or ≤25 s). The entire set of scaled data, for the case when Tc = 1.50 K, strongly suggests that the response time diverges for H 1 2 ∼ T - Tc. This is of the form of a de Almeida-Thouless transition line with, however, a non-mean-field exponent.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics