Zero-field<i>μ</i>SR measurements in<i>Cu</i>Mn and<i>Au</i>Mn spin glasses interpreted in the frame of a fractal cluster model

Abstract

We present a detailed analysis of zero-field muon-spin-relaxation (\ensuremath{\mu}SR) measurements in CuMn and AuMn spin glasses in the framework of a fractal cluster model. The latter is reformulated in terms of a probability distribution of spin-correlation times from which an expression for the spin autocorrelation function S(t) is inferred. The fractal cluster model predicts that the upper limit ${\ensuremath{\tau}}_{\ensuremath{\xi}}$ of the correlation time spectrum diverges at the freezing temperature ${T}_{f}$ and decreases below ${T}_{f}$. The \ensuremath{\mu}SR method measures the average amplitude ${a}_{s}$ of a static part and the effective correlation time ${\ensuremath{\tau}}_{\mathrm{eff}}$ of a rapidly fluctuating part of the local magnetic field at the muon site. The scaled quantities ${a}_{s}$/${a}_{0}$, where ${a}_{0}$ denotes the static field amplitude in the limit T\ensuremath{\rightarrow}0, and ${\ensuremath{\tau}}_{\mathrm{eff}{T}_{f}}$ turn out to be universal functions of the reduced temperature T/${T}_{f}$ for all investigated spin glasses. ${\ensuremath{\tau}}_{\mathrm{eff}}$ decreases below ${T}_{f}$ and qualitatively reflects the temperature dependence predicted by the fractal cluster model for the characteristic correlation time ${\ensuremath{\tau}}_{\ensuremath{\xi}}$. To relate the local-field time correlations and the spin autocorrelation function S(t) quantitatively, we discuss two different models for the local-field dynamics as probed by \ensuremath{\mu}SR. As a result the \ensuremath{\mu}SR data do not reflect a spatial arrangement of spin clusters reorienting with size-dependent relaxation times. Rather the local field appears to be similar at each muon site and seems to consist of many contributions from different spins fluctuating with different correlation times. We analyze neutron and ac susceptibility data for the spin autocorrelation S(t) within the fractal cluster model and show that they agree well with the \ensuremath{\mu}SR results.