Critical dynamics of metallic spin glasses

We have measured the ac nonlinear susceptibilities ${\chi }_3^{\mathcal{’}}$, ${\chi }_5^{\mathcal{’}}$, and ${\chi }_7^{\mathcal{’}}$ of very dilute AgMn spin glasses above and below the transition temperature $T_g$ as a function of frequency, temperature and magnetic field. In the static limit, these quantities display well-defined critical singularities at $T_g$ and imply a divergence of the spin-glass correlation length. The nonlinear susceptibilities can be fitted above $T_g$ to powers of frequency with weakly temperature-dependent exponents. While the effective exponents satisfy the relations imposed by static and dynamic scaling, the observed temperature and frequency roundings suggest that the spin-glass correlation length does not actually become infinite and is cut off at a length scale of 2000 Å. Activated behavior in the vicinity of $T_g$ with a logarithmic dynamic scaling also accounts for the measured dynamical nonlinear susceptibilities. The measured critical exponents (β=0.9, γ=2.3, δ=3.3, ν=1.3, z=5.4) are not mean field, and differ from the exponents obtained by Monte Carlo simulation of short-range Ising systems.