Dynamic scaling in theEu0.4Sr0.6S spin-glass

We have established the zero-field freezing temperature and $T_f(H,\omega )$ lines associated with a constant relaxation time over a large frequency range (${10}^{-2\mathrm{}}$-${10}^5$ Hz) in ${\mathrm{Eu}}_{0.4}$ ${\mathrm{Sr}}_{0.6}$S. The choice of the experimental criterion and the demagnetizing field effects are analyzed in some detail in order to establish the validity and the limits of our analysis. Two different scalings are tested as suggested by Binder and Young: $T_c=0\mathrm{}$, $\ln \left(\frac{\tau }{{\tau }_0}\right)=T^{-z\nu }f\left(\frac{H}{T^{\Delta }}\right)$; and $T_c\ne 0$, $\frac{\tau }{{\tau }_0}={(T-T_c)}^{-z\nu }g\left({(T-T_c)}^{-\Delta }\right(\frac{H}{T}\left)\right)$. Both are found to work satisfactorily with the following sets of parameters: for $T_c=0\mathrm{}$ K, $z\nu =8\mathrm{}$, $\Delta =10.5\mathrm{}$, and ${\tau }_0\sim {10}^{-5\mathrm{}}$ s; for $T_c=1.50\mathrm{}$ K, $z\nu =7\mathrm{}$, $\Delta =2\mathrm{}$, and ${\tau }_0\sim {10}^{-7\mathrm{}}$ s. The latter value of ${\tau }_0$ appears to be more consistent with previous relaxation data than the former. Hence, our fitting procedure suggests that $T_c\ne 0$ K (equal to ∼1.50 K) for ${\mathrm{Eu}}_{0.4}$ ${\mathrm{Sr}}_{0.6}$S.