Magnetic Field Dependence of Spin Glass Free Energy Barriers

We measure the field dependence of spin glass free energy barriers in a thin amorphous Ge:Mn film through the time dependence of the magnetization. After the correlation length $\xi (t,T)$ has reached the film thickness $\mathcal{L}=155\AA$ so that the dynamics are activated, we change the initial magnetic field by $\delta H$. In agreement with the scaling behavior exhibited in a companion Letter [M. Baity-Jesi et al., Phys. Rev. Lett. 118, 157202 (2017)], we find that the activation energy is increased when $\delta H<0$. The change is proportional to $(\delta H{)}^2$ with the addition of a small $(\delta H{)}^4$ term. The magnitude of the change of the spin glass free energy barriers is in near quantitative agreement with the prediction of a barrier model.

Figure 1

Magnetization measurements, $M(t,\delta H;H_0)$, after zero-field cooling at 21.5 K, and reducing the original magnetic field $H_0=50\mathrm{G}$ after twenty hours by representative values $\delta H=-5$, $-10$, and $-15\mathrm{G}$, as a function of time. Also plotted is the field-cooled magnetization, $M_{\mathrm{FC}}(H_0+\delta H)$, to which the measured moment is approaching.

Figure 2

The logarithm of the irreversible part of magnetization, ${\log }_{10}[M_{\mathrm{FC}}(H_0+\delta H)-M(t,\delta H;H_0)$], for the representative values $\delta H=-5$, $-10$, and $-15\mathrm{G}$, plotted against the time. The dashed straight lines, displaying activated behavior, give rise to the values of ${\mathrm{\Delta }}_{\max }(H_0+\delta H)$ displayed in Fig. 3.

Figure 3

Plot of the measured increases of the maximum barrier height, ${\mathrm{\Delta }}_{\max }(H_0+\delta H)$ as a function of the reductions in magnetic field $\delta H$. Shown on the figure are curves for the fit to a linear variation in $\delta H$ (dotted line), and a quadratic variation in $\delta H$ (dashed line), with the addition of a small fourth order term to the quadratic variation (solid line). The numerical fitting values are given in Table 1.