Aging dynamics across a dynamic Almeida-Thouless line in three dimensional short-range Issuing spin glass Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compound

TL;DR

This study investigates the aging dynamics and stability of a three-dimensional short-range Ising spin glass in a magnetic field, revealing a dynamic crossover from spin glass to paramagnetic behavior consistent with droplet theory.

Contribution

It provides experimental evidence of the instability of the spin glass phase in a finite magnetic field and demonstrates scaling behavior predicted by droplet theory.

Findings

Relaxation rate peak time decreases with increasing magnetic field.

Spin freezing temperature indicates instability of the spin glass phase in a field.

Scaling behavior supports a dynamic crossover from spin glass to paramagnetic state.

Abstract

Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ graphite intercalation compound is a three-dimensional short-range Ising spin glass with a spin freezing temperature $T_{c}$ ($= 3.92 \pm 0.11$ K). The stability of the spin glass phase in the presence of a magnetic field $H$ is examined from (i) the spin freezing temperature $T_{f}(\omega,H)$ at which the differential field-cooled (FC) susceptibility $\partial M_{FC}(T,H)/\partial H$ coincides with the dispersion $\chi^{\prime}(\omega,T,H=0)$ with the angular frequency $\omega$, and (ii) the time dependence of zero-field cooled (ZFC) susceptibility $\chi_{ZFC}$ after a ZFC aging protocol with a wait time $t_{W}$ ($= 1.0 \times 10^{4}$). The relaxation rate $S(t)$ (= d$\chi_{ZFC}$/d$\ln t$) exhibits a local maximum at a characteristic time $t_{cr}$, reflecting non-equilibrium aging dynamics. The peak time $t_{cr}(T,H)$ decreases with increasing $H$ at the fixed temperature $T$ (2.9 K $\leq T<T_{c}$). The spin freezing temperature $T_{f}(\omega,H)$ provides evidence for the instability of the spin glass phase in thermal equilibrium in a finite magnetic field. Both $t_{cr}(T,H)$ and $T_{f}(\omega,H)$ exhibit certain scaling behavior predicted from the droplet picture, suggesting a dynamic crossover from SG dynamics to paramagnetic behavior in the presence of $H$.