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

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 $\le T<T_c$). 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 $H$.

10 pages, 12 figures; submitted to Physical Review B