Spin-glass dynamics in the presence of a magnetic field: exploration of microscopic properties

The synergy between experiment, theory, and simulations enables a microscopic analysis of spin-glass dynamics in a magnetic field in the vicinity of and below the spin-glass transition temperature $T_{\mathrm{g}}$. The spin-glass correlation length, $\xi (t,t_{\mathrm{w}};T)$, is analysed both in experiments and in simulations in terms of the waiting time $t_{\mathrm{w}}$ after the spin glass has been cooled down to a stabilised measuring temperature $T<T_{\mathrm{g}}$ and of the time $t$ after the magnetic field is changed. This correlation length is extracted experimentally for a CuMn 6 at. % single crystal, as well as for simulations on the Janus II special-purpose supercomputer, the latter with time and length scales comparable to experiment. The non-linear magnetic susceptibility is reported from experiment and simulations, using $\xi (t,t_{\mathrm{w}};T)$ as the scaling variable. Previous experiments are reanalysed, and disagreements about the nature of the Zeeman energy are resolved. The growth of the spin-glass magnetisation in zero-field magnetisation experiments, $M_{\mathrm{Z}\mathrm{F}\mathrm{C}}(t,t_{\mathrm{w}};T)$, is measured from simulations, verifying the scaling relationships in the dynamical or non-equilibrium regime. Our preliminary search for the de Almeida-Thouless line in $D=3$ is discussed.