On the superposition principle and non-linear response in spin glasses

Abstract

The extended principle of superposition has been a touchstone of spin glass dynamics for almost thirty years. The Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields $H$ up to 10 Oe at the reduced temperature $T_{\mathrm{r}}=T/T_{\mathrm{g}}=0.95$, where $T_{\mathrm{g}}$ is the spin glass condensation temperature. For $H>10$ Oe, they observe a departure from linear response which they ascribe to the development of non-linear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin glass correlation length, $\xi (t,t_{\mathrm{w}};H)$. Here, $t$ is the time after $H$ changes, and $t_{\mathrm{w}}$ is the time from the quench for $T>T_{\mathrm{g}}$ to the working temperature $T$ until $H$ changes. We connect the growth of $\xi (t,t_{\mathrm{w}};H)$ to the barrier heights $\Delta (t_{\mathrm{w}})$ that set the dynamics. The effect of $H$ on the magnitude of $\Delta (t_{\mathrm{w}})$ is responsible for affecting differently the two dynamical protocols associated with turning $H$ off (TRM, or thermoremanent magnetization) or on (ZFC, or zero field-cooled magnetization). In this paper, we display the difference between the zero-field cooled ${\xi }_{\text{ZFC}}(t,t_{\mathrm{w}};H)$ and the thermoremanent magnetization ${\xi }_{\text{TRM}}(t,t_{\mathrm{w}};H)$ correlation lengths as $H$ increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group.

arXiv comment23 pages and 18 figures

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