Spin-glass-like complex susceptibility of frozen magnetic fluids

Abstract

The complex magnetic susceptibility $\ensuremath{\chi}={\ensuremath{\chi}}^{\ensuremath{'}}\ensuremath{-}i{\ensuremath{\chi}}^{\ensuremath{''}}$ of different kinds of magnetic fluids (MFs) was measured as a function of temperature $T$ from 6 to 300 K in a weak ac field of 1 Oe for frequencies ranging from $f=0.1$ to 1000 Hz. A prominent peak appears in both ${\ensuremath{\chi}}^{\ensuremath{'}}$ and ${\ensuremath{\chi}}^{\ensuremath{''}}$ as a function of $T$ in the frozen state of the MF in which cluster formation of the colloidal particles is difficult, whereas no peak appears in the frozen state of other MFs in which clusters form easily. The peak temperature ${T}_{p2}$ of ${\ensuremath{\chi}}^{\ensuremath{''}}$ depends on $f$ following the Vogel-Fulcher (VF) law, i.e., ${f=f}_{0}\mathrm{exp}[\ensuremath{-}{E}_{\mathrm{sg}}{/k}_{B}{(T}_{p2}\ensuremath{-}{T}_{0})],$ where ${f}_{0}$ and ${E}_{\mathrm{sg}}$ are positive constants and ${T}_{0}$ is a function of the particles' volume fraction \ensuremath{\varphi}. The VF law only holds for $0.0007l~\ensuremath{\varphi}l~0.104,$ where an empirical power law of ${T}_{0}\ensuremath{\propto}{\ensuremath{\varphi}}^{0.41}$ holds. There is another kind of peak in the loss factor $\mathrm{tan}\ensuremath{\delta}={\ensuremath{\chi}}^{\ensuremath{''}}/{\ensuremath{\chi}}^{\ensuremath{'}}$ as a function of $T,$ which means the existence of a magnetic aftereffect. This peak temperature ${T}_{p4}$ is far less than ${T}_{p2}$ and shown as an Arrhenius-type dependence on $f$ with the exception of a MnZn ferrite particle MF.