Dynamics of Spin Glass in NiFe$_{2}$O$_{4 }$Nanoparticle

The dynamic magnetic properties of spin glass in NiFe$_{2}$O$_{4}$ nanoparticles have been investigated. The strong irreversibility in the zero-field-cooled and the field-cooled temperature-dependent magnetizations implies the spin glass. The real part of the ac susceptibility$_{ }\chi '(T)$ curve shows a pronounced peak. With increasing frequency, the peak ($T_{f})$ shifts to a higher temperature, which is a characteristic of spin glass. The frequency-dependent $T_{f}$ data is fitted by a critical power law: $\tau =\tau _0 (T_f /T_g -1)^{-z\upsilon }$. The spin-glass transition temperature$ T_{g}$ is 290 K. The microscopic flipping time $\tau _0 $ of the fluctuating spins and the critical parameter $z\upsilon $ are obtained to be 10$^{-10}$ s and 8.3 respectively. They are both within the ranges typical for spin glasses (10$^{-10}$ - 10$^{-12 }$s for $\tau _0 $ and 5 - 10 for $z\upsilon )$, confirming the nature of spin glass. The excellent fit by the Vogel-Fulcher model, revealing the existence of the inter-particle interaction, exhibits that spin glass rather than superparamagentism exists in NiFe$_{2}$O$_{4}$ nanoparticles.