Observation of superspin-glass behavior in Fe$_{3}$O$_{4}$ nanoparticles

TL;DR

This study investigates the magnetic aging, memory effects, and critical slowing down in Fe₃O₄ nanoparticles, revealing superspin-glass behavior below a freezing temperature of approximately 30.6 K.

Contribution

It provides experimental evidence of superspin-glass phase in Fe₃O₄ nanoparticles through detailed magnetic measurements and critical analysis.

Findings

Aging dip observed in ZFC magnetization depends on wait time.

Critical slowing down characterized by a power law with specific exponents.

Critical line with field dependence close to de Almeida-Thouless prediction.

Abstract

The aging and memory effects of Fe$_{3}$O$_{4}$ nanoparticles have been studied using a series of zero-field cooled (ZFC) and field-cooled (FC) magnetization measurements at various aging protocols. The genuine ZFC magnetization after the ZFC procedure with a single stop and wait process shows an aging dip at the stop temperature on reheating. The depth of the aging dip is dependent on the wait time. The frequency dependence of the AC magnetic susceptibility is indicative of critical slowing down at a freezing temperature $T_{f}$ ($= 30.6 \pm 1.6$ K). The relaxation time $\tau$ is described by a power law form with a dynamic critical exponent $x$ ($= 8.2 \pm 1.0$) and a microscopic relaxation time $\tau_{0}$ [$=(1.33 \pm 0.05) \times 10^{-9}$ sec]. The ZFC-peak temperature decreases with increasing magnetic field ($H$), forming a critical line with an exponent $p = 1.78 \pm 0.26$, close to the de Almeida-Thouless exponent ($p = 3/2$). These results indicate that the superspin glass phase occurs below $T_{f}$.