Magnetic relaxation and correlating effective magnetic moment with particle size distribution in maghemite nanoparticles

TL;DR

This study investigates how particle size distribution affects the magnetic relaxation and effective magnetic moments in maghemite nanoparticles, revealing detailed relationships between size, magnetic properties, and temperature.

Contribution

It provides a detailed analysis of the influence of size distribution on magnetic relaxation and moments in maghemite nanoparticles, using TEM, magnetization, and susceptibility measurements.

Findings

Particle size distribution is log-normal with mean 7.04 nm.

Absence of significant interparticle interaction inferred from blocking temperature shift.

Consistent magnetic moment values obtained from different analysis methods.

Abstract

The role of particle size distribution inherently present in magnetic nanoparticles (NPs) is examined in considerable detail in relation to the measured magnetic properties of oleic acid-coated maghemite ({\gamma}-Fe$_2$O$_3$) NPs. Transmission electron microscopy (TEM) of the sol-gel synthesized $\gamma$-$Fe$$_2$$O$$_3$ NPs showed a log-normal distribution of sizes with average diameter $<D>$= 7.04 nm and standard deviation $\sigma$= 0.78 nm. Magnetization, $M$, vs. temperature (2 K to 350 K) of the NPs was measured in an applied magnetic field $H$ up to 90 kOe along with the temperature dependence of the ac susceptibilities, $\chi$$'$ and $\chi$$"$, at various frequencies, $f$$_m$, from 10 Hz to 10 kHz. From the shift of the blocking temperature from $T$$_B$ =35 K at 10 Hz to $T$$_B$ = 48 K at 10 kHz, the absence of any significant interparticle interaction is inferred and the relaxation frequency $f$$_o$= 2.6 x 10$^{10}$ Hz and anisotropy constant $K$$_a$= 5.48 x 10$^5$ ergs/cm$^3$ are determined. For $T$ < $T$$_B$, the coercivity $H$$_C$ is practically negligible. For $T$ > $T$$_B$, the data of $M$ vs. $H$ up to 90 kOe at several temperatures are analyzed two different ways: (i) in terms of the modified Langevin function yielding an average magnetic moment per particle $\mu$$_p$=7300 (500) $\mu$$_B$; and (ii) in terms of log-normal distribution of moments yielding $<$$\mu$$>$= 6670 $\mu$$_B$ at 150 K decreasing to $<$$\mu$$>$= 6100 $\mu$$_B$ at 300 K with standard deviations $\sigma$ $\approx$ $<$$\mu$$>$$/2$. The above two approaches yield consistent and physically meaningful results as long as the width parameter, $s$, of the log-normal distribution is less than 0.83.