Validity of the N\'{e}el-Arrhenius model for highly anisotropic Co_xFe_{3-x}O_4 nanoparticles

TL;DR

This study validates the Néel-Arrhenius model for describing the magnetic relaxation of highly anisotropic Co_xFe_{3-x}O_4 nanoparticles across various sizes, incorporating temperature-dependent anisotropy to match experimental data.

Contribution

It demonstrates that the Néel-Arrhenius relaxation framework, with a temperature-dependent anisotropy, accurately describes the magnetic behavior of highly anisotropic cobalt ferrite nanoparticles.

Findings

The model fits static and dynamic magnetic data without ad-hoc corrections.

The anisotropy constants match bulk values for larger particles.

Small particles show deviations explained by surface effects.

Abstract

We report a systematic study on the structural and magnetic properties of Co_{x}Fe_{3-x}O_{4} magnetic nanoparticles with sizes between $5$ to $25$ nm, prepared by thermal decomposition of Fe(acac)_{3} and Co(acac)_{2}. The large magneto-crystalline anisotropy of the synthesized particles resulted in high blocking temperatures ($42$ K \leqq $T_B$ $\leqq 345$ K for $5 \leqq$ d $\leqq 13$ nm ) and large coercive fields ($H_C \approxeq 1600$ kA/m for $T = 5$ K). The smallest particles ($<d>=5$ nm) revealed the existence of a magnetically hard, spin-disordered surface. The thermal dependence of static and dynamic magnetic properties of the whole series of samples could be explained within the N\'{e}el-Arrhenius relaxation framework without the need of ad-hoc corrections, by including the thermal dependence of the magnetocrystalline anisotropy constant $K_1(T)$ through the empirical Br\"{u}khatov-Kirensky relation. This approach provided $K_1(0)$ values very similar to the bulk material from either static or dynamic magnetic measurements, as well as realistic values for the response times ($\tau_0 \simeq 10^{-10}$ s). Deviations from the bulk anisotropy values found for the smallest particles could be qualitatively explained based on Zener\'{}s relation between $K_1(T)$ and M(T).