Critical behavior of ferromagnetic pure and random diluted nanoparticles with competing interactions: variational and Monte Carlo approaches

TL;DR

This study investigates the critical magnetic behavior of ferromagnetic nanoparticles with disorder and competing interactions using variational and Monte Carlo methods, revealing size-dependent properties and critical exponents.

Contribution

It introduces a combined variational and Monte Carlo approach to analyze the critical behavior of disordered ferromagnetic nanoparticles, including size effects and reentrant spin glass phenomena.

Findings

Variational model reproduces size dependence of Curie temperature.

Low temperature magnetization aligns with reentrant spin glass behavior.

Critical exponent ν differs from pure Ising model, consistent with Harris and Fisher arguments.

Abstract

The magnetic properties and critical behavior of both ferromagnetic pure and metallic nanoparticles having concurrently atomic disorder, dilution and competing interactions, are studied in the framework of an Ising model. We have used both the free energy variational principle based on the Bogoliubov inequality and Monte Carlo simulation. As a case of study for random diluted nanoparticles we have considered the Fe$_{0.5}$Mn$_{0.1}$Al$_{0.4}$ alloy characterized for exhibiting, under bulk conditions, low temperature reentrant spin glass (RSG) behavior and for which experimental and simulation results are available. Our results allow concluding that the variational model is successful in reproducing features of the particle size dependence of the Curie temperature for both pure and random diluted particles. In this last case, low temperature magnetization reduction was consistent with the same type of RSG behavior observed in bulk in accordance with the Almeida-Thouless line at low fields and a linear dependence of the freezing temperature with the reciprocal of the particle diameter was also obtained. Computation of the correlation length critical exponent yielded the values $\nu=0.926\pm 0.004$ via Bogoliubov and$ \nu =0.71\pm 0.04$ via Monte Carlo. This fact indicates that even though thermodynamical models can be indeed used in the study of nanostructures and they can reproduce experimental features, special attention must be paid regarding critical behavior. From both approaches, differences in the $\nu$ exponent with respect to the pure Ising model agree with Harris and Fisher arguments.