Fundamental inequalities in the Stoner-Wohlfarth model

TL;DR

This paper establishes fundamental inequalities in the Stoner-Wohlfarth model, deriving limits for magnetic susceptibility, analytical solutions for low-field magnetization, and exploring effects of interactions on these properties.

Contribution

It introduces new fundamental inequalities and analytical solutions in the Stoner-Wohlfarth model, including a mean-field theory for interacting systems and criteria for exchange interactions.

Findings

Derived the theoretical limit for initial magnetic susceptibility.

Obtained analytical solutions for magnetization in low-field regimes.

Identified violation of susceptibility inequalities as a signature of exchange interactions.

Abstract

We report two fundamental inequalities in the Stoner-Wohlfarth model. Specifically, we investigate the theoretical limit for the initial magnetic susceptibility in a system described by the Stoner-Wohlfarth approach. We also find analytical solutions for the magnetization in the low-field regime and obtain the borderline value for the uniaxial anisotropy constant in such an ideal Stoner-Wohlfarth system. We go beyond and introduce a general mean-field theory for interacting Stoner-Wohlfarth-like systems, thus estimating how the initial magnetic susceptibility is affected by the dipolar and exchange interactions inside the system. By means of a simple insight from a fundamental inequality for the magnetic susceptibility of an ideal Stoner-Wohlfarth system, we show its violation is a signature of the existence of exchange interactions between nanoparticles in an interacting Stoner-Wohlfarth-like system.