Effectiveness of the Self-Consistent Harmonic Approximation in ferromagnets with dipolar interactions

TL;DR

This paper extends the Self-Consistent Harmonic Approximation (SCHA) to include dipolar interactions in ferromagnets, demonstrating its effectiveness in accurately describing magnetic properties of EuO and EuS.

Contribution

The paper generalizes the SCHA method to incorporate dipolar interactions, improving the modeling of real magnetic materials beyond short-range interactions.

Findings

SCHA with dipolar interactions agrees well with experimental data

The generalized SCHA accurately predicts transition temperatures

Dipolar interactions significantly influence magnetic behavior

Abstract

Among the various methods for treating magnetic models, the Self-Consistent Harmonic Approximation (SCHA) has successfully described ferro and antiferromagnetism in many different scenarios. In particular, the SCHA is a valuable and easy formalism for determining transition temperatures as, for example, the Berezinskii-Kosterlitz-Thouless. The heart of the method includes thermal fluctuations through of a renormalization parameter depending on temperature. Nevertheless, most of the work has been done considering only short-range interactions, which results in an incomplete description of actual magnetic samples. Here, we generalize the SCHA to include the dipolar interaction in the thermodynamic analysis. The method is applied to analyze the well-known Europium Chalcogenides EuO and EuS. The SCHA results are in good agreement with the experimental measurements.