Specific heat of Gd$^{3+}$ and Eu$^{2+}$-based magnetic compounds

TL;DR

This paper presents a theoretical analysis of the specific heat in Gd$^{3+}$ and Eu$^{2+}$-based magnetic compounds, revealing that it is primarily governed by the effective number of neighbors and axial anisotropy, allowing for accurate data fitting and parameter extraction.

Contribution

The study introduces a simplified model using two key parameters to accurately describe the specific heat of 4f$^7$ magnetic systems, enabling extraction of magnetic interactions beyond mean-field approximations.

Findings

Specific heat is mainly governed by the effective number of neighbors and axial anisotropy.

The model achieves excellent fit to experimental data for several Gd and Eu compounds.

Universality of the effective number of neighbors holds under certain conditions, deviations occur otherwise.

Abstract

We have studied theoretically the specific heat of a large number of non-frustrated magnetic structures described by the Heisenberg model for systems with total angular momentum $J=7/2$, corresponding to the 4f$^7$ configuration of Gd$^{+3}$ and Eu$^{+2}$. For a given critical temperature (determined by the magnitude of the exchange interactions), we find that, to a high degree of accuracy, the specific heat is governed by two primary parameters: the effective number of neighbors $z$, which dictates the extent of spatial and quantum fluctuations, and the axial anisotropy $K$. The universality of $z$ (its ability to describe specific heat across diverse lattices) holds robustly for systems where exchange interactions do not strongly increase with distance and in the absence of frustration. Otherwise, deviations from universality emerge. Using these two parameters we fit the specific heat of four Gd compounds and two Eu compounds, achieving a remarkable agreement. The present approach enables the extraction of magnetic interaction parameters not accessible through mean-field theory, offering a powerful tool for interpreting specific heat data in 4f$^7$ systems.