A semi-empirical analysis of the paramagnetic susceptibility of solid state magnetic clusters

TL;DR

This paper develops an analytical microscopic theory to accurately model the paramagnetic susceptibility of magnetic cluster materials, incorporating intercluster interactions and frustration effects, validated through application to experimental data.

Contribution

It introduces a semi-empirical analytical approach for calculating susceptibility in cluster magnets, including intercluster interactions and a new frustration parameter.

Findings

The theory fits experimental susceptibility data well.

Intercluster interactions significantly influence magnetic properties.

A new effective frustration parameter is proposed.

Abstract

Recent developments in the synthesis of new magnetic materials lead to the discovery of new quantum paramagnets. Many of these materials, such as the perovskites Ba$_{4}$LnMn$_{4}$O$_{12}$ (Ln = Sc or Nb), Ba$_{3}$Mn$_{2}$O$_{8}$, and Sr$_{3}$Cr$_{2}$O$_{8}$ present isolated magnetic clusters with strong intracluster interactions but weak intercluster interactions, which delays the onset of order to lower temperatures ($T$). This offset between the local energy scale and the magnetic ordering temperature is the hallmark of magnetic frustration. At sufficient high-$T$, the paramagnetic susceptibility ($\chi$) of frustrated cluster magnets can be fit to a Curie-Weiss law, but the derived microscopic parameters cannot in general be reconciled with those obtained from other methods. In this work, we present an analytical microscopic theory to obtain $\chi$ of dimer and trimer cluster magnets, the two most commonly found in literature, making use of suitable Heisenberg-type Hamiltonians. We also add intercluster interactions in a mean-field level, thus obtaining an expression to the critical temperature of the system and defining a new effective frustration parameter $f_{\text{eff}}$. Our method is exemplified by treating the $\chi$ data of some selected materials.