The delta-chain with ferro- and antiferromagnetic interactions in applied magnetic field

TL;DR

This paper investigates the thermodynamics of a delta-chain model with competing magnetic interactions under an external magnetic field, providing exact solutions for the classical case and numerical analysis for the quantum case, relevant to a specific compound.

Contribution

It offers the first exact analytical solution for the classical delta-chain model with ferro- and antiferromagnetic interactions in a magnetic field and explores quantum effects using numerical methods.

Findings

Classical model's magnetization defines a universal scaling function.

Quantum model's susceptibility depends on spin quantum number s.

Results are relevant for understanding Fe$_{10}$Gd$_{10}$ compound.

Abstract

We study the thermodynamics of the delta-chain with competing ferro- and antiferromagnetic interactions in an external magnetic field which generalizes the field-free case studied previously. This model plays an important role for the recently synthesized compound Fe$_{10}$Gd$_{10}$ which is nearly quantum critical. The classical version of the model is solved exactly and explicit analytical results for the low-temperature thermodynamics are obtained. The spin-$s$ quantum model is studied using exact diagonalization and finite-temperature Lanzos techniques. Particular attention is focused on the magnetization and the susceptibility. The magnetization of the classical model in the ferromagnetic part of the phase diagram defines the universal scaling function which is valid for the quantum model. The dependence of the susceptibility on the spin quantum number $s$ at the critical point between the ferro- and ferrimagnetic phases is studied and the relation to Fe$_{10}$Gd$_{10}$ is discussed.