# Thermodynamics of delta-chain with ferro- and antiferromagnetic interactions

## TL;DR

This paper investigates the thermodynamics of a delta-chain with competing ferro- and antiferromagnetic interactions, combining classical and quantum models to understand magnetic properties relevant to a specific cyclic compound.

## Contribution

It provides an exact solution for the classical model and explores quantum effects using numerical techniques, linking theoretical results to experimental compounds.

## Key findings

- Classical model accurately predicts magnetic susceptibility.
- Quantum effects alter low-temperature specific heat behavior.
- Results relate to the magnetic properties of $Fe_{10}Gd_{10}$.

## Abstract

Motivated by a novel cyclic compound $Fe_{10}Gd_{10}$ with record ground state spin in which the arrangement of magnetic ions with $s=\frac{5}{2}$ and $s=\frac{7}{2}$ corresponds to a saw-tooth chain we investigate the thermodynamics of the delta-chain with competing ferro- and antiferromagnetic interactions. We study both classical and quantum versions of the model. The classical model is exactly solved and quantum effects are studied using full diagonalization and a finite temperature Lanczos technique for finite delta-chains as well as modified spin wave theory. It is shown that the main features of the magnetic susceptibility of the quantum spin delta chain are correctly described by the classical spin model, while quantum effects significantly change the low-temperature behavior of the specific heat. The relation of the obtained results to the $Fe_{10}Gd_{10}$ system is discussed.