Thermodynamics of multiferroic spin chains

TL;DR

This paper investigates the thermodynamics of a Heisenberg spin chain model relevant for multiferroic materials, revealing how temperature and anisotropies influence incommensurate correlations and fitting experimental susceptibilities.

Contribution

It provides a detailed analysis of the thermodynamic behavior of the model, including temperature effects on correlations and improved parameter fitting for specific materials.

Findings

Incommensurate correlations depend on temperature and J2/|J1| ratio.

Easy-plane anisotropies can stabilize vector chiral order.

Fitted J2 values for LiCuVO4 are around 90 K, consistent with experiments.

Abstract

The minimal model to describe many spin chain materials with ferroelectric properties is the Heisenberg model with ferromagnetic nearest neighbor coupling J1 and antiferromagnetic next-nearest neighbor coupling J2. Here we study the thermodynamics of this model using a density-matrix algorithm applied to transfer matrices. We find that the incommensurate spin-spin correlations - crucial for the ferroelectric properties and the analogue of the classical spiral pitch angle - depend not only on the ratio J2/|J1| but also strongly on temperature. We study small easy-plane anisotropies which can stabilize a vector chiral order as well as the finite-temperature signatures of multipolar phases, stable at finite magnetic field. Furthermore, we fit the susceptibilities of LiCuVO4, LiCu2O2, and Li2ZrCuO4. Contrary to the literature, we find that for LiCuVO4 the best fit is obtained with J2 ~ 90 K and J2/|J1| ~ 0.5 and show that these values are consistent with the observed spin incommensurability. Finally, we discuss our findings concerning the incommensurate spin-spin correlations and multipolar orders in relation to future experiments on these compounds.