Magnetostriction in the $J$-$K$-$\Gamma$ model: Application of the numerical linked cluster expansion

TL;DR

This study uses the numerical linked cluster expansion to analyze thermodynamic and magnetoelastic properties of the Kitaev magnet $ ext{RuCl}_3$ under magnetic fields, revealing features related to magnetic order suppression.

Contribution

It demonstrates the application of NLCE to compute magnetostriction and thermodynamics in the $J$-$K$-$ extGamma$ model for $ ext{RuCl}_3$, linking magnetoelastic effects to magnetic order.

Findings

Magnetostriction shows a dip-like feature correlating with magnetic order suppression.

Results align with previous studies, validating NLCE for magnetoelastic analysis.

Computed thermodynamic quantities match experimental observations.

Abstract

We apply the numerical linked cluster expansion (NLCE) to study thermodynamic properties of the proximate Kitaev magnet $\alpha$-RuCl$_3$ on the honeycomb lattice in the presence of a magnetic field. Using the extended spin-1/2 $J$-$K$-$\Gamma$ model and based on documented exchange and magnetoelastic coupling parameters, we present results for the internal energy, the specific heat, and the magnetization. Moreover, the linear magnetostriction coefficient perpendicular to the plane is calculated, which is sensitive to changes of the in-plane spin-spin correlations. We find the magnetostriction to display a dip-like feature, in line with the temperature dependent and field-driven suppression of magnetic order in $\alpha$-RuCl$_3$. Our results are consistent with previous findings, establishing NLCE also as a tool to study magnetoelastic features of quantum magnets.