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

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.