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

TL;DR

The paper applies the numerical linked cluster expansion (NLCE) to the J-K-Γ model on the honeycomb lattice to study thermodynamics and magnetoelastic responses of α-RuCl3 in a magnetic field. NLCE yields energy, specific heat, magnetization, and a linear magnetostriction coefficient, with careful convergence analysis and comparison to exact diagonalization. A key finding is a dip in the magnetostriction that tracks field-driven suppression of zigzag order, in qualitative agreement with experiments and prior theory. The work demonstrates NLCE as a robust tool for magnetoelastic features in quantum magnets and provides benchmarks for understanding field- and temperature-tuned phases in Kitaev-like materials.

Abstract

We apply the numerical linked cluster expansion (NLCE) to study thermodynamic properties of the proximate Kitaev magnet $α$-RuCl$_3$ on the honeycomb lattice in the presence of a magnetic field. Using the extended spin-1/2 $J$-$K$-$Γ$ 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 $α$-RuCl$_3$. Our results are consistent with previous findings, establishing NLCE also as a tool to study magnetoelastic features of quantum magnets.

Figures (5)

• Figure 1: (a) Honeycomb lattice and sample clusters thereon. Red, green and blue label x-, y- and z-type bond-directional exchange, respectively. Black and white vertices denote the triangular lattice basis. Smaller clusters such as (1) can be fully contained by larger ones such as (2). (b) NLCE-decomposition of a cluster into its constituent exemplified: Tricoordinated unit (1) consists of four sites (2) and, equivalently of three bonds (3), one of each type.
• Figure 2: (a) Internal energy per site in the $J$-$K$-$\Gamma$ model calculated using bare sums and (b) the Euler resummation
• Figure 3: (e) Specific heat of the $J$-$K$-$\Gamma$ model: Comparison of 10th and 11th order NLCE (solid orange and blue), with ED on clusters of 12-sites (green dotted/dashed, (a)/(c)) and 16-sites (red dotted/dashed, (b)/(d)).
• Figure 4: Comparing NLCE versus ED for the magnetization of the $J$-$K$-$\Gamma$ model at $T = \qty{29.3}{K}$ for magnetic fields with in-plane, i.e., $[\overline{1}\,1\,0] \hat{=} b$ and out-of-plane, i.e., $[1\,1\,1] \hat{=} c^{*}$ directions. ED on cluster Fig. \ref{['fig:3']}(d).
• Figure 5: (a) Linear magnetostriction coefficient $\lambda_{c^\star}$ of the $J$-$K$-$\Gamma$ model from NLCE at 11th order versus in-plane magnetic field along the $[\overline{1}\,1\,0]$ direction for various temperatures. (b) Comparing NLCE for $\lambda_{c^\star}$ at 10th and 11th order (solid orange and blue) versus temperature at fixed $B=\qty{8.9}{\tesla}$.