Fully Generalized Spin Models with Strain Effects of Kitaev Spin Liquid Candidate Materials

TL;DR

This paper introduces a fully generalized spin model that incorporates lattice strain effects, derived from DFT calculations, to better understand and predict magnetic phase transitions and topological states in Kitaev candidate materials under realistic conditions.

Contribution

The authors develop an $ ext{ extonehalf}$-generalized spin model incorporating arbitrary lattice deformations and strain-dependent interactions, derived from first-principles calculations, enhancing the modeling of Kitaev materials.

Findings

Strain of 3% in $ ext{ extonehalf}$-RuCl$_3$ induces new exchange interactions of comparable magnitude.

Strain-driven quantum phase transitions between magnetic states, including topological transitions within the KQSL, are identified.

The model's symmetry analysis applies to both $d^5$ and $d^7$ transition-metal systems.

Abstract

The $KJ\Gamma\Gamma'$ spin model-originally derived for an ideal $P\bar{3}1m$ symmetric geometry-has long served as a central framework for understanding candidate Kitaev materials. In realistic crystals, however, this ideal geometry is seldom realized, either at low temperatures or under external perturbations, limiting the model's quantitative applicability. Here we introduce a fully generalized spin model, denoted $\epsilon$-$KJ\Gamma\Gamma'$, that explicitly incorporates arbitrary lattice deformations $\epsilon$. All spin-exchange interactions and their strain-dependent coefficients are obtained from density-functional theory (DFT) calculations and a microscopic derivation of coupling constants for materials based on $d^5$ transition-metal ions. For $\alpha$-RuCl$_3$ under a strain of $3\%$, new emergent exchange channels acquire magnitudes comparable to their unstrained counterparts. Building on these parameters, we investigate strain-driven quantum phase transitions between competing magnetic states-including the zigzag order and the Kitaev quantum spin liquid (KQSL)-and identify a strain-induced topological transition within the KQSL states that offers a practical diagnostic of Kitaev physics. Furthermore, our symmetry analysis of the $\epsilon$-$KJ\Gamma\Gamma'$ model is applicable to both $d^{5}$ ions, such as $\alpha$-RuCl$_3$, and $d^{7}$ systems, including cobalt-based compounds.