Extent of frustration in the classical Kitaev-Γ model via bond anisotropy

In the pseudospin-1/2 honeycomb Mott insulators with strong spin-orbit coupling, there are two types of bond-dependent exchange interactions named Kitaev (K) and Gamma (Γ) that lead to strong frustration. While the ground state of the Kitaev model is a quantum spin liquid with fractionalized excitations, the ground state of the Γ model remains controversial. In particular, the phase diagram of the KΓ model with ferromagnetic K and antiferromagnetic Γ interactions has been intensively studied because of its relevance to candidate materials such as α-RuCl₃. Numerical studies also included the effects of tuning the bond strengths, i.e., z-bond strength different from the other bonds. However, no clear consensus on the overall phase diagram has been reached yet. Here we discuss the classical KΓ model with anisotropic bond strengths studied using Monte Carlo simulations to understand the phases that emerge out of the competition between the two frustrated limits. We also address how the anisotropic bond strength affects the phase diagram and strength of quantum fluctuations.