Extent of frustration in the classical Kitaev- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">Γ</mml:mi></mml:math> model via bond anisotropy

In the pseudospin-$\frac{1}{2}$ honeycomb Mott insulators with strong spin-orbit coupling, there are two types of bond-dependent exchange interactions, named Kitaev ($K$) and $\Gamma$, leading to frustration. While ground state model is a quantum spin liquid fractionalized excitations, $\Gamma$ remains controversial. particular, phase diagram $K\Gamma$ ferromagnetic $K$ antiferromagnetic interactions has been intensively studied because its relevance candidate materials such as $\alpha$-RuCl$_{3}$. Numerical studies also included effects tuning bond strengths, i.e., $z$-bond strength different from other bonds. However, no clear consensus on overall reached yet. Here we study classical anisotropic using Monte Carlo simulations understand emerging phases out competition between frustrated limits. We address how affects fluctuations. found various large unit cell due competing frustrations, analyzed their intrinsic degeneracy based symmetry Hamiltonian. Using linear wave theory showed that enhances fluctuations in $\Gamma$-dominant regime where small reduced moment observed. The implications our findings relation discussed.