Extent of frustration in the classical Kitaev-Γmodel via bond anisotropy,Physical Review B

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Extent of frustration in the classical Kitaev-Γmodel via bond anisotropy
Physical Review B ( IF 3.2 ) Pub Date : 2021-09-27 , DOI: 10.1103/physrevb.104.094431
Ahmed Rayyan ₁ , Qiang Luo ₁ , Hae-Young Kee _{1,

2}

Affiliation

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

Γ

, leading 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

K Γ

model with ferromagnetic

K

and antiferromagnetic

Γ

interactions has been intensively studied because of its relevance to candidate materials such as

α − {RuCl}_{3}

. 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 study the classical

K Γ

model with anisotropic bond strengths using Monte Carlo simulations to understand the phases that emerge out of competition between the two frustrated limits. We also address how the anisotropic bond strength affects the phase diagram and strength of quantum fluctuations. We found various large unit cell phases due to the competing frustrations, and analyzed their intrinsic degeneracy based on the symmetry of the Hamiltonian. Using the linear spin wave theory we showed that the anisotropic bond strength enhances quantum fluctuations in the

Γ

-dominant regime where a small reduced moment is observed. The implications of our findings in relation to the quantum model are also discussed.

中文翻译：

通过键各向异性在经典 Kitaev-Γ 模型中受挫的程度

在伪自旋

\frac{1}{2}

具有强自旋轨道耦合的蜂窝莫特绝缘体，有两种类型的键依赖交换相互作用，命名为 Kitaev

(钾)

和

Γ

，导致强烈的挫败感。虽然 Kitaev 模型的基态是具有分级激发的量子自旋液体，但基态

Γ

模型仍然存在争议。特别是，相图

钾 Γ

铁磁模型

钾

和反铁磁

Γ

相互作用已被深入研究，因为它与候选材料的相关性，例如

α - {氯化钌}_{3}

. 数值研究还包括调整键强度的影响，即，

z

- 键强度不同于其他键。然而，尚未就整体相图达成明确的共识。我们在这里学习经典

钾 Γ

使用 Monte Carlo 模拟具有各向异性键强度的模型，以了解两个受挫限制之间的竞争产生的阶段。我们还讨论了各向异性键强度如何影响量子涨落的相图和强度。由于相互竞争的挫折，我们发现了各种大晶胞相，并基于哈密顿量的对称性分析了它们的内在简并性。使用线性自旋波理论，我们表明各向异性键强度增强了量子涨落