The Phase Diagram of Kitaev Models under Arbitrary Magnetic Field Strengths and Orientations

The Kitaev model is an exactly solvable bon anisotropic spin model within the real fermion language. In spite of numerous studies along special field directions such as [001] and [111], there are is a limited knowledge on the complete field angle dependence of the thermal Hall current, which can provide valuable information on the existence of fractionalization. To fulfill this purpose, we first extend the present studies on the field angle response of the anti/ferromagnetic Kitaev. Yet, the realistic Kitaev materials, within the edgesharing octahedra paradigm, arise with the additional exchange terms. The studies on the candidate materials indicates the presence of a large spin-orbit Γ term along with perturbative Γ' and the Heisenberg J terms. It is therefore not reliable to depend on the topological properties of the pure Kitaev model as the only source of the thermal Hall conductivity experiments and it demands an understanding of these models with a complete field response.

Investigating the zero-field phase diagram of the realistic (K,Γ,Γ’) models, we identify conventional antiferromagnetic zigzag and (partially) polarized spin phases as well as two exotic Kitaev(-Γ) spin liquid phases. The arbitrary magnetic field response of these phases provides a rich phase diagram hosting mainly the extended versions of the zero-field phases.

We observe a partially suppressed intermediate region with a finite Chern number and a vanishing gauge flux. This phase is concluded to be an extended phase of Kitaev-Γ spin liquid phase, which resides between the ZZ and the polarized phases. To comply our findings with the experiments and to verify the power of our method, we reproduce the narrow or extended regions of the intermediate phase depending on the field directions, θ=±60 in the ac plane, naturally. We finally revisited the relation between the topological GS and the anti/symmetric thermal conductivity tensor and further clarified our findings in this aspect.