The Phase Diagram of Kitaev Materials under Arbitrary Magnetic Field

The Kitaev model is an exactly solvable quantum spin model. 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. We fulfill this purpose in this talk. In this regards, we first extend the present studies on the field angle response of the ferromagnetic Kitaev model to the antiferromagnetic spin exchange interactions. Yet, the realistic Kitaev materials, within the edge-sharing octahedra paradigm, arise with the additional exchange terms. The studies on the candidate materials indicates the presence of a large spin-orbit $\Gamma$ term along with perturbative $\Gamma_p$ and the Heisenberg $J$ terms. It is therefore not reliable to depend on the topological properties of the Kitaev model as the only source of the thermal Hall conductivity experiments and demands an understanding of these models with a complete field response.

Investigating the zero-field phase diagram of the realistic (K, $\Gamma$, $\Gamma_p$) models, we identify antiferromagnetic zig-zag and (partially) polarized spin phases as well as two exotic Kitaev-($\Gamma$) spin liquid phases. The arbitrary magnetic field response of these phases provide a rich phase diagram hosting mainly the extended forms 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-$\Gamma$ 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, $\theta = \pm 60^o$ in the ac plane, naturally. We finally revisited the relation between the topological GS and the antisymmetric thermal conductivity tensor and further clarified our findings in this aspect.