Interplay of Kitaev Interaction and Off-Diagonal Exchanges: Exotic Phases and Quantum Phase Diagrams

Aligning with the ongoing search for quantum spin liquids (QSLs), identifying QSLs in Kitaev magnets has attracted significant research interest during the past decade. Nevertheless, it remains a significant challenge. One of the major difficulties is that Kitaev QSL is typically fragile to competing interactions such as off-diagonal exchanges, which are ubiquitous in real materials owing to spin-orbit coupling and crystal-field effects. This, in turn, generates many intriguing field-induced novel phases and the thermal Hall effect. In this review, we focus on the interplay between the Kitaev interaction and off-diagonal Γ and Γ′ exchange from a numerical perspective. The review discusses certain representative exotic phases such as Γ spin liquid, nematic ferromagnet, spin-flop phase, and distinct chiral spin states with spontaneous time-reversal symmetry breaking. It also presents quantum phase diagrams of anisotropic Kitaev-Γ chains that exhibit kaleidoscopy for both ordered and disordered phases.