We point out that the Kitaev materials may not necessarily support Kitaev spin liquid. It is well known that having a Kitaev term in the spin interaction is not the sufficient condition for the Kitaev spin-liquid ground state. Many other spin liquids may be stabilized by the competing spin interactions of the systems. We thus explore the possibilities of non-Kitaev spin liquids in the honeycomb Kitaev materials. We carry out a systematic classification of gapped ${\mathbb{Z}}_2$ spin liquids using the Schwinger boson representation for the spin variables. The presence of strong spin-orbit coupling in the Kitaev materials brings new ingredients into the projective symmetry group classification of the non-Kitaev spin liquid. We predict the spectroscopic properties of these gapped non-Kitaev spin liquids. Moreover, among the gapped spin liquids that we discover, we identify the spin liquid whose spinon condensation leads to the zigzag magnetic order that was observed in ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ and $\alpha \text{−}{\mathrm{RuCl}}_3$. We further discuss the possibility of gapped ${\mathbb{Z}}_2$ spin liquid and the deconfined quantum criticality from the zigzag magnetic order to spin dimerization in pressurized $\alpha \text{−}{\mathrm{RuCl}}_3$.

• Received 3 March 2019
• Corrected 5 November 2019

DOI:https://doi.org/10.1103/PhysRevB.99.205119