# Non-Kitaev spin liquids in Kitaev materials

## TL;DR

This paper explores the existence of non-Kitaev spin liquids in honeycomb Kitaev materials, classifying gapped $ ext{Z}_2$ spin liquids and predicting their spectroscopic properties, challenging the assumption that Kitaev interactions alone produce Kitaev spin liquids.

## Contribution

It provides a systematic classification of non-Kitaev gapped $ ext{Z}_2$ spin liquids in Kitaev materials considering strong spin-orbit coupling effects.

## Key findings

- Identification of non-Kitaev gapped $ ext{Z}_2$ spin liquids.
- Prediction of spectroscopic signatures for these spin liquids.
- Connection between spinon condensation and observed magnetic order in Na$_2$IrO$_3$ and $ ext{α}$-RuCl$_3$.

## Abstract

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 magnetic Bragg peak structure of the zig-zag magnetic order that was observed in Na$_2$IrO$_3$ and $\alpha$-RuCl$_3$. We further discuss the possibility of gapped $\mathbb{Z}_2$ spin liquid and the deconfined quantum criticality from the zig-zag magnetic order to spin dimerization in pressurized $\alpha$-RuCl$_3$.