Motivated by the recent progress in the spin-orbit-coupled triangular lattice spin liquid candidate
YbMgGaO4, we carry out a systematic projective symmetry group analysis and mean-field study of candidate
U(1) spin-liquid ground states. Due to the spin-orbital entanglement of the Yb moments, the space-group symmetry operation transforms both the position and the orientation of the local moments, and hence it brings different features for the projective realization of the lattice symmetries from the cases with spin-only moments. Among the eight
U(1) spin liquids that we find with the fermionic parton construction, only one spin-liquid state, which was proposed and analyzed by Yao Shen et al. [Nature (London) 540, 559 (2016)] and labeled as U1A00 in the present work, stands out and gives a large spinon Fermi surface and provides a consistent explanation for the spectroscopic results in
YbMgGaO4. Further connection of this spinon Fermi surface
U(1) spin liquid with
YbMgGaO4 and the future directions are discussed. Finally, our results may apply to other spin-orbit-coupled triangular lattice spin-liquid candidates, and more broadly, our general approach can be well extended to spin-orbit-coupled spin-liquid candidate materials.
We use a projective symmetry group analysis to determine all symmetric spin liquids on the stuffed honeycomb lattice Heisenberg model. This lattice interpolates between honeycomb, triangular, and dice lattices, always preserving hexagonal symmetry, and it already has one spin-liquid candidate,
TbInO3, albeit with strong spin-orbit coupling not considered here. In addition to the stuffed honeycomb lattice itself, we gain valuable insight into potential spin liquids on the honeycomb and triangular lattices, as well as how they might be connected. For example, the sublattice pairing state proposed on the honeycomb lattice connects to the uniform spinon Fermi surface that may be relevant for the triangular lattice with ring exchange, while there are no spin liquids competitive on both the ${J}_{1}\ensuremath{-}{J}_{2}$ honeycomb and triangular lattice limits. In particular, we find three stuffed honeycomb descendants of the U(1) Dirac spin liquid widely believed to be found on the ${J}_{1}\ensuremath{-}{J}_{2}$ triangular lattice. We also discuss how spin liquids near the honeycomb limit can potentially explain the physics of
LiZn2Mo3O8.
The weak Mott insulating regime of the triangular lattice Hubbard model exhibits a rich magnetic phase diagram as a result of the ring exchange interaction in the spin Hamiltonian. These phases include the Kalmeyer-Laughlin type chiral spin liquid (CSL) and a valence bond solid (VBS). A natural question arises regarding the robustness of these phases in the presence of a weak spin-orbit coupling (SOC). In this study, we derive the effective spin model for the spin-orbit coupled triangular lattice Hubbard model in the weak Mott insulting regime, including all SOC-mediated spin-bilinear and ring-exchange interactions. We then construct a simplified spin model keeping only the most relevant SOC-mediated spin interactions. Using infinite density matrix renormalization group (iDMRG), we show that the CSL and VBS phases of the triangular lattice Hubbard model can be stabilized in the presence of a weak SOC. The stabilization results from a compensation between the Dzyaloshinskii-Moriya interaction and a SOC-mediated ring-exchange interaction. We also provide additional qualitative arguments to intuitively understand the compensation mechanism in the iDMRG quantum phase diagrams. This mechanism for stabilization can potentially be useful for the experimental realization of quantum spin liquids.