Motivated by the recent experiments on the triangular lattice spin-liquid candidate ${\mathrm{YbMgGaO}}_4$, we explore the effect of spin-orbit coupling on the effective-spin correlation of the Yb local moments. We point out that the anisotropic interaction between the effective spins on the nearest-neighbor bonds is sufficient to reproduce the spin-wave dispersion of the fully polarized state in the presence of strong magnetic field normal to the triangular plane. We further evaluate the effective-spin correlation at zero magnetic field within the mean-field spherical approximation. We explicitly demonstrate that the nearest-neighbor anisotropic effective-spin interaction, originating from the strong spin-orbit coupling, enhances the effective-spin correlation at the M points in the Brillouin zone. We identify these results as strong evidence for the anisotropic interaction and strong spin-orbit coupling in ${\mathrm{YbMgGaO}}_4$.

• Received 25 August 2016
• Revised 7 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.125105