Magnetic field induced phase transitions of the triangular spin model

Motivated by a recent inelastic neutron scattering experiment on ${\mathrm{YbMgGaO}}₄$, I study the homogeneous spin model on the triangular lattice using the cluster mean-field theory and exact diagonalization. Phase diagrams with and without magnetic field are computed. The results show that the magnetic field can induce the phase transition from the spin liquid state (or the stripe state) to the ${120}^{\ensuremath{\circ}}$ antiferromagnetic state. These phase transitions are suppressed by the next-nearest-neighbor exchange interaction ${J}₂/{J}₁$ and vanish as ${J}₂/{J}₁>0.11$. I analyze a parameter space at ${J}₂/{J}₁=0.1$, where a field induced phase transition can occur, and find that the deviation of the theoretical spin excitation energy from the experimental data is only about 0.054. These results imply that an effective homogeneous spin model still applies to ${\mathrm{YbMgGaO}}₄$.