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Temperature and field dependence of collective spin excitations or magnon inmonolayer honeycomb spin lattices is investigated using an anisotropic exchangeXZ-Heisenberg model in an external field. Magnetic phase transition in thepresence of the transverse field is the spin reorientation (SR) transition withmagnon intensity existing above the SR temperature. The transverse field eitherdecreases or sustains the spin-wave intensity in the temperature region belowor above the SR temperature, respectively. The gap of the zero-momentumlow-energy magnon branch closes at the SR transverse field, which is thecritical quantum phase transition field at zero temperature. The application ofthe model to a two-dimensional CrI$_3$ explains the existence of thezero-momentum magnon mode above the Curie temperature and shows the suitablevalues of the exchange parameters compared with the DFT calculations. Theestimated magnon velocity near the Dirac point in this material is about 1.74km/s.

Temperature and Field Dependence of Ferromagnetic Magnon in Monolayer Honeycomb Spin Lattice