Spin waves in layered antiferromagnets with honeycomb structure

We develop a description of spin waves in a $3D$ quantum $XY$ antiferromagnet (AFM) in terms of macroscopic variables, magnetization and N\'eel vector densities. We consider a layered AFM with spins located on the honeycomb lattice. In the discussed system, the spectrum of spin waves consists of four modes, all well captured by our macroscopic description. The gapless mode of the spin waves, i.e., magnons, is described by a system of equations, which has a structure general for the Goldstone mode in AFMs. We demonstrate that the parameters in the spin Hamiltonian can be evaluated by fitting the experimental data with the results obtained for the four modes using the macroscopic variable approach. The description of AFM in terms of macroscopic variables can be easily extended to the case when the lattice of the magnetic substance is deformed by an external strain or acoustic wave.