Collective excitations in two-dimensional antiferromagnet in strong magnetic field

We discuss spin-$\frac12$ two-dimensional (2D) Heisenberg antiferromagnet (AF) on a square lattice at T=0 in strong magnetic field H near its saturation value $H_c$. A perturbation approach is proposed to obtain spectrum of magnons with momenta not very close to AF vector in the leading order in small parameter $(H_c-H)/H_c$. We find that magnons are well-defined quasi-particles at $H>0.9H_c$ although the damping is quite large near the zone boundary. A characteristic rotonlike local minimum in the spectrum is observed at ${\bf k}=(\pi,0)$ accompanied by decrease of the damping near $(\pi,0)$. The suggested approach can be used in discussion of short-wavelength excitations in other 2D Bose gases of particles or quasi-particles.