Magnetic field effect on the spin-wave gaps in the real antiferromagnets

An unusual dependence of the excitation spectrum of a 2D antiferromagnet with a weak Dzyaloshinskii-Moriya interaction $D$ on the external magnetic field $H$ is studied. While the ${\bf k}=0$ gap follows closely the ``uniform precession'' behavior, $\Delta_0\sim H$, the gap at the antiferromagnetic ordering vector $\Delta_{{\bf Q}_{AF}}$ evolves from $\sim D$ at $H=0$ to $\propto \sqrt{D}$ at $H\sim H_s/2$ and then to $\propto D^{2/3}$ at $H=H_s$, where $H_s$ is the saturation field. In small fields this gap shows a non-analytic behavior $\Delta_{{\bf Q}_{AF}}\sim \sqrt{H}$. These results are directly applicable to the 2D AF K$_2$V$_3$O$_8$. The mutual effect of the magnetic field and DM interaction on the quantum fluctuations is also studied.