** J. Chovan and N. Papanicolaou **

Department of Physics, University of Crete, and
Research Center of Crete, Heraklion, Greece

** S. Komineas **

Physikalisches Institut, Universitaet Bayreuth D-95440 Bayreuth, Germany

The magnetic compound Ba$_{2}$CuGe$_{2}$O$_{7}$ has recently been shown to be an essentially two-dimensional spiral antiferromagnet that exhibits an incommensurate-to-commensurate phase transition when a magnetic field applied along the $c$-axis exceeds a certain critical value $H_c$. The $T=0$ dynamics is described here in terms of a continuum field theory in the form of a nonlinear $\sigma$ model. We are thus in a position to carry out a complete calculation of the low-energy magnon spectrum for any strength of the applied field throughout the phase transition. In particular, our spin-wave analysis reveals field-induced instabilities at two distinct critical fields $H_1$ and $H_2$ such that $H_1