Intermediate phase in the spiral antiferromagnet ${\mathrm{Ba}}_2{\mathrm{CuGe}}_2{\mathrm{O}}_7$

The magnetic compound ${\mathrm{Ba}}_2{\mathrm{CuGe}}_2{\mathrm{O}}_7$ 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 $T=0\mathrm{}$ dynamics is described here in terms of a continuum field theory in the form of a nonlinear σ 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 $H_1<H_c<H_2.$ Hence we predict the existence of an intermediate phase whose detailed nature is also studied to some extent.