Weak Ferromagnetism in the Helimagnet $Ba_{2}CuGe_{2}O_{7}$

The Dzyaloshinskii-Moriya anisotropy, responsible for helimagnetism in $Ba_{2}CuGe_{2}O_{7}$, has recently been shown to comprise also a weak-ferromagnetic component. We theoretically demonstrate the signatures of weak-ferromagnetism in the magnon spectrum when a magnetic field is applied perpendicular to the z axis. We also anticipate the occurrence of unconventional domain walls in the so-called intermediate phase, and briefly elucidate the importance of the weak ferromagnetic component of the Dzyaloshinskii-Moriya anisotropy for the dynamics of driven domain walls.