Rotational magnetoelastic interactions in the Dzyaloshinskii-Moriya magnet Ba${}_2$CuGe${}_2$O${}_7$

We report the magnetoelastic properties of a Ba${}_2$CuGe${}_2$O${}_7$ single crystal at low temperatures under a magnetic field applied along the crystallographic [001] axis. Our results extend to low temperature the $H-T$ phase diagram determined for this compound by neutron scattering. Furthermore, we observe that specific elastic modes are better sensitive to the various magnetic transitions. In particular, we observe an unusual coupling between the in-plane transverse acoustic mode and the cycloidal order at low field, which suggests a novel spin-strain mechanism originating from Dzyaloshinskii-Moriya interaction in this compound.