| We study the effects of magnons on the physical properties of phonons in triangular antiferromagnets. Starting point is a frustrated Heisenberg quantum antiferromagnet with Dzyaloshinskii-Moriya anisotropies subject to a uniform magnetic field perpendicular to the plane. Assuming for fields below the critical field hc, where the system becomes a saturated ferromagnet, an ordered "cone"-state in the groundstate that is also stabilized due to the anisotropies, we set up an interacting spin-wave theory using the 1/S-expansion technique. Subsequently we introduce a coupling between lattice vibrations and spin degrees of freedom. An examination of the resulting interaction processes finally allows to calculate the renormalization of the phonons. It turns out that the hybridization of between the magnons and the phonons influences the change of the elastic constant and its damping. As a result we find that the long wavelength phonons with momentum →k remain well-defined quasi-particles with a damping that is proportional to k4 and a slight change of its velocity as long as the magnetic field is smaller than the critical field hc. |
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