Dynamical properties of the anisotropic triangular quantum antiferromagnet with Dzyaloshinskii-Moriya interaction

We present a detailed study of the anisotropic triangular quantum antiferromagent with Dzyaloshinskii-Moriya (DM) interaction building on earlier work by Veillette, James and Essler [Phys.\ Rev.\ B, {\bf 72}, 134429 (2005)]. The DM interaction generates an easy-plane anisotropy and opens a gap in the spin-wave spectrum at the incommensurate ordering wave vector $\vec Q$. Our calculation utilizes the Holstein-Primakoff representation of spins and goes beyond linear spin wave theory by taking into account magnon-magnon interactions in a $1/S$ expansion. We calculate renormalized dispersion relations for the magnons to order $1/S$ for different values of the DM interaction and pay particular attention to the interesting case of zero DM interaction. The dynamical structure factor is calculated to order $1/S$. It is found that, compared to linear spin wave theory, a significant fraction of the scattering intensity is shifted to higher energies. We compare our findings with the recent neutron scattering data measured on the frustrated quantum antiferromagnet $Cs_2 Cu Cl_4$, [R. Coldea, {\it et. al.}, Phys.\ Rev.\ B, {\bf 68}, 134424, (2003)].