  For a thin ferromagnetic film with the Dzyaloshinskii-Moriya interaction
(DMI), we derive an expression of the extrinsic ferromagnetic resonance (FMR)
linewidth in a quantum mechanical way, taking into account scatterings from
structural inhomogeneity. In the presence of the DMI, the magnon dispersion
exhibits rich resonant states, especially in small external magnetic fields and
strong DMI strength. It is found that the FMR linewidth shows several
characteristic features such as a finite linewidth at zero frequency and peaks
in the low frequency range.
