  A spin model including magnetic anisotropy terms and Dzyaloshinsky-Moriya
interactions is studied for the case of a ferromagnetic monolayer with C2v
symmetry like Fe/W(110). Using the quasiclassical stochastic
Landau-Lifshitz-Gilbert equations, the magnon spectrum of the system is derived
using linear response theory. The Dzyaloshinsky-Moriya interaction leads to
asymmetry in the spectrum, while the anisotropy terms induce a gap. It is shown
that in the presence of lattice defects, both the Dzyaloshinsky-Moriya
interactions and the two-site anisotropy lead to a softening of the magnon
energies. Two methods are developed to investigate the magnon spectrum at
finite temperatures. The theoretical results are compared to atomistic spin
dynamics simulations and a good agreement is found between them.
