Magnetic excitations in the spin-spiral state of TbMnO3 and DyMnO3

We calculate spectra of magnetic excitations in the spin-spiral state of perovskite manganates. The spectra consist of several branches corresponding to different polarizations and different ways of diffraction from the static magnetic order. The easy-axis crystal-field anisotropy and the Dzyaloshinski-Moriya anisotropy lead to opening of gaps in Goldstone modes and to discontinuities in magnon dispersions. Comparing results of the calculation with available experimental data, we determine values of effective exchange parameters and anisotropies. To simplify calculations and to get a clearer physical insight into the structure of excitations, we use the sigma-model-like effective-field theory instead of the conventional spin-wave approach to analyze the Heisenberg Hamiltonian and to derive the spectra.