Spin-phonon renormalization of the excitation energy in a diluted two-dimensional ferromagnet

The contribution of spin-lattice coupling to the phonon self-energy is calculated for a diluted two-dimensional "soft" ferromagnet. The calculations are based on a bond percolation model. Numerical results are presented for the dampings of phonon excitations. At low temperature, the damping rate is much smaller than the frequency of excitations, leading to well-defined phonons. The overall features of the Gamma(q) curves possess similar characteristics: Gamma(q) has two maximum points at qa approximate to 0.5 and qa approximate to 1.7, the value of the latter is much larger than the former. The temperature-dependent phonon line widths arising from spin-lattice coupling are also presented. We point out the sensitivity of the interaction on bond concentration of the network.