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 in a dilute two-dimensional antiferromagnet. The calculations are based on a bond percolation model of the CuO2 plane of high-T(c) copper oxides recently proposed by some of the authors. Numerical results are presented for the dampings of phonon excitations relating to three different situations. They are two magnons (Case A), one magnon and one fracton (Case B), and two fractons (Case C) involved in the phonon self-energy process. At low temperatures, the damping rate is much smaller than the frequency of excitations, leading to well-defined phonons for all the cases. The overall features of the GAMMA(q) approximately q curves possess similar characteristics: GAMMA(q) increases linearly with q in the small-q region, reaching a maximum at an intermediate q, and after that scales nearly as q-2 until q approaches the edge of the Brillouin zone. The temperature-dependent phonon linewidths arising from spin-lattice coupling are also presented. We point out the sensitivity of the interaction involving fractons on bond concentration of the network. Relevance of the calculated results to experimental data are discussed.