Theoretical study of phonon spectra in ferromagnetic nanoparticles

Based on the spin–phonon model we analyze the influence of surface and size effects on the phonon properties of ferromagnetic nanoparticles. A Green's function technique in real space enables us to calculate the renormalized phonon energy and its damping depending on the temperature and the anharmonic spin–phonon interaction constants. With decreasing particle size the phonon energy can decrease or increase for different surface spin–phonon interaction constants, whereas the damping increases always. The influence of an external magnetic field is discussed, too. The theoretical results are in reasonable accordance to experimental data.