The polarized Raman spectra of layered ruthenates of the Srn+1RunO3n+1 (n=1,2,3) Ruddlesden-Popper series were measured between 10 and 300 K. The phonon spectra of Sr3Ru2O7 and Sr4Ru3O10 confirmed earlier reports for correlated rotations of neighboring RuO6 octahedra within double or triple perovskite blocks. The observed Raman lines of Ag or B1g symmetry were assigned to particular atomic vibrations by considering the Raman modes in simplified structures with only one double or triple RuO6 layer per unit cell and by comparison to the predictions of lattice dynamical calculations for the real Pban and Pbam structures. Along with discrete phonon lines, a continuum scattering, presumably of electronic origin, is present in the zz, xx and xy, but not in the xy and zx spectra. Its interference with phonons results in Fano shape for some of the lines in the xx and xy spectra. The temperature dependencies of phonon parameters of Sr3Ru2O7 exhibit no anomaly between 10 and 300 K where no magnetic transition occurs. In contrast, two B1g lines in the spectra of Sr4Ru3O10, corresponding to oxygen vibrations modulating the Ru-O-Ru bond angle, show noticeable hardening with ferromagnetic ordering at 105 K, thus indicating strong spin-phonon interaction.
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