Symmetry of phonon, magnetic, and spin-phonon excitations in GdSr₂RuCu₂O₈ single crystals

We present a polarized Raman scattering study of GdSr₂RuCu₂O₈ single crystals. In this compound, the RuO₆ octahedra are rotated around the c axis that in turn gives some Raman activity of the oxygen (O_Ru) vibrations at 265 cm^-1 (A_1g), 411 cm^-1 (B_2g) and 607 cm^-1 (B_1g). These vibrations, as well as those of the apical oxygen of RuO₆ at 654 cm^-1 (A_1g) and the Cu-plane oxygen at 318 cm^-1 (B_2g), clearly respond to the onset of magnetic ordering at T_m≈140 K. In particular, the 265 cm^-1 mode hardens anomalously with decreasing temperature below T_m. Notably, the corresponding phonon line is absent in the Raman spectra of GdSr₂NbCu₂O₈ (Nb⁵⁺:4d⁰), a compound isomorphic to GdSr₂RuCu₂O₈ (Ru⁵⁺:4d³). We argue that the eigenvector of the 265 cm^-1 phonon (rotational mode) facilitates efficient modulation of the Ru(t_1g)-O_Ru(p) bands. This modulation gives both Raman scattering strength to the 265 cm^-1 mode and strong spin-phonon coupling.