Spin-orbit coupling effects on spin-phonon coupling in Cd2 Os2 O7

Spin-orbit coupling (SOC) is essential in understanding the properties of 5d transition metal compounds, whose SOC value is large and almost comparable to other key parameters. Over the past few years, there have been numerous studies on the SOC-driven effects of the electronic bands, magnetism, and spin-orbit entanglement for those materials with a large SOC. However, how the SOC affects the lattice dynamics is less studied and remains an unsolved problem. We therefore measured the phonon spectra of 5d pyrochlore Cd2Os2O7 over the full Brillouin zone to address the question by using inelastic x-ray scattering. Our main finding is a visible mode dependence in the phonon spectra, measured across the metal-insulator transition at 227 K. We examined the SOC strength dependence of the lattice dynamics and its spin-phonon (SP) coupling, with first-principles calculations. Our experimental data taken at 100 K are in good agreement with the theoretical results obtained with the optimized U=2.0eV with SOC. By scaling the SOC strength and the U value in the density-functional theory calculations, we demonstrate that SOC is more relevant than U in explaining the observed mode-dependent phonon energy shifts with temperature. Furthermore, the temperature dependence of the phonon energy can be effectively described by scaling SOC. Our work provides clear evidence of SOC producing a non-negligible and essential effect on the lattice dynamics of Cd2Os2O7 and its SP coupling.