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We present a study of the lattice dynamical properties of superconductingSrPt$_3$P ($T_c = 8.4$ K) via high-resolution inelastic x-ray scattering (IXS)and ab initio calculations. Density functional perturbation theory includingspin-orbit coupling (SOC) results in enhanced electron-phonon coupling (EPC)for the optic phonon modes originating from the Pt(I) atoms, with energies$\sim 5$ meV, resulting in a large EPC constant $\lambda \sim 2$. An overallsoftening of the IXS powder spectra occurs from room to low temperatures,consistent with the predicted strong EPC and with recent specific-heatexperiments ($2\Delta_0 / k_{\mathrm{B}}T_c \sim 5$). The low-lying phononmodes observed in the experiments are approximately 1.5 meV harder than thecorresponding calculated phonon branch. Moreover, we do not find any changes inthe spectra upon entering the superconducting phase. We conclude that currenttheoretical calculations underestimate the energy of the lowest band of phononmodes indicating that the coupling of these modes to the electronic subsystemis overestimated.

Lattice dynamical properties of superconducting SrPt$_3$P studied via inelastic x-ray scattering and density functional perturbation theory