Phonon and Magnetic Excitations in Superconducting Ca$_{10}$Pt$_4$As$_8$(Fe$_{1-x}$Pt$_x$As)$_{10}$

Inelastic neutron scattering studies have been carried out on selected phonons and magnetic excitations of a crystal of superconducting (SC) Ca$_{10}$Pt$_4$As$_8$(Fe$_{1-x}$Pt$_x$As)$_{10}$ with the onset transition temperature $T_{\rm c}^{\rm onset} \sim$ 33 K to investigate the role that orbital fluctuations play in the Cooper pairing. The spectral weight of the magnetic excitations, $χ''({\bm Q}, ω)$ at ${\bm Q} = {\bm Q}_{\rm M}$ (magnetic $Γ$ points) is suppressed (enhanced) in the relatively low (high) $ω$ region. The maximum of the enhancement is located at $ω= ω_{\rm p} \sim$ 18 meV at temperature $T = 3$ K corresponding to the $ω_{\rm p}/k_{\rm B}T_{\rm c}^{\rm onset} \sim$ 6.3. This large value is rather favorable to the orbital-fluctuation mechanism of the superconductivity with the so-called $S_{++}$ symmetry. In the phonon measurements, we observed slight softening of the in-plane transverse acoustic mode corresponding to the elastic constant $C_{66}$. This softening starts at $T$ well above the superconducting $T_{\rm c}$, as $T$ decreases. An anomalously large increase in the phonon spectral weight of in-plane optical modes was observed in the range of $35 < ω< 40$ meV with decreasing $T$ from far above $T_{\rm c}$. Because this $ω$ region mainly corresponds to the in-plane vibrations of Fe atoms, the finding presents information on the coupling between the orbital fluctuation of the Fe 3$d$ electrons and lattice system, useful for studying possible roles of the orbital fluctuation in the pairing mechanism and appearance of the so-called nematic phase.