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, $chi ({bm Q}, omega)$ at ${bm Q} = {bm Q}_{rm M}$ (magnetic $Gamma$ points) is suppressed (enhanced) in the relatively low (high) $omega$ region. The maximum of the enhancement is located at $omega = omega_{rm p} sim$ 18 meV at temperature $T = 3$ K corresponding to the $omega_{rm p}/k_{rm B}T_{rm c}^{rm onset} sim$ 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 $35 < omega < 40$ meV with decreasing $T$ from far above $T_{rm c}$. Because this $omega$ 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.
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