Impact of temperature and mode polarization on the acoustic phonon range in complex crystalline phases: A case study on intermetallic clathrates

The low and weakly temperature-varying lattice thermal conductivity, kappa(L)(T), in crystals with a complex unit cell such as type-I clathrates is assumed to originate from a reduced momentum and energy space available for propagative lattice vibrations, which is caused by the occurrence of low-energy optical phonon modes. In the context of ab initio self-consistent phonon (SCP) theory, it has been shown that the cubic and quartic anharmonic interactions result in a temperature-induced energy renormalization of these low-lying optical branches which contributes to the anomalous behavior of kappa(L)(T) in structurally ordered type-I clathrates [T. Tadano and S. Tsuneyuki, Phys. Rev.Lett. 120, 105901 (2018)]. By means of inelastic neutron scattering, we provide evidence for this energy renormalization in temperature, which has been resolved for transversely and longitudinally polarized phonons in the single crystal type-I clathrate Ba7.81Ge40.67Au5.33. By mapping the neutron intensity in the momentum space, we demonstrate the coherent character of the low-lying optical phonons. The overall phonon spectrum and dynamical structure factors are satisfactorily reproduced by ab initio harmonic calculations using density functional theory with the meta-GGA SCAN functional and a fully ordered structure. However, a polarization-dependent cutoff energy with opposing temperature shifts for longitudinal and transverse acoustic dispersions is experimentally observed which is not reproduced by the simulations. Anharmonicity affects the energies of the low-lying optical phonons in the transverse polarization, which compares quantitatively well with available results from SCP theory, whereas differences are observed for the longitudinal polarization.