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, κL (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 κL (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
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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