Turner, S., Pailhès, S., Bourdarot, F., Ollivier, J., Raymond, S., Keller, T., Sidis, Y., Castellan, J.-P., Lory, P.-F., Euchner, H., Baitinger, M., Grin, Yu., Schober, H., De Boissieu, M., Giordano, V., Institut Laue-Langevin (ILL), Science et Ingénierie des Matériaux et Procédés (SIMaP), Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), (nano)Matériaux pour l'énergie (ENERGIE), Institut Lumière Matière [Villeurbanne] (ILM), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Magnétisme et Diffusion Neutronique (MDN ), Modélisation et Exploration des Matériaux (MEM), Institut de Recherche Interdisciplinaire de Grenoble (IRIG), Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Grenoble Alpes (UGA)-Institut de Recherche Interdisciplinaire de Grenoble (IRIG), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Grenoble Alpes (UGA), Max-Planck-Institut für Festkörperforschung, Max-Planck-Gesellschaft, Forschungsneutronenquelle Heinz Maier-Leibnitz (FRM II), Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne] (TUM), Laboratoire Léon Brillouin (LLB - UMR 12), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Institut für Festkörperphysik, Helmholtz Institute Ulm (HIU), Max-Planck-Institut für Chemische Physik fester Stoffe (CPfS), ILL, and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay
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 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