We use vibrational dynamical mean-field theory (VDMFT) to study the vibrational structure of type-I clathrate solids, specifically X$_8$Ga$_{16}$Ge$_{30}$, where X=Ba,Sr. These materials are cage-like chemical structures hosting loosely bound guest atoms, resulting in strong anharmonicity, short phonon lifetimes, and ultra-low thermal conductivities. Presenting the methodological developments necessary for this first application to three-dimensional, atomistic materials, we validate our approach through comparison to molecular dynamics simulations and show that VDMFT is extremely accurate at a fraction of the cost. Through the use of nonperturbative methods, we find that anharmonicity is dominated by four-phonon and higher-order scattering processes, and it causes rattler modes to shift up in frequency by 50% (10 cm$^{-1}$) and to have lifetimes of less than 1 ps; this behavior is not captured by traditional perturbation theory. Furthermore, we analyze the phonon self-energy and find that anharmonicity mixes guest rattling modes and cage acoustic modes, significantly changing the character of the harmonic phonons.
We investigate the role of rattling guest atoms on the lattice thermal-conductivity of a type-I clathrate Ba$_{8}$Ga$_{16}$Ge$_{30}$ by first-principles lattice dynamics. Comparing phonon properties of filled and empty clathrates, we show that rattlers cause 10-fold reductions in the relaxation time of phonons by increasing the phonon-phonon scattering probability. Contrary to the resonant scattering scenario, the reduction in the relaxation time occurs in a wide frequency range, which is crucial for explaining unusually low thermal-conductivities of clathrates. We also find that the impact of…
We investigate the role of the quartic anharmonicity in lattice dynamics and thermal transport of type-I clathrate Ba$_{8}$Ga$_{16}$Ge$_{30}$ based on \textit{ab initio} self-consistent phonon calculations. We show that the strong quartic anharmonicity of rattling guest atoms causes the hardening of vibrational frequencies of low-lying optical modes and thereby affects calculated lattice thermal conductivities $κ_{L}$ significantly, resulting in an improved agreement with experimental results including the deviation from $κ_{L}\propto T^{-1}$ at high temperature. Moreover, our static simulatio…
Anharmonic guest atom oscillation has direct connection to the thermal transport and thermo- electric behavior of type-I Ba8Ga16Sn30 clathrates. This behavior can be observed through several physical properties, with for example the heat capacity providing a measure of the overall excita- tion level structure. Localized anharmonic excitations also influence the low-temperature resistivity, as we show in this paper. By combining heat capacity, transport measurements and our previous NMR relaxation results, we address the distribution of local oscillators in this material, as well as the shape o…
Inorganic clathrates such as Ba$_8$Ga$_{x}$Ge$_{46-x}$ and Ba$_8$Al$_{x}$Si$_{46-x}$ commonly exhibit very low thermal conductivities. A quantitative computational description of this important property has proven difficult, in part due to the large unit cell, the role of disorder, and the fact that both electronic carriers and phonons contribute to transport. Here, we conduct a systematic analysis of the temperature and composition dependence of low-frequency modes associated with guest species in Ba$_8$Ga$_{x}$Ge$_{46-x}$ and Ba$_8$Al$_{x}$Si$_{46-x}$ ("rattler modes"), as well as of thermal…
The anharmonic phonon properties of type-I filled inorganic clathrates Ba8 Ga16 Ge30 and Sr8 Ga16 Ge30 are obtained from the first-principles calculations by considering the temperature-dependent sampling of the potential energy surface and quartic phonon renormalization. Owing to the weak binding of guest atoms with the host lattice, the obtained guest modes undergo strong renormalization with temperature and become stiffer by up to 50% at room temperature in Sr8Ga16Ge30. The calculated phonon frequencies and associated thermal mean squared displacements are comparable with experiments despit…
The phonon dispersion relations of crystal lattices can often be well-described with the harmonic approximation. However, when the potential energy landscape exhibits more anharmonicity, for instance, in case of a weakly bonded crystal or when the temperature is raised, the approximation fails to capture all crystal lattice dynamics properly. Phonon-phonon scattering mechanisms become important and limit the phonon lifetimes. We take a novel approach and simulate the phonon dispersion of a complex dynamic solid at elevated temperatures with Machine-Learning Force Fields of near-first-principle…
Rattling motion of fillers in cage materials has been of great interest for their import roles in superconductivity and thermoelectric applications. The standing waves of the rattling oscillations are normally lower in energy than the propagating waves of the acoustic phonons, thus exert large influences on the configuration of phonon dispersions as well as the associated thermal and electrical properties. Although it has been extensively studied, the origin of the low energy soft modes is still not clear. In the present paper, we show that van der Waals-type interactions are predominant betwe…
We have applied ab initio molecular dynamics (MD) simulations to study metal-metal coupling on the alkali-metal sublattice in the β-pyrochlore osmates, AOs2O6 (A = K, Rb, Cs) at 300 K. We find that the alkali-metal atoms (rattlers) couple to each other more strongly than they couple to the cage atoms, and that, at 300 K, this coupling is strongest for Cs. We show that this coupling controls the dominant dynamics in the rattling of these atoms. We provide preliminary evidence that the rattlers couple to each other primarily through the T2g mode whereas their coupling to the cage modes occurs th…
Atomic motion of guest atoms inside semiconducting clathrate cages is considered as an important source for the glasslike thermal behavior.69Ga and 71Ga Nuclear Magnetic Resonance (NMR) studies on type-I Ba8Ga16Sn30 show a clear low temperature relaxation peak attributed to the influence of Ba rattling dynamics on the framework-atom resonance, with a quadrupolar relaxation mechanism as the leading contribution. The data are analyzed using a two-phonon Raman process, according to a recent theory involving localized anharmonic oscillators. Excellent agreement is obtained using this model, with t…
A series of infrared-active optical phonons have been detected in type-I clathrate Ba$_8$Ga$_{16}$Ge$_{30}$ by terahertz time-domain spectroscopy. The conductivity spectra with the lowest-lying peaks at 1.15 and 1.80 THz are identified with so-called rattling phonons, i.e., optical modes of the guest ion Ba$^{2+}(2)$ with $T_{1u}$ symmetry in the oversized tetrakaidecahedral cage. The temperature dependence of the spectra from these modes are totally consistent with calculations based on a one-dimensional anharmonic potential model that, with decreasing temperature, the shape becomes asymmetri…
The lattice thermal conductivities of silicon clathrate frameworks II and VIII are investigated by using ab initio lattice dynamics and iterative solution of the linearized Boltzmann transport equation(BTE) for phonons. Within the temperature range 100-350 K, the clathrate structures II and VIII were found to have lower lattice thermal conductivity values than silicon diamond structure (d-Si) by factors of 1/2 and 1/5, respectively. The main reason for the lower lattice thermal conductivity of the clathrate structure II in comparison to d-Si was found to be the harmonic phonon spectra, while i…
Understanding heat transport in semiconductors and insulators is of fundamental importance because of its technological impact in electronics and renewable energy harvesting and conversion. Anharmonic Lattice Dynamics provides a powerful framework for the description of heat transport at the nanoscale. One of the advantages of this method is that it naturally includes quantum effects due to atoms vibrations, which are needed to compute the thermal properties of semiconductors widely used in nanotechnology, like silicon and carbon, even at room temperature. While the heat transport picture subs…
We develop an analytical model to describe the phonon dispersion relations of host-guest lattices with heavy guest atoms (rattlers). Crucially, the model also accounts for phonon damping arising from anharmonicity. The spectrum of low energy states contains acoustic-like and (soft) optical-like modes, which display the typical avoided crossing, and which can be derived analytically by considering the dynamical coupling between host lattice and guest rattlers. Inclusion of viscous anharmonic damping in the model allows us, for the first time, to compute the vibrational density of states (VDOS) …
One of the key requirements for good thermoelectric materials is a low lattice thermal conductivity. Here we present a combined neutron scattering and theoretical investigation of the lattice dynamics in the type I clathrate system Ba-Ge-Ni, which fulfills this requirement. We observe a strong hybridization between phonons of the Ba guest atoms and acoustic phonons of the Ge-Ni host structure over a wide region of the Brillouin zone which is in contrast with the frequently adopted picture of isolated Ba atoms in Ge-Ni host cages. It occurs without a strong decrease of the acoustic phonon lifet…
Recently there has been paid much attention to phenomena caused by local anharmonic vibrations of the guest ions encapsulated in polyhedral cages of materials such as pyrochlore oxides, filled skutterdites and clathrates. We theoretically investigate the optical conductivity solely due to these so-called rattling phonons in a one-dimensional anharmonic potential model. The dipole interaction of the guest ions with electric fields induces excitations expressed as transitions among vibrational states with non-equally spaced energies, resulting in a natural line broadening and a shift of the peak…
We have investigated optical conductivity spectra of $n$- and $p$-type Ba$_8$Ga $_{16}$Sn$_{30}$ ($α$-BGS) with type-VIII clathrate structure, at temperatures from 296\,K down to 6\,K with a terahertz time-domain spectrometer (0.2\,-\,2.5\,THz). The continuous spectra contributed from charge carriers are dispersive in this frequency range and also temperature- and carrier type-dependent. The Drude-Smith model taking multiple-scatterings of charge carriers into account well reproduces those data. The relaxation rate of the $n$-type carriers decreases more sharply than that in the $p$-type mater…
With a terahertz time-domain spectrometer (0.3 - 3.0 THz) we have measured the optical conductivity of the type-I clathrate Ba$_8$Ga$_{16}$Sn$_{30}$ at temperatures from 300 K down to 7 K. Independent six spectra superimposed on the Drude conductivity are identified to infrared active vibrational modes of guest Ba ions and the cages. While the spectra of five higher-frequency modes depend hardly on temperature, the lowest-lying spectrum with a peak at 0.72 THz due to the Ba(2) ion's off-centering vibration in the oversized cage changes with temperature characteristically. With lowering tempera…
In the filled Ga/Ge clathrate, Eu and Sr are off-center in site 2 but Ba is on-center. All three filler atoms (Ba,Eu,Sr) have low temperature Einstein modes; yet only for the Eu and Sr systems is there a large dip in the thermal conductivity, attributed to the Einstein modes. No dip is observed for Ba. Here we argue that it is the off-center displacement that is crucial for understanding this unexplained difference in behavior. It enhances the coupling between the "rattler" motion and the lattice phonons for the Eu and Sr systems, and turns on/off another scattering mechanism (for 1K < T < 20K…
{\it Ab initio\} calculations have been successfully used for evaluating lattice dynamical properties of solids within the (quasi-)harmonic approximation (i.e., assuming non-interacting phonons with infinite lifetimes), but it remains difficult to treat anharmonicity in all but the simplest compounds. We detail a systematic information theory based approach to deriving {\it ab initio\} anharmonic force constants: compressive sensing lattice dynamics (CSLD). The non-negligible terms that are necessary to reproduce the first-principles calculated interatomic forces are automatically selected by …
The factors that affect the thermal conductivity of semiconductors is a topic of great scientific interest, especially in relation to thermoelectrics. Key developments have been the concept of the phonon-glass-electron-crystal (PGEC) and the related idea of rattling to achieve this. We use first principles phonon and thermal conductivity calculations in order to explore the concept of rattling for stoichiometric ordered half-Heusler compounds. These compounds can be regarded as filled zinc blende materials, and the filling atom could be viewed as a rattler if it is weakly bound. We use two sim…
We propose a simple phenomenological model describing vibrational dynamics in a class of materials (like clathrates), which are crystalline compounds with closed cavities in their structures. In the spirit of a minimalist approach, our model includes only the minimum of ingredients necessary to capture the generic features of this class of compounds as brought to light by experiments. We consider only two kinds of particles: strongly coupled host atoms, which form the structural cavities, and guest atoms confined in the cavities. In spite of the confinement, for relatively small amplitude vibr…
