Phonon Self-Energy and Origin of Anomalous Neutron Scattering Spectra in SnTe and PbTe Thermoelectrics

Abstract

The anharmonic lattice dynamics of rock-salt thermoelectric compounds SnTe and PbTe are investigated with inelastic neutron scattering (INS) and first-principles calculations. The experiments show that, surprisingly, although SnTe is closer to the ferroelectric instability, phonon spectra in PbTe exhibit a more anharmonic character. This behavior is reproduced in first-principles calculations of the temperature-dependent phonon self-energy. Our simulations reveal how the nesting of phonon dispersions induces prominent features in the self-energy, which account for the measured INS spectra and their temperature dependence. We establish that the phase space for three-phonon scattering processes, combined with the proximity to the lattice instability, is the mechanism determining the complex spectrum of the transverse-optic ferroelectric mode

Anharmonicity and atomic distribution of SnTe and PbTe thermoelectrics

“…First principles frozen phonon calculations show that, at their respective relaxed lattice parameters, SnTe has a double-well potential with two minima offset from the rock salt position, while PbTe shows a single minimum centered at the equilibrium configuration. 37 This is in good agreement with the experimental observation that stoichiometric SnTe is ferroelectric while PbTe is paraelectric down to 0 K, and thus SnTe is closer to the ferroelectric instability than PbTe. The TDEP method at the calculated temperatures yields stable phonons, and reproduces the experimental observation of stabilization of the soft TO mode with increasing T.…”

“…The low temperature ferroelectric distortion of SnTe is very small 24 and we could not resolve any splitting of Bragg peaks with either powder or single-crystal neutron diffraction. However, the resistivity measurements on our SnTe crystals showed an anomaly characteristic of the ferroelectric transition at T C ≃ 42 K. 42 This transition temperature is consistent with expectations for this carrier density, based on Raman measurements, transport characterization, and diffraction peak intensities. 24,43 On the other hand, PbTe at the present carrier concentration remains incipient ferroelectric, with an extrapolated T C ≃ −60 K. 24 The phonon DOS measurements were performed on the powders with the ARCS time-of-flight neutron spectrometer at the Spallation Neutron Source (SNS).…”

“…1,11 However, our first-principles calculations of the temperature-dependent spectral density functions showed how the double-peak arises from the shape of the anharmonic phonon self-energy, whose imaginary part contains a pronounced peak, owing to nesting of the phonon dispersions. 37 Calculations of the zone-center TO phonon spectral function at zone center in PbTe based on molecular dynamics also reproduced the effect. 31,38 Our measurements and calculations found a less unusual spectral function for the TO mode in SnTe, although its linewidth is also quite broad.…”

“…The TO mode spectral function in SnTe does not exhibit the double peak present in PbTe. 37 This leads to the conclusion that the asymmetry of the 1NN PDF peak probes anharmonicity differently than the phonon spectral function. Indeed, we have found that the harmonic, cubic, and quartic interatomic force-constants in SnTe and PbTe have very similar values (similar bonding and anharmonicity), explaining the similar RDFs.…”

“…31,38 Our measurements and calculations found a less unusual spectral function for the TO mode in SnTe, although its linewidth is also quite broad. 37 While PbTe is an incipient ferroelectric material, intrinsic SnTe undergoes a displacive ferroelectric phase transition from a high-temperature paraelectric rock salt …”