Coupling between acoustic and soft transverse optical phonons leads to negative thermal expansion of GeTe near the ferroelectric phase transition

Abstract

GeTe is a well-known ferroelectric and thermoelectric material that undergoes a structural phase transition from a rhombohedral to the rocksalt structure at ∼ 600 − 700 K. We present a first principles approach to calculate the thermal expansion of GeTe in the rhombohedral phase up to the Curie temperature. We find the minimum of the Helmholtz free energy with respect to the structural parameters, including the internal atomic displacement, in a manner similar to the traditional Grüneisen theory, explicitly accounting for the variation of the static elastic energy with respect to all structural parameters. We obtain the temperature variation of the structural parameters of rhombohedral GeTe in very good agreement with experiments. In particular, we correctly reproduce a negative volumetric thermal expansion of GeTe near the phase transition. We show that the negative thermal expansion is induced by the coupling between acoustic and soft transverse optical phonons, which is also responsible for the low lattice thermal conductivity of GeTe.

Nonthermal Transport of Energy Driven by Photoexcited Carriers in Switchable Solid States of GeTe

“…Considering the dispersion curves found in Ref. [42], we see that, even at a highfrequency component (100 GHz), the phase velocity is nearly the same as the one we can deduce at the lowest frequency (Brillouin zone center). Consequently, the dispersion effect, i.e., the difference in the propagation time between the highest-and lowest-frequency components, over the relevant propagation distance (less than 1 μm) can potentially broaden the coherent acoustic pulse only by a few picoseconds, which is much shorter than the duration of the detected acoustic pulse approaching 200 ps [see inset of Fig.…”

“…4 within the Supplemental Material [35]). Considering the bulk-modulus values for α-GeTe either calculated (T = 0 K), with B ≈ 46 GPa [42] and B ≈ 44.3 GPa [43], or measured (T = 300 K), B ∼ 49.9 GPa [44], the longitudinal velocity of sound becomes included in the range V ≈ √ B/ρ ≈ 2680-2850 m s −1 (mass density ρ = 6140 kg m −3 ), which is in reasonable agreement with our measurements. However, it is worth mentioning that a much smaller value of 1900 m s −1 is measured by nuclear inelastic scattering methods for α-GeTe [45].…”

Large piezoelectric and thermal expansion coefficients with negative Poisson's ratio in strain-modulated tellurene

“…A negative volumetric expansion exists in GeTe depending upon the thermal evolution of its structure. Herein, the acoustic and soft transverse optical modes coupling cause the negative thermal expansion 35 . Black phosphorus possesses anisotropic thermal expansion with negative values in the zigzag direction 36 .…”

Pressure-Induced Phase Transitions in Germanium Telluride: Raman Signatures of Anharmonicity and Oxidation

“…However real crystals have a large number of Ge vacancies which are self-doping [25], leading to screening of long range interactions. Thus two modes are found at the zone center [26,27] due to degeneracy of long wavelength longitudinal and transverse modes. In backscattering, with the sample (a,b) plane perpendicular to the laser light these two modes should be visible in an unpolarised or parallel polarization measurement.…”