  The proximity to structural phase transitions in IV-VI thermoelectric
materials is one of the main reasons for their large phonon anharmonicity and
intrinsically low lattice thermal conductivity $\kappa$. However, the $\kappa$
of GeTe increases at the ferroelectric phase transition near $700$ K. Using
first-principles calculations with the temperature dependent effective
potential method, we show that this rise in $\kappa$ is the consequence of
negative thermal expansion in the rhombohedral phase and increase in the phonon
lifetimes in the high-symmetry phase. Negative thermal expansion increases
phonon group velocities, which counteracts enhanced anharmonicity of phonon
modes and boosts $\kappa$ close to the phase transition in the rhombohedral
phase. A drastic decrease in the anharmonic force constants in the cubic phase
increases the phonon lifetimes and $\kappa$. Strong anharmonicity near the
phase transition induces non-Lorentzian shapes of the phonon power spectra. To
account for these effects, we implement a novel method of calculating $\kappa$
based on the Green-Kubo approach and find that the Boltzmann transport equation
underestimates $\kappa$ near the phase transition. Our findings elucidate the
influence of structural phase transitions on $\kappa$ and provide guidance for
design of better thermoelectric materials.
