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GeTe is a well-known ferroelectric and thermoelectric material that undergoesa structural phase transition from a rhombohedral to the rocksalt structure at$\sim 600-700$ K. We present a first principles approach to calculate thethermal expansion of GeTe in the rhombohedral phase up to the Curietemperature. We find the minimum of the Helmholtz free energy with respect toeach structural parameter in a manner similar to the traditional Gr{\"u}neisentheory, and account for the temperature dependence of elastic constants. Weobtain the temperature variation of the structural parameters of rhombohedralGeTe in very good agreement with experiments. In particular, we correctlyreproduce a negative volumetric thermal expansion of GeTe near the phasetransition. We show that the negative thermal expansion is induced by thecoupling between acoustic and soft transverse optical phonons, which is alsoresponsible for the low lattice thermal conductivity of GeTe.

Acoustic-Soft Optical Mode Coupling Leads to Negative Thermal Expansion of GeTe near the Ferroelectric Phase Transition