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Phase competition underlies many remarkable and technologically important phenomena in transition metal oxides. Vanadium dioxide (VO2) exhibits a first-order metal-insulator transition (MIT) near room temperature, where conductivity is suppressed and the lattice changes from tetragonal to monoclinic on cooling. Ongoing attempts to explain this coupled structural and electronic transition begin with two alternative starting points: a Peierls MIT driven by instabilities in electron-lattice dynamics and a Mott MIT where strong electron-electron correlations drive charge localization. A key missing piece of the VO2 puzzle is the role of lattice vibrations. Moreover, a comprehensive thermodynamic treatment must integrate both entropic and energetic aspects of the transition. Here we report that the entropy driving the MIT in VO2 is dominated by strongly anharmonic phonons rather than electronic contributions, and provide a direct determination of phonon dispersions. Our ab initio calculations identify softer bonding in the tetragonal phase, relative to the monoclinic phase, as the origin of the large vibrational entropy stabilizing the metallic rutile phase. They further reveal how a balance between higher entropy in the metal and orbital-driven lower energy in the insulator fully describes the thermodynamic forces controlling the MIT. Our study illustrates the critical role of anharmonic lattice dynamics in metal oxide phase competition, and provides guidance for the predictive design of new materials.

Cubic scandium trifluoride (ScF 3 ) has a large negative thermal expansion over a wide range of temperatures. Inelastic neutron scattering experiments were performed to study the temperature dependence of the lattice dynamics of ScF 3 from 7 to 750 K. The measured phonon densities of states show a large anharmonic contribution with a thermal stiffening of modes around 25 meV. Phonon calculations with first-principles methods identified the individual modes in the densities of states, and frozen phonon calculations showed that some of the modes with motions of F atoms transverse to their bond direction behave as quantum quartic oscillators. The quartic potential originates from harmonic interatomic forces in the DO 9 structure of ScF 3 , and accounts for phonon stiffening with the temperature and a significant part of the negative thermal expansion. DOI: 10.1103/PhysRevLett.107.195504 PACS numbers: 63.20.Ry, 63.20.DÀ, 65.40.De, 78.70.Nx Nearly all materials expand when heated, so exceptions are interesting. Negative thermal expansion (NTE) of a pure phase has attracted much attention over the past 20 years, driven both by curiosity, and by opportunities to design materials with special thermal properties. For materials like face-centered cubic plutonium and Invar alloys, NTE involves electronic or magnetic excitations. Other types of NTE are structure induced, originating from atom arrangements in the crystal [1]. Several mechanisms of NTE have been proposed, such as deformations of polyhedra, one-or two-dimensional NTE caused by normal thermal expansion of anisotropic bonds, NTE induced by interstitial cations, and NTE associated with transverse motions of linkage atoms (as in Fig. 1) [2,3]. Often NTE is anisotropic, and it usually occurs only in a small range of temperature [4]. Zirconium tungstate (ZrW 2 O 8 ) is a notable exception [5][6][7][8][9][10]. The NTE in ZrW 2 O 8 is associated with under-constrained atom sites in the crystal structure [11]. Although some of the behavior can be understood with a ''quasiharmonic'' model (a harmonic model with interatomic forces adapted to the bond lengths at a given temperature), anharmonic effects are expected, but the full connection between anharmonic lattice dynamics and NTE is obscured by the complexity of the structure [11]. Simplified models like a rigid square [12,13], a 3-atom Bravais lattice [11], and a rigid structure [14] have been used to explain the ''soft-phonon'' NTE mechanism, but accurate lattice dynamics for materials such as ZrW 2 O 8 are not easy to obtain from geometrical models.Very recently, a surprisingly large and isotropic negative thermal expansion was discovered in cubic scandium trifluoride (ScF 3 ) by Greve et al. [15]. It occurs over a wide range of temperature from 10 to about 1100 K, and exceeds À1:0 Â 10 À5 K À1 . Under ambient conditions, ScF 3 has the DO 9 crystal structure of -ReO 3 , shown in Fig. 1, and is stable from 10 to over 1600 K. Although À ReO 3 itself shows modest negative thermal expansion below 300 K [16,17], the ...

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

The anharmonic phonon properties of SnSe in the Pnma phase were investigated with a combination of experiments and first-principles simulations. Using inelastic neutron scattering (INS) and nuclear resonant inelastic X-ray scattering (NRIXS), we have measured the phonon dispersions and density of states (DOS) and their temperature dependence, which revealed a strong, inhomogeneous shift and broadening of the spectrum on warming. First-principles simulations were performed to rationalize these measurements, and to explain the previously reported anisotropic thermal expansion, in particular the negative thermal expansion within the Sn-Se bilayers. Accurate treatment of the phonon free energy, in addition to the electronic ground state energy, is essential to reproduce the negative thermal expansion. From the phonon DOS obtained with INS and additional calorimetry measurements, we quantify the harmonic, dilational, and anharmonic components of the phonon entropy, heat capacity, and free energy. The origin of the anharmonic phonon thermodynamics is linked to the electronic structure.