Phonon excitations play an important role in electronic transport, nonradiative electron-relaxation processes, and other properties of interest for materials characterization, device engineering, and design. We have calculated the phonon dispersions and density of states for wurtzite AlN, GaN, and InN using state-of-the-art density-functional perturbation theory. The calculations are in good agreement with the existing experimental data for zone-center modes and predict the full phonon dispersions throughout the Brillouin zone. In particular, it is found that the three-phonon decay of the LO phonon in two acoustic phonons is not allowed in GaN and InN, since the LO frequency is much larger than the acoustic frequencies over the entire spectrum.
The phonon dispersion relations and elastic constants for ferromagnetic Ni2MnGa in the cubic and tetragonally distorted Heusler structures are computed using density-functional and densityfunctional perturbation theory within the spin-polarized generalized-gradient approximation. For 0.9 < c/a < 1.06, the TA2 tranverse acoustic branch along [110] and symmetry-related directions displays a dynamical instability at a wavevector that depends on c/a. Through examination of the Fermi-surface nesting and electron-phonon coupling, this is identified as a Kohn anomaly. In the parent cubic phase the computed tetragonal shear elastic constant, C ′ =(C11−C12)/2, is close to zero, indicating a marginal elastic instability towards a uniform tetragonal distortion. We conclude that the cubic Heusler structure is unstable against a family of energy-lowering distortions produced by the coupling between a uniform tetragonal distortion and the corresponding [110] modulation. The computed relation between the c/a ratio and the modulation wavevector is in excellent agreement with structural data on the premartensitic (c/a = 1) and martensitic (c/a = 0.94) phases of Ni2MnGa.
Using a combination of first-principles and effective-Hamiltonian approaches, we map out the structure of BaTiO3 under epitaxial constraints applicable to growth on perovskite substrates. We obtain a phase diagram in temperature and misfit strain that is qualitatively different from that reported by Pertsev et al. [Phys. Rev. Lett. 80, 1988], who based their results on an empirical thermodynamic potential with parameters fitted at temperatures in the vicinity of the bulk phase transitions. In particular, we find a region of 'r phase' at low temperature where Pertsev et al. have reported an 'ac phase'. We expect our results to be relevant to thin epitaxial films of BaTiO3 at low temperatures and experimentally-achievable strains. PACS numbers: 77.55.+f, 77.80.Bh, 77.84.Dy, 81.05.Zx The perovskite oxide barium titanate (BaTiO 3 ) is a prototypical ferroelectric, an insulating solid whose macroscopic polarization can be reoriented by the application of an electric field [1]. In the perovskite ferroelectrics, it is well known both experimentally and theoretically that the polarization is also strongly coupled to strain [2], and thus that properties such as the ferroelectric transition temperature and polarization magnitude are quite sensitive to external stress.Experimentally, the properties of ferroelectrics in thin film form generally differ significantly from those in the bulk [3]. While many factors are expected to contribute to these differences, it has been shown that the properties of perovskite thin films are strongly influenced by the magnitude of the epitaxial strain resulting from latticematching the film to the substrate. For example, Yoneda et al.[4] used molecular-beam epitaxy (MBE) to grow BaTiO 3 (lattice constant of 4.00Å) on (001)-oriented SrTiO 3 (lattice constant of 3.91Å); they found that the ferroelectric transition temperature exceeds 600 • C, to be compared to the bulk Curie temperature of T C = 130 • C. Other studies have shown that the amount of strain in BaTiO 3 /SrTiO 3 superlattices on SrTiO 3 substrates strongly influences properties including the observed polarization, phase transition temperature, and dielectric constant [5,6,7,8].In a seminal paper, Pertsev, Zembilgotov and Tagantsev [9] introduced the concept of mapping the equilibrium structure of a ferroelectric perovskite material versus temperature and misfit strain, thus producing a "Pertsev phase diagram" (or Pertsev diagram) of the observable epitaxial phases. The effect of epitaxial strain is isolated from other aspects of thin-film geometry by computing the structure of the bulk material with homogeneous strain tensor constrained to match a given substrate with square surface symmetry [10]. In addition, short-circuit electrical boundary conditions are imposed, equivalent to ideal electrodes above and beneath the film [9]. Given the recognized importance of strain in determining the properties of thin-film ferroelectrics, Pertsev diagrams have proven to be of enormous interest to experimentalists seeking to interpret the ...
The c(2×2) reconstruction of (001) PbTiO3 surfaces is studied by means of first principles calculations for paraelectric (non-polar) and ferroelectric ([001] polarized) films. Analysis of the atomic displacements in the near-surface region shows how the surface modifies the antiferrodistortive (AFD) instability and its interaction with ferroelectric (FE) distortions. The effect of the surface is found to be termination dependent. The AFD instability is suppressed at the TiO2 termination while it is strongly enhanced, relative to the bulk, at the PbO termination resulting in a c(2x2) surface reconstruction which is in excellent agreement with experiments. We find that, in contrast to bulk PbTiO3, in-plane ferroelectricity at the PbO termination does not suppress the AFD instability. The AFD and the in-plane FE distortions are instead concurrently enhanced at the PbO termination. This leads to a novel surface phase with coexisting FE and AFD distortions which is not found in PbTiO3 bulk.
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