arXiv subjects

David Vanderbilt

Publications and source records attributed to David Vanderbilt.

At least 199 records · Page 11Linked to original sources

arXiv2002

Quantitative analysis of the first-principles effective-Hamiltonian approach to ferroelectric perovskites

The various approximations used in the construction of a first-principles effective Hamiltonian for BaTiO3, and their effects on the calculated transition temperatures, are discussed. An effective Hamiltonian for BaTiO3 is constructed not from first-principles calculations, but from the structural energetics of an atomistic shell model for BaTiO3 of Tinte et al. This allows the elimination of certain uncontrolled approximations that arise in the comparison of first-principles effective Hamiltonian results with experimental values and the quantification of errors associated with the selection of the effective Hamiltonian subspace and subsequent projection. The discrepancies in transition temperatures computed in classical simulations for this effective Hamiltonian and for the atomistic shell model are shown to be associated primarily with a poor description of the thermal expansion in the former case. This leads to specific proposals for refinements to the first-principles effective Hamiltonian method. Our results suggest that there are at least two significant sources of error in the effective-Hamiltonian treatment of BaTiO3 in the literature, i.e., the improper treatment of thermal expansion, and the errors inherent in the first-principles approach itself.

cond-mat.mtrl-sci↗

arXiv2002

Lattice dielectric response of CdCu{3}Ti{4}O{12} and of CaCu{3}Ti{4}O{12} from first principles

Structural, vibrational, and lattice dielectric properties of CdCu{3}Ti{4}O{12} are studied using density-functional theory within the local spin-density approximation, and the results are compared with those computed previously for CaCu{3}Ti{4}O{12}. Replacing Ca with Cd is found to leave many calculated quantities largely unaltered, although significant differences do emerge in zone-center optical phonon frequencies and mode effective charges. The computed phonon frequencies of CdCu{3}Ti{4}O{12} are found to be in excellent agreement with experiment, and the computed lattice contribution to the intrinsic static dielectric constant (~60) also agrees exceptionally well with a recent optical absorption experiment. These results provide further support for a picture in which the lattice dielectric response is essentially conventional, suggesting an extrinsic origin for the anomalous low-frequency dielectric response recently observed in both materials.

cond-mat.mtrl-sci↗

arXiv2002

A First-Principles Approach to Insulators in Finite Electric Fields

We describe a method for computing the response of an insulator to a static, homogeneous electric field. It consists of iteratively minimizing an electric enthalpy functional expressed in terms of occupied Bloch-like states on a uniform grid of k points. The functional has equivalent local minima below a critical field E_c that depends inversely on the density of k points; the disappearance of the minima at E_c signals the onset of Zener breakdown. We illustrate the procedure by computing the piezoelectric and nonlinear dielectric susceptibility tensors of III-V semiconductors.

cond-mat.mtrl-sci↗

arXiv2002

Theory of structural response to macroscopic electric fields in ferroelectric systems

We have developed and implemented a formalism for computing the structural response of a periodic insulating system to a homogeneous static electric field within density-functional perturbation theory (DFPT). We consider the thermodynamic potentials E(R,eta,e) and F(R,eta,e) whose minimization with respect to the internal structural parameters R and unit cell strain eta yields the equilibrium structure at fixed electric field e and polarization P, respectively. First-order expansion of E(R,eta,e) in e leads to a useful approximation in which R(P) and eta(P) can be obtained by simply minimizing the zero-field internal energy with respect to structural coordinates subject to the constraint of a fixed spontaneous polarization P. To facilitate this minimization, we formulate a modified DFPT scheme such that the computed derivatives of the polarization are consistent with the discretized form of the Berry-phase expression. We then describe the application of this approach to several problems associated with bulk and short-period superlattice structures of ferroelectric materials such as BaTiO3 and PbTiO3. These include the effects of compositionally broken inversion symmetry, the equilibrium structure for high values of polarization, field-induced structural phase transitions, and the lattice contributions to the linear and the non-linear dielectric constants.

cond-mat.mtrl-sci↗

arXiv2002

First-principles study of structural, vibrational and lattice dielectric properties of hafnium oxide

Crystalline structures, zone-center phonon modes, and the related dielectric response of the three low-pressure phases of HfO2 have been investigated in density-functional theory using ultrasoft pseudopotentials and a plane-wave basis. The structures of low-pressure HfO2 polymorphs are carefully studied with both the local-density approximation (LDA) and the generalized gradient approximation (GGA). The fully relaxed structures obtained with either exchange-correlation scheme agree reasonably well with experiment, although LDA yields better overall agreement. After calculating the Born effective charge tensors and the force-constant matrices by finite-difference methods, the lattice dielectric susceptibility tensors for the three HfO2 phases are computed by decomposing the tensors into the contributions from individual infrared-active phonon modes.

cond-mat.mtrl-sci↗

arXiv2002

A first-principles study of the structure and lattice dielectric response of CaCu{3}Ti{4}O{12}

Structural and electronic properties of CaCu{3}Ti{4}O{12} have been calculated using density-functional theory within the local spin-density approximation. After an analysis of structural stability, zone-center optical phonon frequencies are evaluated using the frozen-phonon method, and mode effective charges are determined from computed Berry-phase polarizations. Excellent agreement between calculated and measured phonon frequencies is obtained; calculated mode effective charges are in poorer agreement with experiment, although they are of the correct order of magnitude; and the lattice contribution to the static dielectric constant is calculated to be ~40. On the basis of these results, various mechanisms are considered for the enormous dielectric response reported in recent experiments. No direct evidence is found for intrinsic lattice or electronic mechanisms, suggesting that increased attention should be given to extrinsic effects.

cond-mat.mtrl-sci↗

arXiv2001

Ab initio study of ferroelectric domain walls in PbTiO3

We have investigated the atomistic structure of the 180-degree and 90-degree domain boundaries in the ferroelectric perovskite compound PbTiO3 using a first-principles ultrasoft-pseudopotential approach. For each case we have computed the position, thickness and creation energy of the domain walls, and an estimate of the barrier height for their motion has been obtained. We find both kinds of domain walls to be very narrow with a similar width of the order of one to two lattice constants. The energy of the 90-dergree domain wall is calculated to be 35 mJ/m^2, about a factor of four lower than the energy of its 180-degree counterpart, and only a miniscule barrier for its motion is found. As a surprising feature we detected a small offset of 0.15-0.2 eV in the electrostatic potential across the 90-degree domain wall.

cond-mat.mtrl-sci↗

arXiv2001

Phonons and Lattice Dielectric Properties of Zirconia

We have performed a first-principles study of the structural and vibrational properties of the three low-pressure (cubic, tetragonal, and especially monoclinic) phases of ZrO2, with special attention to the computation of the zone-center phonon modes and related dielectric properties. The calculations have been carried out within the local-density approximation using ultrasoft pseudopotentials and a plane-wave basis. The fully relaxed structural parameters are found to be in excellent agreement with experimental data and with previous theoretical work. The total-energy calculations correctly reproduce the energetics of the ZrO2 phases, and the calculated zone-center phonon frequencies yield good agreement with the infrared and Raman experimental frequencies in the monoclinic phase. The Born effective charge tensors are computed and, together with the mode eigenvectors, used to decompose the lattice dielectric susceptibility tensor into contributions arising from individual infrared-active phonon modes. This work has been partially motivated by the potential for ZrO2 to replace SiO2 as the gate-dielectric material in modern integrated-circuit technology.

cond-mat.mtrl-sci↗

arXiv2001

Maximally-localized Wannier functions for entangled energy bands

We present a method for obtaining well-localized Wannier-like functions (WFs) for energy bands that are attached to or mixed with other bands. The present scheme removes the limitation of the usual maximally-localized WFs method (N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997)) that the bands of interest should form an isolated group, separated by gaps from higher and lower bands everywhere in the Brillouin zone. An energy window encompassing N bands of interest is specified by the user, and the algorithm then proceeds to disentangle these from the remaining bands inside the window by filtering out an optimally connected N-dimensional subspace. This is achieved by minimizing a functional that measures the subspace dispersion across the Brillouin zone. The maximally-localized WFs for the optimal subspace are then obtained via the algorithm of Marzari and Vanderbilt. The method, which functions as a postprocessing step using the output of conventional electronic-structure codes, is applied to the s and d bands of copper, and to the valence and low-lying conduction bands of silicon. For the low-lying nearly-free-electron bands of copper we find WFs which are centered at the tetrahedral interstitial sites, suggesting an alternative tight-binding parametrization.

cond-mat.mtrl-sci↗

arXiv2001

Electric-field induced polarization paths in PZT alloys

Properties of Pb(Zr_{1-x}Ti_x)O_3 (PZT) for compositions x near the morphotropic phase boundary and under an electric field are simulated using an ab-initio based approach. Applying an electric field of [111] orientation to tetragonal PZT (e.g., x=0.50) leads to the expected sequence of tetragonal, A-type monoclinic, and rhombohedral structures. However, the application of a field of orientation [001] to rhombohedral PZT (e.g., x=0.47) does not simply reverse this sequence. Instead, the system follows a complicated path involving also triclinic and C-type monoclinic structures. These latter phases are found to exhibit huge shear piezoelectric coefficients.

cond-mat.mtrl-sci↗

arXiv2001

Low-temperature properties of PZT solid solutions near the morphotropic phase boundary

A first-principles-derived approach is used to study structural, piezoelectric and dielectric properties of Pb(Zr_{1-x}Ti_{x})O_{3} (PZT) solid solutions near the morphotropic phase boundary at low temperature. Three ferroelectric phases are found to exist: a tetragonal phase for larger x compositions, a rhombohedral phase for smaller x compositions, and the recently discovered monoclinic phase in between. In this monoclinic phase, the polarization associated with the Zr atoms behaves differently from the polarization associated with the Ti atoms. As the composition x decreases, the former rotates more quickly towards the pseudo-cubic [111] direction and grows in magnitude, while the latter lags in its rotation and its magnitude shrinks. The local microscopic structure is found to deviate significantly from the average structure in these PZT alloy phases as a result of fluctuations in the directions and magnitudes of the local polarizations. The monoclinic phase is characterized by a very large piezoelectric and dielectric response.

cond-mat.mtrl-sci↗

arXiv2001

Ab initio study of BaTiO3 and PbTiO3 surfaces in external electric fields

For the ferroelectric perovskite compounds BaTiO3 and PbTiO3, we have studied the effects of external electric fields on the structural properties of the (001) surfaces. The field-induced changes in the surface interlayer spacings and bucklings have been calculated using a first-principles ultrasoft-pseudopotential approach, and the change of the polarization and the ferroelectric distortions in the surface layers have been obtained. The surfaces are represented by periodically repeated slabs, and an external dipole layer is included in the vacuum region of the supercells to control the electric field normal to the surfaces. The influence of the electrical boundary conditions on the ferroelectric properties of the slabs is discussed. In the case of a vanishing internal electric field, our study indicates that even very thin slabs can show a ferroelectric instability.

cond-mat.mtrl-sci↗

arXiv2001

Exponential decay properties of Wannier functions and related quantities

The spatial decay properties of Wannier functions and related quantities have been investigated using analytical and numerical methods. We find that the form of the decay is a power law times an exponential, with a particular power-law exponent that is universal for each kind of quantity. In one dimension we find an exponent of -3/4 for Wannier functions, -1/2 for the density matrix and for energy matrix elements, and -1/2 or -3/2 for different constructions of non-orthonormal Wannier-like functions.

cond-mat.mtrl-sci↗

arXiv2000

Monoclinic and triclinic phases in higher-order Devonshire theory

Devonshire theory provides a successful phenomenological description of many cubic perovskite ferroelectrics such as BaTiO3 via a sixth-order expansion of the free energy in the polar order parameter. However, the recent discovery of a novel monoclinic ferroelectric phase in the PZT system by Noheda et al. (Appl. Phys. Lett. 74, 2059 (1999)) poses a challenge to this theory. Here, we confirm that the sixth-order Devonshire theory cannot support a monoclinic phase, and consider extensions of the theory to higher orders. We show that an eighth-order theory allows for three kinds of equilibrium phases in which the polarization is confined not to a symmetry axis but to a symmetry plane. One of these phases provides a natural description of the newly observed monoclinic phase. Moreover, the theory makes testable predictions about the nature of the phase boundaries between monoclinic, tetragonal, and rhombohedral phases. A ferroelectric phase of the lowest (triclinic) symmetry type, in which the polarization is not constrained by symmetry, does not emerge until the Devonshire theory is carried to twelfth order. A topological analysis of the critical points of the free-energy surface facilitates the discussion of the phase transition sequences.

cond-mat.mtrl-sci↗

arXiv2000

Models of core reconstruction for the 90-degree partial dislocation in semiconductors

We compare the models that have been proposed in the literature for the atomic structure of the 90-degree partial dislocation in the homopolar semiconductors, silicon, diamond, and germanium. In particular, we examine the traditional single-period and our recently proposed double-period core structures. Ab-initio and tight-binding results on the core energies are discussed, and the geometries are compared in light of the available experimental information about dislocations in these systems. The double-period geometry is found to be the ground-state structure in all three materials. We address boundary-conditions issues that have been recently raised about these results. The structures of point excitations (kinks, solitons, and kink-soliton complexes) in the two geometries are also reviewed.

cond-mat.mtrl-sci↗

arXiv2000

Stability of the Period-Doubled Core of the 90-degree Partial in Silicon

In a recent Letter [N. Lehto and S. Oberg, Phys. Rev. Lett. 80, 5568 (1998)], Lehto and Oberg investigated the effects of strain fields on the core structure of the 90-degree partial dislocation in silicon, especially the influence of the choice of supercell periodic boundary conditions in theoretical simulations. We show that their results for the relative stability between the two structures are in disagreement with cell-size converged tight-binding total energy (TBTE) calculations, which suggest the DP core to be more stable, regardless of the choice of boundary condition. Moreover, we argue that this disagreement is due to their use of a Keating potential.

cond-mat.mtrl-sci↗

arXiv2000

Wannier-function description of the electronic polarization and infrared absorption of high-pressure hydrogen

We have constructed maximally-localized Wannier functions for prototype structures of solid molecular hydrogen under pressure, starting from LDA and tight-binding Bloch wave functions. Each occupied Wannier function can be associated with two paired protons, defining a ``Wannier molecule''. The sum of the dipole moments of these ``molecules'' always gives the correct macroscopic polarization, even under strong compression, when the overlap between nearby Wannier functions becomes significant. We find that at megabar pressures the contributions to the dipoles arising from the overlapping tails of the Wannier functions is very large. The strong vibron infrared absorption experimentally observed in phase III, above ~ 150 GPa, is analyzed in terms of the vibron-induced fluctuations of the Wannier dipoles. We decompose these fluctuations into ``static'' and ``dynamical'' contributions, and find that at such high densities the latter term, which increases much more steeply with pressure, is dominant.

cond-mat.mtrl-sci↗

arXiv2000

First-principles study of ferroelectric and antiferrodistortive instabilities in tetragonal SrTiO3

We carry out first-principles density-functional calculations of the antiferrodistortive (AFD) and ferroelectric (FE) soft-mode instabilities in tetragonal SrTiO3, with the structural degrees of freedom treated in a classical, zero-temperature framework. In particular, we use frozen-phonon calculations to make a careful study of the anisotropy of the AFD and FE mode frequencies in the tetragonal ground state, in which an R-point AFD soft phonon has condensed. Because of the anharmonic couplings, the presence of this AFD distortion substantially affects both the AFD and FE mode frequencies. The AFD mode is found to be softer for rotations around a perpendicular axis (Eg mode) than for rotations about the tetragonal axis (A1g mode), in agreement with experimental results. The FE mode, on the other hand, is found to be softer when polarized perpendicular to the tetragonal axis (Eu mode) than parallel to it (A2u mode). The sign of this frequency splitting is consistent with the experimentally reported anisotropy of the dielectric susceptibility and other evidence. Finally, we present a discussion of the influence of various types of structural distortions on the FE instability and its anisotropy.

cond-mat.mtrl-sci↗