arXiv subjects

David Vanderbilt

Publications and source records attributed to David Vanderbilt.

At least 145 records · Page 8Linked to original sources

arXiv2009

First-principles study of high-field piezoelectricity in tetragonal PbTiO3

We calculate from first principles the nonlinear piezoelectric response of ferroelectric PbTiO3 for the case of a polarization-enhancing electric field applied along the tetragonal axis. We focus mainly on the case of fixed in-plane lattice constants, corresponding to epitaxially constrained thin films. We find that the dependence of the c/a ratio on electric field is almost linear in the range up to 500 MV/m, with little saturation. This result contrasts with expectations from Landau-Devonshire approaches based on experimental results obtained at lower fields, but is in qualitative agreement with a recent experiment in which higher fields were attained using pulsed-field methods. We also study cases in which the in-plane epitaxy constraint is removed, or an artificial negative pressure is applied, or both. These calculations demonstrate that PbTiO3 can show a strikingly non-linear piezoelectric response under modified elastic boundary conditions.

cond-mat.mtrl-sci↗

arXiv2009

Berry-phase theory of polar discontinuities at oxide-oxide interfaces

In the framework of the modern theory of polarization, we rigorously establish the microscopic nature of the electric displacement field D. In particular, we show that the longitudinal component of D is preserved at a coherent and insulating interface. To motivate and elucidate our derivation, we use the example of LAO/STO interfaces and superlattices, where the validity of the above conservation law is not immediately obvious. Our results generalize the "locality principle" of constrained-D density functional theory to the first-principles modeling of charge-mismatched systems.

cond-mat.mtrl-sci↗

arXiv2009

Dependence of electronic polarization on octahedral rotations in TbMnO3 from first principles

The electronic contribution to the magnetically induced polarization in orthorhombic TbMnO3 is studied from first principles. We compare the cases in which the spin cycloid, which induces the electric polarization via the spin-orbit interaction, is in either the b-c or a-b plane. We find that the electronic contribution is negligible in the first case, but much larger, and comparable to the lattice-mediated contribution, in the second case. However, we how that this behavior is an artifact of the particular pattern of octahedral rotations characterizing the structurally relaxed Pbnm crystal structure. To do so, we explore how the electronic contribution varies for a structural model of rigidly rotated MnO6 octahedra, and demonstrate that it can vary over a wide range, comparable with the lattice-mediated contribution, for both b-c and a-b spirals. We introduce a phenomenological model that is capable of describing this behavior in terms of sums of symmetry-constrained contributions arising from the displacements of oxygen atoms from the centers of the Mn-Mn bonds.

cond-mat.mtrl-sci↗

arXiv2009

First-principles modeling of ferroelectric capacitors via constrained-D calculations

First-principles modeling of ferroelectric capacitors presents several technical challenges, due to the coexistence of metallic electrodes, long-range electrostatic forces and short-range interface chemistry. Here we show how these aspects can be efficiently and accurately rationalized by using a finite-field density-functional theory formalism in which the fundamental electrical variable is the displacement field D. By performing calculations on model Pt/BaTiO3/Pt and Au/BaZrO3/Au capacitors we demonstrate how the interface-specific and bulk-specific properties can be identified and rigorously separated. Then, we show how the electrical properties of capacitors of arbitrary thickness and geometry (symmetric or asymmetric) can be readily reconstructed by using such information. Finally, we show how useful observables such as polarization and dielectric, piezoelectric and electrostrictive coefficients are easily evaluated as a byproduct of the above procedure. We apply this methodology to elucidate the relationship between chemical bonding, Schottky barriers and ferroelectric polarization at simple-metal/oxide interfaces. We find that BO2-electrode interfaces behave analogously to a layer of linear dielectric put in series with a bulk-like perovskite film, while a significant non-linear effect occurs at AO-electrode interfaces.

cond-mat.mtrl-sci↗

arXiv2009

First-principles theory of magnetically induced ferroelectricity in TbMnO3

We study the polarization induced via spin-orbit interaction by a magnetic cycloidal order in orthorhombic TbMnO3 using first-principle methods. The case of magnetic spiral lying in the b-c plane is analyzed, in which the pure electronic contribution to the polarization is shown to be small. We focus our attention on the lattice-mediated contribution, and study it's dependence on the Coulomb interaction parameter U in the LDA+U method and on the wave-vector of the spin spiral. The role of the spin-orbit interaction on different sites is also analyzed.

cond-mat.mtrl-sci↗

arXiv2009

A converse approach to the calculation of NMR shielding tensors

We introduce an alternative approach to the first-principles calculation of NMR shielding tensors. These are obtained from the derivative of the orbital magnetization with respect to the application of a microscopic, localized magnetic dipole. The approach is simple, general, and can be applied to either isolated or periodic systems. Calculated results for simple hydrocarbons, crystalline diamond, and liquid water show very good agreement with established methods and experimental results.

cond-mat.mtrl-sci↗

arXiv2009

Magnetoelectric polarizability and axion electrodynamics in crystalline insulators

The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $θ$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous materials. This polarizability $θ$ is the same parameter that appears in the "axion electrodynamics" Lagrangian $Δ{\cal L}_{EM} = (θe^2 / 2 πh) {\bf E} \cdot {\bf B}$, which is known to describe the unusual magnetoelectric properties of the three-dimensional topological insulator ($θ=π$). We compute $θ$ for a simple model that accesses the topological insulator and discuss its connection to the surface Hall conductivity. The orbital magnetoelectric polarizability can be generalized to the many-particle wavefunction and defines the 3D topological insulator, like the IQHE, in terms of a topological ground-state response function.

cond-mat.mes-hall↗

arXiv2009

Electric polarization in a Chern insulator

We extend the Berry-phase concept of polarization to insulators having a non-zero value of the Chern invariant. The generalization to such Chern insulators requires special care because of the partial occupation of chiral edge states. We show how the integrated bulk current arising from an adiabatic evolution can be related to a difference of bulk polarizations. We also show how the surface charge can be related to the bulk polarization, but only with a knowledge of the wavevector at which the occupancy of the edge state is discontinuous. Furthermore we present numerical calculations on a model Hamiltonian to provide additional support for our analytic arguments.

cond-mat.mes-hall↗

arXiv2008

Theoretical investigation of polarization-compensated II-IV/I-V perovskite superlattices

Recent work suggested that head-to-head and tail-to-tail domain walls could be induced to form in ferroelectric superlattices by introducing compensating "delta doping" layers via chemical substitution in specified atomic planes [Phys. Rev. B 73, 020103(R), 2006]. Here we investigate a variation of this approach in which superlattices are formed of alternately stacked groups of II-IV and I-V perovskite layers, and the "polar discontinuity" at the II-IV/I-V interface effectively provides the delta-doping layer. Using first-principles calculations on SrTiO3/KNbO3 as a model system, we show that this strategy allows for the growth of a superlattice with stable polarized regions and large polarization discontinuities at the internal interfaces. We also generalize a Wannier-based definition of layer polarizations in perovskite superlattices [Phys. Rev. Lett. 97, 107602 (2006)] to the case in which some (e.g., KO or NbO2) layers are non-neutral, and apply this method to quantify the local variations in polarization in the proposed SrTiO3/KNbO3 superlattice system.

cond-mat.mtrl-sci↗

arXiv2008

Ideal barriers to polarization reversal and domain-wall motion in strained ferroelectric thin films

The ideal intrinsic barriers to domain switching in c-phase PbTiO_3 (PTO), PbZrO_3 (PZO), and PbZr_{1-x}Ti_xO_3 (PZT) are investigated via first-principles computational methods. The effects of epitaxial strain on the atomic structure, ferroelectric response, barrier to coherent domain reversal, domain-wall energy, and barrier to domain-wall translation are studied. It is found that PTO has a larger polarization, but smaller energy barrier to domain reversal, than PZO. Consequentially the idealized coercive field is over two times smaller in PTO than PZO. The Ti--O bond length is more sensitive to strain than the other bonds in the crystals. This results in the polarization and domain-wall energy in PTO having greater sensitivity to strain than in PZO. Two ordered phases of PZT are considered, the rock-salt structure and a (100) PTO/PZO superlattice. In these simple structures we find that the ferroelectric properties do not obey Vergard's law, but instead can be approximated as an average over individual 5-atom unit cells.

cond-mat.mtrl-sci↗

arXiv2008

Enhancement of ferroelectricity at metal/oxide interfaces

By performing first-principles calculations on four capacitor structures based on BaTiO3 and PbTiO3, we determine the intrinsic interfacial effects that are responsible for the destabilization of the polar state in thin-film ferroelectric devices. We show that, contrary to the established interpretation, the interfacial capacitance depends crucially on the local chemical environment of the interface through the force constants of the metal-oxide bonds, and is not necessarily related to the bulk screening properties of the electrode material. In particular, in the case of interfaces between AO-terminated perovskites and simple metals, we demonstrate a novel mechanism of "interfacial ferroelectricity" that produces an overall enhancement of the ferroelectric instability of the film, rather than a suppression as is usually assumed. The resulting "negative dead layer" suggests a route to thin-film ferroelectric devices that are free of deleterious size effects.

cond-mat.mtrl-sci↗

arXiv2008

Electric displacement as the fundamental variable in electronic-structure calculations

Finite-field calculations in periodic insulators are technically and conceptually challenging, due to fundamental problems in defining polarization in extended solids. While significant progress has been made recently with the establishment of techniques to fix the electric field E or the macroscopic polarization P in first-principles calculations, both methods lack the ease of use and conceptual clarity of standard zero-field calculations. Here we develop a new formalism in which the electric displacement D, rather than E or P, is the fundamental electrical variable. Fixing D has the intuitive interpretation of imposing open-circuit electrical boundary conditions, which is particularly useful in studying ferroelectric systems. Furthermore, the analogy to open-circuit capacitors suggests an appealing reformulation in terms of free charges and potentials, which dramatically simplifies the treatment of stresses and strains. Using PbTiO3 as an example, we show that our technique allows full control over the electrical variables within the density functional formalism.

cond-mat.mtrl-sci↗

arXiv2008

Maximally-localized Wannier functions for GW quasiparticles

We review the formalisms of the self-consistent GW approximation to many-body perturbation theory and of the generation of optimally-localized Wannier functions from groups of energy bands. We show that the quasiparticle Bloch wave functions from such GW calculations can be used within this Wannier framework. These Wannier functions can be used to interpolate the many-body band structure from the coarse mesh of Brillouin zone points on which it is known from the initial calculation to the usual symmetry lines, and we demonstrate that this procedure is accurate and efficient for the self-consistent GW band structure. The resemblance of these Wannier functions to the bond orbitals discussed in the chemical community led us to expect differences between density-functional and many-body functions that could be qualitatively interpreted. However, the differences proved to be minimal in the cases studied. Detailed results are presented for SrTiO_3 and solid argon.

cond-mat.mtrl-sci↗

arXiv2008

Structural stability and lattice dynamics of SiO2 cristobalite

Among the phases of SiO2 are alpha and beta cristobalites, which have a long and somewhat controversial history of proposed structural assignments and phase-transition mechanisms. Recently, Zhang and Scott found new indications that the higher-temperature beta phase has space group I-42d and, by assuming a group-subgroup relationship between phases, they argued that the lower-temperature alpha phase should have lower symmetry than that of the widely-accepted P4_12_12 space group. With this motivation, we use first-principles calculations to investigate the energy, structure, and local stability of P4_12_12 and I-42d structures. We also compute the frequencies of the zone-center phonon modes in both structures, as well as certain zone-boundary modes in the I-42d structure, and compare with experiment. We then argue that the various P4_12_12 and I-42d enantiomorphs can be grouped into three clusters, each of which is identified with a three-dimensional manifold of structures of P2_12_12_1 symmetry in which the P4_12_12 and I-42d appear as higher-symmetry special cases. We find that there are relatively high energy barriers between manifolds, but low barriers within a manifold. Exploring the energy landscape within one of these manifolds, we find a minimal-energy path connecting P4_12_12 and I-42d structures with a surprisingly low barrier of ~5 meV per formula unit. Possible implications for the phase-transition mechanism are discussed.

cond-mat.mtrl-sci↗

arXiv2008

Ab initio calculations of the atomic and electronic structure of CaTiO3 (001) and (011) surfaces

We present the results of calculations of surface relaxations, energetics, and bonding properties for CaTiO3 (001) and (011) surfaces using a hybrid B3PW description of exchange and correlation. We consider both CaO and TiO2 terminations of the non-polar (001) surface, and Ca, TiO and O terminations of the polar (011) surface. On the (001) surfaces, we find that all upper-layer atoms relax inwards on the CaO-terminated surface, while outward relaxations of all atoms in the second layer are found for both terminations. For the TiO2-terminated (001) surface, the largest relaxations are on the second-layer atoms. The surface rumpling is much larger for the CaO-terminated than for the TiO2-terminated (001) surface, but their surface energies are quite similar at 0.94eV and 1.13eV respectively. In contrast, different terminations of the (011) CaTiO3 surface lead to very different surface energies of 1.86eV, 1.91eV, and 3.13eV for the O-terminated, Ca-terminated, and TiO-terminated (011) surface respectively. Our results for surface energies contrast sharply with those of Zhang et al. [Phys. Rev. B 76, 115426 (2007)], where the authors found a rather different pattern of surface energies. We predict a considerable increase of the Ti-O chemical bond covalency near the (011) surface as compared both to the bulk and to the (001) surface.

cond-mat.mtrl-sci↗

arXiv2008

Fast Molecular-Dynamics Simulation for Ferroelectric Thin-Film Capacitors Using a First-Principles Effective Hamiltonian

A newly developed fast molecular-dynamics method is applied to BaTiO3 ferroelectric thin-film capacitors with short-circuited electrodes or under applied voltage. The molecular-dynamics simulations based on a first-principles effective Hamiltonian clarify that dead layers (or passive layers) between ferroelectrics and electrodes markedly affect the properties of capacitors, and predict that the system is unable to hop between a uniformly polarized ferroelectric structure and a striped ferroelectric domain structure at low temperatures. Simulations of hysteresis loops of thin-film capacitors are also performed, and their dependence on film thickness, epitaxial constraints, and electrodes are discussed.

cond-mat.mtrl-sci↗

arXiv2008

Predicting polarization and nonlinear dielectric response of arbitrary perovskite superlattice sequences

We carry out first-principles calculations of the nonlinear dielectric response of short-period ferroelectric superlattices. We compute and store not only the total polarization, but also the Wannier-based polarizations of individual atomic layers, as a function of electric displacement field, and use this information to construct a model capable of predicting the nonlinear dielectric response of an arbitrary superlattice sequence. We demonstrate the successful application of our approach to superlattices composed of SrTiO$_3$, CaTiO$_3$, and BaTiO$_3$ layers.

cond-mat.mtrl-sci↗

arXiv2008

First-principles study of improper ferroelectricity in TbMnO3

We have carried out a first-principles theoretical study of the magnetically induced polarization in orthorhombic TbMnO3, a prototypical material in which a cycloidal spin structure generates an electric polarization via the spin-orbit interaction. We compute both the electronic and the lattice-mediated contributions to the polarization and find that the latter is strongly dominant. We analyze the spin-orbit induced forces and lattice displacements from both atomic and mode-decomposition viewpoints, and show that a simple model based on nearest Mn--Mn neighbor Dzyaloshinskii-Moriya interactions is not able to account fully for the results. The direction and magnitude of our computed polarization are in good agreement with experiment.

cond-mat.mtrl-sci↗