Showing papers by "David Vanderbilt published in 2009"

Magnetoelectric polarizability and axion electrodynamics in crystalline insulators

Abstract: The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $\ensuremath{\theta}$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous materials. This polarizability $\ensuremath{\theta}$ is the same parameter that appears in the ``axion electrodynamics'' Lagrangian $\ensuremath{\Delta}{\mathcal{L}}_{EM}=(\ensuremath{\theta}{e}^{2}/2\ensuremath{\pi}h)\mathbf{E}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{B}$, which is known to describe the unusual magnetoelectric properties of the three-dimensional topological insulator ($\ensuremath{\theta}=\ensuremath{\pi}$). We compute $\ensuremath{\theta}$ 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 wave function and defines the 3D topological insulator, like the integer quantum Hall effect, in terms of a topological ground-state response function.

Enhancement of ferroelectricity at metal–oxide interfaces

Abstract: The size reduction of thin-film ferroelectric capacitors has been hampered by effects that arise as ferroelectric films reach only a few unit cells in height However, rather than inevitably resulting in a ‘dead layer’, an enhancement of ferroelectricity at certain metal–oxide interfaces is now predicted

Electric displacement as the fundamental variable in electronic-structure calculations

Abstract: Finite-field calculations in periodic insulators are technically and conceptually challenging, owing to fundamental problems in defining polarization in extended solids. Although 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 enables full control over the electrical variables within the density functional formalism.

Magnetoelectric polarizability and axion electrodynamics in crystalline insulators

Abstract: The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $\ensuremath{\theta}$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous materials. This polarizability $\ensuremath{\theta}$ is the same parameter that appears in the ``axion electrodynamics'' Lagrangian $\ensuremath{\Delta}{\mathcal{L}}_{EM}=(\ensuremath{\theta}{e}^{2}/2\ensuremath{\pi}h)\mathbf{E}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{B}$, which is known to describe the unusual magnetoelectric properties of the three-dimensional topological insulator ($\ensuremath{\theta}=\ensuremath{\pi}$). We compute $\ensuremath{\theta}$ 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 wave function and defines the 3D topological insulator, like the integer quantum Hall effect, in terms of a topological ground-state response function.

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

Abstract: In the framework of the modern theory of polarization, we rigorously establish the microscopic nature of the electric displacement field $\mathbf{D}$. In particular, we show that the longitudinal component of $\mathbf{D}$ 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-$\mathbf{D}$ density-functional theory to the first-principles modeling of charge-mismatched systems.

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

Abstract: The ideal intrinsic barriers to domain switching in $c$-phase ${\text{PbTiO}}_{3}$ (PTO), ${\text{PbZrO}}_{3}$ (PZO), and ${\text{PbZr}}_{1\ensuremath{-}x}{\text{Ti}}_{x}{\text{O}}_{3}$ (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 rocksalt 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 five-atom unit cells.

Electric polarization in a Chern insulator.

Abstract: We extend the Berry-phase concept of polarization to insulators having a nonzero 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 wave vector 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.

Maximally localized Wannier functions for GW quasiparticles

Abstract: 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 ${\text{SrTiO}}_{3}$ and solid argon.

A converse approach to the calculation of NMR shielding tensors

Abstract: 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.

First-principles modeling of ferroelectric capacitors via constrained displacement field calculations

Abstract: 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 $\mathbf{D}$. By performing calculations on model $\text{Pt}/{\text{BaTiO}}_{3}/\text{Pt}$ and $\text{Au}/{\text{BaZrO}}_{3}/\text{Au}$ 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 ${\text{BO}}_{2}$-electrode interfaces behave analogously to a layer of linear dielectric put in series with a bulklike perovskite film while a significant nonlinear effect occurs at AO-electrode interfaces.

First-principles modeling of multiferroic RMn2O5.

Abstract: We investigate the phase diagrams of $R{\mathrm{Mn}}_{2}{\mathrm{O}}_{5}$ via a first-principles effective-Hamiltonian method. We are able to reproduce the most important features of the complicated magnetic and ferroelectric phase transitions. The calculated polarization as a function of temperature agrees very well with experiments. The dielectric-constant step at the commensurate-to-incommensurate magnetic phase transition is well reproduced. The microscopic mechanisms for the phase transitions are discussed.

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

Abstract: 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 in 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 ${\text{SrTiO}}_{3}/{\text{KNbO}}_{3}$ 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 ${\text{NbO}}_{2}$) layers are non-neutral and apply this method to quantify the local variations in polarization in the proposed ${\text{SrTiO}}_{3}/{\text{KNbO}}_{3}$ superlattice system.

Dependence of electronic polarization on octahedral rotations in TbMnO 3 from first principles

Abstract: The electronic contribution to the magnetically induced polarization in orthorhombic ${\text{TbMnO}}_{3}$ 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 $b\text{\ensuremath{-}}c$ or $a\text{\ensuremath{-}}b$ 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 show 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 ${\text{MnO}}_{6}$ octahedra and demonstrate that it can vary over a wide range, comparable with the lattice-mediated contribution, for both $b\text{\ensuremath{-}}c$ and $a\text{\ensuremath{-}}b$ spirals. We present 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.

First-principles theory of magnetically induced ferroelectricity in TbMnO3

Abstract: 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.

First-principles theory of magnetically induced ferroelectricity in TbMnO3

Abstract: 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.