arXiv subjects

David Vanderbilt

Publications and source records attributed to David Vanderbilt.

At least 181 records · Page 10Linked to original sources

arXiv2005

Predicting polarization enhancement in multicomponent ferroelectric superlattices

Ab initio calculations are utilized as an input to develop a simple model of polarization in epitaxial short-period CaTiO3/SrTiO3/BaTiO3 superlattices grown on a SrTiO3 substrate. The model is then combined with a genetic algorithm technique to optimize the arrangement of individual CaTiO3, SrTiO3 and BaTiO3 layers in a superlattice, predicting structures with the highest possible polarization and a low in-plane lattice constant mismatch with the substrate. This modelling procedure can be applied to a wide range of layered perovskite-oxide nanostructures providing guidance for experimental development of nanoelectromechanical devices with substantially improved polar properties.

cond-mat.mtrl-sci↗

arXiv2005

Theory of hypothetical ferroelectric superlattices incorporating head-to-head and tail-to-tail 180$^\circ$ domain walls

While electrical compatibility constraints normally prevent head-to-head (HH) and tail-to-tail (TT) domain walls from forming in ferroelectric materials, we propose that such domain walls could be stabilized by intentional growth of atomic layers in which the cations are substituted from a neighboring column of the periodic table. In particular, we carry out predictive first-principles calculations of superlattices in which Sc, Nb, or other substitutional layers are inserted periodically into PbTiO$_3$. We confirm that this gives rise to a domain structure with the longitudinal component of the polarization alternating from domain to domain, and with the substitutional layers serving as HH and TT domain walls. We also find that a substantial transverse component of the polarization can also be present.

cond-mat.mtrl-sci↗

arXiv2005

First-Principles Calculations at Constant Polarization

We develop an exact formalism for performing first-principles calculations for insulators at fixed electric polarization. As shown by Sai, Rabe, and Vanderbilt (SRV) [N. Sai, K. M. Rabe, and D. Vanderbilt, Phys. Rev. B {\bf 66}, 104108 (2002)], who designed an approximate method to tackle the same problem, such an approach allows one to map out the energy landscape as a function of polarization, providing a powerful tool for the theoretical investigation of polar materials. We apply our method to a system in which the ionic contribution to the polarization dominates (a broken-inversion-symmetry perovskite), one in which this is not the case (a III-V semiconductor), and one in which an additional degree of freedom plays an important role (a ferroelectric phase of KNO$_3$). We find that while the SRV method gives rather accurate results in the first case, the present approach provides important improvements to the physical description in the latter cases.

cond-mat.mtrl-sci↗

arXiv2005

First-principles study of epitaxial strain in perovskites

Using an extension of a first-principles method developed by King-Smith and Vanderbilt [Phys. Rev. B {\bf 49}, 5828 (1994)], we investigate the effects of in-plane epitaxial strain on the ground-state structure and polarization of eight perovskite oxides: BaTiO$_3$, SrTiO$_3$, CaTiO$_3$, KNbO$_3$, NaNbO$_3$, PbTiO$_3$, PbZrO$_3$, and BaZrO$_3$. In addition, we investigate the effects of a nonzero normal stress. The results are shown to be useful in predicting the structure and polarization of perovskite oxide thin films and superlattices.

cond-mat.mtrl-sci↗

arXiv2005

Orbital magnetization in periodic insulators

Working in the Wannier representation, we derive an expression for the orbital magnetization of a periodic insulator. The magnetization is shown to be comprised of two contributions, an obvious one associated with the internal circulation of bulk-like Wannier functions in the interior, and an unexpected one arising from net currents carried by Wannier functions near the surface. Each contribution can be expressed as a bulk property in terms of Bloch functions in a gauge-invariant way. Our expression is verified by comparing numerical tight-binding calculations for finite and periodic samples.

cond-mat.mtrl-sci↗

arXiv2005

Polarization enhancement in two- and three-component ferroelectric superlattices

Composition-dependent structural and polar properties of epitaxial short-period CaTiO_3/SrTiO_3/BaTiO_3 superlattices grown on a SrTiO_3 substrate are investigated with first-principles density-functional theory computational techniques. Polarization enhancement with respect to bulk tetragonal BaTiO_3 is found for two- and three-component superlattices with a BaTiO_3 concentration of more than 30%. Individual BaTiO_3 layer thickness is identified as an important factor governing the polarization improvement. In addition, the degree of inversion-symmetry breaking in three-component superlattices can be controlled by varying the thicknesses of the component layers. The flexibility allowed within this large family of structures makes them highly suitable for various applications in modern nano-electro-mechanical devices.

cond-mat.mtrl-sci↗

arXiv2005

Systematic treatment of displacements, strains and electric fields in density-functional perturbation theory

The methods of density-functional perturbation theory may be used to calculate various physical response properties of insulating crystals including elastic, dielectric, Born charge, and piezoelectric tensors. These and other important tensors may be defined as second derivatives of the total energy with respect to atomic-displacement, electric-field, or strain perturbations, or as mixed derivatives with respect to two of these perturbations. The resulting tensor quantities tend to be coupled in complex ways in polar crystals, giving rise to a variety of variant definitions. For example, it is generally necessary to distinguish between elastic tensors defined under different electrostatic boundary conditions, and between dielectric tensors defined under different elastic boundary conditions. Here, we describe an approach for computing all of these various response tensors in a unified and systematic fashion. Applications are presented for two materials, wurtzite ZnO and rhombohedral BaTiO3, at zero temperature.

cond-mat.mtrl-sci↗

arXiv2004

Amorphous ZrO2 from Ab-initio molecular dynamics: Structural, electronic and dielectric properties

Realistic models of amorphous ZrO2 are generated in a ``melt-and-quench'' fashion using ab-initio molecular dynamics in a plane-wave pseudopotential formulation of density-functional theory. The structural properties of the resulting amorphous models are analyzed, with special attention to coordination statistics. The vibrational and dielectric properties of one of these models are then investigated from first principles using linear-response methods. The electronic dielectric constant and Born effective charges are found to be very similar to those of the crystalline phases. Encouragingly, the predicted total static dielectric constant is about 22, comparable to that of the monoclinic phase. This work is motivated by the search for improved gate dielectric materials for sub-0.1 micron CMOS technology, and may also have implications for HfO2 and for silicates of ZrO2 and HfO2.

cond-mat.mtrl-sci↗

arXiv2004

Metric Tensor Formulation of Strain in Density-Functional Perturbation Theory

The direct calculation of the elastic and piezoelectric tensors of solids can be accomplished by treating homogeneous strain within the framework of density-functional perturbation theory. By formulating the energy functional in reduced coordinates, we show that the strain perturbation enters only through metric tensors, and can be treated in a manner exactly paralleling the treatment of other perturbations. We present an analysis of the strain perturbation of the plane-wave pseudopotential functional, including the internal strain terms necessary to treat the atomic-relaxation contributions. Procedures for computationally verifying these expressions by comparison with numerical derivatives of ground-state calculations are described and illustrated.

cond-mat.mtrl-sci↗

arXiv2004

Tunability of the dielectric response of epitaxially strained SrTiO3 from first principles

The effect of in-plane strain on the nonlinear dielectric properties of SrTiO3 epitaxial thin films is calculated using density-functional theory within the local-density approximation. Motivated by recent experiments, the structure, zone-center phonons, and dielectric properties with and without an external electric field are evaluated for several misfit strains within +-3% of the calculated cubic lattice parameter. In these calculations, the in-plane lattice parameters are fixed, and all remaining structural parameters are permitted to relax. The presence of an external bias is treated approximately by applying a force to each ion proportional to the electric field. After obtaining zero-field ground state structures for various strains, the zone-center phonon frequencies and Born effective charges are computed, yielding the zero-field dielectric response. The dielectric response at finite electric field bias is obtained by computing the field dependence of the structure and polarization using an approximate technique. The results are compared with recent experiments and a previous phenomenological theory. The tunability is found to be strongly dependent on the in-plane lattice parameter, showing markedly different behavior for tensile and compressive strains. Our results are expected to be of use for isolating the role of strain in the tunability of real ultrathin epitaxial films.

cond-mat.mtrl-sci↗

arXiv2004

Ab initio study of the phase diagram of epitaxial BaTiO3

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 (1998)], 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.

cond-mat.mtrl-sci↗

arXiv2004

Atomistic simulations of the incipient ferroelectric KTaO$_3$

A parameterized effective Hamiltonian approach is used to investigate KTaO$_3$. We find that the experimentally observed anomalous dielectric response of this incipient ferroelectric is well reproduced by this approach, once quantum effects are accounted for. Quantum fluctuations suppress the paraelectric--to--ferroelectric phase transition; it is unnecessary to introduce defects to explain the dielectric behavior. The resulting quantum-induced local structure exhibits off-center atomic displacements that display {\sl longitudinal, needle-like correlations} extending a few lattice constants.

cond-mat.mtrl-sci↗

arXiv2003

Dynamics of Berry-phase polarization in time-dependent electric fields

We consider the flow of polarization current J(t)=dP/dt produced by a homogeneous electric field E(t) or by rapidly varying some other parameter in the Hamiltonian of a solid. For an initially insulating system and a collisionless time evolution, the dynamic polarization P(t) is given by a nonadiabatic version of the King-Smith--Vanderbilt geometric-phase formula. This leads to a computationally convenient form for the Schroedinger equation where the electric field is described by a linear scalar potential handled on a discrete mesh in reciprocal space. Stationary solutions in sufficiently weak static fields are local minima of the energy functional of Nunes and Gonze. Such solutions only exist below a critical field that depends inversely on the density of k points. For higher fields they become long-lived resonances, which can be accessed dynamically by gradually increasing E. As an illustration the dielectric function in the presence of a dc bias field is computed for a tight-binding model from the polarization response to a step-function discontinuity in E(t), displaying the Franz-Keldysh effect.

cond-mat.mtrl-sci↗

arXiv2003

Anomalous enhancement of tetragonality in PbTiO3 induced by negative pressure

Using a first-principles approach based on density-functional theory, we find that a large tetragonal strain can be induced in PbTiO3 by application of a negative hydrostatic pressure. The structural parameters and the dielectric and dynamical properties are found to change abruptly near a crossover pressure, displaying a ``kinky'' behavior suggestive of proximity to a phase transition. Analogous calculations for BaTiO3 show that the same effect is also present there, but at much higher negative pressure. We investigate this unexpected behavior of PbTiO3 and discuss an interpretation involving a phenomenological description in terms of a reduced set of relevant degrees of freedom.

cond-mat.mtrl-sci↗

arXiv2003

A first-principles study of oxygen vacancy pinning of domain walls in PbTiO3

We have investigated the interaction of oxygen vacancies and 180-degree domain walls in tetragonal PbTiO3 using density-functional theory. Our calculations indicate that the vacancies do have a lower formation energy in the domain wall than in the bulk, thereby confirming the tendency of these defects to migrate to, and pin, the domain walls. The pinning energies are reported for each of the three possible orientations of the original Ti-O-Ti bonds, and attempts to model the results with simple continuum models are discussed.

cond-mat.mtrl-sci↗

arXiv2003

First-principles study of (BiScO3){1-x}-(PbTiO3){x} piezoelectric alloys

We report a first-principles study of a class of (BiScO3)_{1-x}-(PbTiO3)_x (BS-PT) alloys recently proposed by Eitel et al. as promising materials for piezoelectric actuator applications. We show that (i) BS-PT displays very large structural distortions and polarizations at the morphotropic phase boundary (MPB) (we obtain a c/a of ~1.05-1.08 and P_tet of ~1.1 C/m^2); (ii) the ferroelectric and piezoelectric properties of BS-PT are dominated by the onset of hybridization between Bi/Pb-6p and O-2p orbitals, a mechanism that is enhanced upon substitution of Pb by Bi; and (iii) the piezoelectric responses of BS-PT and Pb(Zr_{1-x}Ti_x)O3 (PZT) at the MPB are comparable, at least as far as the computed values of the piezoelectric coefficient d_15 are concerned. While our results are generally consistent with experiment, they also suggest that certain intrinsic properties of BS-PT may be even better than has been indicated by experiments to date. We also discuss results for PZT that demonstrate the prominent role played by Pb displacements in its piezoelectric properties.

cond-mat.mtrl-sci↗

arXiv2003

Extrinsic models for the dielectric response of CaCu{3}Ti{4}O{12}

The large, temperature-independent, low-frequency dielectric constant recently observed in single-crystal CaCu{3}Ti{4}O{12} is most plausibly interpreted as arising from spatial inhomogenities of its local dielectric response. Probable sources of inhomogeneity are the various domain boundaries endemic in such materials: twin, Ca-ordering, and antiphase boundaries. The material in and neighboring such boundaries can be insulating or conducting. We construct a decision tree for the resulting six possible morphologies, and derive or present expressions for the dielectric constant for models of each morphology. We conclude that all six morphologies can yield dielectric behavior consistent with observations and suggest further experiments to distinguish among them.

cond-mat.mtrl-sci↗

arXiv2003

First-principles Study of Electronic and Dielectric Properties of ZrO2 and HfO2

Using density-functional theory with ultrasoft pseudopotentials, we previously investigated the structural and electronic properties of the low-pressure (cubic, tetragonal, and monoclinic) phases of ZrO2 and HfO2, in order to elucidate phonon modes, Born effective charge tensors, and especially the lattice dielectric response in these phases. We now extend this previous work by carrying out similar calculations on the two high-pressure orthorhombic phases, and by providing density-of-states and band-gap information on all polymorphs. Our results show that the electronic structures and dielectric responses are strongly phase-dependent. In particular, the monoclinic phases of ZrO2 and HfO2 are found to have a strongly anisotropic dielectric tensor and a rather small orientational average (epsilon_0) compared to the two other low-pressure phases. Our calculations show that epsilon_0 is even smaller in the orthorhombic phases.

cond-mat.mtrl-sci↗