arXiv subjects
Publications and source records attributed to K. M. Rabe.
A first-principles method, based on density functional perturbation theory, is presented for computing the leading order tunability of high-dielectric-constant materials.
The structure, polarization, and zone-center phonons of bulk tetragonal BaTiO$_3$ under compressive epitaxial stress are calculated using density functional theory within the local density approximation. The polarization, computed using the Berry-phase formalism, increases with increasing tetragonality and is found to be enhanced by nearly 70% for the largest compressive misfit strain considered (-2.28%). The results are expected to be useful for the analysis of coherent epitaxial BaTiO$_3$ thin films and heterostructures grown on perovskite substrates having a smaller lattice constant, such as SrTiO$_3$.
Ab initio phonon calculations for the nonpolar reference structures of the (001), (110), and (111) PbZrO_3/PbTiO_3 [1:1] superlattices are presented. The unstable polar modes in the tetragonal (001) and (110) structures are confined in either the Ti- or the Zr-centered layers and display two-mode behavior, while in the cubic (111) case one-mode behavior is observed. Instabilities with pure oxygen character are observed in all three structures. The implications for the ferroelectric behavior and related properties are discussed.
A detailed examination of the energy landscape, density of states and magnetic moment of tetragonally distorted ferromagnetic Ni_2MnGa was performed using first-principles local-spin-density (LSD) pseudopotential calculations, varying V as well as c/a. The energy of tetragonal Ni_2MnGa is found to be nearly constant for values of c/a over a wide range, with shallow minima near c/a = 1 and 1.08 in addition to that near 1.2. This flat energy surface is consistent with the wide range of observed values of c/a. It also explains the observation of pseudomorphic growth of Ni_2MnGa on GaAs, despite a nominal 3% lattice mismatch. The related materials Ni_2MnAl, Ni_2MnIn and ferromagnetic NiMn were examined for similar behavior, but all are seen to have a single well-defined minimum at c/a near 1, consistent with available experimental information. For NiMn, the ground state antiferromagnetic ordering and structural parameters are correctly predicted within the LSD approach.
Using first-principles calculations based on a variational density functional perturbation theory, we investigate the lattice dynamics of solid solutions of barium and strontium titanates. Averaging the information available for the related pure compounds yields results equivalent to those obtained within the virtual crystal approximation, providing frequencies which are a good approximation to those computed for a (111) ordered supercell. Using the same averaging technique we report the evolution of the ferroelectric and antiferrodistortive instabilities with composition.
The ground-state polarization of PbTiO3 thin films is studied using a microscopic effective Hamiltonian with parameters obtained from first-principles calculations. Under short-circuit electrical boundary conditions, (001) films with thickness as low as three unit cells are found to have a perpendicularly polarized ferroelectric ground state with significant enhancement of the polarization at the surface.
The full phonon dispersion relations of lead titanate and lead zirconate in the cubic perovskite structure are computed using first-principles variational density-functional perturbation theory, with ab initio pseudopotentials and a plane-wave basis set. Comparison with the results previously obtained for barium titanate shows that the change of a single constituent (Ba to Pb, Ti to Zr) has profound effects on the character and dispersion of unstable modes, with significant implications for the nature of the phase transitions and the dielectric and piezoelectric responses of the compounds. Examination of the interatomic force constants in real space, obtained by a transformation which correctly treats the long-range dipolar contribution, shows that most are strikingly similar, while it is the differences in a few key interactions which produce the observed changes in the phonon dispersions. These trends suggest the possibility of the transferability of force constants to predict the lattice dynamics of perovskite solid solutions.
Molecular-dynamics simulations of KNbO$_3$ reveal preformed dynamic chain-like structures, present even in the paraelectric phase, that are related to the softening of phonon branches over large regions of the Brillouin zone. The phase sequence of ferroelectric transitions is correctly reproduced, showing that the first-principles effective Hamiltonian used in the simulations captures the essential behavior of the microscopic fluctuations driving the transitions. Real space chains provide a framework for understanding both the displacive and order-disorder characteristics of these phase transitions.
The fcc-based structure of Yb2.75C60 is unique among metal-doped fullerene compounds, exhibiting long-range-ordered vacancies, significantly off-centered divalent Yb cations, and distorted, crystallographically inequivalent, orientationally ordered C60 anions. A simple electrostatic-energy analysis, which models the constituents using point charges, is shown to provide insight into how each of these features stabilizes this unusual crystal structure. The results have general implications for a variety of other intercalated metal fullerides.
An effective Hamiltonian for the ferroelectric transition in PbTiO3 is constructed from first-principles density-functional-theory total-energy and linear-response calculations through the use of a localized, symmetrized basis set of ``lattice Wannier functions.'' Explicit parametrization of the polar lattice Wannier functions is used for subspace projection, addressing the issues of LO-TO splitting and coupling to the complementary subspace. In contrast with ferroelectric BaTiO3 and KNbO3, we find significant involvement of the Pb atom in the lattice instability. Monte Carlo simulations for this Hamiltonian show a first-order cubic-tetragonal transition at 660 K. Resulting temperature dependence of spontaneous polarization, c/a ratio and unit-cell volume near the transition are in good agreement with experiment. Comparison of Monte Carlo results with mean field theory analysis shows that both strain and fluctuations are necessary to produce the first order character of this transition.
A systematic method is presented for constructing effective Hamiltonians for general phonon-related structural transitions. The key feature is the application of group theoretical methods to identify the subspace in which the effective Hamiltonian acts and construct for it localized basis vectors, which are the analogue of electronic Wannier functions. The results of the symmetry analysis for the perovskite, rocksalt, fluorite and A15 structures and the forms of effective Hamiltonians for the ferroelectric transition in $PbTiO_3$ and $BaTiO_3$, the oxygen-octahedron rotation transition in $SrTiO_3$, the Jahn-Teller instability in $La_{1-x}(Ca,Sr,Ba)_xMnO_3$ and the antiferroelectric transition in $PbZrO_3$ are discussed. For the oxygen- octahedron rotation transition in $SrTiO_3$, this method provides an alternative to the rotational variable approach which is well behaved throughout the Brillouin zone. The parameters appearing in the Wannier basis vectors and in the effective Hamiltonian, given by the corresponding invariant energy expansion, can be obtained for individual materials using first- principles density-functional-theory total energy and linear response techniques, or any technique that can reliably calculate force constants and distortion energies. A practical approach to the determination of these parameters is presented and the application to ferroelectric $PbTiO_3$ discussed.
An effective Hamiltonian for the ferroelectric transition in $PbTiO_3$ is constructed from first-principles density-functional-theory total-energy and linear-response calculations through the use of a localized, symmetrized basis set of ``lattice Wannier functions.'' Preliminary results of Monte Carlo simulations for this system show a first-order cubic-tetragonal transition at 660 K. The involvement of the Pb atom in the lattice instability and the coupling of local distortions to strain are found to be particularly important in producing the behavior characteristic of the $PbTiO_3$ transition. A tentative explanation for the presence of local distortions experimentally observed above $T_c$ is suggested. Further applications of this method to a variety of systems and structures are proposed for first-principles study of finite-temperature structural properties in individual materials.
We use ab initio pseudopotential total energy calculations with a plane wave basis set to investigate the structural energetics of various phases of polymorphic NbN. Particular attention is given to its recently discovered superconducting phase with a $T_c$ of 16.4 K, reported to have the NbO structure type. Results of total energy calculations show that it is in fact energetically unfavorable for NbN to form in this cubic structure, and its predicted theoretical lattice constant is significantly smaller than the experimental value. Various approaches to the identification of an alternative structure are discussed. In preliminary investigations, we have found two new structures that are energetically more favorable than the NbO structure.
The structural stability and electronic properties of the ternary intermetallic compounds NiSnM (M = Ti, Zr, Hf) and the closely related Heusler compounds Ni$_2$SnM are discussed using the results of ab initio pseudopotential total energy and band-structure calculations performed with a plane wave basis set using the conjugate gradients algorithm. The results characterize the lowest energy phase of NiSnM compounds, with a SnM rocksalt structure sublattice, as narrow gap semiconductors with indirect gaps near 0.5 eV. Two other atomic arrangements for NiSnM in the MgAgAs structure result in energetically unfavorable compounds that are metallic. The gap formation in the lowest energy structure of NiSnZr and relative stability of the three atomic arrangements are investigated within a tight-binding framework and by considering the decompositions of each ternary compound into a binary substructure plus a third element sublattice. The stabilization of the lowest energy phase of NiSnZr is found to be mainly due to the relative stability of the SnZr rocksalt substructure, while the opening of the gap induced by the addition of the symmetry-breaking Ni sublattice makes a relatively minor contribution. From analysis of structural and chemical trends, CoVSn is predicted to be a new semiconducting intermetallic in the MgAgAs structure with a 0.8 eV indirect gap.
We carry out a completely first-principles study of the ferroelectric phase transitions in BaTiO$_3$. Our approach takes advantage of two features of these transitions: the structural changes are small, and only low-energy distortions are important. Based on these observations, we make systematically improvable approximations which enable the parameterization of the complicated energy surface. The parameters are determined from first-principles total-energy calculations using ultra-soft pseudopotentials and a preconditioned conjugate-gradient scheme. The resulting effective Hamiltonian is then solved by Monte Carlo simulation. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. We find the transitions to be intermediate between order-disorder and displacive character. We find all three phase transitions to be of first order. The roles of different interactions are discussed.
We develop a first-principles scheme to study ferroelectric phase transitions for perovskite compounds. We obtain an effective Hamiltonian which is fully specified by first-principles ultra-soft pseudopotential calculations. This approach is applied to BaTiO$_3$, and the resulting Hamiltonian is studied using Monte Carlo simulations. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. The order-disorder vs.\ displacive character of the transitions and the roles played by different interactions are discussed.