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arXiv1996

First-principles study of stability and vibrational properties of tetragonal PbTiO_3

A first-principles study of the vibrational modes of PbTiO_3 in the ferroelectric tetragonal phase has been performed at all the main symmetry points of the Brillouin zone (BZ). The calculations use the local-density approximation and ultrasoft pseudopotentials with a plane-wave basis, and reproduce well the available experimental information on the modes at the Gamma point, including the LO-TO splittings. The work was motivated in part by a previously reported transition to an orthorhombic phase at low temperatures [(J. Kobayashi, Y. Uesu, and Y. Sakemi, Phys. Rev. B {\bf 28}, 3866 (1983)]. We show that a linear coupling of orthorhombic strain to one of the modes at Gamma plays a role in the discussion of the possibility of this phase transition. However, no mechanical instabilities (soft modes) are found, either at Gamma or at any of the other high-symmetry points of the BZ.

mtrl-th↗

arXiv1995

Analytical and computational study of magnetization switching in kinetic Ising systems with demagnetizing fields

An important aspect of real ferromagnetic particles is the demagnetizing field resulting from magnetostatic dipole-dipole interaction, which causes large particles to break up into domains. Sufficiently small particles, however, remain single-domain in equilibrium. This makes such small particles of particular interest as materials for high-density magnetic recording media. In this paper we use analytic arguments and Monte Carlo simulations to study the effect of the demagnetizing field on the dynamics of magnetization switching in two-dimensional, single-domain, kinetic Ising systems. For systems in the ``Stochastic Region,'' where magnetization switching is on average effected by the nucleation and growth of fewer than two well-defined critical droplets, the simulation results can be explained by the dynamics of a simple model in which the free energy is a function only of magnetization. In the ``Multi-Droplet Region,'' a generalization of Avrami's Law involving a magnetization-dependent effective magnetic field gives good agreement with our simulations.

cond-mat↗

arXiv1996

Applications of a tight-binding total energy method for transition and noble metals: Elastic Constants, Vacancies, and Surfaces of Monatomic Metals

A recent tight-binding scheme provides a method for extending the results of first principles calculations to regimes involving $10^2 - 10^3$ atoms in a unit cell. The method uses an analytic set of two-center, non-orthogonal tight-binding parameters, on-site terms which change with the local environment, and no pair potential. The free parameters in this method are chosen to simultaneously fit band structures and total energies from a set of first-principles calculations for monatomic fcc and bcc crystals. To check the accuracy of this method we evaluate structural energy differences, elastic constants, vacancy formation energies, and surface energies, comparing to first-principles calculations and experiment. In most cases there is good agreement between this theory and experiment. We present a detailed account of the method, a complete set of tight-binding parameters, and results for twenty-nine of the alkaline earth, transition and noble metals.

mtrl-th↗

arXiv1996

Variational quantum Monte Carlo ground state of GaAs

Variational quantum Monte Carlo calculations are reported for the bulk GaAs semiconductor in order to present values for the ground-state energy, the lattice constant, the bulk modulus, and some derived properties. The statistical accuracy is significantly higher than the remaining differences to the experimental values, especially for the total-energy upper bound. The agreement with experiment is satisfactory. The results are also compared with those of density functional calculations. The accuracy of our results is comparable to the best of those calculations.

mtrl-th↗

arXiv1995

Dynamical Jahn-Teller Effect and Berry Phase in Positively Charged Fullerene I. Basic Considerations

We study the Jahn-Teller effect of positive fullerene ions $^2$C$_{60}^{+}$ and $^1$C$_{60}^{2+}$. The aim is to discover if this case, in analogy with the negative ion, possesses a Berry phase or not, and what are the consequences on dynamical Jahn-Teller quantization. Working in the linear and spherical approximation, we find no Berry phase in $^1$C$_{60}^{2+}$, and presence/absence of Berry phase for coupling of one $L=2$ hole to an $L=4$/$L=2$ vibration. We study in particular the special equal-coupling case ($g_2=g_4$), which is reduced to the motion of a particle on a 5-dimensional sphere. In the icosahedral molecule, the final outcome assesses the presence/absence of a Berry phase of $π$ for the $h_u$ hole coupled to $G_g$/$H_h$ vibrations. Some qualitative consequences on ground-state symmetry, low-lying excitations, and electron emission from C$_{60}$ are spelled out.

cond-mat↗

arXiv1996

Multiple-Scattering Theory of X-Ray Magnetic Circular Dichroism: Implementation and Results for Iron K-edge

An implementation of the multiple-scattering approach to x-ray magnetic circular dichroism (XMCD) in K-edge x-ray absorption spectroscopy is presented. The convergence problems due to the cluster size and the relativistic corrections are solved using an expansion of the Dirac Green function for complex energies up to the second order in 1/$c$. The Fermi energy is dealt with via a complex plane integration. Numerical methods used to obtain the semi-relativistic Green function in the whole complex plane are explained. We present a calculation of the magnetic circular dichroism at the K-edge of bcc-iron including the core hole effect. A good agreement is found at high energy. The physical origins of the XMCD spectrum near the edge and far from the edge are analyzed. The influence of the core hole, the possibility of a multiple-scattering expansion and the relation of XMCD with the spin-polarized density of states are discussed. A simple interpretation of XMCD at the K-edge is presented in terms of a rigid-band model.

cond-mat↗

arXiv1996

Point-charge electrostatics in disordered alloys

A simple analytic model of point-ion electrostatics has been previously proposed in which the magnitude of the net charge q_i on each atom in an ordered or random alloy depends linearly on the number N_i^(1) of unlike neighbors in its first coordination shell. Point charges extracted from recent large supercell (256-432 atom) local density approximation (LDA) calculations of Cu-Zn random alloys now enable an assessment of the physical validity and accuracy of the simple model. We find that this model accurately describes (i) the trends in q_i vs. N_i^(1), particularly for fcc alloys, (ii) the magnitudes of total electrostatic energies in random alloys, (iii) the relationships between constant-occupation-averaged charges and Coulomb shifts (i.e., the average over all sites occupied by either $A$ or $B$ atoms) in the random alloy, and (iv) the linear relation between the site charge q_i and the constant- charge-averaged Coulomb shift (i.e., the average over all sites with the same charge) for fcc alloys. However, for bcc alloys the fluctuations predicted by the model in the q_i vs. V_i relation exceed those found in the LDA supercell calculations. We find that (a) the fluctuations present in the model have a vanishing contribution to the electrostatic energy. (b) Generalizing the model to include a dependence of the charge on the atoms in the first three (two) shells in bcc (fcc) - rather than the first shell only - removes the fluctuations, in complete agreement with the LDA data. We also demonstrate an efficient way to extract charge transfer parameters of the generalized model from LDA calculations on small unit cells.

mtrl-th↗

arXiv1996

The GaAs Equilibrium Crystal Shape from First-Principles

Surface energies for different GaAs surface orientations have been calculated as a function of the chemical potential. We use an energy density formalism within the first-principles pseudopotential density-functional approach. The equilibrium crystal shape (ECS) has been derived from the surface energies for the (110), (100), (111), and (-1-1-1) orientations. Under As-rich conditions all four considered surface orientations exist in thermodynamic equilibrium, in agreement with experimental observations. Moreover, our calculations allow us to decide on previous contradictory theoretical values for the surface energies of the (111) and (-1-1-1) facets.

mtrl-th↗

arXiv1996

Potential, core-level and d band shifts at transition metal surfaces

We have extended the validity of the correlation between the surface 3d-core-level shift (SCLS) and the surface d band shift (SDBS) to the entire 4d transition metal series and to the neighboring elements Sr and Ag via accurate first-principles calculations. We find that the correlation is quasilinear and robust with respect to the differencies both between initial and final-state calculations of the SCLS's and two distinct measures of the SDBS's. We show that despite the complex spatial dependence of the surface potential shift (SPS) and the location of the 3d and 4d orbitals in different regions of space, the correlation exists because the sampling of the SPS by the 3d and 4d orbitals remains similar. We show further that the sign change of the SCLS's across the transition series does indeed arise from the d band-narrowing mechanism previously proposed. However, while in the heavier transition metals the predicted increase of d electrons in the surface layer relative to the bulk arises primarily from transfers from s and p states to d states within the surface layer, in the lighter transition metals the predicted decrease of surface d electrons arises primarily from flow out into the vacuum.

mtrl-th↗

arXiv1996

Anomalous effective charges and far IR optical absorption of Al$_2$Ru from first principles

For the orthorhombic intermetallic semiconductor Al$_2$Ru, the bandstructure, valence charge density, zone center optical phonon frequencies, and Born effective charge and electronic dielectric tensors are calculated using variational density functional perturbation theory with {\em ab initio} pseudopotentials and a plane wave basis set. Good agreement is obtained with recent measurements on polycrystalline samples which showed anomalously strong far IR absorption by optical phonons, while analysis of the valence charge density shows that the static ionic charges of Al and Ru are negligible. Hybridization is proposed as the single origin both of the semiconducting gap and the anomalous Born effective charges. Analogous behavior is expected in related compounds such as NiSnZr, PbTe, skutterudites, and Al-transition-metal quasicrystals.

mtrl-th↗

arXiv1996

Band Structure and Transport Properties of CrO_2

Local Spin Density Approximation (LSDA) is used to calculate the energy bands of both the ferromagnetic and paramagnetic phases of metallic CrO_2. The Fermi level lies in a peak in the paramagnetic density of states, and the ferromagnetic phase is more stable. As first predicted by Schwarz, the magnetic moment is 2 μ_B per Cr atom, with the Fermi level for minority spins lying in an insulating gap between oxygen p and chromium d states ("half-metallic" behavior.) The A_1g Raman frequency is predicted to be 587 cm^{-1}. Drude plasma frequencies are of order 2eV, as seen experimentally by Chase. The measured resistivity is used to find the electron mean-free path l, which is only a few angstroms at 600K, but nevertheless, resistivity continues to rise as temperature increases. This puts CrO_2 into the category of "bad metals" in common with the high T_c superconductors, the high T metallic phase of VO_2, and the ferromagnet SrRuO_3. In common with both SrRuO_3 and Sr_2RuO_4, the measured specific heat γis higher than band theory by a renormalization factor close to 4.

mtrl-th↗

arXiv1996

Basis Functions for Linear-Scaling First-Principles Calculations

In the framework of a recently reported linear-scaling method for density-functional-pseudopotential calculations, we investigate the use of localized basis functions for such work. We propose a basis set in which each local orbital is represented in terms of an array of `blip functions'' on the points of a grid. We analyze the relation between blip-function basis sets and the plane-wave basis used in standard pseudopotential methods, derive criteria for the approximate equivalence of the two, and describe practical tests of these criteria. Techniques are presented for using blip-function basis sets in linear-scaling calculations, and numerical tests of these techniques are reported for Si crystal using both local and non-local pseudopotentials. We find rapid convergence of the total energy to the values given by standard plane-wave calculations as the radius of the linear-scaling localized orbitals is increased.

mtrl-th↗

arXiv1996

Ab initio statistical mechanics of the ferroelectric phase transition in PbTiO3

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.

mtrl-th↗

arXiv1996

Effects of crack tip geometry on dislocation emission and cleavage: A possible path to enhanced ductility

We present a systematic study of the effect of crack blunting on subsequent crack propagation and dislocation emission. We show that the stress intensity factor required to propagate the crack is increased as the crack is blunted by up to thirteen atomic layers, but only by a relatively modest amount for a crack with a sharp 60$^\circ$ corner. The effect of the blunting is far less than would be expected from a smoothly blunted crack; the sharp corners preserve the stress concentration, reducing the effect of the blunting. However, for some material parameters blunting changes the preferred deformation mode from brittle cleavage to dislocation emission. In such materials, the absorption of preexisting dislocations by the crack tip can cause the crack tip to be locally arrested, causing a significant increase in the microscopic toughness of the crack tip. Continuum plasticity models have shown that even a moderate increase in the microscopic toughness can lead to an increase in the macroscopic fracture toughness of the material by several orders of magnitude. We thus propose an atomic-scale mechanism at the crack tip, that ultimately may lead to a high fracture toughness in some materials where a sharp crack would seem to be able to propagate in a brittle manner. Results for blunt cracks loaded in mode II are also presented.

mtrl-th↗

arXiv1996

Theoretical study of hydrogen-covered diamond (100) surfaces: A chemical potential analysis

The bare and hydrogen-covered diamond (100) surfaces were investigated through pseudopotential density-functional calculations within the local-density approximation. Different coverages, ranging from one to two, were considered. These corresponded to different structures including 1x1, 2x1, and 3x1, and different hydrogen-carbon arrangements including monohydride, dihydride, and configurations in between. The formation energy of each phase was expressed as a function of hydrogen chemical potential. As the chemical potential increased, the stable phase successively changed from bare 2x1 to (2x1):H, to (3x1):1.33H, and finally to the canted (1x1):2H. Setting the chemical potential at the energy per hydrogen in H$_2$ and in a free atom gave the (3x1):1.33H and the canted (1x1):2H phase as the most stable one, respectively. However, after comparing with the formation energy of CH$_4$, only the (2x1):H and (3x1):1.33H phases were stable against spontaneous formation of CH$_4$. The former existed over a chemical potential range ten times larger than the latter, which may explain why the latter, despite of having a low energy, has not been observed so far. Finally, the vibrational energies of the C-H stretch mode were calculated for the (2x1):H phase.

cond-mat↗

arXiv1996

Ab-initio study of the anomalies in the He atom scattering spectra of H/Mo(110) and H/W(110)

Helium atom scattering (HAS) studies of the H-covered Mo(110) and W(110) surfaces reveal a twofold anomaly in the respective dispersion curves. In order to explain this unusual behavior we performed density functional theory calculations of the atomic and electronic structure, the vibrational properties, and the spectrum of electron-hole excitations of those surfaces. Our work provides evidence for hydrogen adsorption induced Fermi surface nesting. The respective nesting vectors are in excellent agreement with the HAS data and recent angle resolved photoemission experiments of the H-covered alloy system Mo_0.95Re_0.05(110). Also, we investigated the electron-phonon coupling and discovered that the Rayleigh phonon frequency is lowered for those critical wave vectors. Moreover, the smaller indentation in the HAS spectra can be clearly identified as a Kohn anomaly. Based on our results for the susceptibility and the recently improved understanding of the He scattering mechanism we argue that the larger anomalous dip is due to a direct interaction of the He atoms with electron-hole excitations at the Fermi level.

mtrl-th↗

arXiv1995

Phase Coexistence of a Stockmayer Fluid in an Applied Field

We examine two aspects of Stockmayer fluids which consists of point dipoles that additionally interact via an attractive Lennard-Jones potential. We perform Monte Carlo simulations to examine the effect of an applied field on the liquid-gas phase coexistence and show that a magnetic fluid phase does exist in the absence of an applied field. As part of the search for the magnetic fluid phase, we perform Gibbs ensemble simulations to determine phase coexistence curves at large dipole moments, $μ$. The critical temperature is found to depend linearly on $μ^2$ for intermediate values of $μ$ beyond the initial nonlinear behavior near $μ=0$ and less than the $μ$ where no liquid-gas phase coexistence has been found. For phase coexistence in an applied field, the critical temperatures as a function of the applied field for two different $μ$ are mapped onto a single curve. The critical densities hardly change as a function of applied field. We also verify that in an applied field the liquid droplets within the two phase coexistence region become elongated in the direction of the field.

mtrl-th↗

arXiv1995

A Method to Study Relaxation of Metastable Phases: Macroscopic Mean-Field Dynamics

We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter $m$ through the restricted free energy $F(m)$ and are designed to give the correct equilibrium distribution for $m$. The connection between macroscopic dynamics and the underlying microscopic dynamic are considered in the context of a projection- operator formalism. Application to the square-lattice nearest-neighbor Ising ferromagnet gives good agreement with droplet theory and Monte Carlo simulations of the underlying microscopic dynamic. This includes quantitative agreement for the exponential dependence of the lifetime on the inverse of the applied field $H$, and the observation of distinct field regions in which the derivative of the lifetime with respect to $1/H$ depends differently on $H$. In addition, at very low temperatures we observe oscillatory behavior of this derivative with respect to $H$, due to the discreteness of the lattice and in agreement with rigorous results. Similarities and differences between this work and earlier works on finite Ising models in the fixed-magnetization ensemble are discussed.

cond-mat↗