Muffin-tin Sphere Research Articles

Surface-embedded Green-function method: A formulation using a linearized-augmented-plane-wave basis set

We present a first-principles method for calculating the Green function of a semi-infinite crystal surface using the embedding technique of Inglesfield and the linearized-augmented-plane-wave (LAPW) basis set. The calculation consists of two independent steps: (i) The embedding potential of a semi-infinite substrate is generated from the bulk crystalline potential, and (ii) a self-consistent surface Green function calculation is performed in the embedded surface region. The numerical advantages of our method over the previous ones are (i) that one does not need to determine the exact shape of the curvy embedding surface between the bulk and surface regions and (ii) that there is no need to explicitly treat the cap region (a portion of the muffin-tin sphere cut by a plane) of boundary atoms near the embedding surface. By virtue of them, the total amount of numerical work for performing a surface-embedded Green function calculation is reduced nearly to the same level as that in standard surface electronic-structure calculations within the slab approximation. As an example, we calculate the electronic structure of the (001) and (111) surfaces of Rh, Pd, and Ag.

Screened exact exchange functional calculations of the spin-wave dispersion in transition metals

The screened “exact” nonlocal exchange approach is applied to the calculation of magnetic susceptibility of transition metals, particularly to the calculation of spin-wave dispersion. We discuss the choice of an appropriate approach and aspects of linear muffin-tin orbital-atomic sphere approximation (ASA) calculations, in particular calculation of the Green function in the three-center approximation. We calculated transverse spin-wave frequencies in Fe with the local density approximation and with the nonlocal functional using both the “frozen” magnon method and calculation of bound state energies (corresponding to spin-wave excitations).

Muffin-tin model without constructing a potential: determination of atomic phaseshifts from experiment

It is shown that in the energy interval from 0 to 2 Ryd phaseshifts for atomic muffin-tin spheres are uniquely determined by energies and mean radii of valent states or energies and lifetimes of resonant states of the corresponding atoms. A scheme for the construction of atomic phaseshifts and the determination of energies and mean radii of bound states of separate atoms by using experimental information on collective shape resonances of many-atom systems is proposed.

Doping in cubic silicon–carbide

We studied the energetics and the properties of impurity states that result from doping cubic silicon–carbide (3C–SiC) with aluminum (Al), boron (B), and nitrogen (N) atoms using the tight-binding linear combination of muffin-tin orbital atomic sphere approximation method. For Al doping, it is only favorable to substitute Al for Si atoms. The corresponding hole states contribute to a partially filled weak peak near the Fermi energy. For B doping, it is possible to replace either Si or C atoms in the crystal. When a B atom is at a Si site, the hole states exhibit behavior similar to the case of Al doping. However, when a B atom is at a C site, the hole states form a partially filled strong peak above the Fermi energy. This localized feature is explained in terms of the screening effect of the neighboring atoms. For n-type doping, a N atom can enter either the Si or C site. The latter site is more energetically favorable. Furthermore, the corresponding donor states form deep impurity states within the gap. In contrast, when a N atom is at a Si site, shallow donor states are formed.

A simplified charge transfer model: calculations using an explicit kinetic energy functional

A charge transfer calculation which uses an explicit kinetic energy functional is reported. By combining the implicit Poisson equation (Andrew E. DePristo, Phy. Rev. A, 54, 3863 (1996)) with the Thomas–Fermi kinetic energy functional, we developed a new scheme to calculate charge transfer in a crystal system. The applicability of this scheme is investigated for S n O 2 crystals, where the variation of total charge in a muffin-tin sphere is analyzed as a function of lattice constant and the results of these analyses are compared with the exact result calculated by using the full potential augmented wave method. Our new scheme is found to predict correct direction of charge transfer.

F -Electron delocalization/localization and the abrupt disappearance of uranium magnetic ordering with dilution alloying

We have applied the model and technique previously applied to the change of Curie temperature with pressure for correlated-electron uranium systems to predict the change in Curie temperature and ordered moment with dilution alloying. The theory is remarkably successful in its predictions, and this success has important implications for the overall understanding of magnetic ordering in correlated-electron systems including heavy fermion systems. For US, the dilution alloying behavior found experimentally is dramatic. In UxLa1−xS, the magnetic ordering abruptly disappears at about 55% uranium. Our ab initio-based theory quantitatively predicts this abrupt disappearance while also quantitatively predicting the monotonic decrease of Curie temperature with pressure for undiluted US. In addition, in agreement with experiment, the theory predicts the correct trend for the magnetic ordering to disappear with dilution, while at the same time absolutely and quantitatively predicting the nonmonotonic variation of Curie temperature with pressure, for USe and UTe. The ab initio-based model gives absolute material-specific predictions using input from the local density approximation paramagnetic uranium f-electron-projected density of states plus ab initio calculated values of the correlation energy U. The key physics of the model is the recognition and quantification of the concept that the f spectral density in the vicinity of a specific uranium nucleus (so-to-speak in the muffin-tin sphere) can either be in a stable f3 configuration for a long enough period of time that, through coupling to other such stable f3 sites, it can magnetically order, or can be in a situation such that the configuration fluctuates rapidly between f3 and f2, and for purposes of magnetic ordering acts like a hole in the f-electron lattice in the same way that substitution of lanthanum for uranium creates a hole. Both pressure and dilution alloying, by causing an increase in f-delocalization, increase the fraction of uranium sites in the rapidly fluctuating, magnetically ineffective, condition. For dilution alloying, at a certain point this increase in fluctuations causes the stable f3 component to fall abruptly below a critical value necessary to sustain any magnetic ordering, and hence brings about a catastrophic collapse in magnetic ordering.

Viable improvement of the full potential linearized augmented plane wave (FLAPW) method

A characteristic feature of the Full Potential Linearized Augmented Plane Wave (FLAPW)-method consists in the spatial subdivision of the charge density analogous to that of the one-particle wavefunctions, i.e. into a portion that is expanded in terms of spherical harmonics Ylm inside the muffin-tin spheres and into a plane wave expansion of the interstitial charge density. To obtain the Hartree potential inside the spheres one is hence forced to solve a boundary value problem at the sphere surface. In addition, in all non-equivalent spheres each (l,m)-component of the charge density is mapped onto 300-400 radial grid points. To ensure an accelerated convergence of the calculation, the pertinent schemes require this rather large data set to be stored and mixed within 3-6 iteration steps. We show and illustrate for the example of a spin-polarized Ni-film with and without an oxygen overlayer and for bulk Si that this data set can be compressed by at least two orders of magnitude if one partitions the charge density in a different way so that the relevant portion determining the interatomic bonding can be Fourier expanded throughout the lattice cell. One thereby arrives at a modified FLAPW-scheme that combines favorable features of the original method with virtues of the pseudopotential method which consist in the simple construction of the Hartree potential and the efficient way of achieving self-consistency. These advantages can be exploited to the fullest by using Fast Fourier Transform. Moreover, forces that atoms experience in off-equilibrium positions attain a particularly simple form in terms of the charge density expansion coefficients.

Contributions of non-spherical potentials near atomic nuclei: Improvement of FLAPW method

We have studied the contributions of non-spherical parts of potential near atomic nuclei, leading to crystal-field splitting in band structure calculations. In a conventional full-potential LAPW method, the non-spherical parts in the muffin-tin spheres contribute the splittings as a first-order perturbation. Then we have improved the methods to treat the non-spherical parts directly. We have applied the methods to 3d transition metals. It is found that the improved method corrects the overestimation of the first-order perturbation.

Accuracy and convergence properties of the extended linear augmented-plane-wave method

A detailed analysis of the accuracy of linear augmented-plane-wave (LAPW) methods is presented. A number of known APW-like formalisms are reviewed and their properties are related to the flexibility of the radial basis set used for the augmentation. The accuracy of the wave functions produced by the standard LAPW and by the extended LAPW method is numerically tested using Nb metal as an example. It is shown that the methods employing an extended set of radial basis functions yield better accuracy and acquire convergence properties similar to those of Slater's APW method. In contrast to the previous analyses of the accuracy of linear methods, we take into account the matching constraints at the muffin-tin sphere and focus on the problem of fitting the radial function to an exact solution with a different logarithmic derivative. Based on this approach, we deduce a value that characterizes the closeness of the linear APW-like method to Slater's APW method. A possibility to improve presently used extended LAPW techniques further is discussed.

Factors affecting convergence in LMTO calculations of the electronic structure of complex crystals

This paper considers factors affecting the convergence of linear muffin- tin (MT) calculations in the atomic sphere approximation (LMTO- ASA) for the case of polyatomic compounds. Recommendations on choosing the radii of MT spheres, the initial energies (centers of gravity of the occupied bands), and the initial distribution of the atomic density of the charge are given. Methods to separate the correct and discard the false self- consistent result are suggested using the calculations of MgO and NaCl as examples. These approaches were tested and gave good results for the compounds ScPd, ScRh, LiH, WC, TlBr, CaO, MgO, KBr, CuPd, NaCl, LiF, CaS, ZnO, Cu2O, TiO2, YBa2Cu3O7, Tl2CaBa2Cu2O8.

Polarized x-ray-absorption spectroscopy of the uranyl ion: Comparison of experiment and theory.

The x-ray linear dichroism of the uranyl ion (${\mathrm{UO}}_{2}^{2+}$) in uranium ${\mathit{L}}_{3}$-edge extended x-ray-absorption fine structure (EXAFS), and ${\mathit{L}}_{1}$- and ${\mathit{L}}_{3}$-edge x-ray-absorption near-edge structure (XANES), has been investigated both by experiment and theory. A striking polarization dependence is observed in the experimental XANES and EXAFS for an oriented single crystal of uranyl acetate dihydrate [${\mathrm{UO}}_{2}$(${\mathrm{CH}}_{3}$${\mathrm{CO}}_{2}$${)}_{2}$\ensuremath{\cdot}${2\mathrm{H}}_{2}$O], with the x-ray polarization vector aligned either parallel or perpendicular to the bond axis of the linear uranyl cation (O-U-O). Single-crystal results are compared to experimental spectra for a polycrystalline uranyl acetate sample and to calculations using the ab initio multiple-scattering (MS) code FEFF 6. Theoretical XANES spectra for uranyl fluoride (${\mathrm{UO}}_{2}$${\mathrm{F}}_{2}$) reproduce all the features of the measured uranyl acetate spectra. By identifying scattering paths which contribute to individual features in the calculated spectrum, a detailed understanding of the ${\mathit{L}}_{1}$-edge XANES is obtained. MS paths within the uranyl cation have a notable influence upon the XANES. The measured ${\mathit{L}}_{3}$-edge EXAFS is also influenced by MS, especially when the x-ray polarization is parallel to the uranyl species. These MS contributions are extracted from the total EXAFS and compared to calculations. The best agreement with the isolated MS signal is obtained by using nonoverlapped muffin-tin spheres in the FEFF 6 calculation. This contrasts the ${\mathit{L}}_{1}$-edge XANES calculations, in which overlapping was required for the best agreement with experiment. \textcopyright{} 1996 The American Physical Society.

The electronic structure of AgF, AgCl and AgBr

Self-consistent local density calculations of the electronic structures of AgF, AgCl and AgBr are carried out by the tight binding linearized muffin-tin orbital-atomic sphere approximation (TB LMTO-ASA) method. The silver 4 d orbital strongly hybridizes with the halogen p orbitals in the valence band and this plays a vital role in the configuration of the total density of states. The relative position of the sharp peaks in the Ag d level and F, Cl, Br p level as well as the band gap values obtained in the total density of states of these silver halides are compared with the previous theoretical and experimental values.

Multiple-scattering calculations of the uranium L3-edge x-ray-absorption near-edge structure.

A theoretical study of the uranium ${\mathit{L}}_{3}$-edge x-ray absorption near-edge structure (XANES) is presented for several uranium compounds, including oxides, intermetallics, uranyl fluoride, and \ensuremath{\alpha}-uranium. Calculations were performed using feff6, an ab initio multiple-scattering (MS) code that includes the most important features of current theories. The results, which account for both the fine structure \ensuremath{\chi} and the atomiclike background ${\mathrm{\ensuremath{\mu}}}_{0}$ of the absorption coefficient \ensuremath{\mu}, are compared to new and previously measured experimental spectra, reavealing very good agreement for most systems. For several compounds, a more detailed theoretical analysis determined the influence of cluster size and scattering order upon the calculated spectra. Results indicate that MS paths and scattering paths that include rather distant atoms make significant contributions for ${\mathrm{UO}}_{2}$, whereas XANES for crystals with lower symmetry and density can be modeled using only shorter single-scattering paths. In most cases, assumption of a screened final state in the calculation gives better agreement with experiment than use of an unscreened final state. The successful modeling of spectra for a variety of different uranium compounds, with differing spectral features, indicates that the semirelativistic treatment of XANES used here is adequate even for heavy elements. The well-known resonance, observed experimentally for uranyl (${\mathrm{UO}}_{2}^{2+}$) compounds \ensuremath{\approxeq}15 eV above the white line, is successfully modeled here for the first time, using multiple-scattering paths within the O-U-O axial bonds. Overlapping muffin-tin spheres were required in the calculation, probably as a result of the short uranyl axial bonds.

Confinement and the confined-localized-orbital-plane-wave method.

A mixed basis for electronic structure calculations has been constructed using a basis set consisting of localized orbitals confined to muffin-tin spheres and plane waves. The confinement smoothly suppresses the tails of atomic orbitals and hence eliminates multicenter integrals. From linear-muffin-tin orbital (LMTO) self-consistent potentials the bulk electronic structures of Cu and Si have been obtained as accurate as the original LMTO-type results. The energy-independent confined-localized-orbital-plane-wave basis functions enable a full solution without using linearization schemes.

Electronic band structure of sulphide spinels CuM2S4 (M=Co, Rh,Ir)

Full-potential linearized augmented-plane-wave band calculations based on the local density approximation are performed for three sulphide spinels CuM2S4 (M=Co,Rh,Ir). The electronic states near the Fermi level consist mainly of the M ndT (n=3 for Co,4 for Rh,5 for Ir) and the S 3p orbitals. A large d gamma -d$54T splitting of the M nd bands is attributed mainly to the effects of hybridization between the M nd gamma and the S 3p orbitals. The Co 3d orbitals are more localized compared with the Rh 4d and the Ir 5d orbitals. Among the three compounds, the density of states or the partial density of states of the M n/sub /components at the Fermi level is largest in CuCo2S4. The Cu 3d orbitals form relatively narrow bands. Judging from the number of Cu 3d electrons in the muffin-tin sphere the valence of the Cu ions is Cu1+ rather than Cu2+. Hence the Cu ions are expected to be non-magnetic.

Crystal field in rare earth intermetallics with CsCl structure

Electronic structure of rare earth intermetallics REX (RE  Y, Er; X  Rh, Cu, Ag, Zn, and Mg) was calculated using the full potential LAPW method in the LDA (LSDA) approximation. The crystal field (CF) splittings of RE 3+ energy levels were obtained from the aspherical components of the self-consistent potential from the region inside the RE muffin-tin sphere as well as from the interstitial region. We show that the calculated CF parameters account for the experimentally observed trend in sign and even values of CF parameter A 4 0〈 r 4〉. As the charge density of the whole crystal contributes to CF in general, we provide the discussion of contributions to CF from the different regions of REX crystals.

The extended-LAPW-based k · p method for complex band structure calculations

An ab initio, k · p method has been developed, which employs the basis functions of the extended linear augmented plane wave method (ELAPW). To construct the solution of the Schrödinger equation inside the muffin-tin sphere the ELAPW method uses an extended set of radial basis functions, which is shown to be responsible for the high accuracy of the ELAPW- k · p method. The k · p method provides an efficient computational scheme for the complex band structure calculations. Results on the complex band structure of Cu are presented.

Cellular solutions for the Poisson equation in extended systems.

The Poisson equation for the electrostatic potential in a solid is solved using three different cellular techniques. The relative merits of these different approaches are discussed for two test charge densities for which an analytic solution to the Poisson equation is known. The first approach uses full-cell multiple-scattering theory and results in the famililar structure constant and multipole moment expansion. This solution is shown to be valid everywhere inside the cell, although for points outside the muffin-tin sphere but inside the cell the sums must be performed in the correct order to yield meaningful results. A modification of the multiple-scattering-theory approach yields a second method, a Green-function cellular method, which only requires the solution of a nearest-neighbor linear system of equations. A third approach, a related variational cellular method, is also derived. The variational cellular approach is shown to be the most accurate and reliable, and to have the best convergence in angular momentum of the three methods. Coulomb energies accurate to within ${10}^{\mathrm{\ensuremath{-}}6}$ hartree are easily achieved with the variational cellular approach, demonstrating the practicality of the approach in electronic structure calculations.

Hyperfine interactions in bcc (110) iron coated with ruthenium

Using FLAPW method we have calculated the electronic structure of the Ru/Fesystem simulating it by a three- layer slab of an ideally constructed bcc Fe(110) film covered on each side with Ru(110) monolayer. For comparison, results for five layer iron slab as well as the Ag 3Fe Ag slab in the same geometry are presented. I have calculated hyperfine magnetic field and electric field gradient (EFG). Valence charge distribution and moments are also calculated. The major feature is the strong change in the valence electrons contribution to hyperfine field in the outermost Fe layers in both Ag/3Fe/Ag and Ru/3Fe/Ru systems, as compared to five-layer Fe slab. The influence of Ag and Ru does not differ much if moments and valence charged in muffin-tin spheres of Fe are concerned. Electric field gradients change for different coating which is the evidenceof strong modifications in distribution of the local electron densities.

On the accuracy of the wavefunctions calculated by LAPW method

The accuracy and the convergence properties of LAPW wavefunctions are studied using Be metal as an example. We show that radial part of thes-component of wavefunction inside the muffin-tin sphere differs substantially from the exact solution to the radial Schrodinger equation. We find that LAPW method underestimates the energy expectation value in the interstitial region. The inaccuracy of the well-converged wavefunctions occasionally produces significant errors in momentum matrix elements.