Intra-atomic Interaction Research Articles

Extended Hubbard model with renormalized Wannier wave functions in the correlated state: beyond the parametrized models

The method used earlier for analysis of correlated nanoscopic systems is extended to infinite (periodic) s-band-like systems described by the Hubbard model. The optimized single-particle Wannier wave functions contained in the parameters of the extended Hubbard model (in the nearest-neghbor hopping (-t), in the magnitude of the intraatomic interaction U, and in other parameters) are determined explicitly in the correlated state for the electronic systems of various symmetries and dimensions: Hubbard chain, square and triangular planar lattices, and the three cubic lattices (SC, BCC, FCC). In effect, the evolution of the electronic properties as a function of interatomic distance R is obtained. The model parameters in most cases do not scale linearly with the lattice spacing and hence, their solution as a function of microscopic parameters reflects only qualitatively the system evolution. Also, the atomic energy changes with R and therefore should be included in the model analysis. The solutions in one dimension (D = 1) can be analyzed both rigorously (by making use of the Lieb–Wu solution) and compared with the approximate Gutzwiller treatments. In higher dimensions (D = 2 and 3) only the latter approach is possible to implement within the scheme. The renormalized single particle wave functions are almost independent of the choice of the scheme selected to diagonalize the Hamiltonian in the Fock space in D = 1 case. For dimensions D > 1 the qualitative behavior is independent of the structure considered. The wave-function size increases above the Mott-Hubbard localization threshold and gradually reaches the atomic limit value. The method can be extended to other approximation schemes, as stressed at the end.

First-principles investigation of symmetric and antisymmetric exchange interactions ofSrCu2(BO3)2

We report on a first-principles investigation of the electronic structure and of the magnetic properties of the quasi-two-dimensional Mott insulator SrCu$_{2}$(BO$_{3}$)$_{2}$. Based on the hopping integrals and Coulomb interactions calculated with LDA and LSDA+U, we provide a microscopic explanation of the symmetric Heisenberg and antisymmetric Dzyaloshinskii-Moriya exchange integrals of SrCu$_{2}$(BO$_{3}$)$_{2}$. The intra-atomic exchange interaction of oxygen is shown to strongly contribute to the intra-dimer isotropic exchange. The results are in good agreement with those derived from experimental data, both regarding the orientation of the Dzyaloshinskii-Moriya vectors and the magnitude of all exchange integrals. The microscopic analysis is confirmed by the results of Green function's and total energies difference methods.

Ionic relaxation contribution to the electronic reconstruction at then-typeLaAlO3/SrTiO3interface

Density-functional theory calculations reveal that the compensationmechanism at the isolated n-type interface in LaAlO(3)/SrTiO(3)superlattices involves both ionic and electronic degrees of freedom.Strong polar distortions screen the local electric field and reduce theband discontinuity across the interface. We find that the electronicreconstruction depends sensitively on whether structural optimization isperformed within GGA (conventional exchange and correlation effects) orGGA+U (which includes strong intra-atomic interactions). For astructural optimization within GGA+U the excess charge is confined tothe interface TiO(2) layer with a charge-ordered, orbitally polarizedarrangement of Ti(3+) and Ti(4+). While the charge-ordered phaserepresents the ground state, optimization within GGA leads to morepronounced lattice polarization, suppression of charge order (withremaining d(xy)-orbital occupation in the interface layer), and adelocalization of the excess charge extending over a few SrTiO(3)layers.

Theoretical study of the structures and electronic properties of all-surface KI and CsI nanocrystals encapsulated in single walled carbon nanotubes

The structural and electronic properties of all-surface KI and CsI crystals encapsulated in single-walled carbon nanotubes are investigated theoretically with an ionic and atomistic approach using the GULP program. The short-range interactions, derived from Dirac-Fock wavefunctions, were augmented with damped dipole-dipole and dipole-quadrupole dispersive attractions. The uncorrelated interionic interactions computed using the relativistic crystal ion and relativistic integral programs accounted for anion in-crystal modifications while being exact given the ion wavefunctions. All the short-range correlation energies and the uncorrelated interactions between the ions and carbon atoms were computed using the density functional theory of a uniform electron gas of infinite extent. Unphysical self-interactions were removed by scaling the exchange interaction with a Rae factor derived from a study of the adsorption of noble gases on graphite. The predictions for the nonencapsulated crystals agreed well with those previously derived from a global analytic theory based on the Born model. This provided a good description of the contraction of the interplane distance (b) relative to the separation (R(e)) in the rocksalt structured bulk material although failing to account for the observed dilation of the intraplane ionic separations (a). Introduction of the interactions with the nanotube wall, including the ion-nanotube dispersive attractions, increased the predicted a values although these were still significantly smaller than experiment. The predicted b separations were reduced compared with those for the nonencapsulated crystals to values significantly less than observed. It is explained why introducing any ion-nanotube interactions that are sufficiently attractive as to reproduce the experimental a values must significantly underestimate the b separations. The partial transfer of anion electrons to the nanotube carbon atoms, not considered hitherto, was described by decomposing the intra-atomic interactions of both the nanotube pi- and the iodide 5p-electrons into an effective one-electron term plus the repulsion between electrons in the same orbital. These energies were derived from electronic structure computations with the additional interspecies electrostatic repulsions derived from the GULP program. Structural predictions are presented as a function of the number (n) of electrons transferred from each anion. For both KI and CsI, the structure predicted by that computation, which minimized the total energy, in contrast to the other calculations, agreed well with experiment reproducing both the significant dilation of a and the smaller contraction of b. The respective n values (n(t)) predicting the lowest energies are 0.278 and 0.285. These results are supported by comparing the experimental frequencies of Raman modes attributable to vibrations of nanotubes encapsulating KI with the corresponding frequencies for systems where independently known numbers of electrons were transferred to the nanotubes. In both the encapsulated KI and CsI systems, the charge transfer is driven by the reduction of the electron repulsion on delocalizing some anion charge over the significantly greater number of nanotube carbon atoms. A simplified analytic model, which reproduces the charge transfers, explains why n(t) is slighter larger for CsI and also predicts that n(t) will be insensitive to the structure of the nanotube.

Correlated Electron Systems of Different Dimensionalities

The optimized single-particle wave functions contained in the parameters of the Hubbard model (hopping integral t and intraatomic interaction U) are determined explicitly in the correlated state for electronic systems of various symmetries and dimensions: Hubbard chain, square and triangular lattices, and the three cubic lattices: SC, BCC, and FCC. In effect, the electronic properties of these structures as a function of the interatomic distance R are obtained. In most cases, the model parameters do not scale linearly with the lattice constant. Also, the atomic part of the total ground state energy changes with the U/t ratio and therefore should be (and is) included in the analysis. The solutions of dimensions D > 1 are analyzed by utilizing the approximate Gutzwiller treatment.

Oxygen Vacancy Induced Ferromagnetism in V2O5-x

Ab initio calculations within density functional theory with generalized gradient approximation have been performed to study the effects of oxygen vacancies on the electronic structure and magnetism in undoped V 2 O 5- x (0 < x < 0.5). It is found that the introduction of oxygen vacancies would induce ferromagnetism in V 2 O 5- x with the magnetization being proportional to the O vacancy concentration x . The calculated electronic structure reveals that the valence electrons released by the introduction of oxygen vacancies would occupy mainly the neighboring V d x y -dominant band which then becomes spin-polarized due to intra-atomic exchange interaction, thereby giving rise to the half-metallic ferromagnetism.

Orbital contribution to the magnetic properties of iron as a function of dimensionality

The orbital contribution to the magnetic properties of Fe in systems of decreasing dimensionality bulk, surfaces, wire, and free clusters is investigated using a tight-binding Hamiltonian in an s, p, and d atomic orbital basis set including spin-orbit coupling and intra-atomic electronic interactions in the full Hartree-Fock HF scheme, i.e., involving all the matrix elements of the Coulomb interaction with their exact orbital dependence. Spin and orbital magnetic moments and the magnetocrystalline anisotropy energy MAE are calculated for several orientations of the magnetization. The results are systematically compared with those of simplified Hamiltonians which give results close to those obtained from the local spin density approximation. The full HF decoupling leads to much larger orbital moments and MAE which can reach values as large as 1B and several tens of meV, respectively, in the monatomic wire at the equilibrium distance. The reliability of the results obtained by adding the so-called orbital polarization ansatz OPA to the simplified Hamiltonians is also discussed. It is found that when the spin magnetization is saturated, the OPA results for the orbital moment are in qualitative agreement with those of the full HF model. However, there are large discrepancies for the MAE, especially in clusters. Thus, the full HF scheme must be used to investigate the orbital magnetism and MAE of low dimensional systems.

Strong influence of configuration interactions on the orientation and alignment dichroism in the3pphotoelectron spectra of free laser-polarized Fe atoms

The $3p$ photoelectron spectra of oriented and aligned free Fe atoms are presented. The atomic polarization was achieved by optical pumping. For this purpose single-mode ultraviolet continuous wave laser radiation was produced by second harmonic generation in an external ring resonator. The ground state Fe $3{d}^{6}4{s}^{2}$ $^{5}D_{4}$ was oriented by circularly polarized laser radiation and aligned by linearly polarized laser radiation. Switching from right handed to left handed circularly polarized laser radiation or by changing the polarization angle of the linearly polarized laser radiation by 90\ifmmode^\circ\else\textdegree\fi{} allowed for the measurement of the orientation or the alignment dichroism in the Fe $3p$ photoelectron spectra excited by linearly polarized synchrotron radiation. The spectra are compared to the predictions of the single configuration $LS$-coupling model and the results of single and multiconfiguration calculations. Strong configuration interactions in the final core-hole states manifest themselves in marked deviations from the characteristic patterns. The comparison of the spectra of the free Fe atoms with spectra of thin magnetized Fe films reveals similarities but also marked differences between the dichroism curves of free and bound Fe atoms. The common atomic origin of the dichroism of free and bound Fe atoms is discussed; changes in the intra-atomic electron interactions as well as changes in valence electronic configuration when going from free to bound Fe atoms are addressed.

Orbital contribution to the magnetic properties of nanowires: is the orbital polarization ansatz justified?

We show that considerable orbital magnetic moments and magneto-crystalline anisotropy energies are obtained for a Fe monatomic wire described in a tight-binding method with intra-atomic electronic interactions treated in a full Hartree Fock (HF) decoupling scheme. Even-though the use of the orbital polarization ansatz with simplified Hamiltonians leads to fairly good results when the spin magnetization is saturated this is not the case of unsaturated systems. We conclude that the full HF scheme is necessary to investigate low dimensional systems.

Fluctuations of the magnetization in thin films due to conduction electrons

A detailed analysis of damping and noise due to a $sd$ interaction in a thin ferromagnetic film sandwiched between two large normal metal layers is carried out. The magnetization is shown to obey, in general, a nonlocal equation of motion, which differs from the the Gilbert equation and is extended to the nonadiabatic regime. To the lowest order in the exchange interaction and in the limit where the Gilbert equation applies, we show that the damping term is enhanced due to interfacial effects, but it also shows oscillations as a function of the film thickness. The noise calculation is, however, carried out to all orders in the exchange-coupling constant. The ellipticity of the precession of the magnetization is taken into account. The damping is shown to have a Gilbert form only in the adiabatic limit, while the relaxation time becomes strongly dependent on the geometry of the thin film. It is also shown that the induced noise characteristic of $sd$ exchange is inherently colored in character and depends on the symmetry of the Hamiltonian of the magnetization in the film. We show that the $sd$ noise can be represented in terms of an external stochastic field, which is white only in the adiabatic regime. The temperature is also renormalized by the spin accumulation in the system. For large intra-atomic exchange interactions, the Gilbert-Brown equation is no longer valid.

Nonextensive thermodynamics of the two-site Hubbard model

Thermodynamical properties of canonical and grand-canonical ensembles of the half-filled two-site Hubbard model have been discussed within the framework of the nonextensive statistics (NES). For relating the physical temperature T to the Lagrange multiplier β , two methods have been adopted: T = 1 / k B β in method A [Tsallis et al., Physica A 261 (1998) 534], and T = c q / k B β in method B [Abe et al., Phys. Lett. A 281 (2001) 126], where k B denotes the Boltzman constant, c q = ∑ i p i q , p i the probability distribution of the ith state, and q the entropic index. Temperature dependences of specific heat and magnetic susceptibility have been calculated for 1 ⩽ q ⩽ 2 , the conventional Boltzman–Gibbs statistics being recovered in the limit of q = 1 . The Curie constant Γ q of the susceptibility in the atomic and low-temperature limits ( t / U → 0 , T / U → 0 ) is shown to be given by Γ q = 2 q 2 2 ( q - 1 ) in method A, and Γ q = 2 q in method B, where t stands for electron hoppings and U intra-atomic interaction in the Hubbard model. These expressions for Γ q are shown to agree with the results of a free spin model which have been studied also by the NES with methods A and B. A comparison has been made between the results for canonical and grand-canonical ensembles of the model.

XMCD study on electronic and magnetic states of rare-earth 5d electrons in Laves compounds, RFe2 (R = rare-earth)

X-ray magnetic circular dichroism (XMCD) at the rare-earth (RE) L2,3 absorption edges of RFe2 (R = RE) in the Laves phase has been investigated based on the tight-binding model with the intra-atomic exchange interaction between 5d and 4f electrons. We find that the magnetic polarization of 5d electrons, being essential for these XMCD, is dominated by the intra-atomic exchange interaction and by the hybridization with spin-polarized Fe 3d states. These contributions as well as the quadrupole one compete, resulting in a variety of XMCD spectra, as observed in experiments.

Theoretical study of x-ray photoemission, x-ray absorption and resonant x-ray emission spectroscopy of Mn films on Ag

We report a theoretical study of core-level x-ray photoemission (XPS), x-ray absorption (XAS) and resonant x-ray emission spectra (RXES) at Mn L2,3 edge in Mn thin films on Ag(001). By combining band structure, atomic multiplet and impurity Anderson model calculation, we construct a realistic impurity model that includes full intra-atomic multiplet interaction and inter-atomic coupling to the Mn-3d and Ag-4d bands. The model is applied to various Mn/Ag thin films and related structures. The different systems were modeled by varying only one parameter, the hybridization strength. Good agreement with experiment is obtained. The main conclusion from the impurity model calculations is that the satellite structure observed in the thin films is due to final state charge transfer process, mainly from the Mn-3d states of the neighboring atom. Moreover we predict that the RXES spectra have a satellite structure which is highly sensitive to the local atomic structure around the Mn atoms through its strong dependence on the hybridization of the Mn-3d orbitals.

Spectrum of dynamic magnetic susceptibility of a randomized f–d magnet with spin–lattice coupling. I. Shift of the magnetic resonance frequencies

In narrow-band ferromagnetic conductors containing local f and quasilocal d magnetic moments the interatomic spin correlations created by the combined effects of the intra-atomic interactions of the quasilocal electrons and their intersite hops are playing a role in the formation of the magnetic resonance spectra. This role is examined, and the transformation of the spectra of the transverse dynamic magnetic susceptibility under conditions of weak spin–lattice coupling and spatial randomization of the g factors of the quasilocal and local spin subsystems is investigated. A calculation done by the method of two-time retarded Green’s functions shows that the interaction of the d and f electrons leads to an effective renormalization of the g factors of both magnetic subsystems, and at zero temperature the spin–lattice coupling lowers the frequency of the inhomogeneous magnetic resonance and causes threshold damping of acoustic and optical magnons.

Theory of orbital ordering and X-ray absorption linear dichroism in LaMnO 3

On the basis of exact diagonalization of a single-ion Hamiltonian including the intra-atomic multipole interactions, we calculated Mn and Ti L 2,3 X-ray absorption linear dichroism (XLD) spectra for LaMnO 3 and YTiO 3, where antiferro-orbital ordering among the degenerate e g and t 2g states, respectively, are reported. For the orbital polarization given by a superposition of the doubly degenerate e g states, the superposition is shown to be reflected in the integrated XLD intensity, while, in the case of the triply degenerate t 2g states, the superposition is shown to be reflected in both the integrated intensity and the spectral shape, i.e. XLD is a promising method to observe details of orbital polarization.

Interplay of intra-atomic and interatomic effects: an investigation of the 2p core level spectra of atomic Fe and molecular FeCl2.

The 2p photoabsorption and photoelectron spectra of atomic Fe and molecular FeCl2 were studied by photoion and photoelectron spectroscopy using monochromatized synchrotron radiation and atomic or molecular beam technique. The atomic spectra were analyzed with configuration interaction calculations yielding excellent agreement between experiment and theory. For the analysis of the molecular photoelectron spectrum which shows pronounced interatomic effects, a charge transfer model was used, introducing an additional 3d(7) configuration. The resulting good agreement between the experimental and theoretical spectrum and the remarkable similarity of the molecular with the corresponding spectrum in the solid phase opens a way to a better understanding of the interplay of the interatomic and intra-atomic interactions in the 2p core level spectra of the 3d metal compounds.

Magnetic interactions in 3d?5d layered ferromagnets

We present results of first-principles calculations for inter- and intra-atomic magnetic interaction parameters in 3d–5d (FePt, CoPt) ordered alloys. We find that the induced Stoner model type of magnetism on the Pt sub-lattice leads to a strong positive inter-sub-lattice exchange interactions. These effective exchange interactions have isotropic and anisotropic contributions, both stabilizing ferromagnetic order along the [0 0 1] direction.

X-ray magnetic circular dichroism at rare-earth L-absorption edges in Laves-phase compounds, RFe 2 (R = rare-earth)

Recent progress of the theoretical interpretation for the X-ray magnetic circular dichroism (XMCD) at the rare-earth (RE) L 2,3 absorption edges is reviewed. We discuss the XMCD spectra of RFe 2 (R = RE) in the Laves phase based on the tight-binding approximation for RE 5d and Fe 3d conducting states. A variety of the XMCD spectra can be attributed to (i) the electric dipole and (ii) the electric quadrupole transitions. For (i), the polarization of the RE 5d electrons, being indispensable for XMCD, is dominated by the RE intra-atomic exchange interaction, which also yields the enhancement of the 2p–5d dipole matrix element. In addition, the hybridization with the spin-polarized Fe 3d states plays a distinctive role. For (ii), the multiplet couplings among the 4f electrons and the 2p core hole determine the XMCD spectra. We also consider XMCD in the mixed valence compound CeFe 2, taking many-body interactions into account based on the impurity Anderson model combined with a cluster approximation.

Magnetic interactions in 3d–5d layered ferromagnets

We present results of first-principles calculations for inter- and intra-atomic magnetic interaction parameters in 3d–5d (FePt, CoPt) ordered alloys. We find that the induced Stoner model type of magnetism on the Pt sub-lattice leads to a strong positive inter-sub-lattice exchange interactions. These effective exchange interactions have isotropic and anisotropic contributions, both stabilizing ferromagnetic order along the [001] direction.

Studies of 6s ionization energy of lanthanides

This work is aimed at the multiconfiguration Hartree–Fock calculations of the 6s ionization energies of lanthanides with configurations [Xe]4f6s. Authors use the ATSP MCHF version in which there are new codes for calculation of spinangular parts of matrix elements of the operators of intraatomic interactions written on the basis of the methodology developed by Gaigalas, Rudzikas, and Froese Fischer, based on the second quantization in coupled tensorial form, the angular momentum theory in three spaces (orbital, spin, and quasispin), graphical technique of spin-angular integrations and reduced coefficients (subcoefficients) of fractional parentage. This methodology allows us to study the configurations with open f -shells without any restrictions, thus providing the possibility to investigate heavy atoms and ions as well as to obtain reasonably accurate values of spectroscopic data for such complex many-electron systems.