J. M. Khalifeh

INFINITE NETWORK OF IDENTICAL CAPACITORS BY GREEN'S FUNCTION

The capacitance between arbitrary nodes in perfect infinite networks of identical capacitors is studied. We calculate the capacitance between the origin and the lattice site (l, m) for an infinite linear chain, and for an infinite square network consisting of identical capacitors using the Lattice Greens Function. The asymptotic behavior of the capacitance for an infinite square lattice is investigated for infinite separation between the origin and the site (l, m). We point out the relation between the capacitance of the lattice and the van Hove singularity of the tight-binding Hamiltonian. This method can be applied directly to other lattice structures.

Resistance Calculation for an infinite Simple Cubic Lattice Application of Green's Function

It is shown that the resistance between the origin and any lattice point (l,m,n) in an infinite perfect Simple Cubic (SC) lattice is expressible rationally in terms of the known value of G0 (0,0,0). The resistance between arbitrary sites in an infinite SC lattice is also studied and calculated when one of the resistors is removed from the perfect lattice. The asymptotic behavior of the resistance for both the infinite perfect and perturbed SC lattice is also investigated. Finally, experimental results are obtained for a finite SC network consisting of 8×8×8 identical resistors, and a comparison with those obtained theoretically is presented.

Interstitial single resistor in a network of resistors application of the lattice Green's function

The resistance between two arbitrary nodes of a network of resistors is studied when the network is perturbed by connecting an extra resistor between two arbitrary nodes in the perfect lattice. The lattice Greens function and the resistance of the perturbed network are expressed in terms of those of the perfect lattice by solving Dysons equation. A comparison is carried out between numerical and experimental results for a square lattice.

Magnetic structure of vanadium overlayers on semi-infinite Nb substrate

We investigate the magnetic ordering of V/Nb systems using a real space tight-binding approach. The magnetism is described in the unrestricted Hartree-Fock approximation of the Hubbard Hamiltonian. The density of states has been calculated within the recursion technique. The magnetic moments of VnNb system with n = 1–3 for different crystallographic directions {(0 0 1), (0 1 1), (1 1 1)} have been calculated. The onset of magnetism depends strongly on the faces considered. Magnetism is more pronounced for the (0 0 1) surface and is found to decrease when V is allowed to relax in order to recover its bulk volume. The magnetic moments of the surface layers are strongly enhanced by addition of more V layers. A sizable induced moment appears in the Nb interface layer which decreases by addition of more V layers.

PERTURBATION OF AN INFINITE NETWORK OF IDENTICAL CAPACITORS

The capacitance between any two arbitrary lattice sites in an infinite square lattice is studied when one bond is removed (i.e. perturbed). A connection is made between the capacitance and the lattice Greens function of the perturbed network, where they are expressed in terms of those of the perfect network. The asymptotic behavior of the perturbed capacitance is investigated as the separation between the two sites goes to infinity. Finally, numerical results are obtained along different directions and a comparison is made with the perfect capacitances.

The electronic structure and spin polarization of Fe3−xMnxSi and Fe3−yMnSiy alloys

First principle calculations using supercell approach and coherent potential approximation (CPA) are performed to investigate the electronic and magnetic structures of Fe3−xMnxSi and Fe3−yMnSiy alloys, where x,y=0, 0.25, 0.50, 0.75, 1.00, 1.25, 1.5, 1.75, and 2.25. Using supercell calculations we obtained a metallic behavior for x=0, 0.25, and 0.5 in Fe3−xMnxSi alloys with spin polarizations of 24%, 39%, and 93%, respectively. The behavior starts to be half-metallic at x=0.75 with a small direct band gap that increases for higher concentrations of Mn. Among the half-metallic systems, only those of L21 structure at x=1 and 2 possess indirect band gaps along Γ-X symmetry line. The change of Si concentration in Fe3−yMnSiy structures retrieve the metallic behavior for all concentrations except y=1.25 that shows a half-metallic behavior with a direct band gap of 0.27 eV. We obtained a good agreement between supercell and CPA calculations for the values of the magnetic moment and the trends of the formation ene...

Spin polarization of vanadium overlayers on a semi-infinite tantalum substrate

Abstract We investigate the substrate bandwidth effect on the onset of magnetism in V overlayers. The local magnetic moments and magnetic order at the V Ta interface of ultrathin V films is studied. Different crystallographic directions (001),(011) and (111) have been considered. The magnetism is described within a real-space tight-binding approach in the unrestricted Hartree-Fock approximation of the Hubbard Hamiltonian. The density of states has been calculated within the recursion technique. The onset of magnetism depends strongly on the faces considered. Magnetism is more pronounced for the (001) surface and is found to decrease when V is allowed to relax in order to recover its bulk volume. The magnetic moments of the surface layers are strongly enhanced by addition of more V layers. A sizeable induced moment appears in the Ta interface layer which decreases by addition of more V layers. The same behavior is shown to occur in the Nb substrate but it is more pronounced as compared to that of Ta. This behavior is expected since the bandwidth of Nb is smaller than that of Ta and their lattice parameters are approximately the same.

SUBSTITUTIONAL SINGLE RESISTOR IN AN INFINITE SQUARE LATTICE APPLICATION TO LATTICE GREEN'S FUNCTION

The resistance between two arbitrary lattice sites in an infinite square lattice of identical resistors is studied when the lattice is perturbed by substituting a single resistor using lattice Greens function. The relation between the resistance and the lattice Greens function for the perturbed lattice is derived. Solving Dysons equation, the Greens function and the resistance of the perturbed lattice are expressed in terms of those of the perfect lattice. Numerical and experimental results are presented.

Magnetic structure of manganese overlayers on semi-infinite chromium substrate

Abstract We report a study of the magnetic behavior of ultrathin Mn films deposited on a Cr substrate using a real space tight binding approach. The magnetism is described in the Hartree–Fock approximation of the Hubbard Hamiltonian. The density of states is calculated within the recursion technique. The magnetic moments of Mn–Cr system up to three Mn overlayers for different crystallographic orientations {(001), (011), (111)} are calculated. The onset of magnetism depends on the faces considered. A sizable induced moment appears in the Cr interface layer. The calculations show ferromagnetic sheets of both metals for the planes {(001) and (111)} and magnetic c(2×2) configuration for the (011) plane. This behavior is consistent with the antiferromagnetic ground states of the constituents.

Lattice Green's Function for the Face Centered Cubic Lattice

An expression for the Greens function (GF) of face centered cubic (FCC) lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are expressed in terms of complete elliptic integrals of the first kind.