Akira Narita

Expressions of energy and potential due to orbital polarization

The simple and tractable representation for the L S -multiplet energy in l 1 l 2 -configuration in an atom is derived in the form of the polynomials being a function of l 1 · l 2 which obey the rec...

Magnetic susceptibilities and spin structures in gadorinium pnictides. I: Semiconductor case

The magnetic susceptibilities χ( Q ) are calculated numerically for some tight binding band structures with semiconducting property by means of Rath-Freeman method, in which the band structures are fitted to those obtained by APW method for LaN, LaP and GdN. From these calculations, the followings are found. (i) The band structure dependences of χ( Q ) are large. Those fitted to the LaN and LaP stabilize the antiferromagnetic state consistent to the experiments, while that to GdN the ferromagnet. (ii) The numerical χ( Q ) can be approximated very well by the decoupling expression, in which the matrix element is replaced by the averaged Q -dependent matrix element M ( Q ) over the B.Z in the formula of χ( Q ). Its dispersion is almost determined by M ( Q ). (iii) In the constant matrix element case only the scatterings between the nearest bands to the Fermi level are important for χ( Q ). But, in inclusion of matrix element effect those between sufficiently separated bands also become very important.

Nonspherical Potential due to Orbital Polarization and Its Effect in Atoms –Approach to Hund's Second Rule in Terms of One-Electron Picture–

The exchange–correlation functional composed of the X α-exchange energy and the new type of correlation energy E M is assumed in order to study the effect of the nonspherical spatial distribution of electrons and the degeneracy of the total energy for states with the different M L values in the electronic open-shell configuration l N ( l = p , d ) of atom, where N is the number of electrons in the open shell characterized by directional quantum number l , M L is an expectation value of the z -component L z of total angular momentum, and E M depends on M L . Nonspherical quantities such as electron density and one-electron effective potential are made from the partially filled occupation obeying Hunds first rule in the open shell, and the Kohn–Sham equation is solved by the self-consistent degenerate first-order perturbation theory. Then, the parameters included in E M are succinctly and conveniently determined by imposing the appropriate conditions of degeneracy on the orbital and total energies. These m...

Magnetic Susceptibilities and Spin Structures in Gadolinium Pnictides. II. Carrier Concentration Effect in the Semimetallic Case

The magnetic susceptibilities of Gd monopnictides are calculated numerically for the semimetallic and metallic cases using the various tight binding band structures fitted to the APW result of LaP, and the carrier concentration effects on the spin orderings, θ p and T N are investigated in detail, in which θ p and T N are the paramagnetic Curie and Neel temperatures, respectively. The contributions to the susceptibilities caused by various scattering processes are analyzed in detail, and the main processes are clarified for the semimetallic and metallic cases. Comparisons with the experiments for Gd monopnictides and GdP–GdS systems are also performed. Our calculations give the best agreement with the experiments in the theoretical works so far carried out, although there are many discrepancies.

A Proposal for Calculating the Orbital-Dependent Exchange-Correlation Potential by Means of the Virial Theorem

We provide a density functional scheme for calculating the orbital-dependent exchange-correlation potential using the virial theorem as a sum rule. This is different from the optimized effective potential (OEP) method. To confirm the validity, atomic-structure calculations are performed for closed-shell atoms. The exchange energies are in good agreement with the previous values obtained by the OEP method, whereas the numerical speed has been considerably improved.

Polynomial Representation for Scalar Product of Unit Tensor Operators in fn and its Application

The polynomial representations in l i · l j are given for the relevant quantities to the unit tensor operators such as Coulomb interaction and Casimirs operators in f 2 . The eigenvalues for the quantities in f n are considered by combining with those of Casimirs operators on a basis of the representations. The expressions of e 1 , e 2 and e 3 for the maximal spin multiplets are interestingly derived. The remarkable is that the procedures for finding the eigenvalues are performed without help of the group theoretical technique.