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Title: Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

Abstract

Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax = (l,m)max, while scattering matrices, which determine spectral properties, are truncated at Ltr = (l,m)tr where phase shifts δl>ltr are negligible. Historically, Lmax is set equal to Ltr, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax > Ltr with δl>ltr set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N(ltr + 1)2] and includes higher-L contributions via linear algebra [R2 process with rank N(lmax +1)2]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L10 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magneticmore » moments versus Lmax for a given Ltr.« less

Authors:
 [1];  [2];  [2];  [3];  [4]
  1. Indian Inst. of Technology (IIT), Mumbai (India). Dept. of Physics
  2. Ames Lab., Ames, IA (United States). Division of Materials Science & Engineering
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  4. Ames Lab., Ames, IA (United States). Division of Materials Science & Engineering; Iowa State Univ., Ames, IA (United States). Dept. of Materials Science & Engineering
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Center for Defect Physics in Structural Materials (CDP); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Ames Lab., Ames, IA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1286786
Alternate Identifier(s):
OSTI ID: 1180863
Grant/Contract Number:  
AC05-00OR22725; FG02-03ER46026; AC02- 07CH11358; 13IRCCSG020; AC02-07CH11358
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 90; Journal Issue: 20; Journal ID: ISSN 1098-0121
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Korringa-Kohn-Rostoker (KKR) Green's function; multiple-scattering

Citation Formats

Alam, Aftab, Khan, Suffian N., Smirnov, A. V., Nicholson, D. M., and Johnson, Duane D. Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism. United States: N. p., 2014. Web. doi:10.1103/PhysRevB.90.205102.
Alam, Aftab, Khan, Suffian N., Smirnov, A. V., Nicholson, D. M., & Johnson, Duane D. Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism. United States. doi:10.1103/PhysRevB.90.205102.
Alam, Aftab, Khan, Suffian N., Smirnov, A. V., Nicholson, D. M., and Johnson, Duane D. Tue . "Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism". United States. doi:10.1103/PhysRevB.90.205102. https://www.osti.gov/servlets/purl/1286786.
@article{osti_1286786,
title = {Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism},
author = {Alam, Aftab and Khan, Suffian N. and Smirnov, A. V. and Nicholson, D. M. and Johnson, Duane D.},
abstractNote = {Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax = (l,m)max, while scattering matrices, which determine spectral properties, are truncated at Ltr = (l,m)tr where phase shifts δl>ltr are negligible. Historically, Lmax is set equal to Ltr, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax > Ltr with δl>ltr set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N(ltr + 1)2] and includes higher-L contributions via linear algebra [R2 process with rank N(lmax +1)2]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L10 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Ltr.},
doi = {10.1103/PhysRevB.90.205102},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 20,
volume = 90,
place = {United States},
year = {2014},
month = {11}
}

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Works referenced in this record:

Multiple-scattering theory with a truncated basis set
journal, September 1992


Spin-dependent tunneling conductance of Fe | MgO | Fe sandwiches
journal, January 2001


Incommensurate and Commensurate Antiferromagnetic Spin Fluctuations in Cr and Cr Alloys from Ab Initio Dynamical Spin Susceptibility Calculations
journal, April 1999


Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations
journal, July 2011


Surface electronic structure
journal, March 1982


Exploring the XPS limit in soft and hard x-ray angle-resolved photoemission using a temperature-dependent one-step theory
journal, November 2013


Fast method for calculating the self-consistent electronic structure of random alloys. II. Optimal use of the complex plane
journal, September 1985


Soft X-ray emission from metals and alloys
journal, May 1971


Temperature-induced configurational excitations for predicting thermodynamic and mechanical properties of alloys
journal, November 2000


An elementary derivation of Lloyd s formula valid for full-potential multiple-scattering theory
journal, August 2004


Solution of the Schrödinger Equation in Periodic Lattices with an Application to Metallic Lithium
journal, June 1954


Special points for Brillouin-zone integrations
journal, June 1976

  • Monkhorst, Hendrik J.; Pack, James D.
  • Physical Review B, Vol. 13, Issue 12, p. 5188-5192
  • DOI: 10.1103/PhysRevB.13.5188

Wave propagation through an assembly of spheres: II. The density of single-particle eigenstates
journal, January 1967


Theory of photoemission from random alloys
journal, November 1981


Multiple scattering theory in condensed materials
journal, January 1972


Calculating condensed matter properties using the KKR-Green's function method—recent developments and applications
journal, August 2011


Mass and Lifetime Enhancement due to Disorder on Ag c Pd 1 c Alloys
journal, January 1982


Validity and accuracy of multiple-scattering theory
journal, February 1990


Conceptual improvements of the KKR method
journal, March 2002

  • Papanikolaou, N.; Zeller, R.; Dederichs, P. H.
  • Journal of Physics: Condensed Matter, Vol. 14, Issue 11
  • DOI: 10.1088/0953-8984/14/11/304

Magneto-optical effects in transition metal systems
journal, December 1996


Commensurate and Incommensurate Ordering Tendencies in the Ternary fcc Cu-Ni-Zn System
journal, January 1995


Bulk and Surface Effects in Photoemission from Disordered Cu -Ni Alloys
journal, November 1984


Angular momentum convergence of Korringa-Kohn-Rostoker Green's function methods
journal, March 2001

  • Moghadam, Nassrin Y.; Stocks, G. M.; Zhang, X-G
  • Journal of Physics: Condensed Matter, Vol. 13, Issue 13
  • DOI: 10.1088/0953-8984/13/13/318

Importance of thermal disorder on the properties of alloys: Origin of paramagnetism and structural anomalies in bcc-based Fe 1 x Al x
journal, February 2005


Chemically Mediated Quantum Criticality in NbFe 2
journal, November 2011


A local exchange-correlation potential for the spin polarized case. i
journal, July 1972


Electronic origins of ordering in multicomponent metallic alloys: Application to the Cu-Ni-Zn system
journal, April 1996


Calculated electrical conductivity and thermopower of silver-palladium alloys
journal, April 1984


Ab initio study of the martensitic bcc-hcp transformation in iron
journal, September 1998

  • Ekman, Mathias; Sadigh, Babak; Einarsdotter, Kristin
  • Physical Review B, Vol. 58, Issue 9
  • DOI: 10.1103/PhysRevB.58.5296

Fast method for calculating the self-consistent electronic structure of random alloys
journal, November 1984


On the calculation of the energy of a Bloch wave in a metal
journal, August 1947


Experimental and theoretical x-ray magnetic-circular-dichroism study of the magnetic properties of Co 50 Pt 50 thin films
journal, July 2000


Total-energy and pressure calculations for random substitutional alloys
journal, May 1990


Accurate and fast numerical solution of Poisson's equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited
journal, November 2011


Scattering theory and cluster calculations
journal, December 1977


Density-Functional Theory for Random Alloys: Total Energy within the Coherent-Potential Approximation
journal, May 1986


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    Magnetocrystalline anisotropy of FePt: A detailed view
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