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Title: Exchange-correlation magnetic fields in spin-density-functional theory

Abstract

In spin-density-functional theory for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in particular, they can give rise to local torques on the magnetization, which are absent in standard local and semilocal approximations. We obtain exact benchmark solutions for two electrons on four-site extended Hubbard lattices over a wide range of interaction strengths, and compare exact xc potentials and magnetic fields with approximations obtained from orbital-dependent xc functionals. Here, the xc magnetic fields turn out to play an increasingly important role as systems becomes more and more correlated and the electrons begin to localize; the effects of the xc torques, however, remain relatively minor. The approximate xc functionals perform overall quite well, but tend to favor symmetry-broken solutions for strong interactions.

Authors:
 [1]; ORCiD logo [1]
  1. Univ. of Missouri, Columbia, MO (United States)
Publication Date:
Research Org.:
Univ. of Missouri, Columbia, MO (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
OSTI Identifier:
1561956
Grant/Contract Number:  
SC0019109
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 100; Journal Issue: 12; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; density-functional theory; noncollinear magnetism; Hubbard model

Citation Formats

Pluhar, III, Edward A., and Ullrich, Carsten A. Exchange-correlation magnetic fields in spin-density-functional theory. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.100.125135.
Pluhar, III, Edward A., & Ullrich, Carsten A. Exchange-correlation magnetic fields in spin-density-functional theory. United States. doi:10.1103/PhysRevB.100.125135.
Pluhar, III, Edward A., and Ullrich, Carsten A. Mon . "Exchange-correlation magnetic fields in spin-density-functional theory". United States. doi:10.1103/PhysRevB.100.125135. https://www.osti.gov/servlets/purl/1561956.
@article{osti_1561956,
title = {Exchange-correlation magnetic fields in spin-density-functional theory},
author = {Pluhar, III, Edward A. and Ullrich, Carsten A.},
abstractNote = {In spin-density-functional theory for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in particular, they can give rise to local torques on the magnetization, which are absent in standard local and semilocal approximations. We obtain exact benchmark solutions for two electrons on four-site extended Hubbard lattices over a wide range of interaction strengths, and compare exact xc potentials and magnetic fields with approximations obtained from orbital-dependent xc functionals. Here, the xc magnetic fields turn out to play an increasingly important role as systems becomes more and more correlated and the electrons begin to localize; the effects of the xc torques, however, remain relatively minor. The approximate xc functionals perform overall quite well, but tend to favor symmetry-broken solutions for strong interactions.},
doi = {10.1103/PhysRevB.100.125135},
journal = {Physical Review B},
number = 12,
volume = 100,
place = {United States},
year = {2019},
month = {9}
}

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Works referenced in this record:

Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

U ( 1 ) × SU ( 2 ) gauge invariance made simple for density functional approximations
journal, July 2017


Modern computational magnetism: role of noncollinear magnetism in complex magnetic phenomena
journal, June 2004


Current development of noncollinear electronic structure theory
journal, April 2017

  • Goings, Joshua J.; Egidi, Franco; Li, Xiaosong
  • International Journal of Quantum Chemistry, Vol. 118, Issue 1
  • DOI: 10.1002/qua.25398

Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]
journal, February 1997


Adapting approximate-memory potentials for time-dependent density functional theory
journal, February 2008


Spin in density-functional theory
journal, August 2012

  • Jacob, Christoph R.; Reiher, Markus
  • International Journal of Quantum Chemistry, Vol. 112, Issue 23
  • DOI: 10.1002/qua.24309

Electron Correlations at Metallic Densities
journal, December 1968


Transverse Spin-Gradient Functional for Noncollinear Spin-Density-Functional Theory
journal, October 2013


Charge-Density-Wave to Spin-Density-Wave Transition in the Extended Hubbard Model
journal, December 1984


Hubbard Trimer with Spin–Orbit Coupling: Hartree–Fock Solutions, (Non)Collinearity, and Anisotropic Spin Hamiltonian
journal, February 2019

  • Ghassemi Tabrizi, Shadan; Arbuznikov, Alexei V.; Kaupp, Martin
  • The Journal of Physical Chemistry A, Vol. 123, Issue 12
  • DOI: 10.1021/acs.jpca.8b11959

Challenges for Density Functional Theory
journal, December 2011

  • Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr200107z

Extended Hubbard model in two dimensions
journal, December 1991


Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
journal, May 1976


Density functionals and model Hamiltonians: Pillars of many-particle physics
journal, July 2013


Source-Free Exchange-Correlation Magnetic Fields in Density Functional Theory
journal, February 2018

  • Sharma, S.; Gross, E. K. U.; Sanna, A.
  • Journal of Chemical Theory and Computation, Vol. 14, Issue 3
  • DOI: 10.1021/acs.jctc.7b01049

Describing strong correlation with fractional-spin correction in density functional theory
journal, September 2018

  • Su, Neil Qiang; Li, Chen; Yang, Weitao
  • Proceedings of the National Academy of Sciences, Vol. 115, Issue 39
  • DOI: 10.1073/pnas.1807095115

Density functional for noncollinear magnetic systems
journal, February 1999


Numerical methods for the inverse problem of density functional theory
journal, July 2017

  • Jensen, Daniel S.; Wasserman, Adam
  • International Journal of Quantum Chemistry, Vol. 118, Issue 1
  • DOI: 10.1002/qua.25425

Accurate and simple analytic representation of the electron-gas correlation energy
journal, June 1992


Noncollinear density functional theory having proper invariance and local torque properties
journal, January 2013


Extended Hubbard model in two dimensions
journal, May 1989


First-Principles Approach to Noncollinear Magnetism: Towards Spin Dynamics
journal, May 2007


Noncollinear magnetism in density functional calculations
journal, March 2007


The Hubbard dimer: a density functional case study of a many-body problem
journal, September 2015


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


Single-band Hubbard model with spin-orbit coupling
journal, December 1983

  • Kaplan, T. A.
  • Zeitschrift f�r Physik B Condensed Matter, Vol. 49, Issue 4
  • DOI: 10.1007/BF01301591

Describing static correlation in bond dissociation by Kohn–Sham density functional theory
journal, March 2005

  • Fuchs, M.; Niquet, Y. -M.; Gonze, X.
  • The Journal of Chemical Physics, Vol. 122, Issue 9
  • DOI: 10.1063/1.1858371

Laser-Induced Demagnetization at Ultrashort Time Scales: Predictions of TDDFT
journal, September 2015

  • Krieger, K.; Dewhurst, J. K.; Elliott, P.
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 10
  • DOI: 10.1021/acs.jctc.5b00621

Climbing the ladder of density functional approximations
journal, September 2013


Spin Currents and Spin Dynamics in Time-Dependent Density-Functional Theory
journal, October 2001


Spin angular gradient approximation in the density functional theory
journal, April 2003


Density functional theory of non-collinear magnetism
journal, March 1988


Noncollinear magnetism in itinerant-electron systems: Theory and applications
journal, January 1998


Transverse and longitudinal gradients of the spin magnetization in spin-density-functional theory
journal, December 2013


Hubbard model with nearest-neighbor and bond-charge interaction: Exact ground-state solution in a wide range of parameters
journal, April 1993


Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965


A New Approach to Noncollinear Spin Density Functional Theory beyond the Local Density Approximation
journal, June 2012

  • Scalmani, Giovanni; Frisch, Michael J.
  • Journal of Chemical Theory and Computation, Vol. 8, Issue 7
  • DOI: 10.1021/ct300441z