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Spin-orbit coupling from a two-component self-consistent approach. II. Non-collinear density functional theories.

Jacques K Desmarais1, Jean-Pierre Flament2, Alessandro Erba1

  • 1Dipartimento di Chimica, Università di Torino, Via Giuria 5, 10125 Torino, Italy.

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This study introduces a new "signed canonical" theory for noncollinear density functional theory (DFT) using generalized gradient approximation (GGA) functionals. It resolves numerical instabilities and improves accuracy in spin-orbit coupling calculations.

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Area of Science:

  • Quantum Chemistry
  • Computational Materials Science
  • Condensed Matter Physics

Background:

  • Standard one-component density functional theory (DFT) extends to noncollinear magnetization within the local density approximation (LDA), ensuring numerical stability.
  • Generalized gradient approximation (GGA) based noncollinear DFT formulations exhibit limitations, including failure to reduce to the collinear limit, rotational invariance issues with spin-orbit coupling (SOC), and numerical instability in low-magnetization regions.

Purpose of the Study:

  • To address the limitations of existing noncollinear DFT formulations within the GGA.
  • To develop a numerically stable and formally correct theory for noncollinear DFT with SOC.
  • To introduce a new formulation, the "signed canonical" theory, for improved calculations.

Main Methods:

  • Revision of formal and numerical aspects of collinear and noncollinear DFT with a two-component self-consistent treatment of spin-orbit coupling (SOC).
  • Development and application of a new "signed canonical" theory for GGA functionals.
  • Implementation of an effective screening algorithm for unstable exchange-correlation potential terms.
  • Testing all methods within the CRYSTAL program using simple molecules.

Main Results:

  • The proposed "signed canonical" theory formally and numerically resolves issues in previous GGA-based noncollinear DFT formulations.
  • Demonstrated improvement in reducing to the collinear limit and ensuring rotational invariance with SOC.
  • Significant reduction in numerical instability, particularly in regions of small magnetization.

Conclusions:

  • The "signed canonical" theory provides a robust and accurate framework for noncollinear DFT calculations involving spin-orbit coupling.
  • This advancement offers a more stable and reliable approach for computational materials science and quantum chemistry research.
  • The findings pave the way for more accurate predictions of material properties influenced by spin-orbit coupling.