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Linear response theories for interatomic exchange interactions.

I V Solovyev1

  • 1Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|January 22, 2024
PubMed
Summary
This summary is machine-generated.

Linear response theory connects physical variables to external fields, enabling calculations of interatomic exchange interactions from electronic structure. This review details methods for calculating magnetic interactions and their nuances.

Keywords:
Dzyaloshinskii–Moriya interactionselectronic structureexchange interactionsligand stateslinear response theorytransition-metal oxides and related compounds

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Materials Science

Background:

  • Linear response theory establishes relationships between physical variables and external fields.
  • In magnetism, susceptibility relates magnetization to magnetic fields.
  • Liechtenstein et al. (1987) formulated interatomic exchange interactions using susceptibility.

Purpose of the Study:

  • To review the fundamental concepts of linear response theories for interatomic exchange interactions.
  • To discuss recent advancements and theoretical nuances in the field.
  • To highlight the connection between exchange interactions and first-principles electronic structure calculations.

Main Methods:

  • Utilizing perturbation theory to calculate energy changes from infinitesimal spin rotations.
  • Employing susceptibility calculations derived from electronic structure.
  • Comparing original Liechtenstein et al. approximations with more rigorous extensions.

Main Results:

  • The linear response approach provides a generic formulation for energy changes, yielding the Heisenberg model for isotropic systems.
  • Establishes a direct link between interatomic exchange interactions and electronic structure.
  • Enables simultaneous calculation of isotropic exchange and antisymmetric Dzyaloshinskii-Moriya interactions.

Conclusions:

  • Linear response theories offer a powerful framework for understanding and calculating magnetic interactions from first principles.
  • The method's applicability is demonstrated across diverse magnetic materials, including van der Waals systems, half-metals, and Weyl semimetals.
  • Careful consideration of approximations, on-site Coulomb interactions, and ligand states is crucial for accurate results.