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Efficient optimization method for finding minimum energy paths of magnetic transitions.

A V Ivanov1,2, D Dagbartsson1, J Tranchida3

  • 1Science Institute and Faculty of Physical Sciences, University of Iceland, VR-III, 107 Reykjavík, Iceland.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|April 22, 2020
PubMed
Summary
This summary is machine-generated.

New algorithms for calculating magnetic transition minimum energy paths significantly outperform older methods. The geodesic nudged elastic band (GNEB) approach with limited memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) and orthogonal spin optimization (OSO) shows improved efficiency.

Keywords:
geodesic nudged elastic band methodmagnetismminimum energy pathsskyrmions

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Area of Science:

  • Computational physics
  • Materials science
  • Magnetism

Background:

  • Calculating minimum energy paths (MEPs) is crucial for understanding magnetic transitions.
  • Traditional methods for MEP calculations can be computationally intensive and less efficient.
  • The geodesic nudged elastic band (GNEB) method offers a framework for MEP calculations but lacks a direct objective function for traditional line searches.

Purpose of the Study:

  • To implement and evaluate efficient algorithms for calculating MEPs of magnetic transitions using the GNEB approach.
  • To compare the performance of new optimization methods against previously used techniques.
  • To demonstrate the effectiveness of these algorithms on various magnetic systems.

Main Methods:

  • Implementation of limited memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) and conjugate gradient algorithms combined with orthogonal spin optimization (OSO).
  • Utilizing energy-weighted springs for optimal distribution of discretization points along the path.
  • Application of these methods to magnetic systems described by Heisenberg-type Hamiltonians, including Dzyaloshinskii-Moriya and extended exchange interactions.

Main Results:

  • The LBFGS-OSO method significantly outperforms previous velocity projection and dissipative Landau-Lifschitz dynamics optimization methods.
  • Energy-weighted springs enhance the performance of the GNEB approach.
  • MEPs were successfully calculated for magnetization reversals in nano-islands, skyrmion collapse, and chiral bobber annihilation.

Conclusions:

  • The developed LBFGS-OSO approach provides a highly efficient method for calculating MEPs in magnetic systems.
  • This advancement offers a factor of up to 8 improvement in performance compared to dynamics-based methods.
  • The implemented algorithms are robust and applicable to complex magnetic phenomena.