Fast and robust algorithm for energy minimization of spin systems applied in an analysis of high temperature spin configurations in terms of skyrmion density

A. V. Ivanov*, V. M. Uzdin, H. Jónsson

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

An algorithm for the minimization of the energy of magnetic systems is presented and applied to the analysis of thermal configurations of a ferromagnet to identify inherent structures, i.e. the nearest local energy minima, as a function of temperature. Over a rather narrow temperature interval, skyrmions appear and reach a high temperature limit for the skyrmion density. In addition, the performance of the algorithm is further demonstrated in a self-consistent field calculation of a skyrmion in an itinerant magnet. The algorithm is based on a geometric approach in which the curvature of the spherical domain is taken into account and as a result the length of the magnetic moments is preserved in every iteration. In the limit of infinitesimal rotations, the minimization path coincides with that obtained using damped spin dynamics while the use of limited-memory quasi-newton minimization algorithms, such as the limited-memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) algorithm, significantly accelerates the convergence.

Original languageEnglish
Article number107749
JournalComputer Physics Communications
Volume260
DOIs
Publication statusPublished - Mar 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • Itinerant magnets
  • Magnetism
  • Skyrmions
  • Spin minimization

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