Fast and robust algorithm for energy minimization of spin systems applied in an analysis of high temperature spin configurations in terms of skyrmion density
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 selfconsistent 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 limitedmemory quasinewton minimization algorithms, such as the limitedmemory BroydenFletcherGoldfarbShanno (LBFGS) algorithm, significantly accelerates the convergence.
 Publication:

Computer Physics Communications
 Pub Date:
 March 2021
 DOI:
 10.1016/j.cpc.2020.107749
 arXiv:
 arXiv:1904.02669
 Bibcode:
 2021CoPhC.26007749I
 Keywords:

 Spin minimization;
 Magnetism;
 Itinerant magnets;
 Skyrmions;
 Physics  Computational Physics
 EPrint:
 Comput. Phys. Commun. 260, 107749 (2021)