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An algorithm for the minimization of the energy of magnetic systems ispresented and applied to the analysis of thermal configurations of aferromagnet to identify inherent structures, i.e. the nearest local energyminima, as a function of temperature. Over a rather narrow temperatureinterval, skyrmions appear and reach a high temperature limit for the skyrmiondensity. In addition, the performance of the algorithm is further demonstratedin 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 thespherical domain is taken into account and as a result the length of themagnetic moments is preserved in every iteration. In the limit of infinitesimalrotations, the minimization path coincides with that obtained using damped spindynamics 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.

computer physics communications

Fast and Robust Algorithm for the Energy Minimization of Spin Systems  Applied in an Analysis of High Temperature Spin Configurations in Terms of  Skyrmion Density