TY - JOUR

T1 - Fast and robust algorithm for energy minimization of spin systems applied in an analysis of high temperature spin configurations in terms of skyrmion density

AU - Ivanov, A.V.

AU - Uzdin, V.M.

AU - Jónsson, H.

N1 - Funding Information: We thank Julien Tranchida for helpful discussion and help with implementation of the algorithm in the LAMMPS software. Also, we thank Gideon Müller, Moritz Sallerman and Pavel Bessarab for helpful discussion and valuable comments on the manuscript. AVI thanks Filipp Rybakov for helpful discussions. This work was funded by the Icelandic Research Fund , the University of Iceland Research Fund, and the Russian Science Foundation (Grant 19-42-06302 ). AVI is supported by a doctoral fellowship from the University of Iceland .

PY - 2021/3/1

Y1 - 2021/3/1

N2 - 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.

AB - 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.

KW - Itinerant magnets

KW - Magnetism

KW - Skyrmions

KW - Spin minimization

KW - LIQUID

KW - DYNAMICS

KW - CONJUGATE-GRADIENT METHOD

KW - OPTIMIZATION

UR - http://www.scopus.com/inward/record.url?scp=85097574344&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/f0b0a903-5a15-36b3-8151-f0381ea25fff/

U2 - 10.1016/j.cpc.2020.107749

DO - 10.1016/j.cpc.2020.107749

M3 - Article

VL - 260

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

M1 - 107749

ER -