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.

中文翻译：

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自旋系统能量最小化的快速而稳健的算法，用于根据斯格明子密度分析高温自旋配置

摘要 提出了一种最小化磁系统能量的算法，并将其应用于铁磁体热配置的分析，以识别作为温度函数的固有结构，即最近的局部能量最小值。在相当窄的温度区间内，斯格明子出现并达到斯格明子密度的高温极限。此外，该算法的性能在流动磁体中斯格明子的自洽场计算中得到进一步证明。该算法基于几何方法，其中考虑了球域的曲率，因此在每次迭代中都保留了磁矩的长度。在无穷小的旋转极限下，