Efficient algorithms for the calculation of minimum energy paths of magnetic transitions are implemented within the geodesic nudged elastic band (GNEB) approach. While an objective function is not available for GNEB and a traditional line search can, therefore, not be performed, the use of limited memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) and conjugate gradient algorithms in conjunction with orthogonal spin optimization (OSO) approach is shown to greatly outperform the previously used velocity projection and dissipative Landau-Lifschitz dynamics optimization methods. The implementation makes use of energy weighted springs for the distribution of the discretization points along the path and this is found to improve performance significantly. The various methods are applied to several test problems using a Heisenberg-type Hamiltonian, extended in some cases to include Dzyaloshinskii-Moriya and exchange interactions beyond nearest neighbors. Minimum energy paths are found for magnetization reversals in a nano-island, collapse of skyrmions in two-dimensional layers and annihilation of a chiral bobber near the surface of a three-dimensional magnet. The LBFGS-OSO method is found to outperform the dynamics based approaches by up to a factor of 8 in some cases.

中文翻译：

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寻找磁跃迁最小能量路径的有效优化方法

用于计算磁跃迁最小能量路径的有效算法在测地线微调弹性带 (GNEB) 方法中实施。虽然 GNEB 没有目标函数，因此无法执行传统的线搜索，但使用有限内存的 Broyden-Fletcher-Goldfarb-Shanno (LBFGS) 和共轭梯度算法与正交自旋优化 (OSO)方法被证明大大优于以前使用的速度投影和耗散 Landau-Lifschitz 动力学优化方法。该实现利用能量加权弹簧沿路径分布离散点，并且发现这可以显着提高性能。使用海森堡型哈密顿量将各种方法应用于几个测试问题，在某些情况下，扩展到包括 Dzyaloshinskii-Moriya 和最近邻以外的交换交互。为纳米岛中的磁化反转、二维层中斯格明子的坍塌和三维磁体表面附近的手性浮子湮灭找到了最小能量路径。在某些情况下，LBFGS-OSO 方法的性能优于基于动力学的方法高达 8 倍。