Efficient Optimization Method for Finding Minimum Energy Paths of Magnetic Transitions

Abstract

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 neighbours. 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.

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Cited by in corpus (6)

• Stability of Hopfions in Bulk Magnets with Competing Exchange Interactions
• The lifetime of micron scale topological chiral magnetic states with atomic resolution
• Lifetime, collapse and escape paths for hopfions in bulk magnets with competing exchange interactions
• Lifetime of skyrmions in discrete systems with infinitesimal lattice constant
• Spin dynamics from a constrained magnetic Tight-Binding model
• Single-stage direct Langevin dynamic simulations of transitions over arbitrary high energy barriers: Concept of the energy-dependent temperature