TY - JOUR

T1 - Efficient optimization method for finding minimum energy paths of magnetic transitions

AU - Ivanov, A. V.

AU - Dagbartsson, D.

AU - Tranchida, J.

AU - Uzdin, V.M.

AU - Jonsson, H.

N1 - Ivanov, A. V., Dagbartsson, D., Tranchida, J., Uzdin, V. M., and Jónsson, H. Efficient optimization method for finding minimum energy paths of magnetic transitions. United States: N. p., 2020. Web. doi:10.1088/1361-648x/ab8b9c.

PY - 2020/8/12

Y1 - 2020/8/12

N2 - Here, 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.

AB - Here, 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.

KW - geodesic nudged elastic band method

KW - magnetism

KW - minimum energy paths

KW - skyrmions

UR - https://www.osti.gov/pages/biblio/1650179-efficient-optimization-method-finding-minimum-energy-paths-magnetic-transitions

UR - https://iopscience.iop.org/article/10.1088/1361-648X/ab8b9c

UR - http://www.scopus.com/inward/record.url?scp=85086598996&partnerID=8YFLogxK

U2 - 10.1088/1361-648X/ab8b9c

DO - 10.1088/1361-648X/ab8b9c

M3 - Article

VL - 32

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

SN - 0953-8984

IS - 34

M1 - 345901

ER -