Efficient optimization method for finding minimum energy paths of magnetic transitions

Ivanov, A. V.; Dagbartsson, D.; Tranchida, J.; Uzdin, V. M.; Jónsson, H.

doi:10.1088/1361-648x/ab8b9c

Efficient optimization method for finding minimum energy paths of magnetic transitions

Journal Article · Wed May 27 00:00:00 EDT 2020 · Journal of Physics. Condensed Matter

DOI:https://doi.org/10.1088/1361-648x/ab8b9c· OSTI ID:1650179

^[1]; Dagbartsson, D. ^[2]; Tranchida, J. ^[3]; ^[4]; ^[5]

Univ. of Iceland, Reykjavík (Iceland). Science Inst. and Faculty of Physical Sciences; Saint Petersburg State Univ. (Russia)
Univ. of Iceland, Reykjavík (Iceland). Science Inst. and Faculty of Physical Sciences
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Multiscale Science Dept.
Saint Petersburg State Univ. (Russia); ITMO Univ., Saint Petersburg (Russia)
Univ. of Iceland, Reykjavík (Iceland). Science Inst. and Faculty of Physical Sciences; Aalto Univ., Espoo (Finland). Dept. of Applied Physics

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.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: Icelandic Research Fund; Russian Foundation of Basic Research; USDOE National Nuclear Security Administration (NNSA); University of Iceland Research Fund

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1650179

Alternate ID(s):: OSTI ID: 23020280

Report Number(s):: SAND--2020-8484J; 689977

Journal Information:: Journal of Physics. Condensed Matter, Journal Name: Journal of Physics. Condensed Matter Journal Issue: 34 Vol. 32; ISSN 0953-8984

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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