A new mathematical approach to finding global solutions of the magnetic structure determination problem

Tomiyasu, K.; Oishi-Tomiyasu, R.; Matsuda, M.; Matsuhira, K.

doi:10.1038/s41598-018-34443-2

Title: A new mathematical approach to finding global solutions of the magnetic structure determination problem

Journal Article · Thu Nov 01 00:00:00 EDT 2018 · Scientific Reports

DOI:https://doi.org/10.1038/s41598-018-34443-2· OSTI ID:1619462

; Oishi-Tomiyasu, R.; Matsuda, M.;

Abstract Determination of magnetic structure is an important analytical procedure utilized in various fields ranging from fundamental condensed-matter physics and chemistry to advanced manufacturing. It is typically performed using a neutron diffraction technique; however, finding global solutions of the magnetic structure optimization problem represents a significant challenge. Generally, it is not possible to mathematically prove that the obtained magnetic structure is a truly global solution and that no solution exists when no acceptable structure is found. In this study, the global optimization technique called semidefinite relaxation of quadratic optimization, which has attracted much interest in the field of applied mathematics, is proposed to use as a new analytical method for the determination of magnetic structure, followed by the application of polarized neutron diffraction data. This mathematical approach allows avoiding spurious local solutions, decreasing the amount of time required to find a tentative solution and finding multiple solutions when they exist.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1619462

Alternate ID(s):: OSTI ID: 1493133

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Vol. 8 Journal Issue: 1; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United Kingdom

Language:: English

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Cited by: 2 works

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