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

K. Tomiyasu, Ryoko Tomiyasu, M. Matsuda, K. Matsuhira

Research output: Contribution to journalArticle

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.

Original languageEnglish
Article number16228
JournalScientific reports
Volume8
Issue number1
DOIs
Publication statusPublished - Dec 1 2018

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Neutron Diffraction
Mathematics
Physics

All Science Journal Classification (ASJC) codes

  • General

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A new mathematical approach to finding global solutions of the magnetic structure determination problem. / Tomiyasu, K.; Tomiyasu, Ryoko; Matsuda, M.; Matsuhira, K.

In: Scientific reports, Vol. 8, No. 1, 16228, 01.12.2018.

Research output: Contribution to journalArticle

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