A new mathematical approach to finding global solutions of the magnetic structure determination problem
Abstract
Determination of magnetic structure is an important analytical procedure utilized in various fields ranging from fundamental condensedmatter 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. Furthermore, 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.
 Authors:

 Tohoku Univ., Sendai (Japan)
 Yamagata Univ., Yamagata (Japan)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Kyusyu Institute of Technology, Kitakyusyu (Japan)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 OSTI Identifier:
 1493133
 Grant/Contract Number:
 AC0500OR22725
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Scientific Reports
 Additional Journal Information:
 Journal Volume: 8; Journal Issue: 1; Journal ID: ISSN 20452322
 Publisher:
 Nature Publishing Group
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
Citation Formats
Tomiyasu, Keisuke, OishiTomiyasu, Ryoko, Matsuda, Masaaki, and Matsuhira, Kazuyuki. A new mathematical approach to finding global solutions of the magnetic structure determination problem. United States: N. p., 2018.
Web. doi:10.1038/s41598018344432.
Tomiyasu, Keisuke, OishiTomiyasu, Ryoko, Matsuda, Masaaki, & Matsuhira, Kazuyuki. A new mathematical approach to finding global solutions of the magnetic structure determination problem. United States. doi:10.1038/s41598018344432.
Tomiyasu, Keisuke, OishiTomiyasu, Ryoko, Matsuda, Masaaki, and Matsuhira, Kazuyuki. Thu .
"A new mathematical approach to finding global solutions of the magnetic structure determination problem". United States. doi:10.1038/s41598018344432. https://www.osti.gov/servlets/purl/1493133.
@article{osti_1493133,
title = {A new mathematical approach to finding global solutions of the magnetic structure determination problem},
author = {Tomiyasu, Keisuke and OishiTomiyasu, Ryoko and Matsuda, Masaaki and Matsuhira, Kazuyuki},
abstractNote = {Determination of magnetic structure is an important analytical procedure utilized in various fields ranging from fundamental condensedmatter 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. Furthermore, 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.},
doi = {10.1038/s41598018344432},
journal = {Scientific Reports},
issn = {20452322},
number = 1,
volume = 8,
place = {United States},
year = {2018},
month = {11}
}
Figures / Tables:
Works referenced in this record:
Infinitelayer iron oxide with a squareplanar coordination
journal, December 2007
 Tsujimoto, Y.; Tassel, C.; Hayashi, N.
 Nature, Vol. 450, Issue 7172, p. 10621065
Figures / Tables found in this record: