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Title: 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 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. 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:
ORCiD logo [1];  [2]; ORCiD logo [3]; ORCiD logo [4]
  1. Tohoku Univ., Sendai (Japan)
  2. Yamagata Univ., Yamagata (Japan)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  4. 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) (SC-22)
OSTI Identifier:
1493133
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Scientific Reports
Additional Journal Information:
Journal Volume: 8; Journal Issue: 1; Journal ID: ISSN 2045-2322
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Tomiyasu, Keisuke, Oishi-Tomiyasu, 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/s41598-018-34443-2.
Tomiyasu, Keisuke, Oishi-Tomiyasu, Ryoko, Matsuda, Masaaki, & Matsuhira, Kazuyuki. A new mathematical approach to finding global solutions of the magnetic structure determination problem. United States. doi:10.1038/s41598-018-34443-2.
Tomiyasu, Keisuke, Oishi-Tomiyasu, 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/s41598-018-34443-2. 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 Oishi-Tomiyasu, Ryoko and Matsuda, Masaaki and Matsuhira, Kazuyuki},
abstractNote = {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. 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/s41598-018-34443-2},
journal = {Scientific Reports},
issn = {2045-2322},
number = 1,
volume = 8,
place = {United States},
year = {2018},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Figures / Tables:

Figure 1 Figure 1: Schematic diagrams illustrating the non-linear optimization process. (A) Before relaxation. (B) SDR technique. (C) Duality theorem combined with SDR. The objective function $f$ is globally minimized to the global optimum value $f$(gl). When the duality gap Δ$f$ is close to zero (corresponding to the square root of themore » machine epsilon), the global optimization process is complete according to the duality theorem. In panels (B) and (C), the solid balls represent the paths toward feasible solutions chosen by the interior point method.« less

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Works referenced in this record:

Infinite-layer iron oxide with a square-planar coordination
journal, December 2007

  • Tsujimoto, Y.; Tassel, C.; Hayashi, N.
  • Nature, Vol. 450, Issue 7172, p. 1062-1065
  • DOI: 10.1038/nature06382

    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.