TY - JOUR
T1 - A new mathematical approach to finding global solutions of the magnetic structure determination problem
AU - Tomiyasu, K.
AU - Oishi-Tomiyasu, R.
AU - Matsuda, M.
AU - Matsuhira, K.
N1 - Funding Information:
Neutron diffraction experiments were conducted using the High Flux Isotope Reactor, a user facility of the DOE Office of Science operated by the Oak Ridge National Laboratory (USA). This study was partially supported by the U.S.-Japan Cooperative Program on Neutron Scattering. This study was financially supported by the MEXT/ JSPS KAKENHI (grant Nos JP18K03503, JP17H06137 and JP15H03692), JST PRESTO (grant No. JPMJPR14E6), Japan-US program administrated by ISSP at the University of Tokyo and FRIS program for the creation of interdisciplinary research at the Tohoku University.
Publisher Copyright:
© 2018, The Author(s).
PY - 2018/12/1
Y1 - 2018/12/1
N2 - 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.
AB - 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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U2 - 10.1038/s41598-018-34443-2
DO - 10.1038/s41598-018-34443-2
M3 - Article
C2 - 30385777
AN - SCOPUS:85055911656
SN - 2045-2322
VL - 8
JO - Scientific Reports
JF - Scientific Reports
IS - 1
M1 - 16228
ER -