Abstract
A microstructural model of behavior of ferromagnetic material (Heusler alloy) in a magnetic field is constructed within the framework of the theory of micromagnetism. The process dynamics is described by the Landau—Lifshitz—Hilbert equation. The Galerkin procedure is used to assign variational equations to differential relations. A herringbone-type martensitic structure (twinned variant of martensite) with magnetic domains arranged at an angle of 180° is considered. The twin boundaries act as 90-degree magnetic domain walls. The evolution of this magnetic structure is investigated, namely the motion and interaction of the 180-degree walls of this magnetic domain in the presence of an external magnetic field applied in different directions. The finite element method simulates the formation of these walls and the magnetization vector distribution in them.
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REFERENCES
A. N. Vasil’ev, V. D. Buchel’nikov, T. Takagi, et al., “Shape Memory Ferromagnets," Uspekhi Fizicheskikh Nauk 173 (6), 577–607 (2003) [Physics-Uspekhi 46 (6), 559–588 (2003)]. DOI: 10.3367/UFNr.0173.200306a.0577.
A. Kazaryan and Y. Wang, “Development of Magnetic Domains in Hard Ferromagnetic Thin Films of Polytwinned Microstructure," J. Appl. Phys. 92, 7408–7414 (2002). DOI: 10.1063/1.1522494.
X.-P. Wan, K. Wang, and E. Weinan, “Simulations of 3-D Domain Wall Structures in Thin Films," Discrete Continuous Dynamic Systemts. B, No. 6, 373–389 (2006). DOI: 10.3934/dcdsb.2006.6.373.
R. Bustamante, A. Dorfmann, and R. W. Ogden, “A Nonlinear Magnetoelastic Tube Under Extension and Inflation in an Axial Magnetic Field: Numerical Solution," J. Engng Math. 59, 139–153 (2007). DOI: 10.1007/s10665-006-9088-4.
K. Haldar, B. Kiefer, and D. C. Lagoudas, “Finite Element Analysis of the Demagnetization Effect and Stress Inhomogeneities in Magnetic Shape Memory Alloy Samples," Philos. Mag. 91, 4126–4157 (2011). DOI: 10.1080/14786435.2011.602031.
A. A. Rogovoy, “Formalized Approach to Construction of the State Equations for Complex Media Under Finite Deformations," Continuum Mech. Thermodynamics. 24, 81–114 (2012). DOI: 10.1007/s00161-011-0220-y.
A. Rogovoy and O. Stolbova, “Modeling the Magnetic Field Control of Phase Transition in Ferromagnetic Shape Memory Alloys," Intern. J. Plasticity 85, 130–155 (2016). DOI: 10.1016/j.ijplas.2016.07.006.
C. Mennerich, F. Wendler, M. Jainta, and B. Nestler, “A Phase-Field Model for the Magnetic Shape Memory Effect," Arch. Mech. 63, 549–571 (2011).
Y. M. Jin, “Domain Microstructure Evolution in Magnetic Shape Memory Alloys: Phase-Field Model and Simulation," Acta Materialia 57, 2488–2495 (2009). DOI: 10.1016/j.actamat.2009.02.003.
L. J. Li, C. H. Lei, Y. C. Shu, and J. Y. Li, “Phase-Field Simulation of Magnetoelastic Couplings in Ferromagnetic Shape Memory Alloys," Acta Materialia 59, 2648–2655 (2011). DOI: 10.1016/j.actamat.2011.01.001.
A. A. Rogovoy, O. V. Stolbov, and O. S. Stolbova, “The Microstructural Model of the Ferromagnetic Material Behavior in an External Magnetic Field," Magnetochemistry 7 (7), 1–19 (2021). DOI: 10.3390/magnetochemistry7010007.
M. A. Shamsutdinov, V. N. Nazarov, and A. T. Kharisov, Introduction to the Theory of Domain Walls and Solitons in Ferromagnets (Bashkir State University, Ufa, 2010) [in Russian].
W. F. Brown, Micromagnetics (Interscience Publisher, New York, 1963).
R. Tickle and R. D. James, “Magnetic and Magnetomechanical Properties of Ni2MnGa," J. Magnet. Magnet. Materials 195, 627–638 (1999). DOI: 10.1016/S0304-8853(99)00292-9.
J. X. Zhang and L. Q. Chen, “Phase-Field Microelasticity Theory and Micromagnetic Simulations of Domain Structures in Giant Magnetostrictive Materials," Acta Materialia 53, 2845–2855 (2005). DOI: 10.1016/j.actamat.2005.03.002.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 62, No. 5, pp. 195-207. https://doi.org/10.15372/PMTF20210519.
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Rogovoi, A.A., Stolbova, O.S. & Stolbov, O.V. NUMERICAL SIMULATION OF EVOLUTION OF MAGNETIC MICROSTRUCTURE IN HEUSLER ALLOYS. J Appl Mech Tech Phy 62, 870–881 (2021). https://doi.org/10.1134/S0021894421050199
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DOI: https://doi.org/10.1134/S0021894421050199