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**Yi, Min and Xu, Bai-Xiang** (2014):

*A constraint-free phase field model for ferromagnetic domain evolution.*

In: Proceedings of Royal Society A-Mathematical Physical and Engineering Sciences, The Royal Society Publishing, p. 20140517, 470, (2171), [Article]

## Abstract

A continuum constraint-free phase field model is proposed to simulate the magnetic domain evolution in ferromagnetic materials. The model takes the polar and azimuthal angles (ϑ1,ϑ2), instead of the magnetization unit vector m(m1,m2,m3), as the order parameters. In this way, the constraint on the magnetization magnitude can be exactly satisfied automatically, and no special numerical treatment on the phase field evolution is needed. The phase field model is developed from a thermodynamic framework which involves a configurational force system for ϑ1 and ϑ2. A combination of the configurational force balance and the second law of thermodynamics leads to thermodynamically consistent constitutive relations and a generalized evolution equation for the order parameters (ϑ1,ϑ2). Beneficial from the constraint-free model, the three-dimensional finite-element implementation is straightforward, and the degrees of freedom are reduced by one. The model is shown to be capable of reproducing the damping-dependent switching dynamics, and the formation and evolution of domains and vortices in ferromagnetic materials under the external magnetic or mechanical loading. Particularly, the calculated out-of-plane component of magnetization in a vortex is verified by the corresponding experimental results, as well as the motion of the vortex under a magnetic field.

Item Type: | Article |
---|---|

Erschienen: | 2014 |

Creators: | Yi, Min and Xu, Bai-Xiang |

Title: | A constraint-free phase field model for ferromagnetic domain evolution |

Language: | English |

Abstract: | A continuum constraint-free phase field model is proposed to simulate the magnetic domain evolution in ferromagnetic materials. The model takes the polar and azimuthal angles (ϑ1,ϑ2), instead of the magnetization unit vector m(m1,m2,m3), as the order parameters. In this way, the constraint on the magnetization magnitude can be exactly satisfied automatically, and no special numerical treatment on the phase field evolution is needed. The phase field model is developed from a thermodynamic framework which involves a configurational force system for ϑ1 and ϑ2. A combination of the configurational force balance and the second law of thermodynamics leads to thermodynamically consistent constitutive relations and a generalized evolution equation for the order parameters (ϑ1,ϑ2). Beneficial from the constraint-free model, the three-dimensional finite-element implementation is straightforward, and the degrees of freedom are reduced by one. The model is shown to be capable of reproducing the damping-dependent switching dynamics, and the formation and evolution of domains and vortices in ferromagnetic materials under the external magnetic or mechanical loading. Particularly, the calculated out-of-plane component of magnetization in a vortex is verified by the corresponding experimental results, as well as the motion of the vortex under a magnetic field. |

Journal or Publication Title: | Proceedings of Royal Society A-Mathematical Physical and Engineering Sciences |

Volume: | 470 |

Number: | 2171 |

Publisher: | The Royal Society Publishing |

Uncontrolled Keywords: | phase field model, ferromagnetic materials, domain evolution, vortex, constraint, coupled problems |

Divisions: | 11 Department of Materials and Earth Sciences 11 Department of Materials and Earth Sciences > Material Science 11 Department of Materials and Earth Sciences > Material Science > Mechanics of functional Materials Zentrale Einrichtungen Exzellenzinitiative Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE) Exzellenzinitiative > Graduate Schools |

Date Deposited: | 23 Oct 2014 12:21 |

Identification Number: | doi:10.1098/rspa.2014.0517 |

Funders: | The support from the LOEWE research cluster RESPONSE (Hessen, Germany), the China Scholarship Council and the Innovation Foundation of BUAA for PhD Graduates (YWF-14-YJSY-052) is acknowledged. |

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