### Abstract

Recent work on magnetic phase transition in nanoscale systems indicates that new physical phenomena, in particular, the Bloch wall width narrowing, arise as a consequence of geometrical confinement of magnetization and leads to the introduction of geometrically constrained domain wall models. In this paper, we present a systematic mathematical analysis on the existence of the solutions of the basic governing equations in such domain wall models. We show that, when the cross section of the geometric constriction is a simple step function, the solutions may be obtained by minimizing the domain wall energy over the constriction and solving the Bogomol'nyi equation outside the constriction. When the cross section and potential density are both even, we establish the existence of an odd domain wall solution realizing the phase transition process between two adjacent domain phases. When the cross section satisfies a certain integrability condition, we prove that a domain wall solution always exists which links two arbitrarily designated domain phases.

Original language | English (US) |
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Article number | 065912JMP |

Journal | Journal of Mathematical Physics |

Volume | 51 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2010 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*51*(2), [065912JMP]. https://doi.org/10.1063/1.3274388

**Phase transition solutions in geometrically constrained magnetic domain wall models.** / Chen, Shouxin; Yang, Yisong.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 51, no. 2, 065912JMP. https://doi.org/10.1063/1.3274388

}

TY - JOUR

T1 - Phase transition solutions in geometrically constrained magnetic domain wall models

AU - Chen, Shouxin

AU - Yang, Yisong

PY - 2010/2

Y1 - 2010/2

N2 - Recent work on magnetic phase transition in nanoscale systems indicates that new physical phenomena, in particular, the Bloch wall width narrowing, arise as a consequence of geometrical confinement of magnetization and leads to the introduction of geometrically constrained domain wall models. In this paper, we present a systematic mathematical analysis on the existence of the solutions of the basic governing equations in such domain wall models. We show that, when the cross section of the geometric constriction is a simple step function, the solutions may be obtained by minimizing the domain wall energy over the constriction and solving the Bogomol'nyi equation outside the constriction. When the cross section and potential density are both even, we establish the existence of an odd domain wall solution realizing the phase transition process between two adjacent domain phases. When the cross section satisfies a certain integrability condition, we prove that a domain wall solution always exists which links two arbitrarily designated domain phases.

AB - Recent work on magnetic phase transition in nanoscale systems indicates that new physical phenomena, in particular, the Bloch wall width narrowing, arise as a consequence of geometrical confinement of magnetization and leads to the introduction of geometrically constrained domain wall models. In this paper, we present a systematic mathematical analysis on the existence of the solutions of the basic governing equations in such domain wall models. We show that, when the cross section of the geometric constriction is a simple step function, the solutions may be obtained by minimizing the domain wall energy over the constriction and solving the Bogomol'nyi equation outside the constriction. When the cross section and potential density are both even, we establish the existence of an odd domain wall solution realizing the phase transition process between two adjacent domain phases. When the cross section satisfies a certain integrability condition, we prove that a domain wall solution always exists which links two arbitrarily designated domain phases.

UR - http://www.scopus.com/inward/record.url?scp=77952268550&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77952268550&partnerID=8YFLogxK

U2 - 10.1063/1.3274388

DO - 10.1063/1.3274388

M3 - Article

AN - SCOPUS:77952268550

VL - 51

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 2

M1 - 065912JMP

ER -