Phase transition solutions in geometrically constrained magnetic domain wall models

Shouxin Chen, Yisong Yang

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Article number065912JMP
JournalJournal of Mathematical Physics
Issue number2
StatePublished - Feb 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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