Néel walls with prescribed winding number and how a nonlocal term can change the energy landscape

Radu Ignat; Roger Moser

doi:10.1016/j.jde.2017.07.006

Néel walls with prescribed winding number and how a nonlocal term can change the energy landscape

Radu Ignat
, Roger Moser

Department of Mathematical Sciences

Université Toulouse III - Paul Sabatier

Research output: Contribution to journal › Article › peer-review

8 Citations (SciVal)

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Abstract

We study a nonlocal Allen-Cahn type problem for vector fields of unit length, arising from a model for domain walls (called Néel walls) in ferromagnetism. We show that the nonlocal term gives rise to new features in the energy landscape; in particular, we prove existence of energy minimisers with prescribed winding number that would be prohibited in a local model.

Original language	English
Pages (from-to)	5846-5901
Journal	Journal of Differential Equations
Volume	263
Issue number	9
Early online date	24 Jul 2017
DOIs	https://doi.org/10.1016/j.jde.2017.07.006
Publication status	Published - 5 Nov 2017

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10.1016/j.jde.2017.07.006

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Cite this

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abstract = "We study a nonlocal Allen-Cahn type problem for vector fields of unit length, arising from a model for domain walls (called N{\'e}el walls) in ferromagnetism. We show that the nonlocal term gives rise to new features in the energy landscape; in particular, we prove existence of energy minimisers with prescribed winding number that would be prohibited in a local model.",

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AB - We study a nonlocal Allen-Cahn type problem for vector fields of unit length, arising from a model for domain walls (called Néel walls) in ferromagnetism. We show that the nonlocal term gives rise to new features in the energy landscape; in particular, we prove existence of energy minimisers with prescribed winding number that would be prohibited in a local model.

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

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Néel walls with prescribed winding number and how a nonlocal term can change the energy landscape

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Roger Moser

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Néel walls with prescribed winding number and how a nonlocal term can change the energy landscape

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