N\'eel walls with prescribed winding number and how a nonlocal term can change the energy landscape

Radu Ignat (1) , Roger Moser

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We study a nonlocal Allen-Cahn type problem for vector fields of unit length, arising from a model for domain walls (called N\'eel 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.

Domaines: Equations aux dérivées partielles [math.AP]

Radu Ignat, Roger Moser. N\'eel walls with prescribed winding number and how a nonlocal term can change the energy landscape. Journal of Differential Equations, 2017, ⟨10.1016/j.jde.2017.07.006⟩. ⟨hal-01673401⟩