N\'eel walls with prescribed winding number and how a nonlocal term can   change the energy landscape
  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. 
Radu Ignat and Roger Moser
math.AP