# Energy minimisers of prescribed winding number in an $\mathbb{S}^1$-valued nonlocal Allen-Cahn type model

@article{Ignat2018EnergyMO, title={Energy minimisers of prescribed winding number in an \$\mathbb\{S\}^1\$-valued nonlocal Allen-Cahn type model}, author={Radu Mihai Ignat and Roger Moser}, journal={arXiv: Analysis of PDEs}, year={2018} }

We study a variational model for transition layers in thin ferromagnetic films with an underlying functional that combines an Allen-Cahn type structure with an additional nonlocal interaction term. The model represents the magnetisation by a map from $\mathbb{R}$ to $\mathbb{S}^1$. Thus it has a topological invariant in the form of a winding number, and we study minimisers subject to a prescribed winding number. As shown in our previous paper Ignat-Moser (JDE 2017), the nonlocal term gives rise…

## References

SHOWING 1-10 OF 24 REFERENCES

### Interaction Energy of Domain Walls in a Nonlocal Ginzburg–Landau Type Model from Micromagnetics

- Physics
- 2015

We study a variational model from micromagnetics involving a nonlocal Ginzburg–Landau type energy for $${{\mathbb S}^{1}}$$S1-valued vector fields. These vector fields form domain walls, called Néel…

### On a Fractional Ginzburg–Landau Equation and 1/2-Harmonic Maps into Spheres

- Mathematics
- 2015

This paper is devoted to the asymptotic analysis of a fractional version of the Ginzburg–Landau equation in bounded domains, where the Laplacian is replaced by an integro-differential operator…

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

- Mathematics
- 2016

### A thin-film limit in the Landau–Lifshitz–Gilbert equation relevant for the formation of Néel walls

- Mathematics
- 2014

We consider an asymptotic regime for two-dimensional ferromagnetic films that is consistent with the formation of transition layers, called Néel walls. We first establish compactness of…

### Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps

- Mathematics
- 2010

### The Logarithmic Tail of Néel Walls

- Mathematics
- 2003

We study the multiscale problem of a parametrized planar 180° rotation of magnetization states in a thin ferromagnetic film. In an appropriate scaling and when the film thickness is comparable to the…

### Logarithmic lower bounds for Néel walls

- Mathematics
- 2004

Abstract.Most mathematical models for interfaces and transition layers in materials science exhibit sharply localized and rapidly decaying transition profiles. We show that this behavior can largely…

### Another Thin-Film Limit of Micromagnetics

- Mathematics
- 2005

Abstract.We consider the variational problem of micromagnetics for soft, relatively small thin films with no applied magnetic field. In terms of the film thickness t, the diameter l and the magnetic…

### Vortex energy and 360° Néel walls in thin‐film micromagnetics

- Physics
- 2010

We study the vortex pattern in ultrathin ferromagnetic films of circular crosssection. The model is based on the following energy functional: $$E_\varepsilon ^{2d} (m) = \varepsilon \int\limits_{B^2…