Speaker
Description
We study minimizers $m∶ \mathbb{R}^2→\mathbb{S}^2$ of the energy functional
$$E_{\sigma} (m)= \int_{\mathbb{R}^2} (\frac{1}{2} |\nabla m|^2 + \sigma^2 m.\nabla \times m + \sigma^2 m_3^2 )dx,$$
for $0<\sigma\ll 1$, with prescribed topological degree
$$Q(m)=\frac{1}{4\pi}\int_{\mathbb{R}^2} (m.\partial_1 m\times \partial_2 m ) dx=\pm1.$$
This model arises in thin ferromagnetic films with Dzyaloshinskii-Moriya interaction and easy-plane anisotropy, where these minimizers represent bimeron configurations. We prove their existence, and describe them precisely as perturbations of specific Möbius maps: we establish in particular that they are localized at scale of order $\frac{1}{|\ln \sigma^2 |}$. This is a joint work with Radu Ignat and Xavier Lamy.
