Calculus of Variations and Geometric Measure Theory

G. Canevari - A. Majumdar - B. Stroffolini - Y. Wang

Two-dimensional Ferronematics, Canonical Harmonic Maps and Minimal Connections

created by paolini on 03 Aug 2022
modified by stroffolini on 26 Sep 2023


Accepted Paper

Inserted: 3 aug 2022
Last Updated: 26 sep 2023

Journal: Archive for Rational Mechanics and Analysis
Year: 2023

ArXiv: 2208.01586 PDF


We study a variational model for ferronematics in two-dimensional domains, in the "super-dilute" regime. The free energy functional consists of a reduced Landau-de Gennes energy for the nematic order parameter, a Ginzburg-Landau type energy for the spontaneous magnetisation, and a coupling term that favours the co-alignment of the nematic director and the magnetisation. In a suitable asymptotic regime, we prove that the nematic order parameter converges to a canonical harmonic map with non-orientable point defects, while the magnetisation converges to a singular vector field, with line defects that connect the non-orientable point defects in pairs, along a minimal connection.