Two-dimensional ferronematics, canonical harmonic maps and minimal connections

Canevari, Giacomo and Majumdar, Apala and Stroffolini, Bianca and Wang, Yiwei (2023) Two-dimensional ferronematics, canonical harmonic maps and minimal connections. Archive for Rational Mechanics and Analysis, 247. 110. ISSN 1432-0673 (https://doi.org/10.1007/s00205-023-01937-x)

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Abstract

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.

ORCID iDs

Canevari, Giacomo, Majumdar, Apala ORCID logoORCID: https://orcid.org/0000-0003-4802-6720, Stroffolini, Bianca and Wang, Yiwei;