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

Two-dimensional Ferronematics, Canonical Harmonic Maps and Minimal Connections