  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.
