We consider a variational model for ferronematics—composite materials formed by dispersing magnetic nanoparticles into a liquid crystal matrix. The model features two coupled order parameters: a Landau-de Gennes Q-tensor for the liquid crystal component and a magnetisation vector field M, both of them governed by a Ginzburg-Landau-type energy. The energy includes a singular coupling term favouring alignment between Q and M. We report on some recent results on the asymptotic behaviour of (not necessarily minimising) critical points as a small parameter $\eps$ tends to zero. Our main results show that the energy concentrates along distinct singular sets: the (rescaled) energy density for the Q-component concentrates, to leading order, on a finite number of singular points, while the energy density for the M-component concentrates along a one-dimensional rectifiable set. Moreover, we will see that the curvature of the singular set for the M-component (technically, the first variation of the associated varifold) is concentrated on a finite number of points, i.e. the singular set for the Q-component. Joint work with G. Canevari (University of Verona) and B. Stroffolini (University of Naples “Federico II”).