  We study a ferromagnetic suspension or a suspension of magnetic nanoparticles
in an anisotropic nematic medium, in three different one-dimensional
variational settings, ordered in terms of increasing complexity. The three
models are featured by a nematic energy, a magnetic energy and a
magneto-nematic coupling energy and the experimentally observed patterns are
modelled as local or global energy minimizers. We numerically observe
polydomains with distinct states of magnetization for weak to moderate
magneto-nematic coupling in our models. We demonstrate that these polydomains
are stabilised by lowering the temperature (as in Mertelj et al., 2013) and
that the polydomain structures lose stability as the magneto-nematic coupling
increases. Some exact solutions for prototypical situations are also obtained.
