Magnetic Nanoparticles in a Nematic Channel: A One-Dimensional Study

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.