Ferronematics in confined geometries

The recently discovered ferronematic liquid crystal phase is characterized by a local polarization vector; this is in contrast to the widely-studied nematic phase which possesses local cylindrical symmetry. In confined geometries, ferronematics have been shown to adopt multiple possible configurations as a function of temperature. In a thin circular disk, for example, Zou et al. recently demonstrated experimentally that a transition occurs from a from CV-type to L-type configuration (Soft Matter, 2024, 20, 3392)]. Predicting the configuration of a ferronematic numerically, however, is challenging and requires simulation of both the local order and the electric field. Here, we construct a finite element model of the ferronematic phase using an energy minimization approach and identify the space of possible solutions in some simple experimentally relevant geometries. Insights into the particular challenges that this phase provides for numerics will also be discussed.