  We investigate solution landscapes for ferronematics i.e., a dilute
suspension of magnetic nano-particles in a nematic liquid crystal host, in a
reduced one-dimensional setting relevant for microfluidic problems. Solution
landscapes show how critical points of an energy functional connect to one
another on the energy landscape, hence revealing potential mechanism by which
multistable systems may switch between different stable states. By varying
model parameters, we show that increasing domain size and increasing
nemato-magnetic coupling have the same impact on the solution landscape, in
that both result in new emergent solutions. Hence, this presents multiple
avenues for experimental realisation of multistable ferronematic systems with
desired properties. We also show the prevalence, and therefore importance, of
ferronematic polydomains, which present themselves as what we call order
reconstruction (OR) solutions. These ferronematic OR solutions possess a great
deal of complexity in terms of the location and multiplicity of domain walls,
and also play a key role in the connectivity of stable states for the solution
landscapes considered.
