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We investigate solution landscapes for ferronematics i.e., a dilutesuspension of magnetic nano-particles in a nematic liquid crystal host, in areduced one-dimensional setting relevant for microfluidic problems. Solutionlandscapes show how critical points of an energy functional connect to oneanother on the energy landscape, hence revealing potential mechanism by whichmultistable systems may switch between different stable states. By varyingmodel parameters, we show that increasing domain size and increasingnemato-magnetic coupling have the same impact on the solution landscape, inthat both result in new emergent solutions. Hence, this presents multipleavenues for experimental realisation of multistable ferronematic systems withdesired properties. We also show the prevalence, and therefore importance, offerronematic polydomains, which present themselves as what we call orderreconstruction (OR) solutions. These ferronematic OR solutions possess a greatdeal 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 solutionlandscapes considered.

Solution landscapes of ferronematics in microfluidic channels