Freedericksz transition in Ferronematic Liquid Crystal under weak anchoring conditions

Freedericksz effect is investigated theoretically for a ferronematic liquid crystal, which is a colloidal suspension of ferromagnetic nanoparticles in a nematic fluid. Considering a splay type Freedericksz geometry, weak anchoring conditions are assumed at the cell boundaries. The specific nature of this anchoring reveals a rich variety of stable ferronematic phases, which include uniform, distorted and saturated states. Apart from weak anchoring conditions at the cell boundaries, soft planar anchoring is assumed for the mesogenic molecules at the surface of a nanoparticle. The interplay between these two anchoring phenomena along with Frank type elastic theory determine the values of Freedericksz threshold between various ferronematic states. It is found that compared to relatively strong anchoring for the mesogens both at the cell boundaries and at the surface of the nanoparticles, weak anchoring significantly reduces the Freedericksz threshold field. Landau theory is then utilized to understand the nature of transition between different ferronematic states. Based on the phenomenon of segregation effect, these transitions are found to be either first order or second order in nature. The present theory is also extended to non-ferromagnetic nanoparticles and significant reduction in Freedericksz threshold is obtained. Finally, these results are corroborated with experimental findings.