Well-ordered reconstruction solutions of ferromagnetic nematic liquid crystals in two-dimensional square wells

The square wells filled with nematic liquid crystals are known to possess the well-ordered reconstruction solutions for wells of size below a threshold value which is typical of sub-micron scale. These solutions are uniquely stable nematic solutions which are characterized by defect lines along the diagonal intersecting at the centre of the square domain. In this paper, we consider a square well system filled with a stable suspension of magnetic nanoparticles in nematic liquid crystals, which is referred to as the ferromagnetic nematic liquid crystals in literature. We investigate the effect of magnetic nano-inclusion on well ordered reconstruction solution of nematic-filled square wells. We numerically compute the stable nematic and magnetization profiles in the Landau-de Gennes framework and obtain spatial inhomogeneities in the profiles as a result of the interplay of material frustration due to confinement and the ferronematic coupling between the nematic medium and magnetic nanoparticles. Our most significant results pertain to the deviation of the nematic patterns from the well ordered solutions domain for large ferronematic coupling and the tailoring of the size of the defect core in the magnetization profiles with the interplay of model parameters.