Director\nResponse of Liquid Crystals in Spatially\nVarying Magnetic Fields with Antagonistic Anchoring Conditions

In\nthe presence of a magnetic field, a liquid crystal (LC) director\ncan be distorted from a ground state set by a combination of LC elasticity\nand surface anchoring at any relevant interfaces. Uniform magnetic\nfields are often used to produce simple LC distortions on demand,\nbut producing more spatially complex distortions is practically challenging.\nWe develop a strategy for the spatially resolved control of the LC\ndirector by leveraging field patterns induced by ferromagnetic materials.\nPatterned magnetic fields are generated from high-permeability ferromagnetic\nmicrostructures embedded into nematic liquid crystals (NLCs) to manipulate\nthe LC director’s orientation. Each ferromagnetic microstructure\nproduces a unique spatially varying magnetic field. In turn, tuning\nmagnetic field strength in competition with NLC elasticity can pattern\na range of spatially complex director configurations. Simulations\nrelate the spatial variation induced in a magnetic field by a ferromagnetic\ngeometry and the resultant director. Our predictive models can inform\nthe inverse design of ferromagnetic microstructures to generate bespoke\ndirector patterns. We also link changes in the magnetic field to the\nmigration of elastically driven periodic extinctions in birefringence\nnear the edges of ferromagnetic structures.