Director Response of Liquid Crystals in Spatially Varying Magnetic Fields with Antagonistic Anchoring Conditions

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