Controlling topological textures of umbilics using spatiotemporal magnetic fields

The generation, evolution and manipulation of topological defects in thin films of liquid crystals is a long-standing subject of study in the soft matter sciences, but one that is still relevant today. Here we report control over the generation of textures of umbilic defects in electrically biased nematic liquid crystals using a spatiotemporally structured magnetic field. This is exemplified by exploiting the symmetries of the magnetic field generated by an array of four permanent magnets for the reconfigurable generation of textures with central umbilics with topological charge ±1. The experimental observations are qualitatively supported by evaluating the orientational response of the liquid crystal to the magnetic torque density from the exact determination of the 3D magnetic field. Furthermore, we derive a 2D amplitude equation from the Frank-Oseen free energy, which allows the quantitative description and prediction of the morphogenesis of different liquid crystal topological textures. This spatiotemporal approach shows how symmetry-guided field-orientation coupling enables deterministic control of topological defects, offering new routes for structuring anisotropic soft materials.