Magnetic-field-controlled topological charge switching of umbilics in nematics

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, particularly in the context of optics and photonics. Here we report the trapping of umbilical defects in electrically biased nematic liquid crystals using spatiotemporally structured magnetic fields. By exploiting the symmetries of bespoke inhomogeneous magnetic fields, we demonstrate the reconfigurable generation and manipulation of umbilics with topological charge ±1, which points to application potential for spectrally adaptive vortex coronagraphy. 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 topological textures.