  Ferroelectric nematic (NF) liquid crystals are an intriguing polar system for
exploring topological defects, and their properties are subject to significant
influence by ionic doping. A prior theory based on a modified XY model predicts
that string defects with half-integer vortex-antivortex pairs can be excited,
while such stable string defects have not been directly observed in polar
materials. Here, we report that doping the ferroelectric nematic material RM734
with cationic polymers can facilitate the formation of abundant string defects
with butterfly textures. The string defects exhibit a polarization field
restricted to 2D plane that is divided by N\'eel type domain walls into domains
with either uniform polarization or negative splay deformation in the butterfly
wing areas (positive bound charges). We establish a charge double layer model
for the string defects: the strings of cationic polymer chains and close
packing RM734 molecules form the Stern charge layer, and the small anionic ions
and the positive bound charges (due to splay deformation) form the charge
diffusion layer. We demonstrate that only cationic polymeric doping is
effective due to the coupling between the flexoelectricity and the pear shape
of the RM734 molecules. We estimate the line charge density of the strings via
measuring the divergence of the polarization and the electrophoretic motion
mobility, and obtain good qualitative agreement. We further show that the
field-driven polarization reversal undergoes either string rotation or
generating and merging with kink walls.
