  The past decade's discovery of topological excitations in nanoscale
ferroelectrics has turned the prevailing view that the polar ground state in
these materials is uniform. However, the systematic understanding of the
topological polar structures in ferroelectrics is still on track. Here we study
stable vortex-like textures of polarization in the nanocylinders of
ferroelectric PbTiO$_3$, arising due to the competition of the elastic and
electrostatic interactions. Using the phase-field numerical modeling and
analytical calculations, we show that the orientation of the vortex core with
respect to the cylinder axis is tuned by the geometrical parameters and
temperature of the system.
