  The isotropic to ferroelectric nematic liquid transition had been
theoretically studied over one hundred years ago, but its experimental studies
are rare. Here we present polarizing optical microscopy studies and theoretical
considerations of ferroelectric nematic liquid crystal droplets coexisting with
the isotropic melt. We find that the droplets have flat pancake-like shapes
that are thinner than the sample thickness as long as there is a room to
increase the lateral droplet size. In the center of the droplets a wing shaped
defect with low birefringence is present that moves perpendicular to a weak
in-plane electric field, and then extends and splits in two at higher fields.
Parallel to the defect motion and extension, the entire droplet drifts along
the electric field with speed that is independent of the size of the droplet
and is proportional to the amplitude of the electric field. After the field is
increased above 1V/mm the entire droplet gets deformed and oscillates with the
field. These observations led us to determine the polarization field and
revealed the presence of a pair of positive and negative bound electric charge
due to divergences of polarization around the defect volume.
