  Ferroelectric ordering in liquids is a fundamental question of physics. Here,
we show that ferroelectric ordering of the molecules causes formation of
recently reported splay nematic liquid-crystalline phase. As shown by
dielectric spectroscopy, the transition between the uniaxial and the splay
nematic phase has the characteristics of a ferroelectric phase transition,
which drives an orientational ferroelastic transition via flexoelectric
coupling. The polarity of the splay phase was proven by second harmonic
generation (SHG) imaging, which additionally allowed for determination of the
splay modulation period to be of the order of 5 - 10 microns, also confirmed by
polarized optical microscopy. The observations can be quantitatively described
by a Landau-de Gennes type of macroscopic theory.
