  In solids, charge polarity can one-to-one correspond to spin polarity
phenomenologically, e.g. ferroelectricity/ferromagnetism,
antiferroelectricity/antiferromagnetism, and even
dipole-vortex/magnetic-vortex, but ferrielectricity/ferrimagnetism kept telling
a disparate story in microscopic level. Since the definition of a charge dipole
involves more than one ion, there may be multiple choices for a dipole unit,
which makes most ferrielectric orders equivalent to ferroelectric ones, i.e.
this ferrielectricity is not necessary to be a real independent branch of
polarity. In this work, by using the spherical aberration-corrected scanning
transmission electron microscope, we visualize a nontrivial ferrielectric
structural evolution in BaFe2Se3, in which the development of two polar
sub-lattices is out-of-sync, for which we term it as irreducible
ferrielectricity. Such irreducible ferrielectricity leads to a non-monotonic
behavior for the temperature-dependent polarization, and even a compensation
point in the ordered state. Our finding unambiguously distinguishes
ferrielectrics from ferroelectrics in solids.
