  We show the first-principles evidence of a hitherto unreported type of
ferroelectricity with ultra-long ion-displacement in sodium and potassium
hydroxides. Even a small amount of proton vacancies can completely change the
mode of proton-transfer from intra-unitcell to trans-unitcell, giving rise to
multiferroic soliton with mobile magnetism and a tremendous polarization that
can be orders of magnitude higher compared with most perovskite ferroelectrics.
Their vertical polarizations of thin-film are robust against depolarizing
field, rendering various designs of 2D ferroelectric field-transistors with
non-destructive readout and ultra-high on/off ratio via sensing the switchable
metallic/insulating state.
