  We theoretically study the stability conditions of the ferroelectric ice of
the Cmc21 structure, which has been considered, for decades, one of the most
promising candidates of the low temperature proton-ordered phase of pure ice
Ih. It turned out that the Cmc21 structure is stable only with a certain amount
of dopant and the true proton-ordered phase of pure ice Ih remains to be found
at lower temperature. Implication for spin ice is mentioned.
