  Since conduction electrons of a metal screen effectively the local electric
dipole moments, it was widely believed that the ferroelectric-like distortion
cannot occur in metals. Recently, metallic LiOsO3, was discovered to be the
first clear-cut example of an Anderson-Blount "ferroelectric" metal, which at
140 K undergoes a ferroelectric-like structural transition similar to
insulating LiNbO3. This is very surprising because the mechanisms for
structural phase transitions are usually quite distinct in metals and
insulators. Through performing first principles calculations, here we reveal
that the local polar distortion in LiOsO3 is solely due to the instability of
the A-site Li atom, in contrast to the LiNbO3 case where the second order
Jahn-Teller effect of the B-site Nb ion also plays an additional role. More
importantly, the "ferroelectric"-like long range order of the local polar
distortion is found to be due to the predominantly ferroelectric short-range
pair interactions between the local polar modes which are not screened by
conduction electrons. Furthermore, we predict that LiNbO3-type MgReO3 is also a
"ferroelectric" metal, but with a much higher structural transition temperature
by 391 K than LiOsO3. Our work not only unravels the origin of FE-like
distortion in LiNbO3-type "ferroelectric" metals, but also provides clue for
designing other multi-functional "ferroelectric" metals.
