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The electronic and structural properties of Li$B$O$_3$ ($B$=V, Nb, Ta, Os)are investigated via first-principles methods. We show that Li$B$O$_3$ belongto the recently proposed hyperferroelectrics, i.e., they all have unstablelongitudinal optic phonon modes. Especially, the ferroelectric-like instabilityin the metal LiOsO$_3$, whose optical dielectric constant goes to infinity, isa limiting case of hyperferroelectrics. Via an effective Hamiltonian, wefurther show that, in contrast to normal proper ferroelectricity, in which theferroelectric instability usually comes from long-range coulomb interactions,the hyperferroelectric instability is due to the structure instability drivenby short-range interactions. This could happen in systems with large ion sizemismatches, which therefore provides a useful guidance in searching for novelhyperferroelectrics.

The origin of hyperferroelectricity in Li$B$O$_3$ ($B$=V, Nb, Ta, Os)