Ferroelectric properties of RbNbO$_3$ and RbTaO$_3$

Phonon spectra of cubic rubidium niobate and rubidium tantalate with the perovskite structure are calculated from first principles within the density functional theory. Based on the analysis of unstable modes in phonon spectra, symmetries of possible distorted phases are determined, their energies are calculated, and it is shown that R3m is the ground-state structure of RbNbO$_3$. In RbTaO$_3$, the ferroelectric instability is suppressed by zero-point lattice vibrations. For ferroelectric phases of RbNbO$_3$, spontaneous polarization, piezoelectric, nonlinear optical, electro-optical, and other properties as well as the energy band gap in the LDA and GW approximations are calculated. The properties of rhombohedral RbNbO$_3$ are compared with those of rhombohedral KNbO$_3$, LiNbO$_3$, and BaTiO$_3$.