From a superconductor NdNiO$_2$ to a Mott multiferroic BiNiO$_2$

Motivated by the recently discovered superconductivity in Sr-doped nickelate oxides NdNiO$_2$, we predict a material BiNiO$_2$ that provides an opportunity to study the intertwined ferroelectricity, metallicity, and magnetism in a crystal with very simple atomic structures. There is a ferroelectric structural transition from the nonpolar phase with the P4/mmm space group to the polar phase with the P4mm space group, which is driven by the lone pair on Bi. Calculations based on the Heyd-Scuseria-Ernzerhof hybrid density functional reveal that both the nonmagnetic and ferromagnetic states are metallic for nonpolar and polar phases, while the lowest energy ground-state for polar BiNiO$_2$ is a Hubbard Mott insulator with the G-type antiferromagnetic spin configurations. As a ferroelectric material with an electric polarization of 0.49 C/m2, it may be possible to control the magnetic order in BiNiO$_2$ by an applied electric field. The replacement of Nd by Bi serves as a connecting link between a high-temperature superconductor and a Mott multiferroic. Our work supports a route towards strongly correlated ferroelectrics.