First-principles study on the electric control of ferromagnetic behaviour of two-dimensional BaTiO 3 (0 0 1) ultrathin film doped with Cr

The electric control of a two-dimensional BaTiO 3 (0 0 1) ultrathin film doped with Cr was studied using the first-principles approach. The findings demonstrate that electric polarization influences the total magnetic moment when Cr substitutes Ba, but is irrelevant on Ti-replacement as no electric polarization is formed in the doped unit cell. The corresponding partial magnetic moment decreases when the partial electric polarization increases under uniaxial compressive strain applied in the [1 0 0] direction; otherwise, it remains unchanged excluding that caused by charge transfer. Furthermore, the coupling efficiency suggests a strong interaction between ferroic orders that can be adjusted by the applied uniaxial compressive strains. This indicates that the electric and magnetic field conversion can be induced in two-dimensional BaTiO 3 (0 0 1) ultrathin films with the aid of Cr-substituting Ba, which was confirmed through applying an electric field in the [0 0 1] direction.