Density functional study of ferromagnetic ferroelectric LaMnO$_{3}$/BaTiO$_{3}$ superlattice

Using the GGA + $U$ density functional, we have calculated the lattice constants, atomic positions, magnetization, and ferroelectric polarization of a (LaMnO$_{3})_{4.5}$(BaTiO$_{3})_{4.5}$ superlattice containing five LaO and TiO$_{2}$ planes and four MnO$_{2}$ and BaO planes. Although LaMnO$_{3}$ is antiferromagnetic, it is ferromagnetic in the superlattice. An approximation to the ferroelectric polarization, obtained from a comparison of superlattice and bulk crystal atomic displacements and unit cell volumes, is found to agree reasonably well with the polarization obtained from a Berry phase calculation. The electric polarization points along the longer in-plane lattice vector, while the atomic spins, after the spin-orbit interaction and spin noncollinearity are included, all point in directions close to that lattice vector.