DFT investigation of weak ferromagnetic and antiferroelectric properties of tetragonal BiCrO$_{3}$

The magnetic and ferroelectric properties of a very thick tetragonal BiCrO$_{3}$ film are studied using density functional theory. The experimental lattice constants were used but the atomic positions within the unit cell had to be calculated. This resulted in a centrosymmetric Pnma ground state, in agreement with the experimental antiferroelectric result. The magnetization is G type antiferromagnetic with a spin-orbit induced canting that is larger than the experimental value. A simple model of the local electric polarization of the Bi and their twelve surrounding oxygens is consistent with the experimental polarization induced by a large electric field. A comparison with experimental and calculated bulk BiCrO$_{3}$ in the C2/c structure will be given.