Comparative study of exchange-correlation functionals for accurate predictions of structural and magnetic properties of multiferroic oxides

We systematically compare predictions of various exchange correlation functionals for the structural and magnetic properties of perovskite ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Ba}}_x{\mathrm{MnO}}₃ (0\ensuremath{\le}x\ensuremath{\le}1)$---a representative class of multiferroic oxides. The local spin density approximation (LSDA) and spin-dependent generalized gradient approximation with Perdew-Burke-Ernzerhof parametrization (sPBE) make substantial different predictions for ferroelectric atomic distortions, tetragonality, and ground state magnetic ordering. Neither approximation quantitatively reproduces all the measured structural and magnetic properties of perovskite ${\mathrm{Sr}}_0.5{\mathrm{Ba}}_0.5{\mathrm{MnO}}₃$. The spin-dependent generalized gradient approximation with Perdew-Burke-Ernzerhof revised for solids parametrization (sPBEsol) and the charge-only Perdew-Burke-Ernzerhof parametrized generalized gradient approximation with Hubbard $U$ and Hund's $J$ extensions both provide overall better agreement with measured structural and magnetic properties of ${\mathrm{Sr}}_0.5{\mathrm{Ba}}_0.5{\mathrm{MnO}}₃$, compared to LSDA and sPBE. Using these two methods, we find that different from previous predictions, perovskite ${\mathrm{BaMnO}}₃$ has large Mn off-center displacements and is close to a ferromagnetic-to-antiferromagnetic phase boundary, making it a promising candidate to induce effective giant magnetoelectric effects and to achieve cross-field control of polarization and magnetism.