Using both the generalized gradient approximation (GGA) and $\mathrm{GGA}+U$ density functionals and including the spin-orbit interaction while allowing for noncollinear spin orientations, we have calculated many of the properties of the multiferroic ${\mathrm{Bi}}_2\mathrm{Ni}\mathrm{Mn}{\mathrm{O}}_6$. The GGA and $\mathrm{GGA}+U$ results are in unexpectedly close agreement; in particular, their lattice constants are in excellent agreement with the measured values. The calculated GGA and $\mathrm{GGA}+U$ magnetizations per formula unit are 4.92 and 4.99 ${\mu }_B$ and the calculated ferroelectric polarizations are 16.84 and $16.63\mu \mathrm{C}{\mathrm{cm}}^{-2}$. A discussion is given of the $C2$ space group of ${\mathrm{Bi}}_2\mathrm{Ni}\mathrm{Mn}{\mathrm{O}}_6$ and of the centrosymmetric $C2∕m$ space group from which it can be generated with small atomic displacements.

• Received 13 March 2007

DOI:https://doi.org/10.1103/PhysRevB.76.064412