First principles study of the multiferroicsBiFeO3,Bi2

We present results of an ab initio density-functional theory study of three bismuth-based multiferroics, $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$, ${\mathrm{Bi}}_{2}\mathrm{Fe}\mathrm{Cr}{\mathrm{O}}_{6}$, and $\mathrm{Bi}\mathrm{Cr}{\mathrm{O}}_{3}$. We disuss differences in the crystal and electronic structure of the three systems and show that the application of the $\mathrm{LDA}+U$ method is essential to obtain realistic structural parameters for ${\mathrm{Bi}}_{2}\mathrm{Fe}\mathrm{Cr}{\mathrm{O}}_{6}$. We calculate the magnetic nearest-neighbor coupling constants for all three systems and show how Anderson's theory of superexchange can be applied to explain the signs and relative magnitudes of these coupling constants. From the coupling constants we then obtain a mean-field approximation for the magnetic ordering temperatures. Guided by our comparison of these three systems, we discuss the possibilities for designing a multiferroic material with large magnetization above room temperature.