The potentially multiferroic Aurivillius phase Bi$_5$FeTi$_3$O$_{15}$: cation site preference, electric polarization, and magnetic coupling from first principles

We study the structural, ferroelectric, and magnetic properties of the potentially multiferroic Aurivillius phase material Bi$_5$FeTi$_3$O$_{15}$ using first principles electronic structure calculations. Calculations are performed both with PBE and PBEsol exchange correlation functionals. We conclude that PBE systematically overestimates the lattice constants and the magnitude of the ferroelectric distortion, whereas PBEsol leads to good agreement with available experimental data. We then assess a potential site preference of the Fe$^{3+}$ cation by comparing 10 different distributions of the perovskite $B$-sites. We find a slight preference for the "inner" site, consistent with recent experimental observations. We obtain a large value of $\sim$55 $\mu$C/cm$^2$ for the spontaneous electric polarization, which is rather independent of the specific Fe distribution. Finally, we calculate the strength of the magnetic coupling constants and find strong antiferromagnetic coupling between Fe$^{3+}$ cations in nearest neighbor positions, whereas the coupling between further neighbors is rather weak. This poses the question whether magnetic long range order can occur in this system in spite of the low concentration of magnetic ions.