Electric polarization of ${\mathrm{Sr}}_{0.5}{\mathrm{Ba}}_{0.5}{\mathrm{MnO}}_3$: A multiferroic Mott insulator

Ab initio calculations of the electric polarization of correlation-driven insulating materials, namely, Mott insulators, are lacking. Using a combination of density-functional theory and dynamical mean-field theory we study the electric polarization of the Mott insulator ${\mathrm{Sr}}_{0.5}{\mathrm{Ba}}_{0.5}{\mathrm{MnO}}_3$. We predict a ferroelectric polarization of $\simeq 16.5\mu \text{C}/{\text{cm}}^2$ in the high-temperature paramagnetic phase and recover a measured value of $\simeq 13.3\mu \text{C}/{\text{cm}}^2$ in the low-temperature antiferromagnetic phase. Our calculations reveal that the driving force for the ferroelectricity, the hybridization between Mn $e_g$ and O p orbitals, is suppressed by correlations, in particular, by the Hund's coupling and by the onset of magnetic order. They also confirm that the half-filled Mn $t_{2g}$ orbitals give rise to the antiferromagnetic Mott phase. This magnetic ordering leads to changes in the ionic polar displacement and, in turn, to the electronic polarization. In addition, for a fixed ionic displacement, we find that there is a reduction in the electronic contribution due to partial magnetic polarization of the Mn ${\mathrm{e}}_g$ orbitals. The reduction of the polarization due to ionic displacement dominates over the additional electronic part, hence the net magnetoelectric coupling is negative.

Figure 1

The total and orbitally resolved LDA paramagnetic DOS. Insets: Predicted LDA + DMFT(PM) DOS and spin-resolved LDA + DMFT(AF) DOS and imaginary part of the electron self-energy as a function of Matsubara frequency. The analytical continuation for the LDA + DMFT method has been performed with the maximum entropy method as implemented in Ref. [19].

Figure 2

Total (top) and electronic (bottom) electric polarization in the $z$ direction as a function of inversion-symmetry-breaking distortion $\xi$ calculated for the PM phase for two values of $J$ in the high-temperature (HT) structure (a) and for the AF phase in the low-temperature (LT) structure (b). (b) also shows the electric polarization in PM phase of the LT structure. $\xi =1$ denotes the experimental structure.