Microscopic Origin of Large Negative Magnetoelectric Coupling in ${\mathrm{Sr}}_{1/2}{\mathrm{Ba}}_{1/2}{\mathrm{MnO}}_3$

With a combined ab initio density functional and model Hamiltonian approach we establish that in the recently discovered multiferroic phase of the manganite ${\mathrm{Sr}}_{1/2}{\mathrm{Ba}}_{1/2}{\mathrm{MnO}}_3$ the polar distortion of Mn and O ions is stabilized via enhanced in-plane Mn-O hybridizations. The magnetic superexchange interaction is very sensitive to the polar bond-bending distortion, and we find that this dependence directly causes a strong magnetoelectric coupling. This novel mechanism for multiferroicity is consistent with the experimentally observed reduced ferroelectric polarization upon the onset of magnetic ordering.

Figure 1

(Color online) Schematic view of a SBMO unit cell and displacements of Mn and O sites in AFM magnetic structure. Arrows indicate the relative atomic ferroelectric displacements.

Figure 2

(Color online) (a), (b) Variation of the O-Mn-O angle $\alpha$ and spontaneous polarization $P$, $P_{\mathrm{ele}}$, $P_{\mathrm{ionic}}$ with the ratio $c/a$ for $U=3.0$ and 4.5 eV, respectively.

Figure 3

(Color online) (a) Schematic view of noncollinear magnetic structures having Mn spins with angle $\theta =0^o$, 45°, 90°; (b) Variation of the O-Mn-O angle $\alpha$ and spontaneous polarization $P$ with the ratio $c/a$ for different values of $\theta$ at $U=3.0\mathrm{eV}$ and $J_H=1.0\mathrm{eV}$.

Figure 4

(Color online) (a) $u_{\min }$ as a function of $J_H$ for paramagnetic and antiferromagnetic spin configurations for $g=0$ and $g=1.4$ . The AFM state leads to a reduction in FE distortion. (b) Phase diagram in $\Delta \mathrm{\text{−}}{J}_H$ phase space showing the regions of FE stability.