Multiferroicity and orbital ordering in ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$ from first principles

Advanced first-principles calculations uncover the emergence of multiferroicity in antiferromagnetic ${\text{Pr}}_{0.5}{\text{Ca}}_{0.5}{\text{MnO}}_3$ upon structural transition to a low-symmetry electrically polarized structure, found to be the ground state according to total energy. The electric polarization is not axial but lies in the basal plane. It is due to the combination of magnetic ordering with two byproducts of the oxygen-rotation-driven structural transformation: a polar ferroelectric mode in the chain-parallel direction and a change in orbital ordering orthogonally to the chains.

Figure 1

(Color online) Magnetization density isosurfaces (top view) of $p\text{−}d$ states within 2 eV below $E_F$ (i.e. the $e_g$’s and the corresponding hybridized ${\text{O}}_p$) for $Pbnm$ [(A) and (B)] and $P{2}_{1}nm$ (C). Dark (red) and light (green) surfaces represent up-polarized and down-polarized charges. Differently ordered Mn and O atoms are also indicated (see text). Mn-Mn distances are in $\text{Å}$. The $\left(a,b\right)$ plane of the $2\sqrt{2}\times 2\sqrt{2}\times 2$ unit cell is $45°$ rotated with respect to the $\left(x,y\right)$ reference system of the perovskite cubic cell. Arrows on O’s in panel B indicate displacements upon $Pbnm\text{−}P{2}_{1}nm$ transition (not to scale). Notice that, despite the equal sign of magnetization isosurfaces, the O magnetic moments are oriented in the direction opposite to that of intrachain Mn; also, the O magnetization has $p$-type character, though it appears roughly spherical on this zoomed-out scale.

Figure 2

(Color online) Orbital-resolved density of states for $Pbnm$ (left) and $P{2}_{1}nm$ (right) structures. For Mn light-shaded (gray) line is for $t_{2g}$ orbitals, dark-shaded (blue), and solid (red) lines for $x^2-y^2$ and $z^2$ orbitals, respectively. For O’s, dark-shaded (blue) and solid (red) lines are for ligand and orthogonal $p$ orbitals, respectively. Up and down arrows indicate majority and minority states. Atoms are labeled according to Fig. 1.