Ferroelectricity driven by charge ordering in the A-site ordered perovskite manganite ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$

Phase transitions in charge and orbital degrees of freedom occur successively in the $A$-site ordered perovskite manganite ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$ at $T_{\mathrm{CO}1}\approx 370\mathrm{K}$ and $T_{\mathrm{CO}2}\approx 190\mathrm{K}$. To determine the $3d$ electronic state in each phase, we performed crystal structure analyses on a single-crystal sample at 150, 300, and 400 K using synchrotron x-ray diffraction. The results indicate that the charge and orbital ordering on the distorted and alternately tilted ${\mathrm{MnO}}_6$ octahedra should accompany electric polarization in each ${\mathrm{MnO}}_2$ layer. The stacking of the polarized ${\mathrm{MnO}}_2$ layers along the $c$ axis changes from a staggered configuration to a ferroic configuration at $T_{\mathrm{CO}2}$.

Figure 1

Crystal structure of ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$ (a) in the CD phase and (b) in the HT-COO phase; the COO stacking patterns are drawn schematically. (c) Two types of COO arrangements in the $ab$ plane. (d) Crystal structure of ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$ in the LT-COO phase.

Figure 2

(a) Representative examples of x-ray oscillation photographs observed at 400 K (CD), 300 K (HT-COO), and 150 K (LT-COO). All reflections are indexed by using a $\surd 2a_{\mathrm{p}}\times \surd 2a_{\mathrm{p}}\times c_{\mathrm{p}}$ unit cell. Dashed and solid arrows denote superlattice reflections with propagation vectors (1/2 0 0) and (1/2 0 1/2), respectively. Insets show the profiles of (7 2 –6) reflections at a magnified scale. (b) Temperature variation of lattice constants $a_{\mathrm{p}},b_{\mathrm{p}}$, and $c_{\mathrm{p}}$ of $A$-site ordered double perovskite. (c) Temperature variation of integrated intensities of the superlattice reflections (–1.5 3 6) and (–1.5 3 6.5).

Figure 3

(a) Crystal structure of ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$ at 400 K projected along the [110] axis. The angles of Mn-O-Mn for apical oxygen ions are ${\theta }_{\mathrm{Ba}}=174.{23}^{\circ }$ and ${\theta }_{\mathrm{Sm}}=164.{38}^{\circ }$. (b) Loosely packed SmO layer and (c) tightly packed BaO layer at 400 K. (d) Crystal structure of ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$ at 300 K projected along the $b$ axis: ${\theta }_{\mathrm{Sm}}^{33}=163.5^{\circ },{\theta }_{\mathrm{Sm}}^{44}=161.8^{\circ }$, and ${\theta }_{\mathrm{Ba}}^{34}=172.5^{\circ }$. (e) Crystal structure of ${\mathrm{SmBaMn}}_2{\mathrm{O}}_6$ at 150 K projected along the $b$ axis: ${\theta }_{\mathrm{Sm}}^{33}=163.7^{\circ },{\theta }_{\mathrm{Sm}}^{44}=155.6^{\circ },{\theta }_{\mathrm{Ba}}^{33}=172.1^{\circ }$, and ${\theta }_{\mathrm{Ba}}^{44}=173.5^{\circ }$.

Figure 4

(a) Valence state of Mn in each phase estimated by the VBS method. (b) Schematic illustrations of the normal modes $Q_2$ and $Q_3$ of a ${\mathrm{MnO}}_6$ octahedron. (c) $Q_2\text{−}{Q}_3$ mode analysis corresponding to anisotropy of the $e_g$ orbital of Mn ions at 150, 300, and 400 K.

Figure 5

(a) Schematic drawing of the ${\mathrm{MnO}}_2$ layer at 150 K. Arrows denote displacement of ions from the ideal positions of the simple perovskite structure. (b), (c) Relation between the local electric polarization and spatial charge arrangement.