Space group determination and first-principles structure optimization of the A -site ordered perovskite-type manganite NdBaMn2O6

Space groups and crystal structures of $A$-site ordered ${\mathrm{NdBaMn}}₂{\mathrm{O}}₆$ perovskite have been investigated by a combination of selected-area electron diffraction (SAED), convergent-beam electron diffraction (CBED), and first-principles methods at high-temperature (HT $\ensuremath{\approx}$ 450 K), room-temperature (RT $\ensuremath{\approx}$ 293 K), and low-temperature (LT $\ensuremath{\approx}$ 95 K) phases. By symmetry analysis of the CBED patterns, space groups of ${\mathrm{NdBaMn}}₂{\mathrm{O}}₆$ at HT, RT, and LT phases have been determined to be $P4/mmm$ (No. 123), $C2mm$ (No. 38), and $P{2}₁am$ (No. 26), respectively. The space groups and the optimized structures using first-principle calculations at the HT and RT phases allow a single crystallographic site for Mn atoms, indicating no charge ordering state. At the LT phase, the observed SAED and CBED patterns revealed the existence of fourfold periodicity along the $c$ axis compared with the pseudocubic unit cell. The optimized structure of the LT phase suggested four inequivalent Mn sites classified into two crystallographically different ${\mathrm{MnO}}₂$ layers. Moreover, the structure showed that the four distinct ${\mathrm{MnO}}₆$ octahedra are similarly compressed in the apical direction.