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. IntroductionTransition metal (TM) oxides with perovskite-type structures exhibit a great variety of electronic and magnetic properties. The so-called manganites are among those 3d-TM perovskites with strong correlation of partially localized electrons that originate a close interplay of spin, charge, orbital, and lattice degrees of freedom, and are responsible for important properties such as colossal magnetoresistance or metal-insulator transitions accompanied by the charge and orbital order.Ordering/disordering phenomena of the cations can also produce signifi cant variations on the correlation/competition of degrees of freedom with important impact on the properties of these oxides. In this sense, ordering/disordering effects on the electronic properties of REBaMn 2 O 6 /RE 0.5 Ba 0.5 MnO 3 perovskites have been widely reported. [1][2][3][4][5][6] In the REBaMn 2 O 6 oxides, the RE 3+ and Ba 2+ cations are ordered in alternating [001] perovskite planes; this is the layeredtype ordering. [ 7 ] The electronic phase diagram of the A -site ordered REBaMn 2 O 6 establishes different groups of compounds depending on the RE ion size: [3][4][5][6] the ground states of the La, Pr, and Nd manganites are ferromagnetic metals (FM) while the oxides with RE cations smaller than Nd show a charge orbital ordering insulator state (COOI). On the contrary, the disordered RE 0.5 Ba 0.5 MnO 3 manganites with RE cations smaller than Nd show paramagnetic behavior.Charge order (CO) structures have been experimentally evidenced by several techniques in REBaMn 2 O 6 perovskites and different CO models have been proposed from powder neutron diffraction, electron diffraction and resonant X-ray and Raman scattering experiments. [8][9][10][11][12][13] Of particular interest is that multiferroic properties have been ascribed to some manganites [ 14,15 ] due to coupling between magnetic and charge ordering.In addition to these multiple ordering effects, a certain range of non-stoichiometry within the anion sublattice is often found in manganites, which is also responsible for interesting electronic properties. [ 7 ] In this case, mixed-conductivity can occur due to the oxygen anions moving throughout the anion vacancies. Moreover, in the layered-type ordered REBaMn 2 O 6− δ the anion vacancies are expected to be mainly located close to the rare earth atoms forming very high conducting planes, which increase the oxygen-ion diffusion in comparison with the A -cation-disordered perovskites, [ 16,17 ] and making these compounds promising candidates as cathodes in solid oxide fuel cells. The atomic mechanism of diffusion can be understood by knowing the vacancy distribution within the oxygen sublattice.Certain instrumental improvements in high resolution transmission electron microscopy (HRTEM) such as reduction of spherical and chromatic aberration of the electron-optical lens system and techniques like scanning-TEM (STEM) have proven to give a new insight into atomic resolution structure dete...