The structures and electromagnetic properties of A-site ordered/disordered perovskite manganites, RBaMn
2O
6/R
0.5Ba
0.5MnO
3(R=Y and rare earth elements), have been investigated. RBaMn
2O
6 exhibits remarkable features; (1) the charge/orbital order (CO) transition at relatively higher temperatures far above 300K, (2) a new stacking variation of the CE-type CO with a 4-fold periodicity along the c-axis, (3) the presence of structural transition possibly accompanied by d
x2-y2 orbital order, (4) electronic phase separation. These novel structural and electromagnetic properties are discussed in terms of the structural characteristic that the MnO
2 square sub-lattice is sandwiched by two types of rock-salt layers, RO and BaO with different lattice sizes, which introduces a strong frustration to the MnO
2 sub-lattice. In R
0.5Ba
0.5MnO
3 with a primitive cubic perovskite cell, on the other hand, the magnetic glassy states are dominant as the ground state. A peculiar behavior, the steplike ultrasharp magnetization and resistivity changes, has been observed in Pr
0.5Ba
0.5MnO
3.
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