  The discovery of novel structural and physical properties in the $A$-site
ordered manganite $R$BaMn$_{2}$O$_{6}$ ($R$ = Y and rare earth elements) has
demanded new comprehension about perovskite manganese oxides. In the present
study, the $A$-site disordered form, $R_{0.5}$Ba$_{0.5}$MnO$_{3}$, has been
investigated and compared with both $R$BaMn$_{2}$O$_{6}$ and
$R_{0.5}A_{0.5}$MnO$_{3}$ ($A$: Sr, Ca) in the structures and electromagnetic
properties. $R_{0.5}$Ba$_{0.5}$MnO$_{3}$ has a primitive cubic perovskite cell
in the structure and magnetic glassy states are dominant as its ground state,
in contrast to the ordinary disordered $R_{0.5}A_{0.5}$MnO$_{3}$ ($A$: Sr, Ca).
In Pr-compounds with various degrees of Pr/Ba randomness at the $A$-sites, the
$A$-site disorder gradually suppresses both ferromagnetic and A-type
antiferromagnetic transitions and finally leads to a magnetic glassy state in
Pr$_{0.5}$Ba$_{0.5}$MnO$_{3}$. A peculiar behavior, multi-step magnetization
and resistivity change, has been observed in Pr$_{0.5}$Ba$_{0.5}$MnO$_{3}$.
These properties could be closely related to any spatial heterogeneity caused
by the random distribution of Ba$^{2 +}$ and $R^{3 +}$ with much different
ionic radius.
