  $^{139}$La- and $^{55}$Mn-NMR spectra demonstrate that the ground state of
the A-site ordered perovskite manganite LaBaMn$_2$O$_6$ is a spatial mixture of
the ferromagnetic (FM) and antiferromagnetic (AFI(CE)) regions, which are
assigned to the metallic and the insulating charge ordered state, respectively.
This exotic coexisting state appears below 200 K via a first-order-like
formation of the AFI(CE) state inside the FM one. Mn spin-spin relaxation rate
indicates that the FM region coexisting with the AFI(CE) one in LaBaMn$_2$O$_6$
is identical to the bulk FM phase of the disordered form
La$_{0.5}$Ba$_{0.5}$MnO$_3$ in spite of the absence of A-site disorder. This
suggests mesoscopic rather than nanoscopic nature of FM region in
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