Magnetic Ordering and Relation to the Metal-Insulator Transition in ${\mathrm{Pr}}_{1-\mathit{x}}{\mathrm{Sr}}_{\mathit{x}}{\mathrm{MnO}}_3$ and ${\mathrm{Nd}}_{1-\mathit{x}}{\mathrm{Sr}}_{\mathit{x}}{\mathrm{MnO}}_3$ with $\mathit{x}$ ∼ $1/2$

We studied three distorted perovskite manganites, ${\mathrm{Pr}}_{1/2}{\mathrm{Sr}}_{1/2}{\mathrm{MnO}}_3$ and ${\mathrm{Nd}}_{1-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3$ with $x=1\mathrm{}/2$ and 0.55 by the neutron diffraction technique. Two samples with $x=1\mathrm{}/2$ exhibit a transition from a ferromagnetic (FM) metal to an antiferromagnetic (AFM) nonmetal. We demonstrate that, in the low temperature phase, ${\mathrm{Nd}}_{1/2}{\mathrm{Sr}}_{1/2}{\mathrm{MnO}}_3$ has a CE-type AFM structure with charge ordering, while ${\mathrm{Pr}}_{1/2}{\mathrm{Sr}}_{1/2}{\mathrm{MnO}}_3$ and ${\mathrm{Nd}}_{0.45}{\mathrm{Sr}}_{0.55}{\mathrm{MnO}}_3$ exhibit an $A$-type layered AFM structure, but show no clear sign of charge ordering. From the present results, we suggest a possible anisotropy of transport as well as magnetic properties in the $A$-type AFM structure near $x\sim 1/2$.