Magnetism and charge ordering in ${\mathrm{Pr}}_{0.5}{\mathrm{Ca}}_x{\mathrm{Sr}}_{0.5-x}{\mathrm{MnO}}_3$ $(x=0.09\mathrm{}\hspace{0.5em}\mathrm{and}\hspace{0.5em}0.5)$

The structural and magnetic transitions in two ${\mathrm{Mn}}^{3+}/{\mathrm{Mn}}^{4+}\mathrm{}(1:1)\mathrm{}$ systems have been investigated using neutron diffraction and electron microscopy. In ${\mathrm{Pr}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3,$ the charge and orbital order develops in the paramagnetic phase of Pnma symmetry below $T_{\mathrm{co}}=250\mathrm{}\hspace{0.5em}\mathrm{K}$ through a sequence of incommensurate configurations. The ordering process is accomplished at $T_N=170\mathrm{}\hspace{0.5em}\mathrm{K}$ where the charge-exchange–(CE) type antiferromagnetism sets in. Despite the superstructure, the tilt pattern of Pnma type is preserved down to the lowest temperatures. The second compound, ${\mathrm{Pr}}_{0.5}{\mathrm{Ca}}_{0.09}{\mathrm{Sr}}_{0.41}{\mathrm{MnO}}_3,$ is ferromagnetic below $T_C=240\mathrm{}\hspace{0.5em}\mathrm{K}.$ The charge ordering occurs at $T_N=180\mathrm{}\hspace{0.5em}\mathrm{K}$ and is accompanied by the onset of the CE antiferromagnetism. The transition is associated with a change of the tilt pattern from $I4/mcm$ to Imma type. The low-temperature phase is commensurate both in the structural and magnetic sense. It is argued that the main energy gain of the charge ordering in ${\mathrm{Mn}}^{3+}/{\mathrm{Mn}}^{4+}$ (1:1) perovskites results from electron-exchange interactions favored by the $e_g$ orbital polarization. The onset of the incommensurate configurations can be understood supposing the existence of a soft lattice mode in which the electron transfer (charge-density wave) is correlated with dynamics of $e_g$ orbitals.