Charge, orbital, and magnetic ordering in ${\mathrm{La}}_{0.5}$ ${\mathrm{Ca}}_{0.5}$ ${\mathrm{MnO}}_3$s

The unusual magnetic properties of ${\mathrm{La}}_{0.5}$ ${\mathrm{Ca}}_{0.5}$ ${\mathrm{MnO}}_3$ were found to be associated with structural and magnetic ordering phenomena, resulting from the close interplay between charge, orbital, and magnetic ordering. Analysis of synchrotron x-ray and neutron powder diffraction data indicates that the anomalous and hysteretic behavior of the lattice parameters occurring between ${\mathrm{T}}_{\mathrm{C}}$ ∼225 K and ${\mathrm{T}}_{\mathrm{N}}$ ∼155 K is due to the development of a Jahn-Teller (J-T) distortion of the ${\mathrm{MnO}}_6$ octahedra, the ${\mathrm{d}}_{\mathrm{z}}^{2>\mathrm{}}$ orbitals being oriented perpendicular to the orthorhombic b axis. We observed an unusual broadening of the x-ray Bragg reflections throughout this temperature region, suggesting that this process occurs in stages. Below ${\mathrm{T}}_{\mathrm{N}}$ , the development of well-defined satellite peaks in the x-ray patterns, associated with a transverse modulation with q=[1/2-ɛ,0,0], indicates that quasicommensurate (ɛ∼0) orbital ordering occurs within the a-c plane as well. The basic structural features of the charge-ordered low-temperature phase were determined from these satellite peaks. The low-temperature magnetic structure is characterized by systematic broadening of the magnetic peaks associated with the ``${\mathrm{Mn}}^{+3\mathrm{}}$ '' magnetic sublattice. This phenomenon can be explained by the presence of magnetic domain boundaries, which break the coherence of the spin ordering on the ${\mathrm{Mn}}^{+3\mathrm{}}$ sites while preserving the coherence of the spin ordering on the ${\mathrm{Mn}}^{+4\mathrm{}}$ sublattice as well as the identity of the two sublattices. The striking resemblance between these structures and the structural ``charge ordering'' and ``discommensuration'' domain boundaries, which were recently observed by electron diffraction and real-space imaging, strongly suggests that these two types of structures are the same and implies that, in this system, commensurate long-range charge ordering coexists with quasicommensurate orbital ordering.