The Pr$_{0.50}$Sr$_{0.5}$0CoO$_3$ perovskite exhibits unique magnetostructural properties among the rest of ferromagnetic/metallic Ln$_{0.50}$Sr$_{0.50}$CoO$_3$ compounds. The sudden orthorhombic-tetragonal (Imma $to$ I4/mcm) structural transition produces an unusual magnetic behavior versus temperature and external magnetic fields. In particular, the symmetry change is responsible for a spontaneous spin rotation in this metallic oxide. We have studied half-doped Ln$_{0.50}$(Sr$_{1-x}$A$_x$)$_{0.50}$CoO$_3$ cobaltites varying the ionic radius rA of A-site cations (divalent cations and lanthanides) in order to complete the T-rA phase diagram. The influence of the structural distortion and the A-cations size for the occurrence of a spontaneous spin reorientation in the metallic state has been investigated. As the reorientation of the magnetization is driven by the temperature induced collapse of the orthorhombic distortion, a careful investigation of the structural symmetry is presented varying the structural distortion of the Sr-rich half-doped cobaltites by means of both compositional and temperature changes. The region in the phase diagram of these perovskites where the phase of magnetic symmetry Fmmm replaces that of Imma symmetry was determined in this family of ferromagnetic/metallic cobaltites. In that region the magnetization direction has rotated 45 degrees within the a-b plane with respect to the second.
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