A comprehensive study of the structural, magnetic, and transport properties of double-substituted ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{Co}}_{1\ensuremath{-}y}{\mathrm{Ni}}_{y}{\mathrm{O}}_{3\ensuremath{-}\ensuremath{\gamma}}$ ($0.1\ensuremath{\le}x\ensuremath{\le}0.5, 0.05\ensuremath{\le}y\ensuremath{\le}0.25$) perovskite systems was carried out. The average oxidation number of Co ions was found to be $3+$ for the most subsystems. The existence of several characteristic concentration regions for various degrees of substitution in the A (La, Sr) and B (Co, Ni) sublattices is shown. Low levels of Sr and Ni ion substitution subsystems demonstrate cluster spin-glass behavior with a semiconducting character of the conductivity and a diamagnetic low-spin (LS) ${\mathrm{Co}}^{3+}$ matrix. An increase of Ni substitution leads to the stabilization of intermediate-spin (IS) ${\mathrm{Co}}^{3+}$ ions in ${\mathrm{CoO}}_{6}$ octahedra, approaching the percolation threshold of ferromagnetic clusters. For strongly Sr-substituted subsystems an effect of stabilization of IS ${\mathrm{Co}}^{3+}$ is not observed, since the contribution of this effect is smaller than the effect of the dilution by antiferromagnetically interacting Ni ions. In this case, an increase of Ni content leads to a decrease in the magnetic ordering temperature ${T}_{\text{mo}}$ and magnetization values. For weakly Sr-substituted systems, on the contrary, it leads to their growth. Anomalies in the conductivity dependences for several subsystems are due to the thermally induced spin crossover of the part of ${\mathrm{Co}}^{3+}$ ions, first from the LS to the IS state, and then to the mixed IS/high-spin (HS) state, similar to the parent ${\mathrm{LaCoO}}_{3}$.
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