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We present a study of the structural and magnetic properties of La_{1.5}(Sr_{0.5-x}Ba_{x})CoMnO_{6} (0 \leqslant x \leqslant 0.5) double perovskites. These compounds have been synthesized by the solid state reaction method and characterized by conventional and high-resolution synchrotron powder x-ray diffraction (PXRD) measurements, along with magnetization experiments. Detailed Rietveld analysis of the PXRD data showed that all samples exhibit rhombohedral symmetry with the \mathit{R-3c} space group. It is possible to observe a systematic shift of the (10\bar{2}) peak toward higher angles as the Sr concentration increases, which explains the enhancement of the crystal lattice with Sr to Ba substitution. This expansion is accompanied by the increase in both the effective magnetic moment (\mathit{\mu_{eff}}) and the antiferromagnetic (AFM) transition temperature observed below a ferromagnetic ordering. Interestingly, a notable increase in the spontaneous exchange bias (SEB) field is observed for intermediate Sr/Ba concentrations. This enhancement of \mathit{\mu_{eff}} and the AFM transition temperature is probably related to the increased fraction of Co^{3+} in the high spin configuration, strengthening the Co^{3+} – O – Mn^{4+} AFM phase and reducing the uncompensation of the AFM coupling between Co and Mn. These combined results due to Ba substitution can explain the changes in the SEB effect.
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