The delicate balance between spin-orbit coupling, Coulomb repulsion and crystalline electric field interactions observed in Ir-based oxides is usually manifested as exotic magnetic behavior. Here we investigate the evolution of the exchange coupling between Co and Ir for partial La substitution by Ca in La$_{2}$CoIrO$_6$. A great advantage of the use of Ca$^{2+}$ as replacement for La$^{3+}$ is the similarity of its ionic radii. Thus, the observed magnetic changes can more easily be associated to electronic variations. A thorough investigation of the structural, electronic and magnetic properties of the La$_{2-x}$Ca$_{x}$CoIrO$_6$ system was carried out by means of synchrotron x-ray powder diffraction, muon spin rotation and relaxation ($mu$SR), AC and DC magnetization, XAS, XMCD, Raman spectroscopy, electrical resistivity and dielectric permittivity. Our XAS results show that up to 25% of Ca substitution at the La site results in the emergence of Co$^{3+}$, possibly in high spin state, while the introduction of larger amount of Ca leads to the increase of Ir valence. The competing magnetic interactions resulting from the mixed valences lead to a coexistence of a magnetically ordered and an emerging spin glass (SG) state for the doped samples. Our $mu$SR results indicate that for La$_{2}$CoIrO$_6$ a nearly constant fraction of a paramagnetic (PM) phase persists down to low temperature, possibly related to the presence of a small amount of Ir$^{3+}$ and to the anti-site disorder at Co/Ir sites. For the doped compounds the PM phase freezes below 30 K, but there is still some dynamics associated with the SG. The dielectric data obtained for the parent compound and the one with 25% of Ca-doping indicate a possible magnetodielectric effect, which is discussed in terms of the electron hopping between the TM ions, the anti-site disorder and the distorted crystalline structure.
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