  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.
