  This study is aimed at exploring the electronic, magnetic, and
magneto-optical properties of double perovskites Ca$_2$FeIrO$_6$ and
Ca$_2$CoIrO$_6$ {with monoclinic structure (space group P21/$c$) } in order to
examine their potential applications in spintronic and photovoltaic devices.
The calculations were done using the full-potential linearized augmented plane
wave within the density functional theory. For the electronic
exchange-correlation function, we used the generalized gradient approximation
(GGA) and GGA+U (Hubbard potential), and spin-orbit coupling (SOC). The study
showed that Ca$_2$FeIrO$_6$ and Ca$_2$CoIrO$_6$ exhibit a monoclinic structure
(space group P21/$c$). The structure relaxation shows an antiferromagnetic
behavior in both systems with a magnetic moment of about 6.00$\mu_B$ for
Ca$_2$FeIrO$_6$ and 4.00$\mu_B$ for Ca$_2$CoIrO$_6$ by using GGA+U
approximation. The results of GGA and GGA+U predict the half-metallic behavior
of Ca$_2$FeIrO$_6$ and Ca$_2$CoIrO$_6$. The magneto-optical polar Kerr effect
(MOKE) was examined by studying the variation of Kerr and ellipticity rotation.
The Kerr rotation angle is $1.3^{\circ}$ at 4.82 eV and $-1.21^{\circ}$ at 4.3
eV, and the ellipticity angle is $-1.21^{\circ}$ at 4.3 eV for Ca$_2$FeIrO$_6$.
In the case of Ca$_2$CoIrO$_6$, the Kerr rotation angle is $-1.04^{\circ}$ at
4.05 eV; the significant Kerr rotation in both compounds may suggest the
application of these materials in optoelectronics bias. The named compounds
have a potential application in the field of spintronics and its devices, such
as in optoelectronics technologies.
