  Commencing from the centrosymmetric MnRMnSbO$_6$ compound, we explore the
realm of magnetic polar double-double perovskite oxides characterized by
significant ferroelectric polarization. Employing symmetry operations,
first-principles methodologies, and Monte Carlo simulations, our investigation
delves into the structural, magnetic, ferroelectric, and electronic attributes
of the polar LaFeMnNiO$_6$ and LaTiMnNiO$_6$ compounds. The structural analysis
uncovers that the paraelectric-ferroelectric phase transition is intricately
linked to the Fe/Ti-displacement of square planar Fe/TiO$_4$. Notably, the
magnetic LaFeMnNiO$_6$ and LaTiMnNiO$_6$ compounds demonstrate robust
ferroelectric polarizations, measuring 20.0 $\mu$C/cm$^2$ and 21.8
$\mu$C/cm$^2$, respectively, accompanied by minimalist forbidden energy gaps of
1.40 eV and 1.18 eV using the GGA+U method. Furthermore, we pinpoint elevated
magnetic transition temperatures for these compounds. Additionally, our study
scrutinizes the energies associated with diverse spin configurations and
identifies potential minimum decomposition pathways into stable oxides. This
comprehensive analysis ensures the meticulous formation of the LaFeMnNiO$_6$
and LaTiMnNiO$_6$ compounds.
