  Magnetic refrigeration at room-temperature is a technology that could
potentially be more environmentally-friendly, efficient and affordable than
traditional refrigeration. The search for suitable materials for magnetocaloric
refrigeration led to the study of double-perovskites La$_2$MnNiO$_6$,
La$_2$MnCoO$_6$ and La$_2$MnFeO$_6$. While La$_2$MnNiO$_6$ and La$_2$MnCoO$_6$
are ferromagnets with near room-temperature $T_C$s, previous theoretical study
of double-perovskite La$_2$MnFeO$_6$ revealed that this material is a
ferrimagnet due to strong electronic interactions in Fe-$d$ orbitals. Here, we
investigate the double-perovskites La$_2$MnRuO$_6$ and LaA''MnFeO$_6$ (A'' =
Ba, Ca and Sr) with density functional theory (DFT) as materials that can
counteract the effects the strong repulsion present in the in Fe-$d$ shells of
La$_2$MnFeO$_6$ and lead to a ferromagnetic state. Our study reaveals that
while La$_2$MnRuO$_6$ is also a ferrimagnet, but with a higher net magnetic
moment per formula than La$_2$MnFeO$_6$, doubly-ordered LaA''MnFeO$_6$ are
ferromagnets. By mapping the total energy of the LaA''MnFeO$_6$ compounds
obtained from DFT calculations to the Ising model, we also calculate their
magnetic exchange couplings. This allows us to estimate the trend in $T_C$ of
the three doped La$_2$MnFeO$_6$ materials with classical Monte-Carlo
calculations and predict that doubly-ordered LaBaMnFeO$_6$ and LaSrMnFeO$_6$
could be suitable materials for room-temperature magnetic refrigeration.
