  In this paper, a theoretical journey from electronic to magneto-caloric
effect has been shown through the magnetic properties of aluminium induced
yttrium chromate. The ground state electronic band structure and density of
states have been studied using first principle calculations under GGA+U
schemes. From the energy minimization, the ferromagnetic structure is more
stable than the antiferromagnetic one. The interaction constant as well as the
magnetic moment, have been determined from mean-field theory and DFT,
respectively. The Monte-Carlo simulation under Metropolis algorithm has been
employed to determine the critical temperature ($T_C$), which is nearly same as
the experimental value. The temperature-dependent magnetization shows that
these materials exhibit a paramagnetic to ferromagnetic phase transition at
~136 K, 130 K, 110 K, and 75 K respectively. The two inherent properties named
the isothermal entropy change ($\Delta S_M$) and the adiabatic temperature
change ($\Delta T_{ad}$) as a function of temperature for different applied
magnetic fields have been determined to measure the magnetocaloric efficiency
of these materials. The relative cooling power (RCP), which is calculated
around $T_C$, changes from 4.7 J/Kg to 2.5 J/Kg with the decreasing
Cr-concentration.
