Origin of Magnetism and trend in $T_c$ in Cr-based double perovskites: Interplay of two driving mechanisms

Employing first principles density functional calculations, together with solution of the low-energy, model Hamiltonian constructed in a first principles manner, we explored the origin of magnetism and $T_c$ trend in Cr-based double perovskite series, Sr${}_2$CrB${}^{\mathrm{\prime }}$O${}_6$ (B${}^{\mathrm{\prime }}$=W/Re/Os). Our study shows that the apparently puzzling $T_c$ trend in Sr${}_2$CrB${}^{\mathrm{\prime }}$O${}_6$ (B${}^{\mathrm{\prime }}$=W/Re/Os) series can be understood in terms of the interplay of the hybridization driven mechanism and the super-exchange mechanism.