DFT+$U$ study of electronic structure and Curie temperature of $A_{2}B$ReO$_6$ ($A$=Sr, Ca and $B$=Cr, Fe)

Re-based double perovskites (DPs) have attracted much attention due to their high Curie temperature ($T_C$) and colossal magneto resistance with large potential for spintronic applications. Here we investigate the electronic and magnetic properties of the Re-based DPs $A_2B$ReO$_6$ ($A$=Sr, Ca and $B$=Cr, Fe) using density functional theory + $U$ (DFT+$U$) calculations. While monoclinic Ca$_2$CrReO$_6$ and Ca$_2$FeReO$_6$ (monoclinic) are insulating within GGA+$U$, tetragonal Sr$_2$CrReO$_6$ ($a^{0}a^{0}c^{0}$) and Sr$_2$FeReO$_6$ ($a^{0}a^{0}c^{-}$) remain metallic. We show that both on-site interaction $U$ and octahedral tilting are critical to obtain the insulating phases. The $a^{0}a^{0}c^{-}$-phase of Sr$_{2}$CrReO$_{6}$ is most stable and insulating with nonzero $U$, suggesting that the high quality Sr$_{2}$CrReO$_{6}$ film on STO substrate can be a semiconductor as reported in recent experiments. We explain that the insulator-to-metal transition (MIT) of Ca$_2$FeReO$_6$ at 140K is predominantly due to a structural phase transition which drives the insulating state. Curie temperatures of Re-based DPs are calculated using the classical Monte Carlo simulations based on the Heisenberg model.