Microscopic Origin Of Room Temperature Ferromagnetism in a Double Perovskite Sr$_2$FeReO$_6$: a first principle and model Hamiltonian study

The puzzling observation of room temperature ferromagnetism in double perovskites (A$_2$BB$'$O$_6$), despite having the magnetic lattice of B-ions diluted by non-magnetic B$'$-ions, have been examined for Sr$_2$FeReO$_6$. {\it Ab-initio} spin spiral electronic structure calculations along various high symmetry directions in reciprocal space are used to determine the exchange interactions entering an extended Heisenberg model, which is then solved classically using Monte Carlo simulations to determine the ferromagnetic transition temperature T$_c$. We find that one must consider onsite Coulomb interactions at the nonmagnetic Re sites ($U$) in order to obtain a T$_c$ close to the experimental value. Analysis of the $ab$-$initio$ electronic structure as well as an appropriate model Hamiltonian trace the origin of enhancement in T$_c$ with $U$ to the enhanced exchange splitting that is introduced at these sites. This in turn destabilizes the antiferromagnetic exchange channels, thereby enhancing the T$_c$. The role of occupancy at the non-magnetic sites is examined by contrasting with the case of Sr$_2$FeMoO$_6$.