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Theory of High T$_c$ Ferrimagnetism in a Multi-orbital Mott Insulator

We propose a model for the multi-orbital material Sr$_2$CrOsO$_6$ (SCOO), an insulator with remarkable magnetic properties and the highest $T_c \simeq 725$ K among {\em all} perovskites with a net moment. We derive a new criterion for the Mott transition $(\widetilde{U}_{1} \widetilde{U}_{2})^{1/2}>2.5W$ using slave rotor mean field theory, where $W$ is the bandwidth and $\widetilde{U}_{1(2)}$ are the effective Coulomb interactions on Cr(Os) including Hund's coupling. We show that SCOO is a Mott insulator, where the large Cr $\widetilde{U}_{1}$ compensates for the small Os $\widetilde{U}_{2}$. The spin sector is described by a frustrated antiferromagnetic Heisenberg model that naturally explains the net moment arising from canting and also the observed non-monotonic magnetization $M(T)$. We predict characteristic magnetic structure factor peaks that can be probed by neutron experiments.