Multi-orbital Mott Transition and High $T_c$ Ferromagnetism in Strongly Correlated Oxides*

Amongst all perovskites with a net magnetic moment, Sr$_2$CrOsO$_6$ (SCOO) [1] has the highest $T_c = 725$K. We model this as a multi-orbital Hubbard model with different Coulomb $U$'s and Hund's coupling $J_H$'s on the Cr and Os sites along with spin-orbit coupling (SOC) $\lambda_{so}$ on Os. Using a slave-rotor approach, we find a new Mott criterion [2] $\left(\tilde{U}_{\rm Cr}\tilde{U}_{\rm Os}\right)^{1/2} > 2.5W$, where $W$ is the bandwidth and $\tilde{U}$'s are the effective charge gaps including the effects of $U$, $J_H$ and $\lambda_{so}$. Using this result, we argue that SCCO is a Mott insulator. Next, we show that the orbital moment on Os is quenched. The effective spin Hamiltonian for $S=3/2$ moments has Cr-Os and Os-Os antiferromagnetic superexchange interactions that are frustrated. Using a variational approach and Monte Carlo simulations, we show that the system has a canted ground state with a net moment at $T=0$, a non-monotonic magnetization $M(T)$ and a high $T_c$. Our results [2] are in excellent agreement with available data [1] and we predict the magnetic $S({\bf q})$ that will test our theory. [1] Y. Krockenberger {\it et al.}, Phys Rev. B {\bf 75} 020404 (2007). [2] O. N. Meetei, O. Erten, M. Randeria, N. Trivedi, and P. Woodward, arXiv:1205.1811