Unusual Valence of Ru and Prediction of Magnetism, Anomalous Hall Conductivity in a Newly Synthesized Double Perovskite Compound Ca₂CoRuO₆

With a goal to expand on the family of double perovskite compounds, hosting 3d transition metal and 4d or 5d transition metal, two new ordered double perovskite compounds, Ca$_2$FeRuO$_6$ and Ca$_2$CoRuO$_6$ are synthesized following the prediction of a recent high throughput machine-learning study [Phys. Rev. Materials 3, 084418]. Experimentally both compounds are found to stabilize in monoclinic symmetry, which is consistent with the high-throughput prediction for Ca$_2$FeRuO$_6$, but at odd for Ca$_2$CoRuO$_6$. Among the two synthesized compounds, the properties of Ca$_2$CoRuO$_6$, investigated employing the first principles technique and model Hamiltonian calculation, appear promising. The monoclinic structured Ca$_2$CoRuO$_6$ is found to stabilize unusual 6+ valence of Ru, and support a half-metallic ground state with uncompensated net moment. As predicted by our first-principles study, the finite spin-orbit coupling at the Ru site contributes to the non-trivial topology of the band structure of monoclinic Ca$_2$CoRuO$_6$, resulting in a moderately large value of anomalous Hall conductivity. Our theoretical predictions should encourage further experimental investigation of this newly synthesized compound.