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We investigated the electronic and magnetic properties of the pyrochloreoxide Cd$_2$Os$_2$O$_7$ using the density-functional theory plus on-siterepulsion ($U$) method, and depict the ground-state phase diagram with respectto $U$. We conclude that the all-in/all-out non-collinear magnetic order isstable in a wide range of $U$. We also show that the easy-axis anisotropyarising from the spin-orbit (SO) coupling plays a significant role instabilizing the all-in/all-out magnetic order. A \textit{pseudo gap} wasobserved near the transition between the antiferromagnetic metallic andinsulating phases. Finally, we discuss possible origins of the peculiarlow-temperature($T$) properties observed in experiments.

Noncollinear magnetism and spin-orbit coupling in 5d pyrochlore oxide Cd2Os2O7