Abstract
Double perovskite ${\mathrm{Sr}}_{2}\mathrm{Cr}\mathrm{Os}{\mathrm{O}}_{6}$ is (or is very close to) a realization of a spin-asymmetric semimetallic compensated ferrimagnet, according to first principles calculations. This type of near-half metallic antiferromagnet is an unusual occurrence, and more so in this compound because the zero gap is accidental rather than being symmetry determined. The large spin-orbit coupling (SOC) of osmium upsets the spin balance (no net spin moment without SOC): it reduces the Os spin moment by $0.27{\ensuremath{\mu}}_{B}$ and induces an Os orbital moment of $0.17{\ensuremath{\mu}}_{B}$ in the opposite directions. The effects combine (with small oxygen contributions) to give a net total moment of $0.54{\ensuremath{\mu}}_{B}$ per cell in ${\mathrm{Sr}}_{2}\mathrm{Cr}\mathrm{Os}{\mathrm{O}}_{6}$, reflecting a large impact of SOC in this compound. This value is in moderately good agreement with the measured saturation moment of $0.75{\ensuremath{\mu}}_{B}$. The value of the net moment on the Os ion obtained from neutron diffraction ($0.73{\ensuremath{\mu}}_{B}$ at low temperature) differs from the calculated value $(1.14{\ensuremath{\mu}}_{B})$. Rather surprisingly, in isovalent ${\mathrm{Sr}}_{2}\mathrm{Cr}\mathrm{Ru}{\mathrm{O}}_{6}$, the smaller SOC-induced spin changes and orbital moments (mostly on Ru) almost exactly cancel. This makes ${\mathrm{Sr}}_{2}\mathrm{Cr}\mathrm{Ru}{\mathrm{O}}_{6}$ a ``half (semi)metallic antiferromagnet'' (practically vanishing net total moment) even when SOC is included, with the metallic channel being a small-band-overlap semimetal. Fixed spin moment (FSM) calculations are presented for each compound, illustrating how they provide different information than in the case of a nonmagnetic material. These FSM results indicate that the Cr moment is an order of magnitude stiffer against longitudinal fluctuations than is the Os moment.
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