Ferrimagnetism in the double perovskite Ca2FeOsO6: a density functional study

Using density functional calculations, we find that the newly synthesized Ca${}_2$FeOsO${}_6$ has the high-spin Fe${}^{3+}$ ($3d^5$)-Os${}^{5+}$ ($5d^3$) state. The octahedral Os${}^{5+}$ ion has a large intrinsic exchange splitting, and its $t_{2g\uparrow }^3$ configuration makes the spin-orbit coupling ineffective. Moreover, there is a strong antiferromagnetic (AF) coupling between the neighboring Fe${}^{3+}$ ($S$ = 5/2) and Os${}^{5+}$ ($S$ = -3/2), but the AF couplings within both the fcc Fe${}^{3+}$ and Os${}^{5+}$ sublattices are one order of magnitude weaker. Therefore, a magnetic frustration is suppressed and a stable ferrimagnetic (FiM) ground state appears. This FiM order is due to the virtual hopping of the $t_{2g}$ electrons from Os${}^{5+}$ ($t_{2g\downarrow }^3$) to Fe${}^{3+}$ ($t_{2g\uparrow }^3{e}_{g\uparrow }^2$). However, if the experimental bended Fe${}^{3+}$-O${}^{2-}$-Os${}^{5+}$ exchange path gets straight, the $e_g$ hopping from Fe${}^{3+}$ ($t_{2g\uparrow }^3{e}_{g\uparrow }^2$) to Os${}^{5+}$ ($t_{2g\uparrow }^3$) would be facilitated and then a ferromagnetic (FM) coupling would occur.