In-plane antiferromagnetism in $N{a}_{0.5}Co{O}_2$ induced by $S{b}_{Co}$ dopants

$N{a}_{x}Co{O}_2$ has a fascinating and complex magnetic phase diagram that can be further manipulated by doping. Here, we investigated the effect of electron doping on the magnetic coupling among $C{o}^{4+}$ ions in $N{a}_{x}Co{O}_2$ using density functional theory based on Hartree-Fock hybrid functional. We found that electron doping through substitutional $S{b}_{Co}$ dopants flip the in-plane ferromagnetic coupling among $C{o}^{4+}$ ions in the undoped compound to antiferromagnetic. Electron doping through interstitial $C{u}_{Int}$, however, does not have a similar effect as $C{u}_{Int}$ dopant leaves the compound ferromagnetic, just like the case of the undoped compound. The results demonstrate the critical dependence of magnetic phase in $N{a}_{0.5}Co{O}_2$ on the dopant and its incorporation site.