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$Na_xCoO_2$ has a fascinating and complex magnetic phase diagram that can befurther manipulated by doping. Here, we investigated the effect of electrondoping on the magnetic coupling among $Co^{4+}$ ions in $Na_xCoO_2$ usingdensity functional theory based on Hartree-Fock hybrid functional. We foundthat electron doping through substitutional $Sb_{Co}$ dopants flip the in-planeferromagnetic coupling among $Co^{4+}$ ions in the undoped compound toantiferromagnetic. Electron doping through interstitial $Cu_{Int}$, however,does not have a similar effect as $Cu_{Int}$ dopant leaves the compoundferromagnetic, just like the case of the undoped compound. The resultsdemonstrate the critical dependence of magnetic phase in $Na_{0.5}CoO_2$ on thedopant and its incorporation site.

In-plane antiferromagnetism in $Na_{0.5}CoO_2$ induced by $Sb_{Co}$ dopants