We present a theoretical analysis of the origin of ferromagnetism in two-dimensional Co-substituted $h$-ZnO (${h\text{−}\mathrm{Co}}_x{\mathrm{Zn}}_{1-x}\mathrm{O}$) observed experimentally at room temperature within a narrow window of Co concentration ($x\approx 0.12$). A combination of first-principles calculations and site-occupancy disorder technique extended to include spin disorder of a large number of configurations reveals that (a) ferromagnetic (FM) and ferrimagnetic states are thermodynamically stable at $x=0.12$ at the experimental annealing temperature of $400{}^{\circ }\mathrm{C}$ and (b) FM order weakens with slight increase in $x$. The low-energy landscape is dominated by configurations with Co atoms at second-nearest-neighbor sites on the Zn sublattice exhibiting FM coupling, while higher energy configurations with Co atoms at first- and third-nearest-neighbor sites exhibit antiferromagnetic coupling. Electronic structure of the most stable FM configuration is gapped.

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• Ferromagnetism
• Doped semiconductors
• First-principles calculations