Using first-principles calculations, we systematically study the atomic structures and electronic properties for two dimensional triangular ZnO nanoislands that are graphite-like with monolayer and bilayer thickness. We find that the monolayer ZnO nanoisland with oxygen-terminated zigzag-edges is magnetic at its ground state, and the magnetism comes from the oxygen-edge states. The other monolayer and bilayer ZnO nanoislands with different edge structures are all nonmagnetic at their ground states. It is further revealed that for different ZnO nanoislands, their magnetic properties are quite dependent on their sizes, with larger nanoislands having larger magnetic moments.
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