  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 O terminated zigzag edges is
magnetic at its ground state, with the magnetism coming from the O 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.
