  Each single hydrogen vacancy created at the surface of graphane gives rise to
a local unpaired spin. For domains of hydrogen vacancies the situation is,
however complex and depends on the size and geometry of domains, as well as
whether the domains are single- or double-sided. In single-sided domains,
hydrogen atoms at the other side are relocated to pair the spins of adjacent
carbon atoms by forming pi-bonds. Owing to the different characters of exchange
coupling in different ranges and interplay between unpaired spin and the
binding geometry of hydrogen, vacancy domains can attain sizable net magnetic
moments. Our results based on the first-principles calculations suggest that
the size and ordering of magnetic moments of hydrogen vacancy domains with thin
walls can be used for future data storage and spintronics applications.
