  Magnetism in single-side hydrogenated (C$_2$H) and fluorinated (C$_2$F)
graphene is analyzed in terms of the Heisenberg model with parameters
determined from first principles. We predict a frustrated ground state for both
systems, which means the instability of collinear spin structures and sheds
light on the absence of a conventional magnetic ordering in defective graphene
demonstrated in recent experiments. Moreover, our findings suggest a highly
correlated magnetic behavior at low temperatures offering the possibility of a
spin-liquid state.
