  Theoretical calculations, based on hybrid exchange density functional theory,
are used to show that in graphene a periodic array of defects generates a
ferromagnetic ground state at room temperature for unexpectedly large defect
separations. This is demonstrated for defects that consist of a carbon vacancy
in which two of the dangling bonds are saturated with H atoms. The magnetic
coupling mechanism is analysed and found to be due to an instability in the
$\pi$ electron system with respect to a long-range spin polarisation
characterised by alternation in the spin direction between adjacent carbon
atoms. The disruption of the $\pi$-bonding opens a semiconducting gap at the
Fermi edge. The size of the energy gap and the magnetic coupling strength are
strong functions of the defect separation and can thus be controlled by varying
the defect concentration. The position of the semiconducting energy gap and the
electron effective mass are strongly spin-dependent and this is expected to
result in a spin asymmetry in the transport properties of the system. A
defective graphene sheet is therefore a very promising material with an
in-built mechanism for tailoring the properties of the spintronic devices of
the future.
