  First principles calculations are used to establish that the electronic
structure of graphene ribbons with zig-zag edges is unstable with respect to
magnetic polarisation of the edge states. The magnetic interaction between edge
states is found to be remarkably long ranged and intimately connected to the
electronic structure of the ribbon. Various treatments of electronic exchange
and correlation are used to examine the sensitivity of this result to details
of the electron-electron interactions and the qualitative features are found to
be independent of the details of the approximaton. The possibility of other
stablisation mechanisms, such as charge ordering and a Peierls distortion, are
explicitly considered and found to be unfavourable for ribbons of reasonable
width. These results have direct implications for the control of the spin
dependent conductance in graphitic nano-ribbons using suitably modulated
magnetic fields.
