Effects of spin polarization on unit cell with even number of electrons

[Quantamania]

Fellows,

I have been investigating graphene for a while, having finished a draft of my thesis paper on its band structure and how it can be modulated by atomic interactions.

When I read a recent Nature article, titled 'Quantum Spin Liquid emerging in two-dimensional correlated Dirac fermions' by Meng et al., I noted that their lattice was hexagonal, much like graphene.  This inspired me to try spin polarization on graphene, even though I had done calculations without using it.  As graphene has an even number of electrons in its orbitals, which are multiply-fold degenerate at K, we have configurations that can have fully paired up electrons in these states.  At K, the eigenstates are four-fold degenerate (two pairs of degenerate states, with different dispersion), meaning that we have four separate states to occupy with four of the eight available electrons for graphene.

This brings me to the question: What would be the effects of spin polarization on such a system?  How would the spin pairings be treated in it (unpolarized or polarized)?  I have observed slight differences at K when doing a spin-polarized calculation with initial spin set at zero.

[Nordland]

If your are performing a calculation on pure graphene using spin. It should if converged sufficiently become unpolarized.
However if you are calculating on graphene with a egde or similar defect, it has been observed that a polarization takes place near the egde.

There is a tutorial on this matter.

[Quantamania]

Yes, I am aware of the polarization effects at defect sites. 

I have indeed found that the eigenstate occupancy in graphene does suggest spin pairing.  In the HOMO and HOMO-1 eigenstates, there are two electrons occupying them.  This is found in both spin-unpolarized and spin-polarized (with initial spin set to zero) calculations of graphene.  The electrons are remaining paired, despite the degeneracy of the initial states.

However, is this actually the experimentally observed microstate (two pairs of electrons in two stabilized orbitals and two empty orbitals, rather than four electrons residing in their own orbitals in an antiferromagnetic orientation with total spin equal to zero) for graphene?  Please find out if there is a reference that clearly states the microstate for graphene at K. 

It seems that the spin pairs would stabilize the orbitals they were located in, lowering those orbitals' energies.  In such a situation, the four-fold degeneracy would be lifted by the electron pairs, and we would not get the zero band gap in graphene at K.  How do we resolve this issue, given that graphene is observed to have a Dirac intersection point and degenerate eigenstates at this point?