Motivated by the structure of TDAE-\c60, we derive a multicomponent superexchange Hamiltonian for the spins and orbital (``isospin'') degrees of freedom in the Mott-insulating phase. We explore its phase diagram and identify points of special interest: an SU(4) antiferromagnet (solved by Sutherland) and two ferromagnet⊗antiferromagnet points where the ground state is known. For the ferromagnetic regime, we apply interchain mean field theory and derive an expression for the Curie temperature where spin ordering occurs and a lower Ne{\'e}l temperature for a conjectured isospin ordering.
@article{arxiv.cond-mat/9506031,
title = {TDAE-\c60: Can a Mott insulator be a ferromagnet?},
author = {Daniel P. Arovas and Assa Auerbach},
journal= {arXiv preprint arXiv:cond-mat/9506031},
year = {2007}
}