Orientational phases for M3C60.

The mechanism of the orientational ordering of C60 in alkali-metal-doped fullerenes M3C60 is studied. Since the M-C60 (M=K,Rb) interactions cause the C60 molecules to assume one of two standard orientations, this model is equivalent to a generalized Ising model on a fcc lattice. The Ising interactions depend on two type of energies: (1) the direct interaction, i.e., the orientationally dependent part of interactions between nearestneighboring C60 molecules (each carrying charge -3e), and (2) the band energy of the electrons transferred from M+ ions to the C603ions. It is shown that the contribution to the pairwise interaction from the direct orientational interaction is ferromagnetic and dominantly nearest neighbor. However, contributions from the band (kinetic) energy of the conduction electrons are found to be antiferromagnetic for firstand thirdnearest neighbors, ferromagnetic for secondand fourth-nearest neighbors, and negligible for further neighbors. The total first-neighbor interaction is probably antiferromagnetic. a non-negligible four-spin interaction is also obtained. The implication of these results for the orientational structure is discussed.