Magnetic properties of undoped ${\mathrm{C}}_{60}$

The Heisenberg antiferromagnet, which arises from the large-U Hubbard model, is investigated on the ${\mathrm{C}}_{60}$ molecule and other fullerenes. The connectivity of ${\mathrm{C}}_{60}$ leads to an exotic classical ground state with nontrivial topology. We argue that there is no phase transition in the Hubbard model as a function of U/t, and thus the large-U solution is relevant for the physical case of intermediate coupling. The system undergoes a first-order metamagnetic phase transition. We also consider the S=1/2 case using perturbation theory. Experimental tests are suggested.