The Heisenberg antiferromagnet, which arises from the large-t/ Hubbard model, is investigated on the CM molecule and other fullerenes. The connectivity of Ceo 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 Ul /, and thus the large-l/ solution is relevant for the physical case of intermediate coupling. The system undergoes a first-order metamagnetic phase transition. We also consider the 5 •= y case using perturbation theory. Experimental tests are suggested.PACS numbers: 75.10.Jm, 75.25.+Z, 75.30.Kz The C60 molecule (buckminsterfullerene) has carbon atoms arranged like the vertices of a soccer ball [1]. We consider a neutral molecule. The active orbitals are one radial p orbital for each carbon atom. When the longrange Coulomb or on-site Hubbard repulsion is large compared with the nearest-neighbor hopping f, the molecule has essentially one electron in each orbital. There is an antiferromagnetic Heisenberg spin-spin interaction between nearest neighbors, caused by superexchange. The exchange constant J ss: t 2 /A, where A is the energy difference between a state with one electron in each orbital, and a state with two electrons in one orbital and none in a neighboring orbital. Including on-site U and nearest-The derivation is similar to that of the t-J model used in connection with the superconducting cuprates.Estimates for real C6o are that U is approximately 9 eV and / is 2 to 3 eV [2,3]. The real molecule is thus in the intermediate U regime, and not in the large-(7 limit for which we calculate. The C6o molecule is too large to numerically solve for the intermediate U ground state. There is evidence, however, that there is no phase transition for the Hubbard model in the C 6 o geometry as a function of U/t. The spin correlations for intermediate VIt are then expected to be qualitatively similar, but smaller in magnitude, to those for large U/t. The evidence for a lack of a phase transition is as follows: For a finite quantum system at zero temperature, a phase transition as a function of the parameters occurs only if the quantum numbers of the ground state change. The only quantum numbers for this problem are spin S and angular momentum L (technically, what remains of L under the symmetry group of the icosahedron). S-0 and £=0 in the limit 1///-0, and probably also in the limit U/t-^oo [4]. The simplest (and we believe correct) hypothesis is that there is no phase transition as a function of U/t. It may be useful in this regard to consider the simple example of the two-site Hubbard model with two electrons. Mean-field theory gives a phase transition with sublattice magnetization developing at finite U/t, which suggests that the large-t/ limit is not continuously connected to the small-t/ limit. The trivial exact solution, however, makes it clear that there is in fact no phase transition, that local moments develop continuously, and that the spin correlations of the large-L/ limit develop continuously as U i...

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We calculate the entropy of a two-dimensional Fermi Liquid(FL) using a model with a contact interaction between fermions. We find that there are T 2 contributions to the entropy from interactions separate from those due to the collective modes.These T 2 contributions arise from non-analytic corrections to the real part of the selfenergy which may be calculated from the leading log dependence of the imaginary part of the self-energy through the Kramers-Kronig relation. We find no evidence of a breakdown in Fermi Liquid theory in 2D and conclude that FL in 2D are similar to 3D FL's. 05.30.Fk, 65.70+y, 67.50g Typeset Using REVTEX 1

We show that the effective spin Hamiltonian used previously to describe the CuO planes of La2Cu04 does not lead to a net ferromagnetic moment for CuO planes and hence does not describe the metamagnetic behavior seen experimentally. %'e construct for the first time a Hamiltonian from the symmetries of the crystal structure which does lead to metamagnetism. The linear spin-wave spectrum is also calculated. This work points to the necessity of constructing effective spin Hamiltonians for metamagnetic systems which have the same symmetries as the system they are to describe.We construct for the first time an effective spin Hamiltonian for the CuO planes of undoped La2Cu04 whose classical ground state has a small ferromagnetic moment and calculate the corresponding linear spin-wave spectrum. The CuO planes are known to have a small ferromagnetic moment from the metamagnetic behavior seen in measurements of the static magnetic susceptibility, ' although the interactions are predominantly antiferromagnetic. This weak ferromagnetism (WF) is present in other materials and Dzyaloshinskii proposed that this could be accounted for by the presence of an extra term in the Hamiltonian beyond the isotropic antiferromagnetic (AF) Heisenberg term of the form D S, XSJ, where S; and S are spins at the sites i and j. He pointed out that this contribution is not forbidden by symmetry in an expansion of the free energy if the symmetry of the system is sufficiently low. Moriya then showed that this extra term arises from the effect of the spin-orbit interaction on the superexchange characterized by the Heisenberg J.He showed that~D~-(b,g/g)J, where g is the value of the free-electron gyromagnetic ratio and bg was the shift in that value due to the spin-orbit interaction. He also gave rules for determining the direction of D from the symmetries of the spin system. This extra term, the Dzyaloshinskii-Moriya (DM) term, has been applied by a number of authors' ' to the description of WF and has more recently been used to describe the metamagnetism' or spin-Aop transition, the magnetoresistance, and the conductivity of undoped La2Cu04. In the present work we show that the inclusion of the original DM term, where 0 is taken to be a constant, in an effective spin Hamiltonian does not lead to a description of WF but that a generalization of the DM term, which is determined by the symmetry properties of the crystal structure, does lead to a net ferromagnetic moment in the ground state. We consider as an explicit example the CuO planes of La2Cu04 and show that the important symmetry of the crystal structure which leads to the CuO planes having a net ferromagnetic moment is that each Cu site should be a center of inversion. We note in passing that an alternative model for WF was introduced by Borovik-Romanov and Orlova" and is discussed in detail in Ref. 4. In this model WF arises because there are different g tensors for different sublattices.The WF is only manifest in applied fields and since there is evidence for WF in the absence of applied ma...

Coffey and Coffey Reply: Varelogiannis [1] has missed the point of our calculation [2] which was motivated by the data of Zasadzinski et al. [3]. In these data there is a feature which scales with D 0 at values of the bias across a junction given by eV 3D 0 in the tunneling conductance of superconductor-insulator-superconductor junctions as well as the peak at eV 2D 0 expected from the mean-field approximation. This scaling holds for superconductors whose T c 's vary by a factor of 20. The scaling clearly points to something intrinsic to the superconducting state and is absent from the meanfield approximation for superconductivity. These data are shown in Refs. [3,4]. Given this scaling, Varelogiannis' point about the precision with which D 0 is known is irrelevant.Our calculation is aimed at bringing out the effect of going beyond the mean-field approximation. One consequence of these corrections is that the mean-field quasiparticle eigenstates spontaneously decay because they are not eigenstates of the full Hamiltonian but only of the BCS reduced Hamiltonian. This phenomenon occurs independently of the details of the effective interaction responsible for the superconductivity. The strong-coupling effects in phonon mediated superconductors reflect the frequency dependence of the self-energy coming from the frequency dependence of the phonon density of states. One could imagine doing the same calculation with magnons. However, it is very unlikely that there happens to be a sharp feature giving very large strong-coupling effects at precisely 3D 0 in a set of superconductors whose D 0 's vary by more than an order of magnitude but which share the same basic component, copper oxygen planes. Furthermore, the strong-coupling features have been investigated for some of the cuprates, and they turn out to be very small, ϳ1%, just as is the case in most superconductors [3,5]. On the other hand, the dip feature is close to a 10% effect.After the original submission, Varelogiannis introduced a second issue in a new version of his Comment, namely, that our simple model gives a dip in the direction in momentum space in which the gap goes to zero. He points out that this is in contradiction to Dessau et al. data [6]. If he had read Ref.[4] of our original reply, we would have found that the direction along which the dip feature is seen depends on the choice of band structure. One of us showed [4] that by putting a next-nearest neighbor hopping term into the nearest neighbor tightbinding band structure the anisotropy could be made to vanish. The fact that a simple band structure does not reproduce all the details of these materials does not invalidate our identification of the dip feature in the tunneling conductance. This result has been published for nearly two years now. We note that this contribution to the quasiparticle self-energy is present in both the k