Magnetism in the High T c Family of Compounds
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large compared to the effective hopping matrix d e m e n t t between d-shells (i.e., via the oxygen atoms), the holes wili thus be localized on their respective sites and the so-called "Mott-Hubbard insulator" picture results. A consideration of the energetics of two holes on neighboring d-shells shows that holes with antiparallel spins can lower their energy by an amount ~t2/U relative to those with parallel spins by a Virtual transition to a doubly occupied State and back again. This is the origin of the well-known super-exchange mechanism which favors an antiferromagnetic ground State for such insulators. In certain cases, if the excitation e n e r g y required to transfer the hole from the cation to the oxygen site is small, but still > > t, a different type of antiferromagnetic insulator may result. In any case, the ground State of a transition metal oxide in the half-filled band limit is expected to be an antiferromagnetic insulator, as has been often observed. For the high Tc Compounds, as we shall see, this State has indeed been observed in the half-filled band case. However, conventional density-functional-based band structure calculations have been unable to account for the antiferromagnetic insulating ground State, even if s p i n - p o l a r i z e d self-consistent b a n d structure calculations are used. 6 This implies that correlation effects must be important in these materials, as discussed above. An important fearure of these materials is t h e i r q u a s i - t w o - d i m e n s i o n a l nature, i.e., the Cu-O planes are only weakly coupled to each other by virtue of the layered structure of these materials. T h e s u p e r c o n d u c t i n g State is achieved by doping with atoms which introduce extra holes into the system. Because of the large values of Tc (and perhaps historically because of the early
determinations of the lack of an oxygen isotope effect in YBa 2 Cu 3 0 7 ) 7 there are now a large number of proposals for superconducting mechanisms which do not involve the conventional electronp h o n o n i n t e r a c t i o n as the p r i m a r y cause. These include attractive electronelectron interactions induced by excitons, 5 plasmons, 8 bipolarons, 9 and various kinds of mechanisms involving the spins on the copper ions. Some of the early modeis were based on the Hubbard Hamiltonian and on the fact that the super-exchange interaction is, in fact, an attractive interaction between holes of opposite spin on different sites. The difficulty, of c o u r s e , is to get a r o u n d the large on-site r e p u l s i o n , which may be partly achieved by modeis involving non-s-wave pairing. However, quantum Monte Carlo simulations of the 2D Hubbard model tend to give an antiferromagnetic, but nonsuperconducting, ground State.10 A m o r e r a d i c a l p r o p o s a l , d u e to Anderson and co-workers, n is that the N6el State is preempted in these Systems and replaced by the so-called Reso n a t i n g Valence Bond (RVB) State, where the ground State of the half-filled band case is described
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