Heisenberg antiferromagnetic spin model

Coulomb repulsion energies can be defined in terms of the corresponding operators of the hamiltonian and the single-particle states V r)  

In these expressions, a stands for any of the three primitive lattice vectors, t is the kinetic energy operator, and we have assumed a screened Coulomb potential between the electrons t and U are both taken to he positive constants. 

The first term Hi,ot order t, is simply the hopping term it requires the presence of an unoccupied site next to the site where the electron is, into which the electron can hop. The second term li.2, of order t /U, leads to spin exchange between electrons at neighboring sites when they happen to have opposite spins. The third term H3, also of order U, leads to electron-pair hopping by one lattice vector, 

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An interesting feature of the spin system of this LB film was revealed by temperature dependent ESR measurements [76-78]. The temperature dependence of spin susceptibility of the LB film together with that of powder sample is shown in Figure 14.10. The magnetic properties in both LB and powder state were adequately explained by the random-exchange Heisenberg antiferromagnetic chain (REHAC) model. 

Temperature dependence of magnetic susceptibility of the PF6 salt was measured from 300 to 4 K at 5 T [35], The spin susceptibility of this salt gradually decreases from 300 to 50 K. Below 50 K, the susceptibility exhibits a rapid decrease accompanied by anisotropic temperature dependence, which is an indication of the long-range antiferromagnetic ordering. A one-dimensional Heisenberg model is... 

There are further models which do not introduce new ideas but use the above frame for more complicated types of interactions. Bari and SivardiSre215) discussed a two sublattice model in analogy to the molecular field theory of antiferromagnetism. In this case there are two different interaction constants, viz. the intrasublattice and the intersublattice interaction. They also expand the one-sublattice model by an Heisenberg type magnetic interaction term between the HS states. Such an interaction may only become important for degenerate spin states. 

Figure 5 Diamagnetic rings currents, Nx z), of half-filled Pariser-Parr-Pople models for regular polygons with D h symmetry. The dashed line at 2 = U/4 t0 = 1.17 corresponds to standard parameters z = 0 is the Hiickel limit of free electrons, while z 1 is the strong-correlation limit of antiferromagnetic Heisenberg spin chain with vanishing ring currents [50].

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