Exchange integrals, effective

Various predictive methods based on molecular graphs of Jt-systems as described in Section 3 have been critically compared by Klein (Klein et al., 1989) and can be extended to more quantitative treatments. In principle, the effective exchange integrals /ab in the Heisenberg Hamiltonian (4) for the interaction of localized electron spins at sites a and b are calculated as the difference in energies of the high-spin and low-spin states. It was Hoffmann who first tried to calculate the dependence of the M—L—M bond... 

Table 4 Effective exchange integrals (/,b/cm" ) calculated by the ab initio APUHF method for the dimers of benzyl radicals in various parallel overlap modes at distances R.

In the case of the anisotropic rectangular lattice formed by two weakly interacted segments (>3=0), there arise effective exchange integrals J(k,l) subject to the condition [23]... 

Unfortunately, for s>l the corresponding effective Hamiltonians have a much more complicated form and the study of corresponding electron systems can be provided numerically only. Also, for triangular lattice there are no simple sum rules for the effective exchange integrals, which have been derived for a rectangular lattice (Eq. (22,26)). 

From the Weiss field model, the relation between Jex, the effective exchange integral of equation 90, and Te for the case L — 0 can be derived from the fact that the energy of interaction with the Weiss field, — fx w = —gSfjLBHw, is equal to the exchange energy, —Jex Si-S, = — 2zJ xS2, where z is the number of nearest neigh-... 

Ji is the effective exchange integral between nearest neighbor Mn + ions... 

The magnetic behavior of EuX materials can be explained by the interplay of two effective exchange integrals between nearest and J2 between next-nearest neighbors... 

Fig. 22. Dependence of (he effective exchange integrals J, and J2 on lattice constant in EuX compounds. [Taken from Zinn (1976).]...

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