Effective exchange interaction

A method for calculating the barriers to internal rotation has recently been proposed (Scott and Scheraga, 1965). It is based on the concept that the barrier arises from two effects, exchange interactions of electrons in bonds adjacent to the bond about which internal rotation occurs, and nonbonded or van der Waals interactions. The exchange interactions are represented by a periodic function, and the nonbonded interactions either by a Buckingham 6-exp or Lennard-Jones 6-12 potential function, the parameters of which are determined semi-empirically. (The parameters of the nonbonded potential energy functions are discussed in Section VB.)... 

The phase shift of the Friedel oscillations by k/2 from a cosine-function to a minus sine-function was recently reported as a common effect of the short mean-free path of the electrons [5.126], an interpretation quite similar to that argued by Kaneyoshi for the effective exchange interaction described in the review. Structure-induced pseudo gaps at EF in amorphous Mg-Zn alloys mentioned above, were confirmed and were also found in the mean time for Ca-Zn [5.127]. 

Table 26.3 Computational results of the effective exchange interactions, J values, for 1-3, together with experimental results...

EPR studies of polycrystalline samples (also other hydrazyls) temperature dependence of line broadening effects, exchange interaction, phase transition 0.05 ) Susceptibility, H-NMR and low field EPR studies of polycrystalline samples. 

FIGURE 37 Layer-resolved components of the effective exchange interaction,... 

J, = Fourier component of ordered spin = effective exchange interaction between Ji, Ji [including (gj -1) factor]... 

According to Campbell s model (1972), the R-R interactions between localized 4f moments should exhibit a stronger variation, because in this interaction flie 4f-5d part of the effective exchange interactions enters twice. To support this view, the ratio r (defined as r = is usually considered (Belorizky et al. 1988, Due et al. 1993a). 

In the spin-fluctuation model the tendency towards magnetism is determined by the strength of the effective exchange interaction between electrons in a narrow band. The presence of this exchange interaction leads to an enhanced susceptibility over the Pauli value, predicted for a free-electron gas. At T = 0 K this enhaneement factor, known as the Stoner factor, is given by... 

A contour map of the MFA-Curie temperatures as a function of the chemical composition (x,y) as presented in Fig. 7 exhibits several important features (i) without donors Tc increases with x and reaches room temperature at approximately x = 0.05. For higher Mn-concentrations Tc saturates which in turn indicates that the effective exchange interactions decrease for heavy Mn doping (ii) the Curie temperature rapidly... 

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