Local field cancellation

We have shown for the case of Li that the step in the occupation number function is surprisingly small z 0.1 and provided semi-empirically obtained values for the local-field correction factor. For the case of Al, we showed the additional cancellation of self-energy and vertex correction. 

Fig. 9. Schematic diagrams of the three types of polarisable potentials. The left-hand diagram shows a point polarisability model (e.g. SK [35] and DC potentials [36]). The centre diagram shows die polarisation on the two 0-H bonds (e.g. NCC potential [37]). The right-hand diagram shows the all-atomic (or three-) polarisation models (e.g. Bernardo et al [44] and Burnham [26]). The lower diagram schematically illustrates the relative orientations of molecular dipole moments of the four nearest neighbour molecules would in possible to cancel out due to the ice rule and give rise a strong local field.

In a subsequent paper, Munn [98] showed that the frequency-dependent local-field tensors accounted for the shift of the poles of the linear and nonlinear susceptibilities from the isolated molecular excitation frequencies to the exciton frequencies. The treatment also described the Davydov splitting of the exciton frequencies for situations where there is more than one molecule per unit cell as weU as the band character or wave-vector dependence of these collective excitations. In particular, the direct and cascading contributions to x contained terms with poles at the molecular excitation energies, but they canceled exactly. Combining both terms is therefore a prerequisite to obtaining the correct pole structure of the macroscopic third-order susceptibility. Munn also demonstrated that this local field approach can be combined with the properties of the effective or dressed molecule and can be extended to electric quadrupole and magnetic dipole nonlinear responses [96]. 

Smith, D.D., Fischer, G., Boyd, R., Gregory, D.A. Cancellation of photoinduced absorption in metal nanoparticle composites through a counterintuitive consequence of local field effects. J. Opt. Soc. Am. B 14, 1625-1631 (1997)... 

Uranium monochalcogenides. These compounds are all simple ferromagnets. It is reasonable to assume that the muon takes up the (i, j) interstitial position since the same crystal structure prevails and since the lattice constants are not significantly different. As pointed out above, the local field will not cancel at such a high-symmetry site for FM order. The contact field remains, pointing in the direction of spontaneous magnetization. UTe, US and the pseudo-binary system Ui-xUa S were studied by (xSR. 

In practice, it is often assumed in calculations or simulations, even of ionic systems, that the interaction energy is pairwise additive. Some justification of this assumption may be given by the fact that in bulk systems the molecules are more or less symmetrically surrounded, so that the local fields at the molecular sites partly cancel and the induced (lower) multipole moments are small (considerably smaller than expected by considering the fields from individual neighbours). However, even in the most perfect crystal of high symmetry this holds only when all the molecules occupy their equilibrium positions, but not when they are (dynamically) displaced. Simplified models have been devised to account for (non-additive) polarization effects in dynamical calculations, such as the shell model for ionic crystals [48]. 

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