Induced moment system

The study of the above hamiltonian for a lattice of RE-ions has had a large influence on the understanding of induced moment systems . Especially to mention is the work of Trammell (1963), Bleaney (1963), Cooper (1967, 1969), Wang and Cooper (1968, 1969, 1970) and Pink (1968), but there are also many other important contributions. A more complete list can be found for example in Fulde and Peschel (1972), Biigeneau (1973) and Cooper (1974). 

The local environment of a surface atom has a lower symmetry than inside the bulk. As a consequence the CEF which a surface atom experiences is very different to the one inside the bulk. This results in a different level splitting of the RE-ions at the surface. Hence strong surface effects are expected in those quantities which depend on the CEF splitting. We shall demonstrate this for a Van Vleck exchange induced moment system (Peschel and Fulde, 1973 Hsieh and Pink, 1974). Very similar considerations hold true for collective Jahn-Teller systems. 

The second term in Eq. (13-17) concerns particles and induced moments located in the MM system. The polarization energy for the QM system interacting with the MM polarization sites is given by the first term in Eq. (13-17) and it is related to the interaction operator, Hv° as... 

In spherically symmetric systems the induced diamagnetism depends primarily on the mean square radius of the valence electrons as the small contribution from the inner-shell electron core can usually be neglected 1 ). In the case of molecules with symmetry lower than cubic, the quantum mechanical treatment by Van Vleck 23> indicates that another term must be added to the Larmor-Langevin expression in order to calculate correctly diamagnetic susceptibilities. This second term arises because the electrons now suffer a resistance to precession in certain directions due to the deviations of the atomic potential from centric symmetry. The induced moment will now be dependent on the orientation of the molecule in the applied magnetic field and thus in general the diamagnetic susceptibility will not be an isotropic quantity 19-a8>. 

The most important component of the water trimer nonadditive energy is the induction interaction of the second order in V. Its simple mechanism is shown in Fig. 33.3 a permanent multipole moment on monomer A induces multipole moments on monomer B which in turn interact with the permanent multipole moments of monomer C. Higher orders involve interactions between induced moments. The nonadditive induction energy is in general the most important nonadditive component for hydrogen-bonded systems. As already mentioned, it is the only term used—and only in the asymptotic approximation, i.e. neglecting charge-overlap effects—in the polarizable empirical potentials. 

The induced transition dipole moments by the SAC-Cl method are shown in Fig. 39.8 as a function of the intemuclear distance. These induced moments are mainly due to the intra-atomic orbital mixing of the p-component of the Cs atom, caused by a reduction of the spatial symmetry of the system. The 6s2-5dS transition moment is induced at larger intemuclear distances than that of 6s2-7s2. The magnitude of the transition moment is reversed between the 5dS and 7s2 states at the avoided crossing point. 

The dependence of the different kinds of induced moments on the geometry of the system is very different, thus when we wish to extract geometric information from CD we must be aware of which situation we have. 

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