Bloch susceptibility

Here u fl" and E " are the periodic part of the Bloch function, energy and Fermi-Dirac distribution functions for the n-th carrier spin subband. In the case of cubic symmetry, the susceptibility tensor is isotropic, Xcj) = Xc ij- It has been checked within the 4 x 4 Luttinger model that the values of 7c, determined from eqs (13) and (12), which do not involve explicitly u and from eqs (14) and (15) in the limit q - 0, are identical (Ferrand et al. 2001). Such a comparison demonstrates that almost 30% of the contribution to 7c originates from interband polarization, i.e. from virtual transitions between heavy and light hole subbands. 

The low value of U in (TMTSF)2X salts in view of their filled electron band (or the hole band) is in striking contrast to the high Us in -filled M(TCNQ)2 conductors, which often have a susceptibility enhancement over the Pauli susceptibility of factors of 10-30, suggesting that C//4i 1. As pointed out by Mazumdar and Bloch (100), U is an effective parameter which is magnified at the band filling of . This makes it much easier to understand why M(TCNQ)2 and (TMTTF)2X salts show strong correlation effects and why in (TMTSF)2X salts U is so low. 

Bloch, Weisman, and V.arma called attention to the importance of disorder for the electronic properties of quasi-one-dimensional materials, pointed out that there existed x-ray evidence for disorder in a number of such materials, and interpreted the conductivity in terms of Mott hopping in one dimension. Among the materials they considered are NMP-TCNQ, Q-(TCNQ)2, and Ad-CFCNQ. Bulaevskii et al. have measured the magnetic susceptibility of these materials and found them to be strongly paramagnetic at low temperatures with a temperature dependence of the form... 

For experimental details, high pressure apparatus and techniques, references to original articles can be found in the review by Bloch and Pavlovic (1969). Briefly, the most common methods used in following a magnetic transition are change in the mutual inductance sensed through a set of coils placed around the specimen in a transformer-like set up, magnetic susceptibility, electrical resistivity and in some cases thermal dilation. To a limited extent more sophisticated... 

This resonance at ks K provides a partial explanation for the surprising temperature dependence of equilibrium and transport properties of dilute alloys and mixed-valent systems. The important conclusion emerging from the relevant theory (Bickers et al. 1985, Allen et al. 1986) is that the low-temperature susceptibility and specific heat reflect a greatly enhanced density of states proportional to IjT, not l/ p. Since these arguments are based on solution of the single-impurity Anderson model, they cannot be expected to apply a priori to concentrated systems. Nonetheless, for temperatures T > the single-impurity results, scaled by the number of impurities, seem to work for most properties. The most prominent deviation at low temperatures occurs for the resistivity, which Bloch s theorem forces to zero whereas the single-impurity result saturates (Lee et al. 1986). 

The negative pressure derivative (dTddp) of RC02 compounds (Voiron and Bloch, 1971) is related dominantly to the pressure dependence of the enhanced susceptibility. Here the pressure dependence of the enhanced susceptibility is used to calculate, within the exchange enhanced model (Bloch and Lemaire, 1970), the pressure dependence of Tc, which agrees well with the experimental data (Voiron et al., 1973). Jaakkola et al. (1975) discussed qualitatively the... 

Bloch and Lemaire (1970) developed a model for describing two-component alloys in which one component A has a permanent localized moment and the other B an exchange enhanced paramagnetic susceptibility. This B component can possess an exchange induced moment of itinerant nature induced by interaction with the localized A moment. In the paramagnetic temperature range the respective, components are assumed to have magnetizations Ma and Mb in... 

The Neel model for ferrimagnets also gives a non-linear (1/y, T) behaviour above Tq for localized A and B moments. This behaviour becomes linear at high temperatures. Burzo (1972b) presented an interpretation, different from the Bloch-Lemaire model, in which he analysed the paramagnetic data according to this Neel model where the paramagnetic susceptibility is expressed by... 

In an NMR experiment the resonance signal contains components in-phase and out-of-phase with the incident radio frequency radiation so that a complex susceptibility x can usefully be defined, such that x = x x"- The dispersion component x is in-phase, and the absorption component x is out-of-phase. By introducing phenomenologically the exponential decay constants Ti and T2 for the nuclear magnetization parallel and perpendicular to the applied field Ho, Bloch et al. (1946) derived expressions for the magnetization as a function of frequency. These may be related to expressions for x and x", the results being ... 

The contributions to the fifth-order nonlinear optical susceptibility of dense medium have been theoretically estimated by using both the local-field-corrected Maxwell-Bloch equations and Bloembergen s approach. In addition to the obvious fifth-order hyperpolarizability contribution, the fifth-order NLO susceptibility contains an extra term, which is proportional to the square of the third-order hyperpolarizability and which originates purely from local-field effects, as a cascaded contribution. Using as model the sodium 3s 3p transition system, it has been shown that the relative contribution of the cascaded term to the fifth-order NLO susceptibility grows with the increase of the atomic density and then saturates. 

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