Spin susceptibility density

Relation (39) determines a low-energy scale for the spectral density of d-electrons, which is of the order of the Kondo temperature kl x for PAM. Because this scale results from the interaction with spin fluctuations of localized moments we also study the spin susceptibility of d-electrons. 

We applied the generating functional approach to the periodic Anderson model. Calculation of the electron GFs gdd, 9ds, 9sd and gss reduces to calculation of only the d-electron GF. For this, an exact matrix equation was derived with the variational derivatives. Iterations with respect to the effective matrix element Aij(to) allow to construct a perturbation theory near the atomic limit. Along with the self-energy, the terminal part of the GF Q is very important. The first order correction for it describes the interaction of d-electrons with spin fluctuations. In the paramagnetic phase this term contains a logarithmic singularity near the Fermi-level and thus produces a Kondo-like resonance peak in the d-electron density of states. The spin susceptibility of d-electrons... 

Inelastic neutron scattering(INS) measurements probe directly the imaginary part of the dynamical spin susceptibility. Therefore, it is of interest to analyze the role played by the electronic correlations in connection with the resonance peak seen by INS[3], This feature is well understood using various approaches[20, 21] as a result of the spin density wave(SDW) collective mode formation at co = coreSt i.e. when the denominator of the RPA spin susceptibility at the antiferromagnetic wave vector Q is close to zero. 

The Pauli-like contribution to spin susceptibility (temperature independent) is associated with nonzero density of states at the Fermi level, but these states are not necessarily extended states. The Pauli-like term is therefore not necessarily related to a metallic state. In spin glasses, for instance, a nonzero density of states appears at the Fermi level. In particular, disorder can give rise to localized states with energy in the gap in the vicinity of EF [92]. It can be shown explicitly that disorder introduces a contribution to the spin susceptibility that is independent of temperature. 

One of the problems with VMC is that it favors simple states over more complicated states. As an example, consider the liquid-solid transition in helium at zero temperature. The solid wave function is simpler than the liquid wave function because in the solid the particles are localized so that the phase space that the atoms explore is much reduced. This biases the difference between the liquid and solid variational energies for the same type of trial function, (e.g. a pair product form, see below) since the solid energy will be closer to the exact result than the liquid. Hence, the transition density will be systematically lower than the experimental value. Another illustration is the calculation of the polarization energy of liquid He. The wave function for fully polarized helium is simpler than for unpolarized helium because antisymmetry requirements are higher in the polarized phase so that the spin susceptibility computed at the pair product level has the wrong sign ... 

The superconducting fulleride (NH3) aK2C6o has been investigated using SQUID magnetometry and NMR in two differently doped samples. NMR relaxation measurements vahdate the interpretation of the spin susceptibility in terms of density of states and rule out the presence of strong antiferromagnetic correlations in the Fermi liquid. 

In Table 14 the data for the spin susceptibilities obtained from Eqs. (32) and (33) are listed. For the AB compounds the data are given for the stoichiometric (st, Cve = 2) and for the defect (de, Cve 1-98) phases (cf. Sects. B and C). As expected from the values of the densities of states at the Fermi surface (Table 7), the spin susceptibilities are small for the defect phases and the values x(AB " ) are about a factor of four larger than X(AB ). The exchange enhancement factors x /X Ln are in the range of 1.1 for the AB phases and roughly 1.3 for AB . The values in Table 14 are calculated from RAPW band structure data . For LiAl, LiZn, and LiCd the Pauli susceptibility is also determined from the ASA model . These values differ from the RAPW results due to differences in the density of states given in Table 7. 

Calculating xw within the framework of plain spin density functional theory (SDFT), there is no modification of the electronic potential due to the induced orbital magnetization. Working instead within the more appropriate current density functional theory, however, there would be a correction to the exchange correlation potential just as in the case of the spin susceptibility giving rise to a Stoner-like enhancement. Alternatively, this effect can be accounted for by adopting Brooks s orbital polarization formalism (Brooks 1985). 

The temperature dependence of the spin susceptibility is one of the most intriguing problems of the conducting charge transfer salts. Basing their arguments on T measurements, some authors maintain that the large decrease of observed between room temperature and the metal-insulator transition temperature is related to the development of a pseudo-gap in the density of states at the Fermi level, as temperature becomes smaller than a mean-field Peierls temperature /3o,... 

Fig. 5 shows the temperature-dependent EPR spin susceptibility of the -phase [14], The susceptibility is related to the density of (spin) free electrons. For B c, the susceptibility has a sudden decrease, when temperature reaches 150 K, which may correspond to a sudden shrinkage of the Fermi surface at that temperature. This phenomenon is also consistent with our assumption, that the ordering of iodine atoms removes the impurity levels, and thus the energy gap recurs. 

The discovery 5 th when in solution in concentrated sulfuric acid, poly aniline is in the protonated form, [B-NH-B-NH-]+ n, and that it is recovered as the partially crystalline salt, [B-NH-B-NH-]+ n(HS04 )n, from solutions in sulfuric acid O y precipitation in water or methanol) has opened the way to a more complete characterization of the polymer, and to studies directed toward the determination of the intrinsic properties of the ordered material. For example, the temperature independence of the spin susceptibility of the more highly ordered crystalline material above 125K is consistent with the Pauli spin susceptibility expected for a metal,with a density of states at the Fermi level estimated as 1 state per eV per formula unit (two rings). 

There are few reports of thermal property measurements (e.g., thermal conductivity, specific heat, etc.) [52, 53]. The linear term in specific heat at low temperatures is evidence of the continuous density of states with a well-defined Fermi energy for any metallic system. The low temperature specific heat, C, for a metallic PPy-PFg sample and for an insulating PPy-p-toluenesulfonate (TSO) sample is shown in Figure 2.13 [54]. The data for both samples fit to the equation C/T = y+ jS P, where yand P are the electronic and lattice contributions, respectively. From the values of P and y, the calculated density of states for metallic and insulating samples are 3.6 0.12 and 1.2 0.04 states per eV per unit, and the corresponding Debye temperatures are 210 7 and 191 6.3 K, respectively. These values are comparable to those obtained from the spin susceptibility data. 

Magnetic susceptibility and electron spin resonance data of self-doped sulfonated polyaniline shows the presence of Curie like susceptibility and temperature independent Pauli like susceptibility. The product of the spin susceptibility and temperature (xT) versus temperature for the emeraldine base sulfonated polyaniline is shown in Figure 2.30 [41]. Based on the Pauli spin concentration, the density of states at the Fermi level N( f) (from the slope) is 0.8 state/eV-two rings and an effective Curie spin concentration (from the T = 0 intercept) is 0.02 spin/two... 

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