Stoner enhancement

Stoner enhancement factor). This solution is evidently unstable when ... 

For solids in which IN([Xf) is very near to 1, often, although no magnetic order occurs, long-range fluctuations of coupled spins may take place, giving particular form to properties such as the (Stoner enhanced) magnetic susceptibility x, the electrical resistivity, and the specific heat of the solid. Spin fluctuations have been observed in actinides, and will be discussed in more detail in Chap. D. 

However, the intra-atomic Coulomb interaction Uf.f affects the dynamics of f spin and f charge in different ways while the spin fluctuation propagator x(q, co) is enhanced by a factor (1 - U fX°(q, co)) which may exhibit a phase transition as Uy is increased, the charge fluctuation propagator C(q, co) is depressed by a factor (1 -H UffC°(q, co)) In the case of light actinide materials no evidence of charge fluctuation has been found. Most of the theoretical effort for the concentrated case (by opposition to the dilute one-impurity limit) has been done within the Fermi hquid theory Main practical results are a T term in electrical resistivity, scaled to order T/T f where T f is the characteristic spin fluctuation temperature (which is of the order - Tp/S where S is the Stoner enhancement factor (S = 1/1 — IN((iF)) and Tp A/ks is the Fermi temperature of the narrow band). 

Xo, Xs-o and Xs are orbital, spin-orbit and spin contributions, S is the Stoner enhancement factor (see Sect. Ill of this chapter). Xs, Xo and Xs-o are given by ... 

Table 7. Stoner enhancement factor S determination for light actinide metals...

Fig. 3.19 Expected effect on susceptibility due to paramagnons (schematic) (a) without enhancement (b) with Stoner enhancement (c) effect of paramagnons.

To summarize, we again want to make a sharp distinction between the enhancement in nearly ferromagnetic metals like Ni3Al, where the Stoner enhancement factor can increase x without limit but not dx/dT or y, and the enhancement in nearly antiferromagnetic metals to be discussed in Chapter 4, where x> V and dx/dT are all enhanced. In the former case, all models involve either a non-integral number of electrons in the band or degenerate orbitals. In the latter, two electrons on the same atom necessarily have antiparallel spins. 

This kind of enhancement, which occurs for a half-full band near the point where an antiferromagnetic lattice forms, is quite different from the Stoner enhancement for nearly ferromagnetic metals described in Chapter 3, Section 11. The latter occurs for non-integral occupation of a d-band, and enhances the Pauli susceptibility only, not the specific heat, apart from probably small paramagnon effects. 

Here S is the so-called Stoner enhancement factor, usually written as... 

Figure 5.10 Left calculated component resolved Pauli spin contributions to the magnetic susceptibilities of Ag Pti- as a function of the Ag concentration. The Pauli spin susceptibilities are given without Stoner enhancement x and with Stoner enhancement x, in-...

UCo is a paramagnet with a weakly temperature-dependent exchange-enhanced magnetic susceptibility of 0.93 X 10 8 m3/mol at 300 K that increases by less than 2% when cooling to 1.6 K (Chen et al. 1985). The originally reported superconductivity below 1.7 K (Chandrasekhar and Hulm 1958) was recently studied in more detail by Chen et al. (1985) who found Tc = 1.22 K and a critical field Ha = 1.7 T (extrapolated to 0 K). This compound represents an example of a regular U superconductor in the sense of the Hill plot because dv v 320 pm. Also the low value of y = 7.84 mJ/mol K2 is consistent with this picture. Compared to the other U-based superconductors (Meisner et al. 1984), UCo exhibits the highest Stoner enhancement parameter, S = 7. This can be correlated with the spin-fluctuation... 

In this formalism, the many-body effects are incorporated through the Stoner enhancement factor... 

With respect to the magnetic and thermal Gruneisen parameters ilj. (sect. 4.4) it has recently been shown that ilg > ilj for transition-metal compounds with strong Stoner enhancement, (Kaiser and Fulde 1988). Since the Sommerfeld-Wilson ratio,... 

The use of Xo indicates that the so-called Stoner enhancement factor has not been included (the toner theory is a mean-field theory for itinerant electrons). In Equation (3 3), is the averaged value of the varying D over the particles, Xyv is the Van Vleck paramagnetism, and Xdia is the Langevin (or Larmor) diamagnetism. 

The stronger enhancement at low densities could be attributed phenomenologically to an increase in the Stoner parameter a. This approach leads to an incorrect description of the physics as may be seen by the following argument (Warren, 1984 Chapman and March, 1988). The plot in Fig. 3.2 shows that the enhancement of the measured susceptibility is limited near the Curie values calculated for cesium on the coexistence curve. Between the peak and the critical point, the liquid-state susceptibility tends to follow the Curie law (x oc p/T). Stoner enhancement, however, can increase without limit and the susceptibility actually diverges at the transition point of a metallic ferromagnet. In contrast. Curie law behavior is the limit expected from Eq. (3.3) if the enhancement is due to a very high density of states. 

The implication of ferromagnetic Stoner enhancement for NMR follows from Eq. (3.13). It is easy to see that for this case the integral over Q in the numerator is enhanced by a smaller factor than the denominator, so that 77 < 1 for ordinary metals. This is not a small effect and, for example, 17 0.6 is typical for the alkali metals. This corresponds to values 0.4 for the Stoner enhancement parameter of (0,0) in these metals. 

Breakdown of the Stoner enhancement and development of 77 values exceeding unity in cesium requires that the enhancement of the nonuniform susceptibility at nonzero g-values must exceed that occurring at (2 = 0. In analogy with the ferromagnetic description of the normal... 

Calculated LMTO charges (by I values), Qi, the total density of states at Ep, iV( p) Stoner enhancement factor, S, and the total energy... 

S Stoner enhancement factor magnetic propagation vector... 

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