Free spin fluctuation effects

When spin-fluctuation effects are taken into account, the state can no longer be regarded as magnetically uniform. Instead of the free energy mentioned in eq. (8) for an itinerant magnet, we must now study the free energy density per unit volume A/(r), which is given as (Shimizu 1981, Yamada 1991, 1993)... 

At any temperature, x(T)/Xc gives the effective number of free spins and is related by the fluctuation-dissipation theorem to the sum of all static spin correlations. The complicated X(T)/Xc behavior in Fig. 17 thus points to disordered exchanges in the power-law regime below 40 °K the flat region 40 < T < 140 K suggests that some 8% are essentially free and follow the Curie law, Eq. (7) the T > 140 K regime... 

Thus m /t is expected to be the same for two similar orbits with the same mean free path. When the effective mass m is enhanced by a factor of (1 -i- A) from spin fluctuations, eq. (65) indicates that r should also be enhanced by a factor of (1+A). This occurs because a large mass is translated into a small velocity from eq. (64) so that the scattering lifetime becomes (1 + A) times larger than that obtained by eq. (64) if the mean free path is the same. In terms of the Dingle temperature, eq. (65) becomes... 

In the spin-fluctuation model the tendency towards magnetism is determined by the strength of the effective exchange interaction between electrons in a narrow band. The presence of this exchange interaction leads to an enhanced susceptibility over the Pauli value, predicted for a free-electron gas. At T = 0 K this enhaneement factor, known as the Stoner factor, is given by... 

In the following, we discuss a method to measure model free the residual dipolar van VIeck moments without contributions from inhomogeneous spin interactions originating from static magnetic field inhomogeneities, local susceptibility effects, and heteronuclear dipolar interactions (70). Moreover, in the first approximation this method is insensitive to the transverse relaxation produced by the fluctuating dipolar interactions. 

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