Stoner model

These concepts are very importcint also for actinide solids. In particular, the Stoner model for collective magnetism in narrow bands, the frame in which d-transition metals and actinide metals magnetism has been discussed, will be reviewed briefly. 

The Stoner model, which we discuss in its simplest form, describes the formation of a net magnetic moment for itinerant electrons in a narrow band by adding to the basic Hamiltonian (11) of band theory a perturbing term accounting for total energy increase in case the itinerant electrons spins are not polarized (as in an atom for states not maximizing the spin). 

The Stoner model retains only the first term, proportional to (molecular field approximation which leads to terms such as (26) in the Hamiltonian). 

In Chap. A, we have seen that, in the Stoner model, (ferromagnetic) spin-polarization of electrons originates two electron states E+ and E from each electron state E of a non-spin-polarized electron band, the difference between the two being (E+ - E ) = Im, where I is the Stoner parameter and m = n+ - n is the magnetization density. 

In the case of weak ferromagnets (1 IN(ep)) Wohlfarth has shown that the Stoner model predicts a magnetic susceptibility for T >Tf which is non-Curie like and has the following form ... 

The effect of interactions on the Korringa ratio 17 can be illustrated for the case of the Stoner model of susceptibility enhancement. The generalization of Eq. (3.6) for the nonuniform susceptibility is... 

With these characteristics of relaxation in normal metals in mind, let us now consider the behavior of the dynamic, nonuniform susceptibility in a low-density metal approaching the critical region. It follows from the foregoing discussion that, within the Stoner model, the Korringa ratio T7 should decrease as the static enhancement increases. This can be tested directly with the NMR data for cesium. It is evident in Fig. 3.6 that the prediction of the Stoner model is not borne out—17 increases in the low-density region where the static susceptibility enhancement also increases. Thus, we are again led to the conclusion that the susceptibility enhancement in the low-density metal is of a fundamentally different character than that of the normal, dense metal near T . 

The Stoner model. The itinerant electron model of magnetism in metals is based on the simple assumption that the magnetic electrons collectively obey the Fermi-Dirac statistics. In addition, the essential electron-electron interactions are included by the use of the molecular field hypothesis. With these assumptions, it is possible to write down the total energy per atom of an itinerant ferromagnet as the smn of two terms. The first term is the total molecular field energy (Fm) which may be expressed as... 

In the Stoner model at 0 K the total energy in the presence of a magnetic field is written as a summation of the electronic (B ei) and elastic (i iat) parts. The electronic energy can... 

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