Theory Stoner

Fig. 13. Modification of N(E) under the effect of a perturbing agent and equalization of the electron population to the same (Fermi) level. The picture illustrates qualitatively (N(E)a E for simplicity) the statistical procedure in the derivation of Pauli paramagnetism and in the Stoner theory...

The one-particle band point of view (Stoner theory)... 

In the Stoner theory for magnetism, it is shown that magnetic ordering is possible in a band scheme, when spin-polarization is energetically favorable the full discussion (see Chap. A) for the simpler case of ferromagnetism leads to a simple criterion known as the Stoner criterion ... 

Compared with the situation for the 3d series, the 4d orbitals are relatively more diffuse and hence can overlap more efficiently. One result of this diffuseness is the absence of permanent magnets amongst the 4d solids the 4d wavefunctions cannot support local moments. This can be rationalized in terms of the Stoner theory of itinerant magnetism which also has a cluster or molecular analog L Briefly, a magnetic instability may occur if... 

In the past the effort to improve the understanding of finite temperature magnetic properties has mainly concentrated on itinerant ferromagnetic materials like Fe, Co, and Ni. The theoretical starting point was the one-electron finite temperature band theory which is known under the name Stoner-theory [108, 109]. Within... 

Information about the magnetic behaviour of heavy-fermion systems is contained in the wavenumber- and frequency-dependent magnetic susceptibility x q, v). In less strongly correlated metals, x is usually expressed via Stoner s formula [for critical reviews on itinerant magnetism and Stoner theory see, e.g., Moriya (1979), Gautier (1982), Stamp (1985)],... 

In the Stoner theory of spontaneous magnetization of a system consisting of N electrons, the energy e of an electron with magnetic moment /ub is modified by the term =F/u-b(/u.bM), where M is the magnetization number (the difference of spin-up and spin-down numbers of electrons). We introduce a characteristic temperature 5... 

Anisimov V i, Zaanen J and Andersen O K 1991 Band theory and Mott insuiators Hubbard U instead of Stoner / Phys. Rev. B 44 943... 

This critical field called coercivity or switching field is also equal to If a field is appHed in between 0 and 90° the coercivity varies from maximum to zero. In the case of this special example the appHed field = H/. Based on the classical theory, Stoner-Wohlfarth (33)... 

O. K. (1991) Band theory and Mott insulators Hubbard Uinstead of Stoner I. Physical Review B - Condensed Matter, 44, 943-954. 

In Sect. 4 and 5, the consequences of spin polarization in unsaturated 5f shells are analysed, and the Stoner and Mott-Hubbard theories briefly reviewed. In this way, concepts which are central for actinides, and which the reader may find only when perusing many textbooks (references of which are duly given) are adequately concentrated. 

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). 

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). 

This is the conclusion obtained by the most recent development of the Stoner-Wohlfarth theory (Edwards and Wohlfarth 1968). 

This critical field called coercivity ff. or switching field Ff., is also equal to FF. If a field is applied in between 0 and 90° the coercivity varies from maximum to zero. In the case of this special example the applied field Ha = Hs = Hc = Hk. Based on the classical theory, Stoner-Wohlfarth (33) considered the rotation unison for noninteracted, randomly oriented, elongated particles. The anisotropic axis can be due to the shape anisotropy (depending on the size and shape of the particle) or to the crystalline anisotropy. In the prolate ellipsoids b is the short axis and a the longest axis. The demagnetizing factors are IV (in the easy direction) and The demagnetizing fields can then be calculated by Hda = — Na Ms, and Hdb = — Nb Ms. The shape anisotropy field is Hd = (Na — Nb)Ms. Then the switching field Hs = Hd = (Na — Nb)Ms. 

Many ferromagnets are metals or metallic alloys with delocalized bands and require specialized models that explain the spontaneous magnetization below Tc or the paramagnetic susceptibility for T > Tc. The Stoner-Wohlfarth model,6 for example, explains these observed magnetic parameters of d metals as by a formation of excess spin density as a function of energy reduction due to electron spin correlation and dependent on the density of states at the Fermi level. However, a unified model that combines explanations for both electron spin correlations and electron transport properties as predicted by band theory is still lacking today. 

The Stoner-Wohlfarth approach works fairly well for very small particles, where VM = 0 is a good approximation. However, it has been known for decades that neither the Stoner-Wohlfarth theory nor the additional consideration of the curling mode account for the coercivity of real materials. For example, the coercivity of optimized permanent magnets is only 20-40% of the anisotropy field 2Kx nMs, and only a part of the discrepancy can be ascribed to the curling terms in Eq. (11). The reason is that real-structure imperfections make it impossible to consider the magnets as perfect ellipsoids of revolution. 

MODIFIED STONER-WOHLFARTH THEORY FOR HARD-MAGNETIC PARTICLE ARRAYS... 

For the above mentioned FePt particles, the particle diameter is clearly smaller than the critical particle size given by Eq. (8) for coherent rotation. Furthermore the strength of the magnetostatic interaction field acting on nearest neighbor particles is only about 2% of the anisotropy field for a particle distance of 2 nm. Thus the Stoner-Wohlfarth theory can be applied. 

---