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By Professor Tôru Moriya (auth.)
Ferromagnetism of metal structures, specially these together with transition metals, has been a arguable topic of recent technological know-how for a very long time. This controversy sterns from the plain twin personality of the d-electrons chargeable for magnetism in transition metals, i.e., they're itinerant elec trons defined via band thought of their flooring kingdom, whereas at finite tem peratures they convey a variety of houses that experience lengthy been attributed to a procedure such as neighborhood magnetic moments. the main primary instance of those houses is the Curie-Weiss legislations of magnetic susceptibility obeyed via just about all ferromagnets above their Curie temperatures. at the start the matter looked to be headquartered round even if the d-elec trons themselves are localized or itinerant. this query used to be settled within the Nineteen Fifties and early Nineteen Sixties via quite a few experimental investigations, specifically through observations of d-electron Fermi surfaces in ferromagnetic transition metals. those observations are often in step with the result of band calculations. Theoretical investigations on the grounds that then have targeting explaining this twin personality of d-electron structures, taking account of the results of electron-electron correlations within the itinerant electron version. the matter in actual phrases is to review the spin density fluctuati·ons, that are ne glected within the mean-field or one-electron concept, and their impact at the actual properties.
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Extra resources for Spin Fluctuations in Itinerant Electron Magnetism
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L. 23) o,1F(M, T)loM= - TL. L. 24) A = AMI (q, i Wm) . 25) This approximation should be reasonable in weakly ferromagnetic metals where the amplitude of spin fluctuation is small, so thus Ä. ~ I XMO ~ 1. 24) since 1 - I XMO (0, 0) is very small. We now discuss the cases for T> Tc and T< Tc separately. 26) A(T, (j) = Xo (0 2,1 F/ oM2)M=O = TL. G (i w m, (5) m 1 00 =-2 J dwcoth(wl2T)Im{G(w+is,<5)}, 7t -00 AI = _ '" [fM(02fMIOM2) G (w,V) aXOLJ q (j+l-fM + (1 + (5) (OfMIO M)2] 2. 27) 52 4. Se1f-Consistent Renormalization (SCR) Theory ofSpin F1uctuations Fig.
This excitation mayaiso be regarded as an electron-hole pair excitation with opposite spins to each other, since this excitation leaves a hole in the down-spin Fermi sea. 1 Stoner Excitations and Spin Waves in Ferromagnetic Metals 31 Fig. 1. Fermi spheres for ! 3) - q) h+ (q) . k+q) ak'-q'~ ak+q~ ak+q'i ak'~] + (nu - nk+q~) h+ (q) . 4) We use here and in what follows an energy unit for frequency, setting fl = l. The first term on the right-hand side represents the diagonal part of the Hamiltonian giving the kinetic energy and the mean-field energy of the electron-hole pair.
14] gives Tc = 4400-6200, 3300-4800, and 2900 K for Fe, Co, Ni, while the corresponding experimental values are 1040, 1390, and 630 K, respective1y. (III) A T 2 temperature dependence of magnetization is expected at 10w temperatures, in contrast with the T 3/ 2 law observed in many ferromagnets including Fe, Co and Ni, and is expected from spin wave excitations. To improve the Stoner theory we have to take account of the effect of spin density fluctuation, which is neglected in this theory. Such improvements are discussed in the following chapters.