By Professor Tôru Moriya (auth.)

Ferromagnetism of metal structures, particularly these together with transition metals, has been a debatable topic of contemporary technological know-how for a very long time. This controversy sterns from the obvious twin personality of the d-electrons chargeable for magnetism in transition metals, i.e., they're itinerant elec trons defined via band conception of their flooring nation, whereas at finite tem peratures they exhibit quite a few homes that experience lengthy been attributed to a method which include neighborhood magnetic moments. the main commonly used instance of those homes is the Curie-Weiss legislations of magnetic susceptibility obeyed through just about all ferromagnets above their Curie temperatures. initially the matter appeared to be headquartered round no matter if the d-elec trons themselves are localized or itinerant. this query was once settled within the Nineteen Fifties and early Nineteen Sixties via a variety of experimental investigations, specifically via observations of d-electron Fermi surfaces in ferromagnetic transition metals. those observations are normally in keeping with the result of band calculations. Theoretical investigations on account that then have focused on 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 conception, and their impact at the actual properties.

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Sketch of the Hartree-Fock and true Neel temperatures for a system with a half-filled band vs the intra-atomic exchange energy U divided by the bandwidth W ,, I U/W reasonable ground state but also a reasonable spin wave excitation spectrum at T = 0 in the limit of strang correlation (U --+ 00). However, the HFA free energy expression in Sect. 3 gives very high values for the Neel temperature which increases linearly with U. 1t is weIl known that in an insulator magnet with large U the Anderson kinetic exchange is inversely proportional to U, so TN a:.

S_ (q), S+ (- q)]+. 2) where <)1 means the statistical average as a function of the coupling constant 1. This formula is proved as folIows. The free energy F (/) as a function of the coupling constant I is given by exp [- F(I)/T] = Tr {exp(- [~o + V(/)]/T)}. Taking logarithmic derivatives with respect to I on both sides of this equation yields oF(I)/oI = Tr {(oV/oI) exp([F(/) -~o - V(/)]/T)} =

33) By the following Fourier transformation aja = (2INo) 1/2 L, aka exp(ik· Rj ), k ala = (21 No) 1/2 L. bka exp (i k . 33) is reexpressed as with Yk = L, ~j' exp [ik· (Rj j Rj')] = L, ~I' exp [ik· (RI I tk = L, tjl exp [ik· (Rj - R I )]. 35) We now define the sublattice magnetizations M A = tL, (nj! - njt), j MB = t L, (nI! 36) and express the free energy in terms of these variables. 3 Antiferromagnetism 23 becomes t JrO = L. L. [( Yk + a hs) aL aku + (Yk k u ta hs ) bL bku + tk (aL bku + bL aku)] .