By Yoshiro Kakehashi
This e-book describes theoretical points of the metal magnetism from metals to disordered alloys to amorphous alloys either on the floor country and at finite temperatures. The publication supplies an creation to the steel magnetism, and treats results of electron correlations on magnetism, spin fluctuations in metal magnetism, formation of complicated magnetic constructions, a number of magnetism as a result of configurational ailment in alloys in addition to a brand new magnetism as a result of the structural illness in amorphous alloys, specially the itinerant-electron spin glasses. The readers will locate that every one those issues may be understood systematically via the spin-fluctuation theories in keeping with the sensible critical method.
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Additional resources for Modern Theory of Magnetism in Metals and Alloys
In order to describe the on-site electron correlations, Gutzwiller introduced a correlated wavefunction as follows. L |Ψ = 1 − (1 − g)ni↑ ni↓ |φ . 64) i Here ni↑ ni↓ is a projection operator that chooses the doubly occupied state on site i, and g is a variational parameter controlling the amplitudes of doubly occupied states in the Hartree–Fock wavefunction. Note that the g = 1 state corresponds to an uncorrelated state, and the g = 0 state corresponds to the atomic state in which all the doubly occupied states have been removed.
53), we obtain the interaction energy as follows. E(k1 k2 ) = 1 U . 57) Alternatively, E = εk1 + εk2 + 1 U . 58) The above result indicates that the Coulomb interaction U has been renormalized by the electron–electron scatterings as U/(1 + U G(k1 k2 )), since the Hartree– Fock energy in the singlet state is given by εk1 + εk2 + U/L. We then find the band narrowing factor q = 1 and the renormalization factor of Coulomb energy r = 1/(1 + U G(k1 k2 )). Note that there is no band narrowing in the low density limit because there is no electron on the surrounding sites which interrupts the motion of an electron.
Nickel which has about 9 d-electrons per atom is regarded as a low density system according to the hole picture. The ferromagnetism of Ni is considered to be stabilized by this mechanism because of the high density of states at the Fermi level (see Fig. 6). 3 Gutzwiller Theory of Electron Correlations When electron number is increased, one cannot apply the low density approximation. In this subsection, we introduce the Gutzwiller variational method for electron correlations at the ground state [6–8], which is useful for any electron density.