Fermi surface spin polarized

Consider again non-relativistic fermions. Their BCS spectrum (for homogeneous systems) is isotropic when the polarizing field drives apart the Fermi surfaces of spin-up and down fermions the phase space overlap is lost, the pair correlations are suppressed, and eventually disappear at the Chandrasekhar-Clogston limit. The LOFF phase allows for a finite center-of-mass momentum of Cooper pairs Q and the quasiparticle spectrum is of the form... 

Formula (36) represents the condition that the energy will be lowered by a small polarization of the spins of electrons at the Fermi surface. The condition for a large polarization will involve the value of N(E) over a considerable range of E. This formula was generalized for this case by Shimizu and Katsuki (1964) and Shimizu (1964,1965) (cf. also Mott 1964, p. 346, footnote). 

When the QD levels deviate from the Fermi surface, as shown in Fig. 2c and 2d with b = r/2, an interesting result is that Gm. and Gdl do not vary with in phase. When (f) = 7t, the peak of one conductance Ggi or God just encounters the valley of another one. In Fig. 2e and 2f, when

spin polarization. Importantly, in such a case Gri o and G g almost... 

Various reasons have been advanced for the relative accuracy of spin-polarized Kohn-Sham calculations based on local (spin) density approximations for E c- However, two very favourable aspects of this procedure are clearly operative. First, the Kohn-Sham orbitals control the physical class of density functions which are allowed (in contrast, for example, to simpler Thomas-Fermi theories). Second, local density approximations for c[n], are mild-mannered, unbiased, and everywhere finite and do not interfere with that controlling role. This applies near nuclei, in the low density regimes of atoms and molecules, and even far from a metallic surface. 

As mentioned in section 2.3.1, the energy bands of Gd are polarized when the 4f moments are ferromagnetically ordered. There are a number of experiments on the spin polarization effects. These studies have more in common with each other than with the band structure and Fermi surface studies using the same methods. We will review here a positron annihilation experiment (Hohenemser et al., 1968), two field emission experiments (Hofmann et al., 1967 Chrobok et al., 1968), and a UPS experiment (Busch et al, 1969). 

The observation of the CT gap should be contrasted with the predictions of band theory. Local-density-approximation (LDA) calculations performed for a number of undoped materials predict these systems to be metals since die Cu 3d and O 2p orbitals form a conduction band which is half-filled (for a review see Pickett 1989). The spin-polarized version of this band theory is not sufficiently accurate to yield an antiferromagnetic state of the insulating compound (Pickett et al. 1992). Thus LDA calculations fail to account for the two principal features of undoped materials the insulating gap and antiferromagnetic ordering. However, despite these serious problems these calculations do yield accurate values for the Fermi surface crossings as observed by angle-resolved photoemission (for a review see Pickett et al. 1992 see also ch. 201 of this Handbook). 

A small maximum is observed on the Fermi surface, which is formed mainly by the p-states of tin. Boulet et al. (1982) have measured the de Haas-van Alphen effect, the Fermi surface was constructed and the band structure was calculated. The conduction band is formed by the 5p-state of Sn and 5d-state of La. The results obtained on the single crystal by the polarized neutrons method agree with the theoretical calculation of the spin magnetic form factor. It is supposed that the Fermi level is formed mainly by the 5p-state of Sn. 

In the RKKY interaction, a localized spin S,- interacts with a conduction electron with spin s, which leads to a spin polarization of the conduction electron. This polarization interacts with another spin 5) localized on ion j and therefore creates an indirect interaction between the spins St and Sj. This indirect interaction extends to the far distance and damps with a sinusoidal 2k oscillation, where kf is half of the caliper dimension of the Fermi surface. When the number of 4f electrons increases in such a way that the lanthanide element changes from Ce to Gd or reversely from Yb to Gd in the compound, the magnetic moment becomes larger and the RKKY interaction stronger, leading to... 

These spin-split branches are explained by LMTO band calculations (Guo 1990) which treat the 4f electron as a spin-polarized core state. The dHvA branch with the frequency of 1.3xlO Oe, centered at (111), was assigned from a band 9 hole Fermi surface. 

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