Conduction electron polarization

Another method is the conduction-electron polarization effect (CEP) discussed by Shirley and Westenbarger (35). deWaard and Drentje (37) have utilized this effect by driving atoms into a thin iron foil with... 

In the case of PuP, Psat is unkown, but from neutron diffraction the easy axis is (100) thus Psat = 1.27 Ppowder 0-6 Pb and not 0.42 pg. This correction is important because the difference between Poid = 0.77 ps obtained by neutron diffraction and Ppowder = 0.42 Pb has been attributed to a huge conduction electron polarization of - 0.35 Pb Although important, this term should in reality reach only half this value (- 0.17 pb). 

Table 9. Conduction electron polarization effect in uranium ferromagnetic monocompounds conduction electron polarization moment Psai saturation moment from magnetization studies ordered magnetic moment as determined by neutron scattering...

However, the ratio of Hint to the effective magnetic moment of the host atom is almost constant for the three alloys, as is to be expected if conduction electron polarization is the cause of the internal fields. Accurate theoretical estimates of the contributions to Hint from conduction electron polarization and from core polarization have not been made yet. 

One finds Bioi= yiMoMiom where Afdom is the magnetization of the domain in which the Lorentz sphere is situated. Strictly speaking this result is true only for non-conducting compounds since in metallic ferromagnets an additional (but usually small) contribution to Mdom arises from conduction electron polarization which is of course not part of Sdip- The demagnetizing field can be expressed as Bdem= where Af is the... 

RKKY-type analysis of the conduction electron polarization Each time when the hyperfine fields at different sites in the same intermetallic compound were available-as for the Al sites in RjAlu in an NMR analysis by van Diepen et al. (1969)-or when the hyperfine fields and asymptotic paramagnetic Curie temperatures 0p could be correlated, or when the conduction electron concentration could be varied in pseudobinary intermetallic compounds, the RKKY model [as introduced by Jaccarino (1961) for the discussion of A1 NMR in RAI2] was the favourite framework for the NMR spectroscopists. For eq. (10b), is calculated as... 

Cannon et al. (1975) used the Jaccarino-Walker model for the transition-metal moment in some cubic Laves phase compounds. Specifically, they showed that in the Gd(COj Ni )2 system the Co moment appears to be criticaUy dependent on the number and type of its nearest neighbours. Ichinose (1987) measured the NMR of " Al, Mn, " Co and Gd in Gd(X, Coj2 for X = Al, Mn, Fe and Ni. He found from the analysis of the NMR spectra that the concentration dependence of the Co hyperfine field is proportional to the sum of the conduction electron polarization arising from nearest-neighbour transition atoms and that the Co atoms carry a magnetic moment induced by the neighbouring X atoms. 

It is widely accepted that the moment coupling in rare earth alloys proceeds by means of the long-range RKKY mechanism involving a spatial non-uniform conduction electron polarization. The coupling constant of eq. (25) then takes the form (De Gennes, 1962a,b) ... 

Gambino et al. also observed a correlation between 7 and the tangent Hall angle Ph/P or between and R. This correlation was interpreted in terms of the side jump mechanism resulting from the conduction electron polarization, i.e. the authors suggest that it is mainly the side jumps which contribute to Ph/p and 7 - Since the side jump mechanism is proportional to the s conduction electron polarization caused by the localized spins S, the side jump scattering can be expected to be proportional to s S. 

The Curie temperature in alloys where the RKKY mechanism is the main source of the localized moment coupling, was taken as a convenient experimental quantity reflecting the strength of this conduction electron polarization. In the RKKY approach the conduction electron polarization produced by a given localized rare earth spin is proportional to A second rare earth spin will orient itself... 

In ferromagnetic materials the magnetic field experienced by the nucleus is much larger than in the paramagnetic materials discussed above. This hyperfine field can be determined experimentally by sweeping the resonance frequency in zero external field. There are several contributions to These comprise contributions due to core polarization of the inner s shell by the net d-spin or f-spin density and contributions due to conduction electron polarization by the atomic moment associated with the nucleus under consideration (/fj and a contribution due to conduction electron polarization caused by the atomic moments of the surrounding atoms H ). This latter contribution is often referred to as the transferred hyperfine field. Adding up, one therefore has... 

The hyperflne parameters of europium as found from heat capacity measurements (Krusius et al. 1974, Lounasmaa 1964b) agree well with those found from Mossbauer work (Hufner and Wemick 1968). However, as shown in table 5.1, these values are somewhat smaller than Bleaney s (1963) theoretical values for Eu. It has been suggested (Hufner and Wernick 1%8) that the conduction electron polarization in the metal contributes a mainly positive hyperflne field, as opposed to the field acting on Eu ions diluted in ionic CaFi used in Bleaney s (1963) calculations. 

The temperature dependence of the reduced magnetization m T,0), as calculated by Lindg d and Danielsen (1975) is compared in fig. 6.3 with the available experimental results. The conduction electron polarization has been subtracted from the measured magnetization using eq. 6.20 but the effect of ignoring this correction is very small. To a good approximation the data may be characterized by the analytic expression of Mackintosh (1963) after the suggestion of Niira (1960)... 

The zero-field moment of 7.63/iB permits a direct estimate of the conduction electron polarization as 0.63/xb, since the anisotropy-induced zero point motion is negligible for Gd. This increased estimate of the conduction electron polarization is of particular significance for energy band calculations. Harmon and Freeman s spin-polarized APW calculation (1974) requires little adjustment to concur with the experimental result. 

Recently, Koehler and Moon (1972) obtained the form factor of Sm " on both cubic and hexagonal sites of Sm metal from intensity measurements in the ordered phases. Their results are shown in fig. 7.24. Unlike most other form factors, it does not have a maximum at sin 0I = 0. This is partly due to the opposition of the spin and orbital contributions to the moment for this ion. In addition, Koehler and Moon ascribe the very low value of the apparent moment on the Sm ion to compensatory conduction electron polarization. However, they did not fully consider the strong crystal field effects which must be present. De Wijn et al. (1974) have attempted to calculate the form factor including crystal field effects but do not obtain good agreement. However, they use non-relativistic wave functions and also employ the dipole approximation. 

As we have seen, on the whole the agreement with theory for the localized form factor associated with the 4f electrons in lanthanide metals and compounds is satisfactory provided one is careful to use relativistic calculations. The situation for the conduction electron polarization distribution is less clear. Conduction electron form factors were obtained for Gd by Moon et al. (1972) and for Er by Stassis et al. (1976). In both cases, these were obtained by separating from the measured form factor the localized 4f contribution, and in both cases appear to be different from either a 5d or 6s atomic form factor. A spin-polarized augmented-plane-wave (APW) calculation of the conduction electron polarization in ferromagnetic Gd was performed by Harmon and Freeman (1974). Their results are, however, only in qualitative agreement with the results of Moon et al. The theoretical form factor of Harmon and Freeman is in somewhat better agreement with the experimental results of Stassis et al. on Er. 

It is well known (e.g., Elliott 1972) that to excellent first approximation the 4f electrons in the ground configurations of the metals are in the Hund-rule states (i.e., maximum S, maximum L consistent with that S, and J = L + S for n 7). Aside from relatively small conduction electron polarization contributions and crystal field effects which are more important for the lighter elements, the magnetic moments of the metals agree reasonably well with those specified by the Hund-rule quantum numbers of the 4f shell (Rhyne 1972, McEwen 1978). Our RHF calculations are done in the LS-average scheme, however, so that Eband for fh initial states must be corrected to properly describe the Hund-rule 4f states. Since the atomic 4f wave... 

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