Spin-dependent scattering observables

In conventional collision experiments the strong Coulomb interaction generally masks the much weaker relativistic spin-dependent interactions. The role of the spin-dependent interactions, such as the exchange and spin—orbit interactions, has also been clarified by sophisticated measurements with spin-polarised electrons and/or spin-polarised targets, sometimes employing spin analysis after the collision process (Kessler, 1985, 1991 Hanne, 1983). 

Such measurements were first applied with considerable success to elastic scattering. Indeed one was able to discuss experiments which would determine all the theoretically calculable amplitudes (Bederson, 1970). For inelastic processes, such measurements necessitate the simultaneous application of spin selection techniques and the alignment and orientation measurements discussed in the previous chapter. The experiments have become feasible with the advancement of experimental techniques. The first successful differential electron impact excitation study with spin-polarised electrons and alignment and orientation measurements was performed by Goeke et al. (1983) for the e—Hg case. McClelland, Kelley and Celotta (1985, 1986) carried out a systematic study for superelastic scattering of polarised electrons from polarised laser-excited Na (3 P) atoms. This system is essentially a two-electron collision system in which spin exchange is the dominant spin-dependent interaction. It thus allows one to obtain 

A polarised electron beam is one with a preferred orientation of the electron spin direction. If there are electrons with spin components parallel to a given direction and with spins antiparallel to that direction then 

The use of polarised beams in collision studies has enabled experimentalists to perform very detailed tests of theoretical models, particularly with regard to the role of electron exchange and the spin—orbit interaction in spin-dependent scattering. We will now briefly discuss the role of these interactions before using the general density matrix method to describe the more general case where more than one mechanism may contribute to the spin-dependent effects. 

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Figure 2. Asymmetric spin dependent scattering at CoFe/Cu and NiFe/Cu interfaces leads to the giant magnetoresistance effect observed in a (CoFe/Cu/NiFe/Cu)x2o multilayer stack (S. Cardoso, INESC MN).

The onset of magnetic order causes sharp kinks in S versus T of Sminj, Gdinj, TblUj, DylUj and Erinj. However, the question remains which mechanism is responsible for the humps in the temperature variation of the thermopower below about 100 K. The hump is observed in all the S T) curves, with slightly different positions. Since this non-linearity in S versus T is observable for all compounds, it is evident that spin-dependent scattering processes alone cannot be the reason. Note that these maxima appear for Lalnj and Lulnj too, where no magnetic moments exist. This fact also excludes the influence of the crystal field as the only reason for the maxima in S versus T. 

A further effect is discussed in Chapter 5, namely that of spin-orbit scattering. This effect preserves the coherence of the two scattered waves but changes the constructive interference into a destructive one. The characteristic time tw is believed to be independent of Ty and inversely proportional to Z4, where Z is the atomic number. An analysis by Fukuyama and Hoshino (1981) shows that Ac depends on and leads to a behaviour as shown in Fig. 1.24. The negative part should be observed only for heavy metals. 

The investigation of sodium as a critical test of the theoretical treatment of scattering is given a new dimension by the spin-dependent measurements of Kelley et al. (1992) in elastic and superelastic scattering experiments with polarised electrons on the polarised 3s and laser-excited 3p states. Not only have asymmetries been measured for these states, but spin-dependent observations of the magnetic substate parameter L have been made for the 3p state. 

This conversion procedure must be attempted for the longitudinal as well as for the transverse transport. The results for p (7) in (TMTSFljPF at ambient pressure is given in Fig. 14 where a cross-over from a superlinear to a linear (or sublinear) power law temperature dependence is observed in the vicinity of 80 K. A detailed analysis based on the Fermi liquid theory shows that a law is apparently well satisfied below 50 K down to the vicinity of the spin density-wave transition where the resistivity is dominated by critical scattering effects [75]. 

Depending on the magnetic ground state of the ytterbimn atoms we observe a variety of diflerent transport properties. Several of the YhTX intermetallics behave like classical metals. In those cases where the ytterbium 4f eleetrons interact with the conduction electrons we observe Kondo-lattiee behavior at low temperatures. The onset of magnetie ordering expresses itself as a drop at low temperatures due to a decrease of spin disorder scattering. 

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