GMR is more appropriately
Then, the periodic intrinsic potential determines Bloch functions for the superlattice; these functions, as well as the Fermi surfaces and Fermi velocities, are different for the periodic potentials of fig. 20(a), (b) and (c). In fig. 21, we show an example of Fermi surfaces calculated for a Co3/Cu3 superlattice. Conduction in parallel by the spin '+' Fermi surface of fig. 21(a) and spin ' - ' Fermi surface of fig. 21(b) for the P configuration is not equivalent to conduction by the spin '+' and spin ' - ' Fermi surfaces of fig. 21(c) for the AP configuration. This gives rise to GMR effects even with only spin independent scatterings.
If the MFP is not much larger than the period (as in many real multilayers), the fine gap structure of fig. 21 is blurred out and a superlattice approach becomes less appropriate. In this regime the contribution from the intrinsic potential to the GMR is more appropriately described by taking into account specular reflections of electrons of metal A at the interface with metal B and neglecting the interference between reflections at successive interfaces that builds the superlattice Bloch functions. In this layer by layer approach for the CPP geometry, the effect of the intrinsic potential is expressed by a spin dependent interface resistance, see section .
The possible twofold contribution to GMR from scattering and intrinsic potentials initially leads to theoretical models which focused on one or the other mechanisms. Progressively, theorists have tried to take into account both mechanisms within the same models. But as it will be seen below, treating both mechanisms on equal footing is not an easy task.
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We will also see from the analysis of experimental results that, although the GMR strongly depends on spin-dependent scattering effects, the influence of the intrinsic potential is also fairly important and cannot be neglected.
Apart from the microscopic origin of the GMR discussed above, another important problem for theory is that of the scaling lengths governing the decrease and collapse of GMR as the thickness of the layers increases. Experimentally GMR decreases much more rapidly with the thickness of the layers in the CIP than in the CPP geometry; this is due to the different scaling lengths governing the thickness dependence in CIP and CPE Scaling lengths will be discussed more in detail in sections We will see that the scaling length involved in CIP is a relatively short MFP, whereas spin accumulation effects make the scaling length in CPP a much longer spin diffusion length (SDL).
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