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I'm reading about giant magnetoresistance (GMR), and the most important feature of this phenomenon is the spin dependance of the electron scattering inside a magnetised lattice. However, I don't quite understand why electrons with spin parallel to the magnetisation (hence, to the majority-spin direction of the electrons) scatter less than those with spin antiparallel to the magnetisation (so, parallel to the minority-spin). I'd appreciate if someone could clear this up for me.

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A qualitative explanation is given in this GMR linκ :

The probability of scattering depends upon the number of available quantum states for the electron to scatter into, and that depends strongly on the relative direction of the electron's spin and the magnetic field inside the ferromagnet. The more states that are available, the higher the probability of scattering, and the higher the electrical resistance. If the spin and magnetic field are anti-parallel, more states are available for electron scattering, so the electrical resistance is larger than if the spin and the magnetic field are parallel (see diagram). This is the basic idea of spin-dependent scattering--

If you have access to a library here is a publication on scattering crossections of electrons

The spin dependences of the inelastic scattering cross section (inverse mean free path) and the elastic scattering cross section are calculated for polarized electrons scattered from oriented atoms in the Born-Ockhur approximation with a view to understanding spin-dependent scattering in ferromagnets. In the medium-to-high-energy range (≳ 100 eV) the elastic scattering for parallel spins is greater than for antiparallel spins, while the inelastic cross section for parallel spins is less than for antiparallel. Elastic spin dependence appears to be greater than inelastic, and the exchange effects fall off rapidly with increasing energy. The relation of this atomistic scattering approach to solid-state models is discussed.

In a classical frame I would think of it as electrons with spin antiparallel to the main field would tend to be attracted to the magnetic domains that create the field, and thus slow down, whereas the parallel are repulsed from all sides and could move ahead unimpeded.

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