GMR can be qualitatively understood using the Mott model, which was introduced as early as 1936 to explain the sudden increase in resistivity of ferromagnetic metals as they are heated above the Curie temperature. There are two main points proposed by Mott:
First, the electrical conductivity in metals can be described in terms of two largely independent conducting channels, corresponding to the up-spin and down-spin electrons, which are distinguished according to the projection of their spins along the quantization axis. The probability of spin-flip scattering processes in metals is normally small as compared to the probability of the scattering processes in which the spin is conserved. This means that the up-spin and down-spin electrons do not mix over long distances and, therefore, the electrical conduction occurs in parallel for the two spin channels.
Second, in ferromagnetic metals the scattering rates of the up-spin and down-spin electrons are quite different, whatever the nature of the scattering centers is. The band structure in a ferromagnet is exchange-split, so that the density of states is not the same for up-spin and down-spin electrons at the Fermi energy. Scattering rates are proportional to the density of states, so the scattering rates and therefore resistivities are different for electrons of different spin.
Using Mott’s arguments it is straightforward to explain GMR. We assume that the scattering is strong for electrons with spin antiparallel to the magnetization direction, and is weak for electrons with spin parallel to the magnetization direction. This is supposed to reflect the asymmetry in the density of states at the Fermi level, in accordance with Mott’s second argument. For the parallel-aligned magnetic layers, the up-spin electrons pass through the structure almost without scattering, because their spin is parallel to the magnetization of the layers. On the contrary, the down-spin electrons are scattered strongly within both ferromagnetic layers, because their spin is antiparallel to the magnetization of the layers. Since conduction occurs in parallel for the two spin channels, the total resistivity of the multilayer is determined mainly by the highly-conductive up-spin electrons and appears to be low. For the antiparallel-aligned multilayer, both the up-spin and down-spin electrons are scattered strongly within one of the ferromagnetic layers, because within the one of the layers the spin is antiparallel to the magnetization direction. Therefore, in this case the total resistivity of the multilayer is high.