Past exam of the advanced Quantum Condensed Matter Physics course of the University of Cambridge / 2013 / Paper 1 / 2 / Solution (magnetoresistance)

Combining the two results gives the GMR ratio for identical thickness-averaged layers:Thus a field that aligns initially antiparallel moments produces a resistance decrease. One spin channel conducts well throughout the aligned stack; in the antiparallel stack both channels sample strong scattering. For the low-resistance-state normalization,Normalizing the field-induced drop by $R_{AP}$ instead gives $(a-b{)}^2/(a+b{)}^2$. Large channel contrast can produce a large giant magnetoresistance; equal channels give none, and common nonmagnetic scattering dilutes the contrast. This is the spin-dependent alignment effect, distinct from anisotropic magnetoresistance of an individual magnetic layer.