Ordinary MR: In a magnetic field, charge carriers curve (Lorentz force), increasing resistivity. ρ ≈ ρ₀(1 + μ²B²) (transverse).
Giant MR (GMR): In a spin valve (FM / NM / FM), resistance is low when layers are parallel (both spins conduct), high when antiparallel. Nobel Prize 2007 (Fert, Grünberg). Used in every hard drive read head since 1997. GMR = (R_AP − R_P)/R_P can reach 10–200%. Mechanism: spin-dependent scattering at FM interfaces — minority spin electrons scatter strongly at antiparallel layers.