Kondo Effect — Resistance Minimum

Magnetic impurities in a metal scatter conduction electrons with a logarithmic temperature dependence that produces a resistance minimum — the Kondo effect, explained by Jun Kondo in 1964.

Physics: R(T) = R₀ + A·T⁵ − c·ρ_K·ln(T/T_K) + c·ρ_K·f(T/T_K). At low T, the Kondo logarithm (from spin-flip scattering off magnetic impurities via third-order perturbation theory) dominates and raises R. At high T, phonon scattering (T⁵ Bloch–Grüneisen) dominates, also raising R. The minimum occurs where these two opposing trends balance — around T_min ∝ (c·ρ_K / 5A)^(1/5). Below T_K, the impurity spin is screened into a Kondo singlet, saturating the resistance.