Kondo Effect Lab (2D)

Why a metal with magnetic impurities gets more resistive when it is cooled: terms, minimum and screening cloud.

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Presets

Playback

Live readout

Total resistivityResidualPhonon termKondo termScreening progressStateResistivity minimum at

What to try

1. Press Cool down sweep and watch the total curve fall, bottom out, then rise again. 2. Raise the Kondo coefficient to move the minimum to higher T. 3. Set it to 0: the minimum disappears (an ordinary metal).

Model checks

The science

A dilute magnetic impurity in a metal scatters conduction electrons by flipping their spin. At low temperature the impurity spin and the electrons build a many-body singlet; second-order perturbation theory (Kondo, 1964) gives a resistivity that grows as rho_K ~ -ln T. Ordinary lattice vibrations give rho_ph ~ a (T/T_D)^5 (Bloch-Gruneisen limit), which falls quickly on cooling. The sum plus a constant residual term, rho = rho_0 + a (T/T_D)^5 + k ln(3 T_K / T), has a minimum where 5 a T^4 / T_D^5 = k / T, i.e. T_min = (k T_D^5 / (5a))^(1/5). Because the log term is clipped to zero above 3 T_K, a minimum predicted above that sits exactly at the kink 3 T_K.

The screening progress is drawn as a logistic crossover centred on T_K. Honest simplifications: the logarithm is clipped at T = 0.3 (the real curve saturates at the unitarity limit, which needs the full renormalisation-group or Bethe-ansatz solution), temperatures are in reduced units, and the impurity is a fictitious single one, not a measured alloy.