Week 9: Spin valve, spin potentials and a magnetic probe

Spin valve: two spin channels, two spin potentials (Datta Sec. 12.2, Figs. 12.7–12.9)

Up spins (red) and down spins (blue) are two parallel channels. Each magnetic contact has a small interface resistance r for its majority spin and a large one R for its minority spin; the channel adds R_ch to each spin. Spin flips (length λ_s) leak current between the two channels. Below: µ_up(z) and µ_dn(z) from the resistor network (µ₁ = 1, µ₂ = 0), and a magnetic probe that reads a weighted average (Eq. 12.17).

no spin flips (Datta's circuit)

Contact polarization P = (R − r)/(R + r) Channel resistance R_ch / r (per spin) Spin-flip length λ_s / L Probe polarization P_probe

R_P and R_AP (units r) · Eqs. 12.13–12.14–

MR = R_AP/R_P − 1 · P²/(1 − P²) (R_ch = 0)–

Spin potential µ_S = (µ_up − µ_dn)/2 at mid-channel–

Probe: µ_P(+m) − µ_P(−m) · 2P_probeµ_S (Eq. 12.20)–