Week 16: Bloch sphere, probe signal and spin precession

Rotating an electron: Bloch sphere, probe and precession (Datta Part B, Ch. 23)

A spin-½ is a rotatable arrow. A probe magnet with polarization P pointing along ˆm measures µ_P = µ + P(m·S)µ_S. Mode 1 rotates the probe (electron versus photon). Mode 2 lets the spin precess in a field along z.

Mode Probe polarization P Angle between contacts θ Precession ω = 2µB/ℏ (rad per unit time) Spin relaxation rate

probe signal (µ_P − µ)/µ_S–

Γ of the probe (α=1, β=(1−P)/(1+P))–

MTJ magnetoresistance 2P²/(1−P²)–

spin vector n–