Spin Echo — Hahn Pulse

Dephasing, π-pulse refocusing, and T₂ decay

Hahn spin echo (1950) refocuses dephasing due to static field inhomogeneity. A π/2 pulse tips spins into the transverse plane; each spin then precesses at its local frequency ω_i. A π pulse at time τ flips all spins, reversing dephasing — at time 2τ an echo forms.
M(2τ) = M₀ · e^(−2τ/T₂)
Static disorder is fully refocused; only irreversible T₂ processes (diffusion, spin flips) cause decay. This is the foundation of MRI pulse sequences.