Bloch Sphere — NMR Spin Dynamics

Magnetic resonance: RF pulses, T1/T2 relaxation, spin echo
500 ms
100 ms
20 Hz
—
Mx
—
My
—
Mz
—
|Mxy|
The Bloch equations describe nuclear spin magnetization: dM/dt = M×γB − (Mx/T2, My/T2, (Mz−M0)/T1). T1 (longitudinal) relaxation restores equilibrium along z. T2 (transverse) relaxation dephases the xy-plane coherence. A spin echo (Hahn echo, 1950): 90°→wait τ→180°→wait τ, the 180° refocuses T2* dephasing (inhomogeneity), recovering the echo signal. True T2 is measured this way.