# Spin Echo

The transverse (or spin-spin) relaxation time T2 is the decay constant for the component of M perpendicular to B0, designated Mxy, MT, or $M_{\perp}$. For instance, initial xy magnetization at time zero will decay to zero (i.e. equilibrium) as follows:

$M_{xy}(t) = M_{xy}(0) e^{-t/T_2} \,$

i.e. the transverse magnetization vector drops to 37% of its original magnitude after one time constant T2.

T2 relaxation is a complex phenomenon, but at its most fundamental level, it corresponds to a decoherence of the transverse nuclear spin magnetization. Random fluctuations of the local magnetic field lead to random variations in the instantaneous NMR precession frequency of different spins. As a result, the initial phase coherence of the nuclear spins is lost, until eventually the phases are disordered and there is no net xy magnetization. Because T2 relaxation involves only the phases of other nuclear spins it is often called "spin-spin" relaxation.

T2 values are generally much less dependent on field strength, B, than T1 values.

A Hahn echo decay experiment can be used to measure the T2 time, as shown in the animation below. The size of the echo is recorded for different spacings of the two applied pulses. This reveals the decoherence which is not refocused by the 180° pulse. In simple cases, an exponential decay is measured which is described by the $T_2$ time.