Spin–spin relaxation

In physics, the spin–spin relaxation is the mechanism by which Mxy, the transverse component of the magnetization vector, exponentially decays towards its equilibrium value in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). It is characterized by the spin–spin relaxation time, known as T2, a time constant characterizing the signal decay. It is named in contrast to T1, the spin–lattice relaxation time. It is the time it takes for the magnetic resonance signal to irreversibly decay to 37% (1/e) of its initial value after its generation by tipping the longitudinal magnetization towards the magnetic transverse plane. Hence the relation T2 relaxation generally proceeds more rapidly than T1 recovery, and different samples and different biological tissues have different T2. For example, fluids have the longest T2 (on the order of seconds for protons), and water based tissues are in the 40–200 ms range, while fat based tissues are in the 10–100 ms range. Amorphous solids have T2 in the range of milliseconds, while the transverse magnetization of crystalline samples decays in around 1/20 ms. When excited nuclear spins—i.e., those lying partially in the transverse plane—interact with each other by sampling local magnetic field inhomogeneities on the micro- and nanoscales, their respective accumulated phases deviate from expected values. While the slow- or non-varying component of this deviation is reversible, some net signal will inevitably be lost due to short-lived interactions such as collisions and random processes such as diffusion through heterogeneous space. T2 decay does not occur due to the tilting of the magnetization vector away from the transverse plane. Rather, it is observed due to the interactions of an ensemble of spins dephasing from each other. Unlike spin-lattice relaxation, considering spin-spin relaxation using only a single isochromat is trivial and not informative. Like spin-lattice relaxation, spin-spin relaxation can be studied using a molecular tumbling autocorrelation framework.