Spin relaxation

Spin relaxation is the approach of nonequilibrium spin populations and coherences toward their equilibrium values through coupling to other degrees of freedom or environmental fluctuations. A spin polarized away from equilibrium can lose its net polarization even when the total angular momentum of the larger closed system is conserved.

For a simple ensemble in a fixed magnetic field, longitudinal relaxation with time $T_1$ restores the population difference along the field, while transverse relaxation with time $T_2$ damps the rotating transverse spin polarization. Static field inhomogeneity can produce an additional reversible spread of precession phases, so an observed free-induction decay time need not equal the intrinsic $T_2$. Spin-flip scattering changes populations; phase-randomizing processes can also suppress transverse coherence without individual flips. A Hanle spin-precession measurement probes the competition of precession, transport and relaxation.

A transverse magnetic field rotates a nonequilibrium spin polarization while diffusion and spin relaxation redistribute it. The field dependence of a detector signal can constrain spin lifetime and transport parameters. A distribution of diffusion times and rotation of the injecting/detecting electrodes must be included when relevant.

Loss of transported spin polarization at an interface, distinct from bulk spin relaxation in an adjacent layer.

The distance over which a nonequilibrium spin imbalance decays appreciably in a diffusive conductor. In a simple diffusion-relaxation model it is ${\ell }_s=\sqrt{D{\tau }_s}$; interfaces can contribute additional spin-memory loss.

Exchange of energy between magnetic spin degrees of freedom and the surrounding lattice, allowing their temperatures to approach thermal equilibrium. It permits adiabatic demagnetization to cool a solid and its attached load.

A model using exponentially correlated magnetic fluctuations. For homonuclear dipolar relaxation, $T_1^{-1}=C[{\tau }_c/(1+{\omega }_0^2{\tau }_c^2)+4{\tau }_c/(1+4{\omega }_0^2{\tau }_c^2)]$. Its rate maximum occurs near ${\omega }_0{\tau }_c=0.616$; a single-frequency Lorentzian instead peaks at one.

Spin-flip scattering is a collision or scattering event that changes a particle's spin projection along a specified quantization axis. For electrons, coupling to another magnetic moment or coupling of motion to spin through spin-orbit coupling can transfer angular momentum between the electron spin and other degrees of freedom.

Repeated events can relax a nonequilibrium spin polarization, making spin-flip scattering one mechanism of spin relaxation. The axis and state basis must be stated: in a spin-orbit-coupled material, the propagating energy eigenstates need not be pure up or down states along one fixed axis. Conversely, decay of transverse coherence need not imply flips; different precession phases can cancel the ensemble's transverse signal while individual spin populations remain unchanged.