Interactions of Electron Spins with Their Environment

1 INTERACTIONS OF ELECTRON SPINS WITH THEIR ENVIRONMENT 

The electron Zeeman interaction with the static external field Bq scales with the g value, which is ge = 2.002319 for a free electron. For bound electrons, the electron spin slightly (light elements) or strongly (heavy elements) couples to 

Local fields at the site of the observed electron spin Nare induced by nuclear spins and other electron spins in the vicinity. The nuclear spins are much more abundant and are usually of more interest. The h5q erfine coupling to a nuclear spin / results in a local field that is proportional to the magnetic quantum number mi, so that each level with magnetic quantum number ms splits into 2/ -h 1 hyperfine sublevels. Accordingly, each allowed EPR transition with Anis = 1 splits into 21 + 1 transitions that give rise to the lines of a hyperfine multiplet. The hyperfine coupling consists of the Fermi-contact contribution caused by spin density of the electron at the site of the nucleus and a dipolar contribution that acts through space. As only orbitals have nonzero spin density at 

For an external magnetic field Bo along the z direction, the electron spins are oriented parallel or antiparallel to the z direction. Modulation of the components of the local field in the xy plane due to a stochastic process then induces stochastic electron spin transitions (spin flips) that contribute to longitudinal relaxation with time constant T. For historical reasons longitudinal relaxation is often termed spin-lattice relaxation. The relaxation rate T is proportional to the spectral density /(co) of the stochastic process at the resonance frequency Mo of the transition under consideration. This spectral density is maximum for a correlation time Tc of the stochastic process that fulfils the condition wqTc = 1. As correlation times usually are a monotonic function of temperature, there is a temperature for which the relaxation rate attains a maximum and T attains a minimum. Measurements of 7] as a function of temperature can thus be used to infer the correlation time of a dynamic process. By varying the external field Bo and thus mq, the time scale can be shifted to which EPR experiments are most sensitive. 

Modulation of the z component of the local field cannot infiuence the z component of the spin magnetization and thus cannot induce spin flips. However, the X and y components of the magnetization that stem from coherent superposition of spin states with lAm l = 1 are influenced, as the modulation of the z component can induce a cooperative flip-flop of two spins. The energy change during such a flip-flop is close to zero, as the two transition frequencies are almost equal. Such transverse or spin-spin relaxation with time constant 7] is thus related to spectral density /(O) at zero frequency. This spectral density 7(0) increases with increasing Tc, i.e., with a slowdown of the process. The total rate of transverse relaxation includes a contribution of spin flips, so that T2- =(T2 ) +(271)- . 

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