Thermal relaxation of electron spin motion in a thermal equilibrium ensemble: Relation to paramagnetic nuclear magnetic resonance relaxation

The electron spin relaxation times measured in ESR spectroscopy are physica lly distinct from the electron spin relaxation times which appear in the th eory of NMR Paramagnetic Relaxation Enhancement (NMR-PRE). ESR involves dec ay of a perturbed spin density matrix toward thermal equilibrium, while in NMR-PRE measurements, the electron spin density matrix remains at thermal e quilibrium throughout the NMR experiment. The pertinent spin relaxation inv olves the thermal decay of the time correlation functions, G(r)(tau)=[S-r(0 ).S-r(tau)] (r = x,y,z), of the spin components, quantities which describe the persistence in microscopic correlation of the spin motion in the therma l equilibrium sample. The decay of the G(r)(tau) is shown to be level-speci fic; i.e., G(r)(tau) is composed of a sum of contribution associated with i ndividual eigenstates, each of which decays exponentially via a process tha t is uncoupled to the decay in other eigenstates. This behavior differs mar kedly from the decay of the nonequilibrium parts of a perturbed density mat rix, which involves coupled degree of freedom of the electron spin system. An expression for the level-specific relaxation times has been derived in t erms of Redfield matrix elements. This expression is valid for any S greate r than or equal to 1 when the static spin Hamiltonian consists of Zeeman an d zfs contributions of arbitrary magnitude. Simple closed-form expressions are given for level-specific relaxation times in the cylindrical and orthor hombic zfs limits for S = 1 and S = 3/2. The theory is used to interpret el ectron and nuclear spin relaxation for S = 3/2 with specific reference to h igh-spin Co(II), for which the zfs splittings are typically large. For this spin system, the presence of orthorhombic terms in the zfs tensor causes p rofound shortening of the electron spin relaxation times relative to the re ference cylindrical zfs case and, in consequence, a comparably large rhombi city-induced depression of the NMR relaxation efficiency. (C) 2001 American Institute of Physics.