Theory of Nuclear Spin Relaxation of Dilute Spin Systems

A study of the effects of spatial disorder on the dynamical properties of spin systems is presented. We have made a detailed study of the magnetic resonance and relaxation behavior of spins randomly diluted in a nonmagnetic host. We have developed a method which quantifies to what extent nuclear or electronic spin wavefunctions are localized as a consequence of dilution. This methodology has been applied to the dilute dipolar lattice, and has had important implications to mixtures of (magnetic) ortho and (nonmagnetic) para molecular hydrogen. We have calculated nuclear spin -lattice relaxation times for solid mixtures of ortho H _2 and para H_2 using standard moment techniques for high concentrations, and a stochastic theory of nuclear relaxation for low ortho concentrations. This work led to an understanding of many unresolved issues of hydrogen physics including a clear and accurate description of the temperature dependence of the nuclear relaxation times. Related methods have been applied to HD, where we have included spin diffusion between the H nuclei. The model we developed for relaxation for this system proved to be interesting in its own right because of its possessing exact solutions in physically interesting limits, and for the development of a method for solving the model by numerical simulation. For the H_2 calculations we obtained good agreement with experiment, particularly for ortho H_2 diluted in HD.