Theoretical Study of Nuclear-Spin-Lattice Relaxation via Paramagnetic Centers

The effect of paramagnetic impurities with local moments on the nuclear-spin-lattice relaxation is studied by using the method of Blume and Hubbard. An average over random impurities is taken on the equations of motion for nuclear and electron spins in the low-concentration limit. An integral equation for the electron-spin correlation function is obtained and solved self-consistently. The correlation function behaves like $\exp [-{\left(\frac{t}{{\Gamma }_1}\right)}^2]$ for small $t$, $\exp [-(\frac{t}{{\Gamma }_2}\left)\right]$ for intermediate $t$, and $\exp [-{\left(\frac{t}{{\Gamma }_3}\right)}^{\frac{1}{2}}]$ for large $t$. The nuclear-spin correlation function is calculated from the electron-spin correlation function. The dependence of the spin-lattice relaxation time on the concentration of impurities, magnetic field; and temperature is obtained. Our calculations are discussed in terms of results obtained from the phenomenological approach.