Theory of Spin Pumping and Relaxation in Systems with a Low Concentration of Electron Spin Resonance Centers

A model is developed to describe nuclear relaxation and spin pumping caused by sparsely distributed electronic spins. It is assumed that the nuclei which are outside the interaction sphere of the paramagnetic centers are influenced indirectly via a fast diffusion process. Nuclei close to the electron spins are assumed to combine with these to form spin pairs of finite lifetime $\tau$. Spin pumping and relaxation in these pairs is described phenomenologically. The coupling with a radio-frequency power source is described in terms of a spectral distribution function with Lorentzian shape. Simultaneous spin flips, made possible by the static part of the spin-spin interaction, are included. The equations for two-spin relaxation are generalized to account for the fluid motion and electron spin relaxation as two independent sources of randomness. The results for relaxation and spin pumping are adapted to various special cases and compared with experiments. In particular, qualitative changes in the pumping process are shown to take place when the constant external magnetic field is changed from low to high values.