|Structure of TTF-TCNQ (image downloaded from http://www.intechopen.com/books/nanowires-fundamental-research/nanowires-of-molecule-based-conductors)|
In an ideal world without perturbations one would observe a sharp delta function agh the nuclear Larmor frequency. However, perturbations generate random magnetic fields at the sites of the nucleus and lead to a broadening of the resonance line. A source of perturbation is the electronic spins which couple to the nuclear spins through hyperfine interaction and thus generating a fluctuating magnetic field (at the nucleus site) reflecting the dynamics of the electron spin motion.
Assuming the electrons perform a random walk in one dimension it can be shown using the spin-spin correlation function that the spin lattice relaxation rate for this case needs to be proportional to x=1/Sqrt(H), where H is the initial external magnetic field.
In the measurement the spin-lattice relaxation rate is measured which is then plotted versus x. There is a wide range where the relaxation rate is proportional to 1/Sqrt(H) indicating 1D diffusion of electronic spins.