Low-frequency dielectric susceptibility of-doped KCl

We report measurements of the complex dielectric susceptibility of lithium defects in potassium chloride (KCl:Li). Experiments were performed at a frequency of 10 kHz and at temperatures between 10 mK and 10 K on single crystals doped with either (Formula presented) or (Formula presented). The lithium concentrations ranged from 4 ppm to 1100 ppm. At concentrations of a few ppm the lithium defects are well described as isolated tunneling systems. For the samples containing 60 ppm or more, we surprisingly observe that the dielectric susceptibility does not scale with the Li concentration. Moreover, we find a relaxation contribution, which indicates collective motion of the defects. Comparing our results with a recent theory based on a Mori approach, we find the motional spectrum of the defects to exhibit a crossover from coherent one-particle tunneling at concentrations below a few ppm to collective incoherent relaxation above 600 ppm. This dissipation mechanism is quite different from the usually considered relaxation based on the interaction with the phonon bath. Without any adjustable parameters, the theory accounts well for several measured quantities.