Long-lived spin echoes in a magnetically dilute system: An NMR study of Ge single crystals

Owing to the well-developed technology, isotopic engineering of Si and Ge semiconductors permits one to control the density of nuclear spins and vary the spin coherence time, a crucial parameter in spintronics and quantum computing where nuclear spin is used as a qubit. In the present paper, we report on the NMR study of Ge73 nuclear spin decoherence in germanium single crystals with different abundances of the Ge73 isotope. Our measurements of Hahn- and solid-echo decays show that they are well fit by a superposition of two exponentials; at that, the deviation from the single exponential is more pronounced in the more spin-diluted sample, causing long-lived echoes. We show that the decay of these echoes becomes slower with the reduction of Ge73 abundance and is therefore caused by dipole-dipole interaction, reflecting the fundamental decoherence process in the spin system. The fast decay at the beginning of the relaxation process is shown to be mainly caused by the quadrupole interaction. Our experimental findings are supported by the calculations of Hahn- and solid-echo decays in the germanium crystals under study. Quite good agreement between the theory and experiment is demonstrated.