Isotope-Purification-Induced Reduction of Spin-Relaxation and Spin-Coherence Times in Semiconductors

Paramagnetic defects and nuclear spins are often the major sources of decoherence and spin relaxation in solid-state qubits realized by optically addressable point defect spins in semiconductors. It is commonly accepted that a high degree of depletion of nuclear spins can enhance the coherence time by reducing magnetic noise. Here we show that the isotope purification beyond a certain optimal level can become contraproductive when both electron and nuclear spins are present in the vicinity of the qubits, particularly for half-spin systems. Using state-of-the-art numerical tools and considering the silicon-vacancy qubit in various spin environments, we demonstrate that the coupling of the spin-3/2 qubit to a spin bath of spin-1/2 point defects in the lattice can be significantly enhanced by isotope purification. The enhanced coupling shortens the spin-relaxation time that in turn may limit the coherence time of spin qubits. Our results can be generalized to triplet point defect qubits, such as the nitrogen-vacancy center in diamond and the divacancy in silicon carbide.