  The decoherence of mixed electron-nuclear spin qubits is a topic of great
current importance, but understanding is still lacking: while important
decoherence mechanisms for spin qubits arise from quantum spin bath
environments with slow decay of correlations, the only analytical framework for
explaining observed sharp variations of decoherence times with magnetic field
is based on the suppression of classical noise. Here we obtain a general
expression for decoherence times of the central spin system which exposes
significant differences between quantum-bath decoherence and decoherence by
classical field noise. We perform measurements of decoherence times of bismuth
donors in natural silicon using both electron spin resonance (ESR) and nuclear
magnetic resonance (NMR) transitions, and in both cases find excellent
agreement with our theory across a wide parameter range. The universality of
our expression is also tested by quantitative comparisons with previous
measurements of decoherence around `optimal working points' or `clock
transitions' where decoherence is strongly suppressed. We further validate our
results by comparison to cluster expansion simulations.
