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Ensembles of bismuth donor spins in silicon are promising storage elementsfor microwave quantum memories due to their long coherence times which exceedseconds. Operating an efficient quantum memory requires achieving criticalcoupling between the spin ensemble and a suitable high-quality factor resonator-- this in turn requires a thorough understanding of the lineshapes for therelevant spin resonance transitions, particularly considering the influence ofthe resonator itself on line broadening. Here, we present pulsed electron spinresonance measurements of ensembles of bismuth donors in natural silicon, abovewhich niobium superconducting resonators have been patterned. By studying spintransitions across a range of frequencies and fields we identify distinct linebroadening mechanisms, and in particular those which can be suppressed byoperating at magnetic-field-insensitive `clock transitions'. Given the donorconcentrations and resonator used here, we measure a cooperativity $C\sim 0.2$and based on our findings we discuss a route to achieve unit cooperativity, asrequired for a quantum memory.

Spin resonance linewidths of bismuth donors in silicon coupled to planar microresonators