Rare-earth doped crystals have long coherence times and the potential to
provide quantum interfaces between microwave and optical photons. Such
applications benefit from a high cooperativity between the spin ensemble and a
microwave cavity -- this motivates an increase in the rare earth ion
concentration which in turn impacts the spin coherence lifetime. We measure
spin dynamics of two rare-earth spin species, 145Nd and Yb doped into
Y2SiO5, coupled to a planar microwave resonator in the high
cooperativity regime, in the temperature range 1.2 K to 14 mK. We identify
relevant decoherence mechanisms including instantaneous diffusion arising from
resonant spins and temperature-dependent spectral diffusion from impurity
electron and nuclear spins in the environment. We explore two methods to
mitigate the effects of spectral diffusion in the Yb system in the
low-temperature limit, first, using magnetic fields of up to 1 T to suppress
impurity spin dynamics and, second, using transitions with low effective
g-factors to reduce sensitivity to such dynamics. Finally, we demonstrate how
the `clock transition' present in the 171Yb system at zero field can be
used to increase coherence times up to T2=6(1) ms.Comment: 8 pages, 5 figure