  The coherent interaction of solid-state spins with both optical and microwave
fields provides a platform for a range of quantum technologies, such as quantum
sensing, microwave-to-optical quantum transduction and optical quantum
memories. Rare-earth ions with electronic spins are interesting in this
context, but it is challenging to simultaneously and efficiently drive both
optical and microwave transitions over a long crystal. In this work, we use a
loop-gap microwave resonator to coherently drive optical and microwave clock
transitions in $^{171}$Yb$^{3+}$:Y$_2$SiO$_5$, at close to zero external
magnetic field. The low magnetic field regime is particularly interesting for
interfacing these spin transitions with superconducting circuits. We achieve a
Rabi frequency of 0.56 MHz at 2.497 GHz, over a 1-cm long crystal. Furthermore,
we provide new insights into the spin dephasing mechanism at very low fields,
showing that superhyperfine-induced collapse of the Hahn echo signal plays an
important role at low fields. Our calculations and measurements reveal that the
effective magnetic moment can be manipulated in $^{171}$Yb$^{3+}$:Y$_2$SiO$_5$,
allowing to suppress the superhyperfine interaction at the clock transition. At
a doping concentration of 2 ppm and a temperature of $3.4$ K, we achieve the
longest spin coherence time of $10.0 \pm 0.4 ~\text{ms}$ reported in
$^{171}$Yb$^{3+}$:Y$_2$SiO$_5$.
