  Solid-state platforms based on electro-nuclear spin systems are attractive
candidates for rotation sensing due to their excellent sensitivity, stability,
and compact size, compatible with industrial applications. Conventional
spin-based gyroscopes measure the accumulated phase of a nuclear spin
superposition state to extract the rotation rate and thus suffer from spin
dephasing. Here, we propose a gyroscope protocol based on a two-spin system
that includes a spin intrinsically tied to the host material, while the other
spin is isolated. The rotation rate is then extracted by measuring the relative
rotation angle between the two spins starting from their population states,
robust against spin dephasing. In particular, the relative rotation rate
between the two spins can be enhanced by their hyperfine coupling by more than
an order of magnitude, further boosting the achievable sensitivity. The
ultimate sensitivity of the gyroscope is limited by the lifetime of the spin
system and compatible with a broad dynamic range, even in the presence of
magnetic noises or control errors due to initialization and qubit
manipulations. Our result enables precise measurement of slow rotations and
exploration of fundamental physics.
