  We consider the possibility to detect cosmic light dark matter (DM), i.e.,
axions and dark photons, of mass $\sim 10^{-6}$ eV and $\sim 10^{-4}$ eV, by
magnetic excitation in a magnet with strong hyperfine interaction. In
particular, we consider a canted anti-ferromagnet, MnCO$_3$, as a concrete
candidate material. With spin transfer between nuclear and electron spins
allowed by the hyperfine interaction, nuclear spins become naturally highly
polarized due to an effective (electron-spin-induced) magnetic field, and have
long-range interactions with each other. The collective precession of nuclear
spins, i.e., a nuclear magnon, can be generated by the DM field through the
nucleon-DM interaction, while they are also sensitive to the electron-DM
interaction through the electron-nuclear spin mixing. Compared with
conventional nuclear-spin precession experiments, this system as a DM sensor is
sensitive to higher frequency needing only a small static magnetic field
applied. The system also has collective precession of electron spins, mixed
with nuclear spins, as the additional channels that can be used for DM probes.
We estimate the sensitivity under appropriate readout setups such as an
inductive pick-up loop associated with an LC resonant circuit, or a photon
cavity with a photon counting device. We show that this method covers an
unexplored parameter region of light bosonic DM.
