Dark matter detection using nuclear magnetization in magnet with hyperfine interaction

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.