Broadband phonon production from axion absorption

We show that axion dark matter in the range meV $\lesssim m_a\lesssim$ 100 meV can incoherently excite phonons in crystal targets with unpolarised nuclear spins. This can occur through its coupling to nuclear spins and/or through its induced time-dependent electric dipole moment in nuclei. Due to the random orientation of the nuclear spins, translation symmetry is broken in the phonon effective theory, allowing axion absorption to create phonons with unrestricted momentum. The absorption rate is therefore proportional to the phonon density of states, which generically has support across a wide range of energies, allowing for a broadband detection scheme. We calculate the absorption rate for solid $\text{H}_2$, $\text{D}_2$, $\text{Al}_2\text{O}_3$, $\text{GaAs}$, $\text{H}_2\text{O}$, $\text{D}_2\text{O}$, $\text{Be}$ and $\text{Li}_2 \text{O}$, and find that materials containing light, non-zero spin nuclei are the most promising. The predicted rates for the QCD axion are of the order of a few events / 10 kg-year exposure, setting an ambitious target for the required exposure and background suppression.