this magnetic field. Equivalently, the nuclear spins precess around the relative velocity as seen in a rotating frame in which the magnetic field is eliminated. This results (as seen in the lab frame) in a magnetization at an angle to the magnetic field, which precesses around this field with the Larmor frequency. This gives rise to a transverse magnetization, which can be measured with a magnetometer such as a superconducting quantum interference device (SQUID) with a pickup loop oriented as shown in Fig. \[Fig:setup\]. The transverse magnetization rotates at the Larmor frequency set by the external magnetic field. When the ALP oscillation frequency is different from the Larmor frequency, no measurable transverse magnetization ensues. However, when the two frequencies coincide, there occurs a resonance akin to that in the usual NMR, where the spins precess around a transverse axis rotating at the Larmor frequency [@BudkerBook]. This effect enhances the precessing transverse magnetization that can be detected with the SQUID magnetometer. The magnitude of the external magnetic field (${B_\text{ext}}$) is swept to search for a resonance. At time $t=0$ the spins are prepared along ${\vec{B}_\text{ext}}$, then the magnitude of the transverse magnetization is given by $$\label{eqn: magnetization signal}
M(t) \approx n p \mu \, \left(g_{\text{aNN}} \sqrt{2 \, \rho_{\text{DM}}} v\right) \, \frac{\sin \left( \left( 2 \mu {B_\text{ext}}- m_a \right) t \right)}{2 \mu {B_\text{ext}}- m_a}  \sin \left(  2 \mu {B_\text{ext}}t \right),$$ where $n$ is the number density of nuclear spins, $p$ is the polarization, and $\mu$ is the nuclear magnetic dipole moment. The resonant enhancement occurs when $2 \mu {B_\text{ext}}\approx m_a$. Taking $n \sim \frac{10^{22}}{\text{cm}^3}$, $p \sim \mathcal{O}\left(1\right)$, $\mu \sim \mu_N$ (the nuclear Bohr magneton) and interrogation time $ t \sim \tau_a \sim \frac{10^{6}}{m_a}$ (the ALP coherence time), we get $$M \approx 2 \times 10^{-14} \, \text{T} \, \left(\frac{g_{\text{aNN}}}{10^{-