Search for axion-like dark matter using solid-state nuclear magnetic resonance

We report the results of an experimental search for ultralight axion-like dark matter in the mass range 162 neV to 166 neV. The detection scheme of our Cosmic Axion Spin Precession Experiment (CASPEr) is based on a precision measurement of $^{207}$Pb solid-state nuclear magnetic resonance in a polarized ferroelectric crystal. Axion-like dark matter can exert an oscillating torque on $^{207}$Pb nuclear spins via the electric-dipole moment coupling $g_d$, or via the gradient coupling $g_{\text{aNN}}$. We calibrated the detector and characterized the excitation spectrum and relaxation parameters of the nuclear spin ensemble with pulsed magnetic resonance measurements in a 4.4 T magnetic field. We swept the magnetic field near this value and searched for axion-like dark matter with Compton frequency within a 1 MHz band centered at 39.65 MHz. Our measurements place the upper bounds $|g_d|<9.5\times10^{-4}\,\text{GeV}^{-2}$ and $|g_{\text{aNN}}|<2.8\times10^{-1}\,\text{GeV}^{-1}$ (95% confidence level) in this frequency range. The constraint on $g_d$ corresponds to an upper bound of $1.0\times 10^{-21}\,\text{e}\cdot\text{cm}$ on the amplitude of oscillations of the neutron electric dipole moment, and $4.3\times 10^{-6}$ on the amplitude of oscillations of CP-violating $\theta$ parameter of quantum chromodynamics. Our results demonstrate the feasibility of using solid-state nuclear magnetic resonance to search for axion-like dark matter in the nano-electronvolt mass range.