We report the results of an experimental search for ultralight axionlike dark matter in the mass range 162–166 neV. The detection scheme of our Cosmic Axion Spin Precession Experiment is based on a precision measurement of ${}^{207}\mathrm{Pb}$ solid-state nuclear magnetic resonance in a polarized ferroelectric crystal. Axionlike dark matter can exert an oscillating torque on ${}^{207}\mathrm{Pb}$ nuclear spins via the electric dipole moment coupling $g_d$ or via the gradient coupling $g_{aNN}$. We calibrate the detector and characterize the excitation spectrum and relaxation parameters of the nuclear spin ensemble with pulsed magnetic resonance measurements in a 4.4 T magnetic field. We sweep the magnetic field near this value and search for axionlike dark matter with Compton frequency within a 1 MHz band centered at 39.65 MHz. Our measurements place the upper bounds $|g_d|<9.5\times {10}^{-4}{\mathrm{GeV}}^{-2}$ and $|g_{aNN}|<2.8\times {10}^{-1}{\mathrm{GeV}}^{-1}$ (95% confidence level) in this frequency range. The constraint on $g_d$ corresponds to an upper bound of $1.0\times {10}^{-21}e\mathrm{cm}$ 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 axionlike dark matter in the neV mass range.

We derive spectral line shapes of the expected signal for a haloscope experiment searching for axionlike dark matter. The knowledge of these line shapes is needed to optimize an experimental design and data analysis procedure. We extend the previously known results for the axion-photon and axion-gluon couplings to the case of gradient (axion-fermion) coupling. A unique feature of the gradient interaction is its dependence not only on magnitudes but also on directions of velocities of galactic halo particles, which leads to the directional sensitivity of the corresponding haloscope. We also discuss the daily and annual modulations of the gradient signal caused by the Earth’s rotational and orbital motions. In the case of detection, these periodic modulations will be an important confirmation that the signal is sourced by axionlike particles in the halo of our Galaxy.

Nuclear magnetic resonance is a promising experimental approach to search for ultra-light axion-like dark matter. Searches such as the cosmic axion spin-precession experiments (CASPEr) are ultimately limited by quantum-mechanical noise sources, in particular, spin-projection noise. We discuss how such fundamental limits can potentially be reached. We consider a circuit model of a magnetic resonance experiment and quantify three noise sources: spin-projection noise, thermal noise, and amplifier noise. Calculation of the total noise spectrum takes into account the modification of the circuit impedance by the presence of nuclear spins, as well as the circuit back-action on the spin ensemble. Suppression of the circuit back-action is especially important in order for the spin-projection noise limits of searches for axion-like dark matter to reach the quantum chromodynamic axion sensitivity.

Axions and axion-like particles are compelling candidates for ultralight bosonic dark matter, forming coherent oscillating fields that can be probed by experiments known as haloscopes. A broad range of haloscope concepts has been developed, including resonant cavity haloscopes, lumped-element circuit detectors, and spin-based experiments, each sensitive to different axion couplings and mass ranges. Rather than attempting an exhaustive survey of all existing approaches, this comparative review provides a unified framework for the major haloscope classes, establishing a common language for the descriptions of signal generation, noise properties, analytical methodologies, and scanning strategies. Key properties of ultralight bosonic dark matter relevant for detection are summarized first, including coherence time, spectral linewidth, and stochasticity under the standard halo model. The discussion then compares cavity, Earth-scale, lumped-element, and spin haloscopes, focusing on expected signal shapes, dominant noise sources, and statistical frameworks for axion searches. Particular emphasis is placed on consistent definitions of signal-to-noise ratio and on how detector bandwidth, axion coherence, and noise characteristics determine optimal scan strategies. By systematically comparing operating principles and performance metrics across these detector families, this framework clarifies shared concepts as well as the essential differences that govern sensitivity in different mass and coupling regimes. The resulting perspective synthesizes current search methodologies and offers guidance for optimizing future haloscope experiments.

We report the results of an experimental search for ultralight axion-like dark matter in the mass ranges 18.9–20.6 and 21.6–21.9 neV. The Cosmic Axion Spin Precession Experiment-electric probes the axion-nuclear electric dipole moment coupling. We perform solid-state nuclear magnetic resonance on ²⁰⁷Pb spin ensembles which reside in a polarized ferroelectric crystal. The background axion-like dark matter field induces an oscillating torque on the ²⁰⁷Pb spins via the electric dipole moment coupling $g_d$. The experiment is calibrated with pulsed magnetic resonance measurements covering two frequency bands (4.57–4.97 and 5.23–5.29 MHz) that correspond to the axion Compton frequencies associated with the identified axion mass ranges. By sweeping the leading magnetic field applied to the sample, we are able to detect the ²⁰⁷Pb nuclear magnetic resonance in these frequency ranges using a superconducting quantum interference device, inductively coupled to the sample with a broadband circuit. We establish the upper bounds $|g_d|<{4\times 10}^{-4}$ GeV⁻² with 95% confidence in these frequency bands. Our results demonstrate the detection and small-tip angle calibration of low-field ²⁰⁷Pb nuclear magnetic resonance, allowing for sensitivity to axion-like dark matter in the nanoelectron-volt axion mass range.