  We propose an experiment to search for QCD axion and axion-like-particle
(ALP) dark matter. Nuclei that are interacting with the background axion dark
matter acquire time-varying CP-odd nuclear moments such as an electric dipole
moment. In analogy with nuclear magnetic resonance, these moments cause
precession of nuclear spins in a material sample in the presence of an electric
field. Precision magnetometry can be used to search for such precession. An
initial phase of this experiment could cover many orders of magnitude in ALP
parameter space beyond the current astrophysical and laboratory limits. And
with established techniques, the proposed experimental scheme has sensitivity
to QCD axion masses m_a < 10^-9 eV, corresponding to theoretically
well-motivated axion decay constants f_a > 10^16 GeV. With further
improvements, this experiment could ultimately cover the entire range of masses
m_a < 10^-6 eV, complementary to cavity searches.
