  Ultralight axion-like particles are well-motivated relics that might compose
the cosmological dark matter and source anomalous time-dependent magnetic
fields. We report on new terrestrial bounds on the coupling of axion-like
particles to neutrons and protons using the nuclei of noble-gas and
alkali-metal atoms in a comagnetometer detector operating in the Spin-Exchange
Relaxation-Free~(SERF) regime. Conducting a month-long search, we cover the
mass range of $1.4\times 10^{-12}$ eV/$c^2$ to $2\times 10^{-10}$~eV/$c^2$ and
provide world-leading limits which supersede robust astrophysical bounds and
improve upon previous terrestrial constraints by up to two orders of magnitudes
for many masses within this range. These are the first reliable terrestrial
bounds reported on the coupling of protons with axion-like dark matter,
covering a new and unexplored terrain in its parameter space.
