  We demonstrate that ultralight axion dark matter with a coupling to photons
induces an oscillating global terrestrial magnetic field signal in the presence
of the background geomagnetic field of the Earth. This signal is similar in
structure to that of dark-photon dark matter that was recently pointed out and
searched for in [arXiv:2106.00022] and [arXiv:2108.08852]. It has a global
vectorial pattern fixed by the Earth's geomagnetic field, is temporally
coherent on long time scales, and has a frequency set by the axion mass $m_a$.
In this work, we both compute the detailed signal pattern, and undertake a
search for this signal in magnetometer network data maintained by the SuperMAG
Collaboration. Our analysis identifies no strong evidence for an axion
dark-matter signal in the axion mass range $2\times10^{-18}\text{eV} \lesssim
m_a \lesssim 7\times10^{-17}\text{eV}$. Assuming the axion is all of the dark
matter, we place constraints on the axion-photon coupling $g_{a\gamma}$ in the
same mass range; at their strongest, for masses $3\times 10^{-17}\text{eV}
\lesssim m_a \lesssim 4\times 10^{-17}\text{eV}$, these constraints are
comparable to those obtained by the CAST helioscope.
