  We propose the use of the Earth as a transducer for ultralight dark-matter
detection. In particular we point out a novel signal of kinetically mixed
dark-photon dark matter: a monochromatic oscillating magnetic field generated
at the surface of the Earth. Similar to the signal in a laboratory experiment
in a shielded box (or cavity), this signal arises because the lower atmosphere
is a low-conductivity air gap sandwiched between the highly conductive interior
of the Earth below and ionosphere or interplanetary medium above. At low masses
(frequencies) the signal in a laboratory detector is usually suppressed by the
size of the detector multiplied by the dark-matter mass. Crucially, in our case
the suppression is by the radius of the Earth, and not by the (much smaller)
height of the atmosphere. We compute the size and global vectorial pattern of
our magnetic field signal, which enables sensitive searches for this signal
using unshielded magnetometers dispersed over the surface of the Earth. In
principle, the signal we compute exists for any dark photon in the mass range
$10^{-21} \text{eV}\lesssim m_{A'} \lesssim 3\times 10^{-14} \text{eV}$. We
summarize the results of our companion paper [arXiv:2108.08852], in which we
detail such a search using a publicly available dataset from the SuperMAG
Collaboration: we report no robust signal candidates and so place constraints
in the (more limited) dark-photon dark-matter mass range $2\times 10^{-18}
\text{eV} \lesssim m_{A'} \lesssim 7\times 10^{-17} \text{eV}$ (corresponding
to frequencies $6\times 10^{-4} \text{Hz}\lesssim f \lesssim 2\times 10^{-2}
\text{Hz}$). These constraints are complementary to existing astrophysical
bounds. Future searches for this signal may improve the sensitivity over a wide
range of ultralight dark-matter candidates and masses.
