Axion dark matter search from terrestrial magnetic fields at extremely low frequencies

The natural environment of the Earth can act as a sensitive detector for dark matter in ultralight axions. When axions with masses between $1\times10^{-15}\,{\rm eV}$ and $1\times10^{-13}\,{\rm eV}$ pass through the Earth, they interact with the global geomagnetic field, generating electromagnetic (EM) waves in the extremely low-frequency range ($0.3$--$30\,{\rm Hz}$) through axion-photon coupling. This paper is one of a series of companion papers for~\cite{Taruya:2025zql}, focusing on the data analysis method and search results for an axion signal. Utilizing the theoretical predictions of axion-induced EM spectra from a companion study, we analyzed long-term observational data of terrestrial magnetic fields in this frequency band to search for axion-induced signals. Our analysis identified 65 persistent signal candidates with a signal-to-noise ratio (SNR) greater than 3. Aside from these candidates, we placed a new upper bound on the axion-photon coupling parameter, significantly refining the previous constraint from CAST by at most two orders of magnitude down to $g_{a\gamma} \lesssim 4\times10^{-13} \,{\rm GeV}^{-1}$ for the axion mass around $3 \times 10^{-14}\,{\rm eV}$.