Signature of axion dark matter in low-frequency terrestrial electromagnetic fields: formulation and predictions

We develop a theoretical framework for axion dark matter (DM) searches using terrestrial electromagnetic (EM) fields, enabling a global and quantitative characterization of the signal across the Earth. Axions couple to the geomagnetic field and generate a monochromatic EM signal at a frequency set by the axion mass. Incorporating a realistic atmospheric conductivity, we describe the axion-induced EM waves confined in the Earth-ionosphere cavity, avoiding the divergences present in idealized treatments. Our semi-analytical method yields quantitative predictions for the axion-induced magnetic field near the Earth's surface, and we found that (i) at $m_{\rm a}\gtrsim10^{-14}$ eV, the signal exhibits resonance structures aligned with Schumann resonances, and the magnetic field amplitude is especially enhanced at $m_{\rm a}\sim3\times10^{-14}$ eV. (ii) The signal amplitude and orientation also vary with geographic location, with Southeast Asia offering the strongest sensitivity. These predictions are insensitive to uncertainties in conductivity models and boundary conditions. Those distinctive features provide a reliable template to distinguish axion-induced signals from natural or anthropogenic EM backgrounds, and the formalism can be extended to other DM candidates such as dark photons.