Late-time magnetogenesis driven by ALP dark matter and dark photon

We propose a mechanism generating primordial magnetic fields after the $e^+e^-$ annihilations. Our mechanism involves an ultra-light axion-like particle (ALP) which constitutes the dark matter, and a dark $U(1)_X$ gauge boson introduced to bypass the obstacle placed by the conductivity of cosmic plasma. In our scheme, a coherently oscillating ALP amplifies the dark photon field, and part of the amplified dark photon field is concurrently converted to the ordinary magnetic field through the ALP-induced magnetic mixing. For the relevant ALP mass range $10^{-21} {\rm eV}\lesssim m_\phi\lesssim 10^{-17}{\rm eV}$, our mechanism can generate $B\sim 10^{-24} \,{\rm G} \,(m_\phi/10^{-17} {\rm eV})^{5/4}$ with a coherent length $\lambda \sim (m_\phi/10^{-17} {\rm eV})^{-1/2}$ kpc, which is large enough to provide a seed of the galactic magnetic fields. The mechanism also predicts a dark $U(1)_X$ electromagnetic field $E_X \sim B_X\sim 80\,{\rm nG}\, (m_\phi/10^{-17}{\rm eV})^{-1/4}$, which can result in interesting astrophysical/cosmological phenomena by inducing the mixings between the ALP, ordinary photon, and dark photon states.