A new detection channel on atomic ionization for possible neutrino electromagnetic interactions is identified and studied. Significant sensitivity enhancement is demonstrated when the energy transfer to the target is of the atomic-transition scale. The interaction cross section induced by neutrino magnetic moments (μ(ν)) is evaluated with the equivalent photon method. A new limit of μ(ν)(ν[over ¯](e))<1.3×10(-11) μ(B) at 90% confidence level is derived by using current reactor neutrino data. Potential reaches for future experiments are explored. Experiments with sub-keV sensitivities can probe μ(ν) to 10(-13) μ(B). Positive observations of μ(ν) in this range would imply that neutrinos are Majorana particles.