Recently, interactions between putative axions and magnetic monopoles have been revisited by two of the authors.[1] It is shown that significant modifications to conventional axion electrodynamics arise due to these interactions, so that the axion–photon coupling parameter space is expanded from one parameter to three . Poynting theorem is implemented to determine how to exhibit sensitivity to and using resonant haloscopes, allowing new techniques to search for axions and a possible indirect way to determine if magnetically charged matter exists.