Axion Sum Rule in Polar Solids

Axions from the local dark matter halo of the galaxy convert infrared electric fields into terahertz magnetic fields within polar solids. The sum of the infrared and terahertz frequencies gives the rest-mass of the axion to percent level precision. Recent broadband infrared transmission spectroscopy of apatites indicates the axion has rest-mass one million times smaller than the electron. The resulting axion sum rule seems to hold in a wide range of polar solids including cuprates, Weyl semimetals, and multiferroic oxides.