Axial Magnetoelectric Effect in Dirac Semimetals

We propose a mechanism to generate static magnetization via {\em axial magnetoelectric effect} (AMEE). Magnetization ${\bf M} \sim {\bf E}_5(\omega)\times E}_5^{*}(\omega)$ appears as result of the transfer angular momentum electric field E}_5(t)$ into magnetic moment in Dirac and Weyl semimetals. point out similarities differences between proposed AMEE conventional inverse Faraday effect (IFE). As an example, we estimated generated by circularly polarized acoustic waves find it be on scale microgauss for gigahertz frequency sound. In contrast IFE, rises linearly at small frequencies fixed sound intensity well demonstrates nonmonotonic peak behavior AMEE. The provides way investigate unusual electromagnetic fields magnetometry techniques.