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