  We propose a mechanism to generate a static magnetization via the axial
electromagnetic fields in Dirac and Weyl semimetals via $axial$
$magnetoelectric$ $effect$ (AME). Magnetization ${\bf M} \sim {\bf E}_5(\omega)
\times {\bf E}_5^{*}(\omega)$ appears as a result of transfer of the angular
momentum of the axial electric field ${\bf E}_5(t)$ into the magnetic moment of
the sample. We point similarities and differences between the proposed AME and
conventional inverse Faraday effect (IFE). As an example, we estimated the AME
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 AME. The effect
provides a way to investigate unusual axial electromagnetic fields via
conventional magnetometry techniques.
