  We show that electric currents are induced in inversion asymmetric
ferromagnets if the exchange splitting varies in time after excitation by laser
pulses. We interpret this phenomenon as the magnetic variant of the inverse
Edelstein effect. Based on \textit{ab initio} calculations we determine the
size of this effect in Co/Pt(111) and Mn/W(001) magnetic bilayer systems and
investigate its dependence on the magnetization direction. The comparison of
our theoretical results to experiments measuring the THz signal emitted after
laser excitation suggests that ultrafast demagnetization in 3$d$ transition
metal ferromagnets is dominated by transverse spin fluctuations rather than by
a reduction of the exchange splitting.
