  The total angular momentum of a close system is a conserved quantity, which
should remain constant in time for any excitation experiment once the pumping
signal has extinguished. Such conservation, however, is never satisfied in
practice in any real-time first principles description of the demagnetization
process. Furthermore, there is a growing experimental evidence that the same
takes place in experiments. The missing angular momentum is usually associated
to lattice vibrations, which are not measured experimentally and are never
considered in real-time simulations. Here we critically analyse the issue and
conclude that current state-of-the-art simulations violate angular momentum
conservation already at the electronic level of description. This shortcoming
originates from an oversimplified description of the spin-orbit coupling, which
includes atomic contributions but neglects completely that of itinerant
electrons. We corroborate our findings with time-dependent simulations using
model tight-binding Hamiltonians, and show that indeed such conservation can be
re-introduced by an appropriate choice of spin-orbit coupling. The consequences
of our findings on recent experiments are also discussed.
