  Spin and orbital angular momenta are two intrinsic properties of an electron
and are responsible for the physics of a solid. How the spin and orbital evolve
with respect to each other on several hundred femtoseconds is largely unknown,
but it is at the center of laser-induced ultrafast demagnetization. In this
paper, we introduce a concept of the spin-orbital correlation diagram, where
spin angular momentum is plotted against orbital angular momentum, much like
the position-velocity phase diagram in classical mechanics. We use four sets of
highly accurate time-resolved x-ray magnetic circular dichroism (TR-XMCD) data
to construct four correlation diagrams for iron and cobalt. To our surprise, a
pattern emerges. The trace on the correlation diagram for iron is an arc, and
at the end of demagnetization, it has a pronounced cusp. The correlation
diagram for cobalt is different and appears more linear, but with kinks. We
carry out first-principles calculations with two different methods:
time-dependent density functional theory (TDDFT) and time-dependent Liouville
density functional theory (TDLDFT). These two methods agree that the
experimental findings for both Fe and Co are not due t experimental errors. It
is the spin-orbit coupling that correlates the spin dynamics to the orbital
dynamics.Microscopically, Fe and Co have different orbital occupations, which
leads to distinctive correlation diagrams. We believe that this correlation
diagram presents a useful tool to better understand spin and orbital dynamics
on an ultrafast time scale. A brief discussion on the magnetic anisotropy
energy is also provided.
