  Intra-atomic exchange couplings (IEC) between $5d6s$ and $4f$ electrons are
ubiquitous in rare-earth metals and play a critical role in spin dynamics.
However, detecting them in real time domain has been difficult. Here we show
the direct evidence of IEC between $5d6s$ and $4f$ electrons in gadolinium.
Upon femtosecond laser excitation, $5d6s$ electrons are directly excited, their
majority bands shift toward the Fermi level while their minority bands do the
opposite. For the first time, our first-principles minority shift now agrees
with the experiment quantitatively. Excited $5d6s$ electrons lower the exchange
potential barrier for $4f$ electrons, so the $4f$ states are also shifted in
energy, a prediction that can be tested experimentally. Although a significant
number of $5d6s$ electrons, some several eV below the Fermi level, are excited
out of the Fermi sea, there is no change in the $4f$ states, a clear
manifestation of intra-atomic exchange coupling. Based on our results, we
propose that the demagnetization time of a material be inversely proportional
to the density of states at the Fermi level and the excited, not the whole,
spin moment. This can be tested experimentally.
