  Excitation of a metallic ferromagnet such as Ni with an intensive femtosecond
laser pulse causes an ultrafast demagnetization within approximately 300 fs. It
was proposed that the ultrafast demagnetization measured in femtosecond
magneto-optical experiments could be due to relativistic light-induced
processes. We perform an ab initio investigation of the influence of
relativistic effects on the magneto-optical response of Ni. To this end, we
develop, first, a response theory formulation of the additional appearing
ultra-relativistic terms in the Foldy-Wouthuysen transformed Dirac Hamiltonian
due to the electromagnetic field, and, second, compute the influence of
relativistic light-induced spin-flip transitions on the magneto-optics. Our ab
initio calculations of relativistic spin-flip optical excitations predict that
these can give only a very small contribution ($\leq 0.1$%) to the
laser-induced magnetization change in Ni.
