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Coherent spin-light-induced mechanisms in the semi-relativistic limit of the self-consistent Dirac-Maxwell equations

We present a self-consistent mean-field model based on a two-component Pauli-like equation that incorporates quantum and relativistic effects (up to second-order in 1/c) for both external and internal electromagnetic fields. By taking the semi-relativistic limit of the Dirac-Maxwell equations in the presence of an external electromagnetic field we obtain an analytical expression of a coherent light-induced mean-field Hamiltonian. The latter exhibits several mechanisms that involve the internal mean fields created by all the electrons and the external electromagnetic field (laser). The role played by the light-induced current density and the light-induced second-order charge density acting as sources in Maxwell's equations are clarified. In particular, we identify clearly four different mechanisms involving the spins that may play an important role in coherent ultrafast spin dynamics.