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Heisenberg representation of nonthermal ultrafast laser excitation of magnetic precessions

We derive the Heisenberg representation of the ultrafast inverse Faraday effect that provides the time evolution of magnetic vectors of a magnetic system during its interaction with a laser pulse. We obtain a time-dependent effective magnetic operator acting in the Hilbert space of the total angular momentum that describes a process of nonthermal excitation of magnetic precessions in an electronic system by a circularly polarized laser pulse. The magnetic operator separates the effect of the laser pulse on the magnetic system from other magnetic interactions. The effective magnetic operator provides the equations of motion of magnetic vectors during the excitation by the laser. We show that magnetization dynamics calculated with these equations is equivalent to magnetization dynamics calculated with the time-dependent Schrödinger equation, which takes into account the interaction of an electronic system with the electric field of light. We model and compare laser-induced precessions of magnetic sublattices of an easy-plane and an easy-axis antiferromagnetic systems. Using these models, we show how the ultrafast inverse Faraday effect induces a net magnetic moment in antiferromagnets and demonstrate that a crystal field environment and the exchange interaction play essential roles for laser-induced magnetization dynamics even during the action of a pump pulse. Using our approach, we show that light-induced precessions can start even during the action of the pump pulse with a duration several tens times shorter than the period of induced precessions and affect the position of magnetic vectors after the action of the pump pulse.