Ce travail de thèse s’intéresse aux corrections relativistes induites par une impulsion lumineuse ultra-brève et intense dans la matière condensée. Il s’inscrit dans la thématique nouvelle de la désaimantation ultra-rapide cohérente de systèmes ferromagnétiques induite par une impulsion laser femto-seconde [Nature 5, 515 (2009)] [1]. Un couplage de nature relativiste entre les spins et les photons a été proposé pour expliquer les résultats expérimentaux observés dans [1]. La première partie de ce travail étudie la limite non relativiste du formalisme de Dirac en présence d’un champ électromagnétique dépendant du temps. En utilisant la transformation de Foldy-Wouthuysen , le hamiltonien électronique de Dirac en présence d’un champ électromagnétique dépendant du temps est développé au cinquième ordre en 1/m. Les résultats obtenus ont permis de postuler une expression générale de l’interaction directe entre le spin et le champ électromagnétique sous la forme d’un développement en série entière. Un travail similaire est réalisé dans le cadre du problème relativiste à deux électrons en interaction coulombienne. La diagonalisation du hamiltonien de Breit au troisième ordre en 1/m fait apparaître une interaction singulière entre le spin, le champ coulombien et le champ électromagnétique externe dépendant du temps. Dans la deuxième partie, on propose un modèle classique pour modéliser une expérience de magnéto-optique non-linéaire réalisée sur des échantillons ferromagnétiques. Les prédictions théoriques des angles de rotation Faraday sont comparées aux résultats expérimentaux de la référence [1] et permettent d’ouvrir une discussion à propos des mécanismes physiques gouvernant les phénomènes magnéto-optiques observés. Le rôle joué par l’interaction spin-orbite entre les spins et le champ électrique du laser est discuté. / This thesis focuses on the relativistic corrections induced by an ultra-short and intense light pulse in condensed matter. It is part of the new theme of the coherent ultra-fast demagnetization of ferromagnetic systems induced by a femtosecond laser pulse [ Nature, 5, 515 (2009)] [1]. A relativistic coupling between spins and photons has been proposed to explain the experimental results obtained in [1]. The first part of this work focuses on the nonrelativistic limit of the Dirac’s formalism. By means of the Foldy–Wouthuysen transformation the nonrelativistic approximation of the external-electromagnetic-field Dirac equation to fifth order in powers of 1/m is obtained. Generalizing this result we postulate a general expression of the direct spin–field electronic hamiltonian valid at any order in 1/m. A similar work is performed on a two-interacting electrons system described with the Breit hamiltonian, whose the diagonalization at third order in 1/m illustrates an original coupling between the spin, the coulombian interaction and the time-dependent external electromagnetic field. In a second part, a classical model is developed for modeling ultrafast nonlinear coherent magneto-optical experiments performed on ferromagnetic thin films. Theoretical predictions of the Faraday rotation angles are compared to available experimental values and give meaningful insights about the physical mechanisms underlying the observed coherent magneto-optical phenomena. The crucial role played by the spin-orbit mechanism resulting from the direct interaction between the external electric field of the laser and the electron spins of the sample is underlined.

Ultrafast dynamical processes in magnetic systems have become the subject of intense research during the last two decades, initiated by the pioneering discovery of femtosecond laser-induced demagnetization in nickel. In this thesis, we develop theory for fast and ultrafast magnetization dynamics. In particular, we build relativistic theory to explain the magnetization dynamics observed at short timescales in pump-probe magneto-optical experiments and compute from first-principles the coherent laser-induced magnetization. In the developed relativistic theory, we start from the fundamental Dirac-Kohn-Sham equation that includes all relativistic effects related to spin and orbital magnetism as well as the magnetic exchange interaction and any external electromagnetic field. As it describes both particle and antiparticle, a separation between them is sought because we focus on low-energy excitations within the particle system. Doing so, we derive the extended Pauli Hamiltonian that captures all relativistic contributions in first order; the most significant one is the full spin-orbit interaction (gauge invariant and Hermitian). Noteworthy, we find that this relativistic framework explains a wide range of dynamical magnetic phenomena. To mention, (i) we show that the phenomenological Landau-Lifshitz-Gilbert equation of spin dynamics can be rigorously obtained from the Dirac-Kohn-Sham equation and we derive an exact expression for the tensorial Gilbert damping. (ii) We derive, from the gauge-invariant part of the spin-orbit interaction, the existence of a relativistic interaction that linearly couples the angular momentum of the electromagnetic field and the electron spin. We show this spin-photon interaction to provide the previously unknown origin of the angular magneto-electric coupling, to explain coherent ultrafast magnetism, and to lead to a new torque, the optical spin-orbit torque. (iii) We derive a definite description of magnetic inertia (spin nutation) in ultrafast magnetization dynamics and show that it is a higher-order spin-orbit effect. (iv) We develop a unified theory of magnetization dynamics that includes spin currents and show that the nonrelativistic spin currents naturally lead to the current-induced spin-transfer torques, whereas the relativistic spin currents lead to spin-orbit torques. (v) Using the relativistic framework together with ab initio magneto-optical calculations we show that relativistic laser-induced spin-flip transitions do not explain the measured large laser-induced demagnetization. Employing the ab initio relativistic framework, we calculate the amount of magnetization that can be imparted in a material by means of circularly polarized light – the so-called inverse Faraday effect. We show the existence of both spin and orbital induced magnetizations, which surprisingly reveal a different behavior. We establish that the laser-induced magnetization is antisymmetric in the light’s helicity for nonmagnets, antiferromagnets and paramagnets; however, it is only asymmetric for ferromagnets.

The spin transport and dynamics of optically injected spin polarized carri- ers are studied with a high spatial and/or time resolution in semiconductor GaAs-based heterostructures in multiple transport regimes. An unexpectedly long-scale and high-speed spin diffusion transport is observed in a long-lived electron sub-system induced optically at an undoped single GaAs/AlGaAs heterointerface. A diffusion and drift-dominated spin transport is investi- gated using an electrical spin-detection via the inverse spin Hall effect in doped GaAs-based systems at room and low temperatures. It is shown that the inverse spin Hall signal and the spin transport parameters can be con- trolled by a direct application of an electric field or by expanding a depleted zone of a planar pn-junction.

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