The Hall resistivity in ferromagnetic materials has an anomalous contribution proportional to the magnetization, which is defined as the anomalous Hall effect (AHE). Being a central topic in the study of ferromagnetic materials for many decades, the AHE was revived in recent years by generating many new understandings and phenomena, e.g. spin-Hall effect, topological insulators. The phase diagram of the AHE was shown recently to exhibit three distinct regions: a skew scattering region in the high conductivity regime, a scattering-independent normal metal regime, and an insulating regime. While the origin of the metallic regime scaling has been understood for many decades through the expected dependence of each contribution, the origin of the surprising scaling in the insulating regime was completely unexplained, leaving the primary challenge to the last step to understand fully the AHE. In this dissertation work we developed a theory to study the AHE in the disordered insulating regime, whose scaling relation is observed to be omega_xy^AH is proportional to omega_xx^(1.40∼1.75) in a large range of materials. This scaling is qualitatively different from the ones observed in metals. In the metallic regime where kFl > > 1, the linear response theory predicts that omega_xx is proportional to the quasi-particle lifetime tau, while omega_xy^AH scales as alpha*tau beta*tau^0, indicating that the upper limit of the scaling exponent is 1.0. Basing our theory on the phonon-assisted hopping mechanism and percolation theory, we derived a general formula for the anomalous Hall conductivity (AHC), and showed that the AHC scales with the longitudinal conductivity as omega_xy^AH ~ omega_xx^gamma with gamma predicted to be 1.33 <= gamma <= 1.76, quantitatively in agreement with the experimental observations. This scaling remains similar regardless of whether the hopping process is long range type (varible range hopping) or short range type (activation E3 hopping), or is influenced by interactions, i.e. Efros-Shklovskii (E-S) regime. Our theory completes the understanding of the AHE phase diagram in the insulating regime.

Cette thèse porte sur l’étude des courants de spin et de l’effet Hall de spin dans des nanostructureslatérales. Des vannes de spin latérales Py/Al, Py/Cu et Py/Au, ont été fabriquées parlithographie électronique, puis optimisées et caractérisées par des mesures de magnéto-transport.Des mesures non locales, de GMR, et d’effet Hanle ont ainsi été enregistrées à 300K et 77K. De l’optimisation des vannes de spin latérales a découlé l’observation de fortes amplitudes designal de spin. De plus, les effets du confinement latéral et vertical de l‘accumulation de spin,par utilisation d’un canal non-magnétique confiné ou de barrières tunnel AlOx, ont été mis enévidence expérimentalement et décrits théoriquement. Des simulations par éléments finis et desanalyses basées sur les modèles de diffusion 1D ont été développées, permettant l’extraction de lapolarisation effective Peff et de la longueur de diffusion de spin lNsf des données expérimentales.Enfin, l’effet Hall de spin dans des matériaux à fort angles de Hall (Pt, aliage d’Au) a étéétudié dans des hétérostructures latérales et par pompage de spin à la résonance ferromagnétique. / This PhD thesis focus on the study of spin currents and of the spin Hall effect in lateralnano-structures. Lateral spin-valves based on Py/Al, Py/Cu and Py/Au, fabricated by meansof electron-beam lithography, have been optimized and characterized using magneto-resistancemeasurements. Non-local, GMR and Hanle effect measurements have been recorded at 300K and77K. The optimization of these lateral spin-valves allowed the observation of high spin signalamplitudes. Lateral and vertical confinement effects on the spin accumulation, by using confinednon-magnetic channel and AlOx tunnel barriers, were evidenced experimentally and describedtheoretically. Finite Elements Method simulations and analyses based on a 1D diffusion modelhave been developed, allowing the extraction from our experimental data of the effective spinpolarization Peff and of the spin diffusion length lNsf .Finally, the spin Hall effect of materials with high spin Hall angles (Pt, Au alloys) has beenstudied using both hybrid lateral nano-structures and spin pumping ferro-magnetic resonance.