Topological Hall effect in systems with magnetic skyrmions

Abstract

This work is focused on the theoretical investigation of spin-dependent transport phenomena and the skew-scattering induced Hall conductivity in two-dimensional systems with spin textures. Firstly, we analyse the topological Hall effect (THE) due to an electron skew scattering on chiral spin textures in real space of a magnetic material, such as magnetic skyrmions, topologically charged configuration of the magnetization. Employing exact and perturbative evaluations of the electron scattering cross-section on a magnetic texture, and using the Boltzmann kinetic equation, we show that the magnitude of the THE varies from topologically quantized value in the strong coupling regime to the texture size-dependent value persisting even for topologically trivial textures in the weak coupling. The predicted theoretical behavior of the THE is discussed for the fluctuations enhancement of the Hall effect observed in experiments with magnetic multilayers hosting nano-scale magnetic skyrmions across a phase transition. Secondly, when spin textures are induced in k-space, e.g. due to a spin-orbit coupling and breaking of the inversion symmetry, we show that a skew scattering on magnetic impurities, in addition to the spin Hall effect, also leads to the anomalous Hall effect even in the absence of the electron spin polarization and due to the paramagnetic impurities orientation. Finally, we investigate microscopic mechanisms of the equilibrium chiral spin orientation of the electron gas in the presence of spatially inhomogeneous electrostatic potential, e.g. due to impurities or gate voltage fluctuations, and resulting from the combination of magnetism and spin textures in the momentum space.