Spin Hall effects are a collection of relativistic spin-orbit coupling phenomena in which electrical currents can generate transverse spin currents and vice versa. Although first observed only a decade ago, these effects are already ubiquitous within
spintronics as standard spin-current generators and detectors. Here we review the experimental and theoretical results that have established this sub-field of spintronics. We focus on the results that have converged to give us a clear understanding of the phenomena and how they have evolved from a qualitative to a more quantitative measurement of spin-currents and their associated spin-accumulation. Within the experimental framework, we review optical, transport, and magnetization-dynamics based measurements and link them to both phenomenological and microscopic theories of the effect. Within the theoretical framework, we review the basic mechanisms in both the extrinsic and intrinsic regime which are linked to the mechanisms present in their closely related phenomenon in ferromagnets, the anomalous Hall effect. We also review the connection to the phenomenological treatment based on spin-diffusion equations applicable to certain regimes, as well as the spin-pumping theory of spin-generation which has proven important in the measurements of the spin Hall angle. We further connect the spin-current generating spin Hall effect to the inverse spin galvanic effect, which often accompanies the SHE, in which an electrical current induces a non-equilibrium spin polarization. These effects share common microscopic origins and can exhibit similar symmetries when present in ferromagnetic/non-magnetic structures through their induced current-driven spin torques. Although we give a short chronological overview, the main body is structured from a pedagogical point of view, focusing on well-established and accepted physics.
We report a series of high-resolution cosmological N-body simulations designed to explore the formation and properties of dark matter halos with masses close to the damping scale of the primordial power spectrum of density fluctuations. We further in
vestigate the effect that the addition of a random component, v_rms, into the particle velocity field has on the structure of halos. We adopted as a fiducial model the Lambda Warm Dark Matter cosmology with a non-thermal sterile neutrino mass of 0.5 keV. The filtering mass corresponds then to M_f = 2.6x10^12 M_sun/h. Halos of masses close to M_f were simulated with several million of particles. The results show that, on one hand, the inner density slope of these halos (at radii <~0.02 the virial radius Rvir) is systematically steeper than the one corresponding to the NFW fit or to the CDM counterpart. On the other hand, the overall density profile (radii larger than 0.02Rvir) is less curved and less concentrated than the NFW fit, with an outer slope shallower than -3. For simulations with v_rms, the inner halo density profiles flatten significantly at radii smaller than 2-3 kpc/h (<~0.010-0.015Rvir). A constant density core is not detected in our simulations, with the exception of one halo for which the flat core radius is ~1 kpc/h. Nevertheless, if ``cored density profiles are used to fit the halo profiles, the inferred core radii are ~0.1-0.8 kpc/h, in rough agreement with theoretical predictions based on phase-space constrains, and on dynamical models of warm gravitational collapse. A reduction of v_rms by a factor of 3 produces a modest decrease in core radii, less than a factor of 1.5. We discuss the extension of our results into several contexts, for example, to the structure of the cold DM micro-halos at the damping scale of this model.
