intrinsic properties of the material, where the carrier's trajectories are distorted due to spin–orbit interaction as a consequence of the asymmetries in the material. One can intuitively picture the intrinsic effect by using the classical analogy between an electron and a spinning tennis ball. The tennis ball deviates from its straight path in air in a direction depending on the sense of rotation, also known as the Magnus effect. In a solid, the air is replaced by an effective electric field due to asymmetries in the material, the relative motion between the magnetic moment (associated to the spin) and the electric field creates a coupling that distorts the motion of the electrons. Similar to the standard Hall effect, both the extrinsic and the intrinsic mechanisms lead to an accumulation of spins of opposite signs on opposing lateral boundaries. Mathematical description The spin current is described by a second-rank tensor , where the first index refers to the direction of flow, and the second one to the spin component that is flowing. Thus denotes the flow density of the y-component of spin in the x-direction. Introduce also the vector qi of charge flow density (which is related to the normal current density j=eq), where e is the elementary charge. The coupling between spin and charge currents is due to spin-orbit interaction. It may be described in a very simple way by introducing a single dimensionless coupling parameter ʏ. Spin Hall magnetoresistance No magnetic field is needed for spin Hall effect. However, if a strong enough magnetic field is applied in the direction perpendicular to the orientation of the spins at the surfaces, spins will precess around the direction of the magnetic field and the spin Hall effect will disappear. Thus in the presence of magnetic field, the combined action of the direct and inverse spin Hall effect leads to a change of the sample resistance, an effect that is of second order in spin-orbit interaction. This was noted by Dyakonov and Perel already in 1971 and later elaborated in more detail by Dyakonov. In recent years, the spin Hall magnetoresistance was extensively studied experimentally both in magnetic and non-magnetic materials (heavy metals, such as Pt, Ta, Pd, where the spin-orbit interaction is strong). Swapping spin currents A transformation of spin currents consisting in interchanging (swapping) of the spin and flow directions (qij → qji) was predicted by Lifshits and Dyakonov. Thus