A new mechanism of bilinear magnetoresistance (BMR) is proposed and studied theoretically within the minimal model describing surface electronic states in topological insulators. The BMR appears as a consequence of the second-order response to electric field, and depends linearly on both magnetic field and current (electric field). The mechanism is based on the interplay of current-induced spin polarization and scattering processes due to inhomogeneities of spin-momentum locking, that unavoidably appear as a result of structural defects in topological insulators. The proposed mechanism leads to the BMR even if the electronic band structure is isotropic (e.g., absence of hexagonal warping), and is shown to be dominant at lower Fermi energies.

Two-dimensional (2D) Rashba systems have been intensively studied in the last decade due to their unconventional physics, tunability capabilities, and potential for spin-charge interconversion when compared to conventional heavy metals. With the advent of a new generation of spin-based logic and memory devices, the search for Rashba systems with more robust and larger conversion efficiencies is expanding. Conventionally, demanding techniques such as angle- and spin-resolved photoemission spectroscopy are required to determine the Rashba parameter ${\alpha }_R$ that characterizes these systems. Here, we introduce a simple method that allows a quantitative extraction of ${\alpha }_R$, through the analysis of the bilinear response of angle-dependent magnetotransport experiments. This method is based on the modulation of the Rashba-split bands under a rotating in-plane magnetic field. We show that our method is able to correctly yield the value of ${\alpha }_R$ for a wide range of Fermi energies in the 2D electron gas at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface. By applying a gate voltage, we observe a maximum ${\alpha }_R$ in the region of the band structure where interband effects maximize the Rashba effect, consistent with theoretical predictions.

Spin, anomalous, and valley Hall effects in graphene-based hybrid structures are studied theoretically within the Green function formalism and linear response theory. Two different types of hybrid systems are considered in detail: (i) graphene/boron nitride/ferromagnetic metal (cobalt or nickel), and (ii) graphene/magnetic insulator (YIG). The main interest is focused on the proximity-induced exchange interaction between graphene and magnetic substrate and on the proximity-enhanced spin–orbit coupling. The proximity effects are shown to have a significant influence on the electronic and spin transport properties of graphene. To find the spin, anomalous and valley Hall conductivities we employ certain effective Hamiltonians which have been proposed recently for the hybrid systems under considerations. Both anomalous and valley Hall conductivities are shown to have universal values when the Fermi level is inside the energy gap in the electronic spectrum.

Spin polarization induced by an external electric field in graphene is considered theoretically in the linear-response regime. The graphene is assumed to be deposited on a substrate which leads to the spin-orbit interaction of Rashba type. The induced spin polarization is shown to be in the graphene plane and perpendicular to the electric field. However, orientation of the spin polarization becomes reversed when the Fermi level, the position of which can be controlled by an external gate voltage, crosses the Dirac points.

Using the Green-function formalism, we calculate a current-induced spin polarization of weakly magnetized graphene with Rashba spin-orbit interaction. In a general case, all components of the current-induced spin polarization are nonzero, contrary to the nonmagnetic limit, where the only nonvanishing component of spin polarization is that in the graphene plane and normal to the electric field. When the induced spin polarization is exchange coupled to the magnetization, it exerts a spin-orbit torque on the latter. Using the Green-function method, we have derived some analytical formulas for the spin polarization and also determined the corresponding spin-orbit torque components. The analytical results are compared with those obtained numerically. Vertex corrections due to scattering on randomly distributed impurities are also calculated and shown to enhance the spin polarization calculated in the bare bubble approximation.