In a semiconductor heterostructure, the Coulomb interaction is responsible for the electric current drag between two 2D electron gases across an electron impenetrable insulator. For two metallic layers separated by a ferromagnetic insulator (FI) layer, the electric current drag can be mediated by a nonequilibrium magnon current of the FI. We determine the drag current by using the semiclassical Boltzmann approach with proper boundary conditions of electrons and magnons at the metal\char21{}FI interface.

Exchange interaction between conduction electrons and magnetic moments at magnetic interfaces leads to mutual conversion between spin current and magnon current. We introduce a concept of spin convertance which quantitatively measures magnon current induced by spin accumulation and spin current created by magnon accumulation at a magnetic interface. We predict several phenomena on charge and spin drag across a magnetic insulator spacer for a few layered structures.

We propose an extension of the Landau-Lifshitz-Gilbert (LLG) equation by explicitly including the role of conduction electrons in magnetization dynamics of conducting ferromagnets. The temporal and spatial dependent magnetization order parameter $\mathbf{m}(\mathbf{r},t)$ generates both electrical and spin currents that provide dissipation of the energy and angular momentum of the processing magnet. The resulting LLG equation contains highly spatial dependence of damping term and thus micromagnetic simulations based on the standard LLG equation should be reexamined for magnetization dynamics involving narrow domain walls and spin waves with short wavelengths.

Recent experiments have revealed nonlinear features of the magnetoresistance in metallic bilayers consisting of a heavy metal (HM) and a ferromagnetic metal (FM). A small change in the longitudinal resistance of the bilayer has been observed when reversing the direction of either the applied in-plane current or the magnetization. We attribute such nonlinear transport behavior to the spin-polarization dependence of the electron mobility in the FM layer acting in concert with the spin accumulation induced in that layer by the spin Hall current originating in the bulk of the HM layer. An explicit expression for the nonlinear magnetoresistance is derived based on a simple drift-diffusion model, which shows that the nonlinear magnetoresistance appears at the first order of the spin Hall angle, and changes sign when the current is reversed, in agreement with the experimental observations. We also discuss possible ways to control sign of the nonlinear magnetoresistance and to enhance the magnitude of the effect.

We predict a nonlinear Hall effect in certain Weyl semimetals with broken inversion symmetry. When the energy dispersions about pairs of Weyl nodes are skewed—the Weyl cones are “tilted”—the concerted actions of the anomalous velocity and the chiral anomaly give rise to the nonlinear Hall effect. This Hall conductivity is linear in both electric and magnetic fields and depends critically on the tilting of the Weyl cones. We also show that this effect does not rely on a finite Berry curvature dipole, in contrast with the intrinsic quantum nonlinear Hall effect that was recently observed in type-II Weyl semimetals.

In a bilayer consisting of an insulator and a ferromagnetic metal (FM), interfacial spin-orbit scattering leads to spin mixing of the two conducting channels of the FM, which results in an unconventional anisotropic magnetoresistance (AMR). We theoretically investigate the magnetotransport in such bilayer structures by solving the spinor Boltzmann transport equation with the generalized Fuchs-Sondheimer boundary condition that takes into account the effect of spin-orbit scattering at the interface. We find that the new AMR exhibits a peculiar angular dependence which can serve as a genuine experimental signature. We also determine the dependence of the AMR on film thickness as well as resistivity spin asymmetry of the FM.