We theoretically show spin and charge transport on the disordered surface of a three‐dimensional topological insulator with a magnetic insulator when localized spin of the magnetic insulator depends on time and space. To ascertain the transports, we use a low‐energy effective Hamiltonian on the surface of a topological insulator using the exchange interaction and calculate analytically using Green's function techniques within the linear response to the exchange interaction. As a result, the time‐dependent localized spin induces the charge and spin current. These currents are detected from change in the half‐width value of the ferromagnetic resonance of the localized spin when the magnetic resonance of the localized spin is realized in the attached magnetic insulator. We also show spin and charge current generation in a three‐dimensional Weyl–Dirac semimetal, which has massless Dirac fermions with helicity degrees of freedoms. The time‐dependent localized spin drives the charge and spin current in the system. The charge current as well as the spin current in the Weyl–Dirac system are slightly different from those on the surface of the topological insulator.
Part of the book: Magnetic Materials