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Starting from the Dirac equation, the relativistic quantum hydrodynamicequations for Dirac electrons on a surface of a three dimensional-topologicalinsulator (TI) are derived and numerically solved to study the spin plasmons.The surface of the TI is modulated by a perpendicular magnetic field and apulsed exchange field provided by an array of ferromagnetic insulating (FI)stripes. The collective density and velocity oscillations in thetwo-dimensional Dirac electron gas are simulated and analyzed. It is shown thatin spin plasmons, the collective electron density and momentum are modulated bythe spin state. Direct experimental observations of such oscillations arepossible at laboratory conditions.

Study of spin plasmons on the surface of a topological insulator based on spin quantum hydrodynamics