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

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