Spatial dispersion of magnetic-edge magnetoplasmons: Effect of semi-infinite gate

Magnetic-edge magnetoplasmons (MEMPs) are obtained for a two-dimensional electron system (2DES) with atop semi-infinite metallic gate, at a distance $d$, and atop semi-infinite ferromagnetic film at a strong perpendicular magnetic field. For two most fast MEMPs, one with positive chirality and other with negative chirality, a strong spatial dispersion, due to effect of metallic half-plane gate, is obtained; some slower MEMPs manifest spatial dispersion too. Present MEMPs are localized at the magnetic-edge that is close to the wedge of metallic half-plane gate; the metallic wedge enhances localization of MEMPs at magnetic-edge. Obtained spatial dispersion has unconventional form. In particular, for two most fast MEMPs the phase velocities, $\omega/k_{x}$, are the linear polynomials on the wave vector $k_{x}$ in the long-wavelength region, $k_{x}d \ll 1$. Strong effect of the ferromagnetic film hysteresis on the MEMPs phase velocities and their anti-crossings are obtained for $0<k_{x}d \leq1$. Two MEMPs of opposite chirality, especially two most fast MEMPs, at some resonance frequency can create a resonance circuit, with closed wave path along a fraction of the magnetic edge perimeter, with a total change of the wave phase given by an integer of $2\pi$.