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Modulation effect on the spin Hall resonance

The effect of a weak electrical modulation on spin Hall resonance is presented here. In presence of the magnetic field normal to the plane of the motion of electron, the Landau levels are formed which get broadened due to the weak modulation. The width of the Landau levels broadening are periodic with the inverse magnetic field. There is a certain magnetic field for which the crossing of Landau levels between spin-up and spin-down branches takes place. This gives rise to the resonance in the spin Hall conductivity (SHC). The Landau levels broadening or the energy correction due to the modulation removes the singularity appears at the resonance field in SHC, leading to the suppression of SHC accompanied by two new peaks around this point. The separation of these two peaks increases with the increase of the modulation period. Moreover, we find that the height of the two peaks are also modulation period dependent.