We propose a magnetic photonic crystal (MPC) nanostructure with a gradient thickness of the magnetic layer. Such a nanostructure exhibits on-the-fly adjustment of optical and magneto-optical (MO) properties. Spatial displacement of the input beam allows tuning of the spectral position of the defect mode resonance in the bandgap of both transmission and magneto-optical spectra. Meanwhile, by varying the diameter of the input beam or its focus one can control the resonance width in both optical and magneto-optical spectra.