The Magneto-optical effect is a fundamental and well-studied phenomenon in the linear regime, but it is rarely studied in extreme conditions where both the magnetic and the laser fields are strong. Here, we study this effect theoretically in graphene in the nonlinear regime, where high-order harmonics are generated. It is found that the harmonic conversion efficiency can be enhanced by orders of magnitude, and the cutoff energy could be extended from visible to extreme ultraviolet ranges. When the laser intensity reaches a critical value, the cutoff energy is linearly dependent on the laser wavelength, outperforming many semiconductors with a wavelength-independent cutoff. These effects closely link to the dense Landau levels. Our Letter sheds light on a promising prospect for the application of the magneto-optical effect in harmonic generation processes in solids.

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• High-order harmonic generation
• Magneto-optical effect
• Semiconductor Bloch equations
• Graphene