We propose a mechanism for the inverse Faraday and the inverse Cotton-Mouton effects arising from quantum geometry, characterized by the quantum metric quadrupole and the weighted quantum metric. Within a semiclassical framework based on the Boltzmann transport theory, we establish a general formalism describing light-induced magnetization in electronic systems as a second-order response to the electric field of light. Using continuum and tight-binding models, we discuss the symmetry constraints on these effects and estimate the magnitudes of the resulting magnetizations. Our results highlight a direct manifestation of quantum-geometric quantities in nonlinear magneto-optical responses and suggest possible routes toward experimental detection.

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• Geometric & topological phases
• Light-induced magnetic effects
• Magnetism
• Magneto-optics
• Optical & microwave phenomena
• Photoinduced effect
• Quantum geometry
• Magnetic systems
• Bloch wave theory
• Boltzmann theory
• Tight-binding model