The Magneto-Optical Activity of Any Dipolar Particle Has a Universal Upper Bound

Abstract Based on energy conservation, we prove that the magneto-optical activity of any dipolar nanoparticle (NP) has a universal upper bound. We derive a simple analytical expression for this ultimate limit and prove that it can be attained only by nonabsorbing dipolar NPs. The bound is general: it is independent of the incident illumination, specific material properties, NP shape, and the origin of magnetization, whether spontaneous (bias-free) or induced by a static external magnetic field. Strikingly, the bound is also independent of the magnetization strength in any material or metamaterial. This work establishes the ultimate magneto-optical limit of any dipolar NP at the single-particle level, setting fundamental constraints on all observables constructed from their polarizability tensor.