Probing nanoscale fluctuation of ferromagnetic meta-atoms with a stochastic photonic spin Hall effect

The photonic spin Hall effect, a deep subdiffraction-limited shift between the opposite spin components of light, emerges when light undergoes an evolution of polarization or trajectory that induces the geometric phase. Here, we study a stochastic photonic spin Hall effect arising from space-variant Berry–Zak phases, which are generated by disordered magneto-optical effects. This spin shift is observed from a spatially bounded lattice of ferromagnetic meta-atoms displaying nanoscale disorders. A random variation of the radii of the meta-atoms induces the nanoscale fluctuation. The standard deviation of the probability distribution of the spin shifts is proportional to the fluctuation of the meta-atoms. This enables us to detect a five-nanometre fluctuation by measuring the probability distribution of the spin shifts via weak measurements. Our approach may be used for sensing deep-subwavelength disorders by actively breaking the photonic spin symmetry and may enable investigations of fluctuation effects in magnetic nanosystems. Magneto-optical interaction of light with magnetic metasurfaces can give rise to the photonic spin Hall effect such that the light trajectory depends on the polarization of the light. For disordered systems, the probability distribution of the spin-dependent trajectories is a sensitive tool to detect random nanoscale variations in the metasurface.