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.

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Fig. 1: Conceptual illustration of a PSHE from a disordered ferromagnetic metasurface.
Fig. 2: The Kerr rotation, Berry–Zak phase and PSHE from a disordered ferromagnetic metasurface.
Fig. 3: Observation of the PSHE from the nanoscale fluctuation of ferromagnetic meta-atoms.
Fig. 4: The stochastic properties of PSHEs from disordered metasurfaces.

Data availability

The data for Figs. 2–4 are available as source data. Other data that support the conclusions of this study are available from the corresponding author upon reasonable request.


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We gratefully acknowledge financial support from the Israel Science Foundation (ISF); the US Air Force Office of Scientific Research (FA9550-18-1-0208) through their programme on Photonic Metamaterials; the Israel Ministry of Science, Technology and Space; the United States−Israel Binational Science Foundation (BSF); and, in part, the Technion via an Aly Kaufman Fellowship. The fabrication was performed at the Micro-Nano Fabrication & Printing Unit (MNF&PU), Technion.

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All the authors contributed substantially to this work.

Corresponding author

Correspondence to Erez Hasman.

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The authors declare no competing interests.

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Peer review information Nature Nanotechnology thanks Vassilios Kapaklis, Francisco Rodríguez-Fortuño and the other, anonymous, reviewers for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary text, Figs. 1–10 and refs. 1–12.

Source data

Source Data Fig. 2

Source data for the simulation results of the Kerr effect and photonic spin Hall effect from disordered Kerr effects.

Source Data Fig. 3

Source data for the experimental results of weak measurements.

Source Data Fig. 4

Source data for the calculated and experimental results for stochastic photonic spin Hall effect.

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Wang, B., Rong, K., Maguid, E. et al. Probing nanoscale fluctuation of ferromagnetic meta-atoms with a stochastic photonic spin Hall effect. Nat. Nanotechnol. 15, 450–456 (2020).

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