Brownian spin-locking effect

Nature Materials (2025)Cite this article Brownian systems are characterized by spatiotemporal disorder, which arises from the erratic motion of particles driven by thermal fluctuations. When light interacts with such systems, it typically produces unpolarized and uncorrelated fields. Here we report the observation of a large-scale spin-locking effect of light within a Brownian medium. In an observation direction perpendicular to the incident wave’s momentum, scattering naturally divides into two diffusion regions, each associated with an opposite spin from the Brownian nanoparticles. This effect arises from the intrinsic spin–orbit interactions of scattering from individual nanoparticles, which ubiquitously generate radiative spin fields that propagate through the Brownian medium with multiple incoherent scattering. It offers an experimental platform for exploring macroscale spin behaviour of diffused light, with potential applications in precision metrology for measuring various nanoparticle properties. Our findings may inspire the study of analogous phenomena for different waves from unusual spin–orbit interactions in complex disordered systems.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articlePrices may be subject to local taxes which are calculated during checkoutSource data are provided with this paper. Additional data supporting the conclusions of this study are available from the corresponding author upon request.Anderson, P. W. Absence of diffusion in certain random lattices. Phys. 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This work is supported by National Key Research and Development Program of China (grant no. 2022YFA1205101), National Science Foundation of China (grant nos. 12274296 and 12192252), Shanghai International Cooperation Program for Science and Technology (grant no. 22520714300) and Shanghai Jiao Tong University 2030 Initiative. B.W. is sponsored by Yangyang Development Fund. E.H. acknowledges financial support from the Israel Science Foundation (grant no. 1170/20).These authors contributed equally: Xiao Zhang, Peiyang Chen.State Key Laboratory of Photonics and Communications, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, ChinaXiao Zhang, Peiyang Chen, Mei Li, Bo Wang & Xianfeng ChenZhiyuan College, Shanghai Jiao Tong University, Shanghai, ChinaPeiyang ChenInstitute of Precision Optical Engineering, School of Physics Science and Engineering, Tongji University, Shanghai, ChinaYuzhi ShiAtomic-Scale Photonics Laboratory, Russell Berrie Nanotechnology Institute, and Helen Diller Quantum Center, Technion – Israel Institute of Technology, Haifa, IsraelErez HasmanShanghai Research Center for Quantum Sciences, Shanghai, ChinaXianfeng ChenCollaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan, ChinaXianfeng ChenSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarE.H., B.W. and X.C. supervised this work. B.W. initialized theory and experiment, observed the phenomena and wrote the manuscript. X.Z. systematically performed experimental work, theory and figure preparation. P.C. contributed importantly in Mie theory analysis and assisted in experimental characterization. M.L. performed g2 and SEM measurement. Y.S. assisted in manuscript revision. B.W., X.Z., P.C. and M.L. prepared the supplementary material. E.H. and X.C. contributed to discussions at all stages of this work and revised the manuscript.Correspondence to Erez Hasman, Bo Wang or Xianfeng Chen.The authors declare no competing interests.Nature Materials thanks Francisco Rodríguez Fortuño and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.(a) and (c): plane-wave illumination (Gaussian beam waist ~2 mm); (a) is x- and y-polarized, and (c) is left- and right-handed circularly polarized. (b) and (d): focused-beam illumination (focused beam waist ( ) represents the average light intensity in region ➀ (➁). (d) Variation of with particle concentration. ( ) represents the average absolute value of sx in region ➀ (➁). As the concentration increases, the spin effect becomes weaker, although its spatial distribution remains similar. While the intensity evolution in both regions (➀ and ➁) is comparable across the concentration range, the spin distributions differ significantly. Specifically, when the concentration of nanoparticles is approximately 2.28\(\times\)108 cm−3, the statistically averaged spin at region ➀, , approaches 0, while is about 0.09. Notably, the sx distribution near region ➁ persists over a wide range of concentrations, indicating the robustness of the Brownian spin-locking effect across single and multiple scattering regimes. Data are presented as mean ± s.d. (technical replicates, n = 10).Source data(a) Schematic of Mie scattering. The location of the analytical point (black dot) in the figure is \((5\sqrt{2}\lambda ,\,5\sqrt{2}\lambda ,\,0)\). (b) Phase diagram of sρ at the black dot in (a) with respect to Mie scattering coefficients. sρ represents the radial component of the spin angular momentum density in the xy plane. \({\Phi }_{{a}_{1}},\,{\Phi }_{{b}_{1}},\,{\Phi }_{{a}_{2}}\) represent the phases of \({a}_{1},\,{b}_{1},\,{a}_{2}\), respectively. The spin is strong if there is a ±π/2 phase difference between the two coupled modes, and disappears if the phase difference approaches 0 or π. (c) Spin angular momentum distribution of the Mie scattering field under different combinations of Mie coefficients. The short arrows (orange arrows) represent the spin angular momentum. These scattering cases are divided into three different types. One, for instance, the electric dipole, represents topological-insulator-like spin textures with two orbital spin distributions perpendicular to the radiation cones (a1, b1, a2 = 1, 0, 0). This is a typical transverse spin. For the Janus dipole, the spins are parallel to the radiation cones (a1, b1, a2 = 1, i, 0), that is, longitudinal spin. In general, the spin from scattering is neither perpendicular nor parallel to the kinetic momentum.Source data(a) The histograms are experimentally observed statistical distributions of the spatial intensity (upper panel) and spin (lower panel), which are obtained from the diffusion regions of Figs. 1d and 1e, respectively. The solid curves are fitted using a Burr distribution for the intensity and a Beta distribution for the spin. (b) The calculated spatial distributions of the normalized intensity and spin from the incoherent scattering theory. (c) The calculated spatial distributions of the normalized intensity and spin from the coherent scattering theory. (d) The theoretical evolution of the intensity and spin distributions by changing m/N from 100% (incoherent) to 0.01% (coherent). As the degree of coherence increases, the spin distributions become wider with enhanced skewness, corresponding to increased spin fluctuations that reduce the spin-locking phenomenon.Source dataSupplementary Sections 1–13 and Figs. 1–19.Statistical source data.Statistical source data.Statistical source data.Statistical source data.Statistical source data.Statistical source data.Statistical source data.Statistical source data.Statistical source data.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsZhang, X., Chen, P., Li, M. et al. Brownian spin-locking effect. Nat. Mater. (2025). https://doi.org/10.1038/s41563-025-02413-5Download citationReceived: 10 December 2024Accepted: 17 October 2025Published: 18 November 2025Version of record: 18 November 2025DOI: https://doi.org/10.1038/s41563-025-02413-5Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative