- Open Access
Interacting magnetic nanoparticles as building blocks for miniaturized magnetic tags in anticounterfeiting strategies
Phys. Rev. Applied 25, 024084 – Published 26 February, 2026
DOI: https://doi.org/10.1103/zk8l-5173
Abstract
Miniaturized, unique, stable, and information-rich tags are crucial for anticounterfeiting efforts in the handling and distribution of consumable goods. Despite ongoing research into various tag technologies, a systematic approach to engineering their physical properties for optimal security is often missing. Through a numerical approach focused on in-depth modeling of the interacting magnetic nanoparticle properties, we demonstrate how their collective magnetic behavior, after suitable field conditioning, boosts the security of magnetic tags. Our miniaturized tag leverages the nonlinear response of assemblies of interacting nanoparticles to store custom information into binary keys. The magnetic properties of the nanoparticles and their spatial correlations result to be crucial to effectively decorrelate all keys from a large batch of tags produced under identical conditions. This ensures each tag encodes unique, virtually unclonable information, guaranteeing secure product identification, traceability, and quality control, enhancing consumer safety and fighting counterfeiting. The tag stability against transient disturbances of thermal and magnetic nature has been assessed. Our numerical analysis establishes magnetic nanoparticle tags as highly promising primitives characterized by high entropic information and security resilience to cloning, paving the way to better-engineered devices that harness the collective magnetic properties of nanoparticles.
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References (102)
- T. R. C. Konfo, F. M. C. Djouhou, M. H. Hounhouigan, E. Dahouenon-Ahoussi, F. Avlessi, and C. K. D. Sohounhloue, Recent advances in the use of digital technologies in agri-food processing: A short review, Appl. Food Res. 3, 100329 (2023).
- E. Skrzetuska and P. Rzeźniczak, Circularity of smart products and textiles containing flexible electronics: Challenges, opportunities, and future directions, Sensors 25, 1787 (2025).
- R. Hailu, T. Gizaw, N. Berhanu, T. Mulugeta, B. Boche, and T. Gudeta, Exploring the role of ICT in pharmaceutical supply chain practices and operational performance in Ethiopia: A structural equation modeling approach, BMC Health Serv. Res. 23, 634 (2023).
- L. Hvam, Mass customisation in the electronics industry: Based on modular products and product configuration, Int. J. Mass Customisation 1, 410 (2006).
- K. Ge, Y. Hu, J. Yan, J. Ding, Y. Gao, H. Yi, Z. Li, L. Cui, S. Hu, H. Ji, et al., Bio-inspired structural color irises as physical unclonable functions for anti-counterfeiting, Adv. Sci. 12, 34 (e04771).
- C. Jiang, J. Yan, R. Du, Y. Li, M. Wu, B. Xu, and J. Qiu, Stimuli-responsive and defect-regulated luminescent organic metal halide for high-security anti-counterfeiting and force sensing, Adv. Sci. 12, 2025 (e10163).
- S. Singh, K. Dev, S. Bhardwaj, D. Ramakanth, K. R. Singh, K. M. Poluri, K. Ghosh, and P. K. Maji, Biodegradable cellulose nanocrystal composites doped with carbon dots for packaging and anticounterfeiting applications, Nanoscale 17, 904 (2025).
- M. N. M. Bhutta and M. Ahmad, Secure identification, traceability and real-time tracking of agricultural food supply during transportation using internet of things, IEEE Access 9, 65660 (2021).
- N.-N. Htun, A. Wiśniewska, G. Nocella, E. Santa Cruz, A. Peracaula-Moner, K. Vehmas, L. Hakola, K. Liczmańska-Kopcewicz, L. Bridgett, and K. Verbert, Smart tag packaging technologies: A qualitative investigation of consumers’ needs and expectations, Packag. Technol. Sci. 36, 595 (2023).
- R. Raman, K. Dhivya, P. Sapra, S. Gurpur, S. Maniraj, and S. Murugan, in 2023 International Conference on Artificial Intelligence for Innovations in Healthcare Industries (ICAIIHI), Vol. 1 (IEEE, Danvers, MA, USA, 2023), p. 1.
- G. Saeed, J. C. Kohler, R. E. Cuomo, and T. K. Mackey, A systematic review of digital technology and innovation and its potential to address anti-corruption, transparency, and accountability in the pharmaceutical supply chain, Expert Opin. Drug Saf. 21, 1061 (2022).
- A. Kordestani, P. Oghazi, and R. Mostaghel, Smart contract diffusion in the pharmaceutical blockchain: The battle of counterfeit drugs, J. Bus. Res. 158, 113646 (2023).
- A. Subrahmannian and S. K. Behera, Chipless RFID sensors for IoT-based healthcare applications: A review of state of the art, IEEE Trans. Instrum. Meas. 71, 1 (2022).
- L. Hakola, F. Abedi, S. Nordman, M. Smolander, and J. Paltakari, Smart tags as enablers for digital product passports in circular electronics value chains, Circ. Econ. Sustain. 5, 2033 (2025).
- E. A. Banu, R. Priyanka, P. Thiruramanathan, T. Senthilnathan, V. VT, and K. Vinoth, in 2024 Ninth International Conference on Science Technology Engineering and Mathematics (ICONSTEM) (IEEE, Danvers, MA, USA, 2024), p. 1.
- X. Xu, S. Liu, Y. Kuai, Y. Jiang, Z. Hu, B. Yu, and S. Li, Laser fabrication of multi-dimensional perovskite patterns with intelligent anti-counterfeiting applications, Adv. Sci. 11, 2309862 (2024).
- U.S. customs and border protection, IPR annual seizure statistics, https://www.cbp.gov/trade/priority-issues/ipr/statistics.
- A. Cook, Variable data printing: What is it, benefits, and how does it work? https://myldi.com/blog/variable-data-printing-benefits/.
- N. Bartneck, V. Klaas, and H. Schönherr, Optimizing Processes with RFID and Auto ID (John Wiley & Sons, Berlin and Munich, Germany, 2009).
- J. Frith, A Billion Little Pieces: RFID and Infrastructures of Identification (Mit Press, Cambridge, MA, USA, 2024).
- R. Focardi, F. L. Luccio, and H. A. Wahsheh, in Computer and Network Security Essentials (Springer, Cham, Switzerland, 2018), p. 207.
- C. Niu, X. Dong, Z. Liang, F. Jiang, X. Bai, T. Sun, and Z. Wang, in 2024 IEEE 2nd International Conference on Control, Electronics and Computer Technology (ICCECT) (IEEE, Jilin, China, 2024), p. 348.
- J. Grosinger, W. Pachler, and W. Bosch, Tag size matters: Miniaturized RFID tags to connect smart objects to the internet, IEEE Microw. Mag. 19, 101 (2018).
- R. J. Lennox, P. M. Mastrodimitropoulos, H. Flávio, K. Cyr, Z. D. Deng, S. J. Cooke, and M. L. Piczak, How small can they go? Microelectronic tags for movement ecology of small aquatic organisms, Fisheries 50, 209 (2025).
- S. Benson, F. De Moliner, W. Tipping, and M. Vendrell, Miniaturized chemical tags for optical imaging, Angew. Chem. Int. Ed. 61, e202204788 (2022).
- S. Shikha, T. Salafi, J. Cheng, and Y. Zhang, Versatile design and synthesis of nano-barcodes, Chem. Soc. Rev. 46, 7054 (2017).
- H. Cheng, Y. Lu, D. Zhu, L. Rosa, F. Han, M. Ma, W. Su, P. S. Francis, and Y. Zheng, Plasmonic nanopapers: Flexible, stable and sensitive multiplex PUF tags for unclonable anti-counterfeiting applications, Nanoscale 12, 9471 (2020).
- D. Zhu, C. Wang, F. Jiao, J. Xu, H. Xu, S. Han, P. Cao, Y. Zeng, M. Fang, W. Liu, et al., Multilevel, solar-blind, and thermostable physical unclonable functions based on host-sensitized luminescence of -, Nanoscale 17, 7128 (2025).
- X. Meng, S. Qiang, J. Li, J. J. Kim, M. Zhang, C. Wang, Z. Ye, Y. Cao, W. Zhang, and G. J. Lee, Hierarchical assembly of upconversion nanoparticle–grating hybrids on flexible nanofibers for multi-level physical unclonable functions, Nanoscale 17, 22513 (2025).
- P. Mishra, A. Manna, and N. Ray, Advances in semiconductor quantum dot-based physical unclonable functions for enhanced security applications, Nanoscale 17, 20865 (2025).
- A. R. Anwar, M. Mur, and M. Humar, Microcavity- and microlaser-based optical barcoding: A review of encoding techniques and applications, ACS Photonics 10, 1202 (2023).
- Y. Hu, S. Yu, X. Deng, J. Zhou, R. Zhang, and Q. Shao, Opposite luminescence thermal behavior of upconversion core/shell nanocrystals for anticounterfeiting, Nanoscale 15, 15552 (2023).
- M. Sharma, C. Cao, G. A. Sepalage, S. Tang, L. Nguyen, H. Deng, N. Nurrosyid, J. Yan, J. Moon, T. Alan, et al., Co-doped perovskite nanocrystals for multiplexed anticounterfeiting applications, Nanoscale 17, 9996 (2025).
- S. R. Nicewarner-Pena, R. G. Freeman, B. D. Reiss, L. He, D. J. Peña, I. D. Walton, R. Cromer, C. D. Keating, and M. J. Natan, Submicrometer metallic barcodes, Science 294, 137 (2001).
- C. Laure, D. Karamessini, O. Milenkovic, L. Charles, and J.-F. Lutz, Coding in 2D: Using intentional dispersity to enhance the information capacity of sequence-coded polymer barcodes, Angew. Chem. Int. Ed. 55, 10722 (2016).
- A. H. Hung, L. M. Lilley, F. Hu, V. S. Harrison, and T. J. Meade, Magnetic barcode imaging for contrast agents, Magn. Reson. Med. 77, 970 (2017).
- C. Li, R. Xu, Y. Duan, X. Zhang, D. Zhu, A. Du, Z. Peng, S. Wang, K. Shi, and W. Zhao, Unraveling spin–orbit torque-induced multistate magnetization switching in Co/Gd ferrimagnetic multilayers for physically unclonable functions, Nanoscale 17, 8016 (2025).
- Y.-W. Hu, T.-P. Zhang, C.-F. Wang, K.-K. Liu, Y. Sun, L. Li, C.-F. Lv, Y.-C. Liang, F.-H. Jiao, W.-B. Zhao, et al., Flexible and biocompatible physical unclonable function anti-counterfeiting label, Adv. Funct. Mater. 31, 2102108 (2021).
- U. Jung, C.-J. Beak, K. Kim, J.-H. Na, and S.-H. Lee, Scalable photo-responsive physical unclonable functions via particle kinetics, ACS Nano 18, 27642 (2024).
- Z. C. Meijs, H. S. Yun, P. Fandre, G. Park, D. K. Yoon, and L. Isa, Pixelated physical unclonable functions through capillarity-assisted particle assembly, ACS Appl. Mater. Interfaces 15, 53053 (2023).
- S. Müssig, F. Fidler, D. Haddad, K.-H. Hiller, S. Wintzheimer, and K. Mandel, Supraparticles with a magnetic fingerprint readable by magnetic particle spectroscopy: An alternative beyond optical tracers, Adv. Mater. Technol. 4, 1900300 (2019).
- S. Müssig, J. Reichstein, J. Prieschl, S. Wintzheimer, and K. Mandel, A single magnetic particle with nearly unlimited encoding options, Small 17, 2101588 (2021).
- N. D. Kohls, A. X. Zheng, J. Kim, G. Mohler, and Y. C. Mazumdar, Magnetic tags with unique self-assembly patterns for tracking applications, J. Magn. Magn. Mater. 535, 168045 (2021).
- D. Salas, D. Ebeperi, M. Elverud, R. Arróyave, R. Malak, and I. Karaman, Embedding hidden information in additively manufactured metals via magnetic property grading for traceability, Addit. Manuf. 60, 103261 (2022).
- X. Song, W. Ma, P. Song, and H. Wang, One-step preparation method and rapid detection implementation scheme for simple magnetic tagging materials, Magnetochemistry 10, 44 (2024).
- L. de Castro Alves, M. A. Cerqueira, M. A. González-Goméz, P. Garcia-Acevedo, Á. A. Prieto, Y. P. Redondo, L. Pastrana, and J. Rivas, Innovative films by embedding magnetic nanoparticles in cellulose acetate, Food Packag. Shelf Life 42, 101264 (2024).
- V. Pilati, M. Salvador, L. B. Fraile, J. L. Marqués-Fernández, F. G. da Silva, M. Fadel, R. L. Antón, M. del Puerto Morales, J. C. Martinez-García, and M. Rivas, Mn-ferrite nanoparticles as promising magnetic tags for radiofrequency inductive detection and quantification in lateral flow assays, Nanoscale Adv. 6, 4247 (2024).
- P. García-Acevedo, M. A. González-Gómez, Á. Arnosa-Prieto, L. de Castro-Alves, Y. Piñeiro, and J. Rivas, Role of dipolar interactions on the determination of the effective magnetic anisotropy in iron oxide nanoparticles, Adv. Sci. 10, 2203397 (2023).
- C. Martinez-Boubeta, K. Simeonidis, D. Serantes, I. Conde-Leborán, I. Kazakis, G. Stefanou, L. Peña, R. Galceran, L. Balcells, C. Monty, et al., Adjustable hyperthermia response of self-assembled ferromagnetic Fe-MgO core–shell nanoparticles by tuning dipole–dipole interactions, Adv. Funct. Mater. 22, 3737 (2012).
- B. D. Cullity and C. D. Graham, Introduction to Magnetic Materials (John Wiley & Sons, Hoboken, New Jersey, USA, 2011).
- A. Kumar, A. K. Jain, and M. Dua, A comprehensive taxonomy of security and privacy issues in RFID, Complex Intell. Syst. 7, 1327 (2021).
- P. Tanuska, L. Spendla, M. Kebisek, R. Duris, and M. Stremy, Smart anomaly detection and prediction for assembly process maintenance in compliance with industry 4.0, Sensors 21, 2376 (2021).
- M. A. Bantahar, S. A. Al-Gailani, and A. A. Salem, in Proceedings of the 11th International Conference on Robotics, Vision, Signal Processing and Power Applications: Enhancing Research and Innovation through the Fourth Industrial Revolution (Springer, Singapore, 2022), p. 156.
- M. Gohar, S. H. Ahmed, M. Khan, N. Guizani, A. Ahmed, and A. U. Rahman, A big data analytics architecture for the internet of small things, IEEE Commun. Mag. 56, 128 (2018).
- P. Allia, G. Barrera, and P. Tiberto, Hysteresis effects in magnetic nanoparticles: A simplified rate-equation approach, J. Magn. Magn. Mater. 496, 165927 (2020).
- M. T. Rietberg, S. Waanders, M. M. Horstman-Van de Loosdrecht, R. R. Wildeboer, B. Ten Haken, and L. Alic, Modelling of dynamic behaviour in magnetic nanoparticles, Nanomaterials 11, 3396 (2021).
- K. Merazzo, A. Lima, M. Rincón-Iglesias, L. Fernandes, N. Pereira, S. Lanceros-Mendez, and P. Martins, Magnetic materials: A journey from finding north to an exciting printed future, Mater. Horiz. 8, 2654 (2021).
- B. Rezaei, I. H. Karampelas, M. Saeidi-Javash, J. Gómez-Pastora, K. Wu, and M. Zeng, Printing rare-earth-free (REF) magnetic inks: Synthesis, formulation, and device applications, Nanoscale 17, 4830 (2025).
- K. N. Al-Milaji, R. L. Hadimani, S. Gupta, V. K. Pecharsky, and H. Zhao, Inkjet printing of magnetic particles toward anisotropic magnetic properties, Sci. Rep. 9, 16261 (2019).
- S. Taccola, T. da Veiga, J. H. Chandler, O. Cespedes, P. Valdastri, and R. A. Harris, Micro-scale aerosol jet printing of superparamagnetic nanoparticle patterns, Sci. Rep. 12, 17931 (2022).
- M. Rafiq, R. S. Khan, A. H. Rather, T. U. Wani, A. Qureashi, A. H. Pandith, S.-U. Rather, and F. A. Sheikh, Overview of printable nanoparticles through inkjet process: Their application towards medical use, Microelectron. Eng. 266, 111889 (2022).
- M. Rasekh, Z. Ahmad, R. Cross, J. Hernández-Gil, J. D. Wilton-Ely, and P. W. Miller, Facile preparation of drug-loaded tristearin encapsulated superparamagnetic iron oxide nanoparticles using coaxial electrospray processing, Mol. Pharm. 14, 2010 (2017).
- J. Heo, D. Choi, J. Hong, and M. A. Correa-Duarte, Layer-by-layer self-assembled ferrite multilayer nanofilms for microwave absorption, J. Nanomater. 2015, 164619 (2015).
- E. Sowade, T. Blaudeck, and R. R. Baumann, Inkjet printing of colloidal nanospheres: Engineering the evaporation-driven self-assembly process to form defined layer morphologies, Nanoscale Res. Lett. 10, 362 (2015).
- J. R. Childress and R. E. Fontana Jr, Magnetic recording read head sensor technology, C. R. Phys. 6, 997 (2005).
- G. Bertero, G. Guo, S. Dahandeh, and A. Krishnan, in Ultra-High-Density Magnetic Recording (Jenny Stanford Publisher, New York, USA, 2016), p. 51.
- A. Magni, G. Barrera, F. Celegato, F. Riboli, D. S. Wiersma, S. Nocentini, and P. Tiberto, Magnetic unclonable functions leveraging remanence and anhysteretic states, Adv. Funct. Mater. 35, e16376 (2025).
- M. A. Wright, The advanced encryption standard, Netw. Secur. 2001, 11 (2001).
- B. Bhushan, Current status and outlook of magnetic data storage devices, Microsyst. Technol. 29, 1529 (2023).
- G. Barrera, P. Allia, and P. Tiberto, Dipolar interactions among magnetite nanoparticles for magnetic hyperthermia: A rate-equation approach, Nanoscale 13, 4103 (2021).
- A. Ali, T. Shah, R. Ullah, P. Zhou, M. Guo, M. Ovais, Z. Tan, and Y. Rui, Review on recent progress in magnetic nanoparticles: Synthesis, characterization, and diverse applications, Front. Chem. 9, 629054 (2021).
- Z. Ma, J. Mohapatra, K. Wei, J. P. Liu, and S. Sun, Magnetic nanoparticles: Synthesis, anisotropy, and applications, Chem. Rev. 123, 3904 (2023).
- Z. Nedelkoski, D. Kepaptsoglou, L. Lari, T. Wen, R. A. Booth, S. D. Oberdick, P. L. Galindo, Q. M. Ramasse, R. F. Evans, S. Majetich, et al., Origin of reduced magnetization and domain formation in small magnetite nanoparticles, Sci. Rep. 7, 45997 (2017).
- M. Knobel, W. Nunes, L. Socolovsky, E. De Biasi, J. Vargas, and J. Denardin, Superparamagnetism and other magnetic features in granular materials: A review on ideal and real systems, J. Nanosci. Nanotechnol. 8, 2836 (2008).
- A. Akbarzadeh, M. Samiei, and S. Davaran, Magnetic nanoparticles: Preparation, physical properties, and applications in biomedicine, Nanoscale Res. Lett. 7, 1 (2012).
- S. Mørup, M. F. Hansen, and C. Frandsen, Magnetic interactions between nanoparticles, Beilstein J. Nanotechnol. 1, 182 (2010).
- T. Nardi, M. Sangermano, Y. Leterrier, P. Allia, P. Tiberto, and J.-A. E. Månson, UV-cured transparent magnetic polymer nanocomposites, Polymer 54, 4472 (2013).
- M. Sonmez, M. Georgescu, L. Alexandrescu, D. Gurau, A. Ficai, D. Ficai, and E. Andronescu, Synthesis and applications of core-shell materials, Curr. Pharm. Des. 21, 5324 (2015).
- S. Dagher, A. Soliman, A. Ziout, N. Tit, A. Hilal-Alnaqbi, S. Khashan, F. Alnaimat, and J. A. Qudeiri, Photocatalytic removal of methylene blue using titania- and silica-coated magnetic nanoparticles, Mater. Res. Express 5, 065518 (2018).
- Y. Jirásková, F. Zazimal, J. Bursik, T. Svoboda, P. Dzik, and T. Homola, Structural and physical characterization of iron-oxide based inks for inkjet printing, J. Magn. Magn. Mater. 562, 169810 (2022).
- E. M. Pugh and G. H. Winslow, The analysis of physical measurements, (No Title) (1966).
- A. Lawrence and A. Lawrence, in Probability in Physics: An Introductory Guide (Springer, Cham, Switzerland, 2019), p. 55.
- I. Murataj, C. Magosso, S. Carignano, M. Fretto, F. Ferrarese Lupi, and G. Milano, Artificial fingerprints engraved through block-copolymers as nanoscale physical unclonable functions for authentication and identification, Nat. Commun. 15, 10576 (2024).
- P. Ilg, Nonequilibrium response of magnetic nanoparticles to time-varying magnetic fields: Contributions from Brownian and Néel processes, Phys. Rev. E 109, 034603 (2024).
- G. Barrera, P. Allia, and P. Tiberto, Temperature-dependent heating efficiency of magnetic nanoparticles for applications in precision nanomedicine, Nanoscale 12, 6360 (2020).
- W. F. Brown Jr, Thermal fluctuations of a single-domain particle, Phys. Rev. 130, 1677 (1963).
- P. Allia, G. Barrera, and P. Tiberto, Nonharmonic driving fields for enhancement of nanoparticle heating efficiency in magnetic hyperthermia, Phys. Rev. Appl. 12, 034041 (2019).
- M. Getzlaff, Fundamentals of Magnetism (Springer Science & Business Media, Berlin, Germany, 2007).
- C. Binns, Nanomagnetism: Fundamentals and Applications (Newnes, Oxford, UK, 2014), Vol. 6.
- N. A. Usov, Low frequency hysteresis loops of superparamagnetic nanoparticles with uniaxial anisotropy, J. Appl. Phys. 107, 123909 (2010).
- J. M. Vargas, W. C. Nunes, L. M. Socolovsky, M. Knobel, and D. Zanchet, Effect of dipolar interaction observed in iron-based nanoparticles, Phys. Rev. B—Condens. Matter Mater. Phys. 72, 184428 (2005).
- S. N. Chiu, D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and Its Applications (John Wiley & Sons, West Sussex, UK, 2013).
- N. Cressie, Statistics for Spatial Data (John Wiley & Sons, New York, USA, 2015).
- D. Luo, C. Yan, and T. Wang, Interparticle forces underlying nanoparticle self-assemblies, Small 11, 5984 (2015).
- H. C. Tuckwell, Elementary Applications of Probability Theory (Chapman and Hall/CRC, London, UK, 2018).
- J. Illian, A. Penttinen, H. Stoyan, and D. Stoyan, Statistical Analysis and Modelling of Spatial Point Patterns (John Wiley & Sons, West Sussex, UK, 2008).
- D. Moltchanov, Distance distributions in random networks, Ad Hoc Netw. 10, 1146 (2012).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/zk8l-5173 for additional graphs and explicit calculation for partially correlated values of nanoparticle surface density.
- M. Vopsaroiu, J. Blackburn, and M. G. Cain, A new magnetic recording read head technology based on the magneto-electric effect, J. Phys. D: Appl. Phys. 40, 5027 (2007).
- R. W. Hamming, Error detecting and error correcting codes, Bell Syst. Tech. J. 29, 147 (1950).
- J. Daugman, How iris recognition works, IEEE Trans. Circuits Syst. Video Technol. 14, 21 (2004).
- M. R. Dale and M.-J. Fortin, Spatial Analysis: A Guide for Ecologists (Cambridge University Press, Cambridge, UK, 2014).