Eco-sustainable magnetoresistive sensors towards disposable magnetoelectronics

Domain: biology
Published: 2026-03-27
Editorial outcome: minor_revision

Abstract
This work presents a holistic integration of environmental sustainability and enhanced sensing performance throughout the full lifecycle of magnetoresistive sensors. Utilizing industry-scale screen-printing techniques combined with eco-friendly inks (formulated from engineered Fe/Fe3O4 core-shell magnetic microparticles, bioderived polymeric binders, and water solvent), the fabrication process avoids harsh treatments and hazardous chemicals. The resulting sensors, constructed entirely from naturally sourced materials, inherently exhibit biocompatibility, biodegradability, and environmentally benign recyclability. These properties collectively demonstrate key attributes for a sustainable lifecycle. Through rational engineering of the Fe/Fe3O4 core-shell structure particles, two synergistic mechanisms are activated within the composite: spin-dependent hopping across Fe3O4 shell grain boundaries and in situ magnetic flux concentration induced by Fe cores, thereby yielding an order-of-magnitude enhancement in low-field sensitivity relative to sputtered Fe film and printed Fe3O4 particle-based counterparts, resulting in a higher magnetoresistance ratio at 10 mT relative to all printed magnetoresistive sensors reported previously. The convergence of eco-sustainability and high performance enables previously unattainable disposable magnetoelectronics, unlocking new opportunities for environmentally responsible and user-safe transient electronics and Internet of Things (IoT) applications.

Introduction
The rapid advancement of digital technologies has profoundly reshaped contemporary society, enabling unprecedented levels of connection, interaction, and automation. However, the widespread incorporation of electronic devices has also introduced substantial environmental challenges. Central to the operation of these electronic systems are diverse sensor technologies, which serve as essential transducers between physical phenomena and digital information. Among them, magnetoresistive sensors, capable of resilient non-contact detection of magnetic fields and consequently relative motion, have been extensively used across a broad spectrum of applications, ranging from environmental monitoring and industrial automation to biomedical diagnostics and the Internet of Things (IoT)1–5. Owing to their functional versatility and robustness, over 100 billion magnetoresistive sensor units were deployed globally in 2022, with market projections estimating that this number could exceed 1 trillion units by 20306. The massive scale of production and deployment raises pressing sustainability concerns, necessitating urgent scientific and technological attention.

In alignment with the United Nations Sustainable Development Goals (SDGs)7, which call for environmentally responsible design, production, and disposal of electronic products, there has been growing momentum toward the development of sustainable electronics. For example, significant efforts have been taken to develop biodegradable electronics8–11 that safely decompose at the end of their functional life without releasing hazardous substances into the environment. Recent advances in biocompatible materials have enabled a variety of biodegradable sensors (e.g., temperature, opticals, pressure/strain, chemical, humidity, acoustic)12–14. Despite these advances, the majority of magnetoresistive sensors still rely heavily on Co and Ni, both of which are classified as hazardous by the Globally Harmonized System of Classification and Labelling of Chemicals15,16. Their widespread usage and improper disposal pose serious ecological and health risks. Moreover, achieving high magnetoresistive performance necessitates precise control over spin-dependent effects, which are generally realized through high-vacuum material deposition and subtractive lithographic patterning, i.e., processes associated with high energy consumption and material waste.

Printable magnetoresistive sensors based on functional inks (composed of magnetic fillers and polymeric binder solutions) present a promising avenue to address the above challenges, thanks to their compatibility with material- and energy-efficient manufacturing techniques17–20. However, most reported printable magnetoresistive sensors that demonstrate acceptable levels of magnetoresistance still rely on Ni- or Co-based fillers21–31 (Supplementary Table 1). In addition, the ink formulations and printing processes often involve hazardous organic chemicals and solvents, further undermining their sustainability. As a greener alternative, ferromagnetic Fe has attracted attention. Nonetheless, Fe-based sensors are fundamentally limited by their intrinsically low magnetoresistance (<0.5%)32,33 (Supplementary Table 2). In contrast, Fe3O4-film based sensors can exhibit higher magnetoresistance (1–10%), but only under strong magnetic fields (>1 T)34–37 (Supplementary Table 3). This poses a significant limitation for real-world applications, particularly in wearable and consumer electronics, where continuous exposure to high magnetic fields, exceeding the 40 mT threshold recommended by the World Health Organization (WHO)38, is undesirable. Even worse, when these materials are processed via printing techniques, inevitable structural heterogeneities, poor inter-filler connectivity, and reduced magnetic domain alignment further suppress magnetoresistive response. In addition, in contrary to thin-film technology that affords nanoscale control, printing techniques typically feature dimensions on the order of tens or hundreds of micrometers. This scale mismatch, combined with the inherently high resistivity of Fe3O4, poses a vital challenge for realizing printed Fe3O4-based sensors with practical functionality due to substantial electrical resistivity. Collectively, these challenges highlight an urgent need for the development of new material systems and fabrication strategies that can bridge the sustainability and functionality in magnetoresistive sensors.

In this work, we integrate environmental sustainability considerations across key lifecycle stages of printable magnetoresistive sensors while equipping them with enhanced low-field sensing performance. To this end, we develop an eco-friendly ink formulated with naturally abundant Fe as the primary sensing composition, bioderived polymers as binders, and water as the solvent. This ink is compatible with industrial-scale screen printing techniques, enabling cost-effective high-throughput sensor fabrication, as evidenced by 5 × 8 sensor arrays printed on A4-sized papers. The resulting sensors exhibit excellent biocompatibility, with minimal cytotoxicity observed in murine fibroblast cells in vitro. After end-of-life, the sensors can be disposed of through both controllable biodegradation and green recyclability, ensuring eco-safe disposal. To endow the device-applicable performance, we rationally engineer the Fe/Fe3O4 core-shell magnetoresistive microparticles and their matrix within the composite, leveraging two synergistic mechanisms: (i) spin-dependent hopping across the Fe3O4 grain boundaries at the interface between adjacent shells, enhancing the magnetoresistance response; (ii) an in situ magnetic flux guiding effect induced by the Fe core, thereby amplifying the local field at the interface of adjacent Fe3O4 shell-shell grain boundaries. Together, the two effects yield remarkable improvements in low-field magnetoresistance and sensitivity. Specifically, two parameters are enhanced by factors of 27.5 and 8, respectively, compared to Fe films, and by 3.4 and 20 times, respectively, relative to printed Fe3O4-based counterparts. Further, the Fe/Fe3O4 core-shell structures offer an additional advantage: the Fe core serves as a highly conductive pathway that electrically connects the Fe3O4 sensing domains, resulting in resistivity reduction by over two orders of magnitude compared to that of printed Fe3O4-based composite, facilitating seamless integration into electronic systems. The simultaneous realization of a sustainable lifespan and superior low-field sensitivity opens new opportunities for disposable magnetoelectronics, with potential applications in smart packaging, food/medicine monitoring, and plant/human wearables and implantables.

Results
Fully green printable fabrication of high-performance biodegradable magnetoresistive sensors

Figure 1a schematically illustrates the formulation strategy of the functional ink, of which all components are free from scarce resources or hazardous substances. The engineered Fe/Fe3O4 core-shell structure endows the ink with magnetoresistive response, and the constituent Fe element is not only abundant in the crust but also plays an essential role in various biological processes39. Sodium carboxymethyl cellulose (NaCMC), derived from plant-based cellulose, is a renewable non-toxic polymer, and has been extensively employed in pharmaceutical and tissue engineering applications. Replacing conventional volatile organic solvents with water eliminates ecological hazards during ink preparation while promoting a safer printing process. Through systematic engineering of these constituent materials, the formulated ink exhibits high compatibility with standard screen-printing techniques (Fig. 1b and Supplementary Fig. 1). Rheological measurements further corroborate the screen-printing suitability of the selected ink, featuring the suitable viscosity for screen printing and pronounced shear-thinning under increasing shear rate (Supplementary Fig. 2). After printing, the aqueous solution in the ink evaporates at ambient conditions, causing substantial volume shrinkage. This simple yet effective method induces internal stress, which tightly compresses the microparticles to establish electrical percolation pathways. The solidified NaCMC immobilizes the magnetoresistive microparticles, thereby forming the robust building block of the sensing device. The printing workflow is free from any harsh post-treatments, reducing associated environmental burdens. As a demonstration of scalability, 5 × 8 sensor arrays are fabricated on A4-sized paper substrates (Fig. 1b, c, Supplementary Fig. 1 and Supplementary Movie 1). The printed sensors also exhibit robust device-to-device performance reproducibility (Supplementary Fig. 3 and Supplementary Table 4). This process highlights the feasibility of low-cost high-throughput production of magnetoresistive sensors using a fully green method.

Owing to the removal of toxic chemicals from the ink formulation and the prevention of harmful by-product generation during the mild printing process, our sensor platform achieves high biocompatibility. To experimentally validate this property, standard in vitro biocompatibility tests are applied, in which printed sensor pieces are cultured with a mouse fibroblast cell line (L929 cells). Cell morphology and proliferation are recorded, and the cytoskeleton is examined by immunofluorescence staining over a 3-day period. The L929 cells exhibit normal spreading behavior, with increased cell density and a typical filamentous, stretched morphology on days 2 and 3 (Fig. 1f). No obvious differences in cell morphology, distribution, or density are observed between the Fe/Fe3O4-NaCMC group and the control group. A quantitative 3-(4,5-dimethylthiazol-2-yl)−2,5-diphenyltetrazolium bromide (MTT) assay analysis shows that cells cultured with Fe/Fe3O4-NaCMC sensor pieces retain a viability exceeding 95% throughout the 3-day period, confirming the absence of cytotoxic effects and biocompatibility of the printed sensor pieces (Fig. 1g).

Importantly, the biocompatible sensor exhibits remarkable sensing performance, featuring a magnetoresistance ratio of about −3.1% at 100 mT, with a maximum sensitivity of 3.93 T−1 at 1.3 mT (Fig. 1d, e). When benchmarked against Fe films prepared by high-vacuum magnetron sputtering, these sensing metrics are about 27.5 times and 8 times higher, respectively. Our sensors also outperform printed Fe3O4-microparticle-based sensors by factors of 3.4 in magnetoresistance and 20 in sensitivity, and 200 in electrical conductivity. The outstanding sensing performance and electrical conductivity stem from a synergistic strategy involving systematic material and structural engineering of Fe/Fe3O4 core-shell microparticles, enabling spin-dependent hopping-mediated Fe3O4 grain boundary magnetoresistance, in situ Fe-core magnetic flux guider (i-MFG), and highly conductive Fe connector (Fig. 1c), as fully validated in the following discussion. These designs work in concert, delivering exceptional low-field response, as evidenced by a higher magnetoresistance ratio at 10 mT relative to all printed magnetoresistive sensors reported previously21–31,40 (Fig. 1h and Supplementary Table 1).

At the end of their service life, the sensors exhibit eco-friendly recyclability and inherent biodegradability, as demonstrated in subsequent assessments. Building on these technical advancements, the proposed sensor platform establishes a new paradigm for magnetoelectronics by concurrently addressing lifespan sustainability and high sensing performance.

Eco-friendly recycling and controllable biodegradation for environmentally responsible disposal of end-of-service sensors

Thank thanks to the incorporation of water-soluble NaCMC as a polymeric binder and hosting substrate, the discarded sensors exhibit rapid disintegration within 1 h upon exposure to water. This eliminates the need for any harsh physical treatment or corrosive reagents commonly used in conventional recycling protocols41. The intrinsic magnetism of the released Fe/Fe3O4 microparticles allows for their efficient collection using permanent magnets, thereby promoting a closed-loop recycling process (Fig. 2a and Supplementary Movie 2). To demonstrate the versatility of this approach, we also successfully recover sensors printed on paper substrates (Fig. 2a). Notably, even when the fillers consist of multiple components (e.g., Mo powders released from the printed electrodes), these mixed fillers can be readily separated via magnetic sorting (Fig. 2a and Supplementary Movie 3). Notably, under practical recycling conditions (water exposure <1 h per cycle), the reclaimed Fe/Fe3O4 microparticles retain their functional quality, as evidenced by the essentially unchanged MR performance of reprinted sensors over multiple recycling cycles (Supplementary Fig. 4), confirming the excellent reusability of the magnetic fillers.

However, under real-world conditions, the efficient retrieval of discarded electronic waste remains a major obstacle to recycling. Addressing this concern, our sensor platform is designed for safe disposal. Upon release into the environment, the Fe/Fe3O4 microparticles gradually degrade into Fe ions over time, without generating any hazardous by-products42,43. Nevertheless, the water-sensitive nature of the printed sensor is a double-edged sword because it may compromise long-term operational stability, particularly in humid or aqueous environments. To address this, various biodegradable protective layers are investigated to regulate the water-triggered degradation behavior (Fig. 2b, c). Among these, the sensor encapsulated with Ecoflex exhibits the most robust performance, retaining their magnetoresistance with minimal degradation for up to 90 days. In contrast, the beeswax-encapsulated sensor maintains a relatively stable magnetoresistance for the first 30 days, which then declines to 2.7% after 60 days, eventually leading to device failure by the 90th day. The sensor sealed with cellulose acetate shows the shortest lifetime (about 3 days). Consistent with these immersion results, accelerated aging under controlled humidity and temperature further confirms that encapsulation markedly expands the operational window from ambient conditions to high-humidity and warm-water environments (Supplementary Fig. 5). These results demonstrate that encapsulation strategies can be rationally tailored to customize sensor degradation kinetics and functional lifespan, thereby meeting different requirements across diverse applications.

The sensor platform is further validated by incorporating alternative biocompatible and even edible binders (e.g., sodium alginate, egg white, starch). These materials not only ensure biosafety but also provide tunable degradation profiles. Sensors fabricated with these binders exhibit stable and reliable performance, with magnetoresistance ratios maintained around −3% and sensitivities exceeding 3.5 T−1 (Fig. 2d, Supplementary Fig. 6). The combination of green fabrication, biocompatibility, and biodegradability broadens the scope of printable substrates beyond traditional polyethylene terephthalate (PET) foils, paper and ceramics (Supplementary Fig. 7). Our sensors can even be directly printed on sensitive biological objects with various surface textures such as tomato, leaf and daisy petals (Fig. 2e, Supplementary Fig. 8). Despite the mechanical and chemical variability of these natural substrates, the printed sensors exhibit consistent performance with magnetoresistance above −2.9% and sensitivity exceeding 3.2 T−1. After service, these sensors can be completely removed by simple rinsing with water, without leaving residue or damage to their surfaces (Fig. 2e). The controllable biodegradation, coupled with the eco-friendly recycling, will ensure a more environmentally responsible end-of-life management for the sensor.

Spin-dependent hopping-mediated grain boundary magnetoresistance in printed Fe/Fe3O4 core-shell microparticle matrix

To overcome the intrinsically low magnetoresistance of metallic Fe-based materials, Fe3O4 grain boundary magnetoresistance is engineered to enhance sensing performance. However, the inherently high resistivity of Fe3O4 poses a challenge for printable electronics, which typically suffer from limited resolution and requires sufficient material conductivity to build electrical percolation. To address this conflict, we designed the Fe/Fe3O4 core-shell microparticles. In this architecture, the metallic Fe core provides a highly conductive backbone that drastically reduces the overall resistance of the composite, while the Fe3O4 shell accommodates magnetoresistive response through spin-dependent transport across grain boundaries. Compared with composites printed with Fe3O4 microparticles, the Fe/Fe3O4 sensors exhibit resistance reduction by over two orders of magnitude (Supplementary Table 3), rendering them suitable for practical electronic applications.

Intriguingly, the printed Fe/Fe3O4 sensor demonstrates nonlinear current-voltage characteristics (Fig. 3a, Supplementary Fig. 9), consistent with a variable-range hopping transport mechanism involving spin-dependent interfacial barriers23,44–46. Following the Efros-Shklovskii variable-range hopping model23,44–46, the application of an increasing electric field (via higher bias voltage) reduces the energy barrier associated with electron hopping across grain boundaries (Supplementary Fig. 10). This facilitates long-range electron hopping and results in a nonlinear increase in current. In stark contrast, selective removal of the Fe3O4 shell using acidic treatment leads to a transition to linear current-voltage behavior (Supplementary Fig. 9), indicative of ohmic conduction dominated by the Fe core. Further support for the variable-range hopping mechanism is provided by temperature-dependent resistance measurements, where the resistance (R) scales with temperature (T) (Fig. 3b, Supplementary Fig. 11), following ln(R) ∝ T−1/2 (Fig. 3c, Supplementary Fig. 11). This relationship aligns well with the Efros–Shklovskii variable-range hopping transport model23,44–46, in which the electron hopping between localized states is controlled by the barrier height. The magnetoresistive behavior of the Fe/Fe3O4 core-shell particle sensors can be attributed to spin-dependent hopping across magnetically disordered interfaces between adjacent Fe3O4 shells. Upon application of an external magnetic field, the alignment of local magnetic moments reduces spin disorder and enhances carrier hopping mobility, giving rise to negative magnetoresistance effects47,48. In particular, as the applied bias increases from 0.1 V to 5 V, the magnetoresistance is progressively suppressed (Fig. 3d, Supplementary Fig. 10), which is attributed to the reduction in the effective spin-dependent hopping barrier under stronger electric fields. As a result, the enhanced hopping of minority-spin carriers lowers the overall spin polarization of the transport electrons, resulting in a gradual suppression of the magnetoresistance ratio.

To further enhance the grain boundary magnetoresistance at Fe3O4 shell interfaces, a controlled thermal oxidation strategy is employed to optimize the structural and magnetic quality of the oxide shell (Fig. 3e). Specifically, a moderate vacuum level (0.5 mbar) is purposely selected to finely regulate the oxidation kinetics, ensuring the formation of nanoscale high-quality Fe3O4 shells. The balanced oxygen supply avoids overly rapid oxidation that could lead to undesirable phase formation or excessive structural disorder. Subsequent tuning of the oxidation temperature enables precise control over shell thickness and crystallinity, both of which are crucial for modulating spin-dependent transport across grain boundaries. As a reference, Fe microparticles oxidized at ambient conditions possess a thin Fe3O4 layer (<6 nm), accompanied by a high density of antiphase boundaries49 (Fig. 3f, Supplementary Fig. 12). These antiphase boundaries act as spin-flip scattering centers that severely limit spin polarization37,49–51, thus suppressing the magnetoresistance ratio to only −0.92% in the corresponding sensors. Increasing the oxidation temperature promotes the growth of a coherent and thicker Fe3O4 shell (10−20 nm), reflected by a remarkable increase in electrical resistivity (Fig. 3e). High-resolution transmission electron microscopy (HR-TEM) reveals well-defined lattice fringes and a notable reduction in antiphase boundary density within these thermally oxidized shells (Fig. 3f). These structural improvements result in enhanced spin coherence and interfacial spin filtering, leading to an improved magnetoresistance ratio of −3.1% at an optimal oxidation temperature of 235 °C. However, excessive oxidation (e.g., at 300 °C) induces the formation of insulating antiferromagnetic α-Fe2O3 phase52, as confirmed by X-ray diffraction (XRD) and Raman spectroscopy (Fig. 3g, Supplementary Figs. 13, 14), which disrupts spin-polarized transport (Fig. 3e). Moreover, the accelerated oxidation process tends to introduce additional structural defects (Fig. 3f), eventually reducing the magnetoresistance ratio to about −1.6% (Fig. 3e). These findings highlight the delicate interplay between oxidation environment, shell composition and microstructure in dictating the spin-dependent hopping behavior, offering a tunable pathway to further optimize the magnetoresistive performance.

In situ magnetic flux guiding effect to boost low-field sensitivity

Although engineered Fe3O4 grain boundaries enable significant spin-dependent transport and exhibit a substantial magnetoresistance ratio, this grain boundary–induced magnetoresistance effect of Fe3O4 typically requires the application of strong magnetic fields (>1 T) to be effective34–37 (Supplementary Table 3). To address this limitation, a structural core-shell configuration was designed for the magnetoresistive fillers within the composite. By leveraging the intrinsically high magnetic permeability of metallic Fe, the Fe core encapsulated in Fe3O4 shell is purposely designed to function as an in situ magnetic flux guider, which locally amplifies the magnetic flux density (that is, characterized by a gain factor) and thus enhances the sensitivity of the Fe/Fe3O4 sensor at weak external magnetic fields. This hypothesis is strongly supported by the experimental results (Fig. 4a, b and Supplementary Fig. 15), for example, as numerically dividing a gain factor of 10 from the magnetoresistance response of the Fe/Fe3O4 sensor, the resulting curve closely resembles that of the Fe3O4 sensor. To elucidate the underlying mechanism, micromagnetic simulations are conducted. As illustrated in Fig. 4c, the Fe cores are capable of concentrating magnetic flux lines, thus altering the spatial distribution of magnetic flux density, especially at Fe3O4 grain boundaries. Considering the wide size distribution of the Fe/Fe3O4 microparticles, a representative geometry (featuring a 240-nm-diameter Fe core and a 10-nm-thick Fe3O4 shell) is selected for simulation. In this case, the local gain factor at the Fe3O4 region can reach 14 (Fig. 4c). Additional simulations further indicate that a reasonable size mismatch between two contacting particles introduces only a modest variation in the local gain factor (Supplementary Fig. 16), whereas the gain factor is highly sensitive to the relative orientation between the external magnetic field and the percolation path connecting adjacent particles (Supplementary Fig. 17 and 18). As the alignment shifts from parallel to tilted, the gain factor decreases progressively. Due to the random arrangement of particles within the composite, the overall averaged effect is expected to be lower, which is in accordance with the experimentally observed gain factor of approximately 10.

To shed light on future device optimization, a comprehensive investigation combining numerical simulations and experimental studies is conducted (Fig. 4d–j). Firstly, the dependence of magnetic flux density gain on the Fe3O4 shell thickness is theoretically evaluated. For a fixed Fe core diameter, the gain factor is found to decrease gradually with increasing shell thickness (Fig. 4d). That is because the increased shell volume introduces a larger region of comparatively lower magnetic permeability, which disperses the magnetic flux lines and diminishes the localized field enhancement effect. To experimentally validate this trend and correlate it with magnetoresistance behavior, shell thicknesses are systematically modulated by varying the thermal oxidation time while maintaining constant temperature and vacuum conditions. The resulting magnetoresistance curves exhibit pronounced broadening and sensitivity decreasing with increasing shell thickness (Fig. 4f, g and Supplementary Fig. 15), indicative of a reduced flux-concentrating effect. Subsequently, the effect of core size on magnetic flux enhancement is investigated under the condition of a constant Fe3O4 shell thickness. The simulation results indicate that larger Fe cores lead to an increase in the gain factor, which eventually approaches a saturation value (Fig. 4e). That is because as the core diameter increases, the greater permeability contrast improves flux concentration. However, beyond a critical size, the resulting flux distribution reaches a geometric limit, no longer enhancing the field in grain boundaries. This simulated trend is confirmed by experimental observations. As shown in Fig. 4h, i and Supplementary Fig. 15, composites incorporating particles with larger core sizes exhibit noticeably sharpened (from 90 nm to 3 μm particle diameter) and then saturated (from 3 μm to 15 μm diameter) magnetoresistance responses (Fig. 4i), also reflected in sensitivity (Fig. 4j). Therefore, achieving optimal magnetic flux guidance (and hence maximum sensitivity) requires a finely tuned core-shell architecture, wherein the shell is sufficiently thin to enable strong interfacial flux transfer while the core should be relatively large to enable substantial flux concentration.

Application in disposable magnetoelectronics

The biocompatible materials-based ink, combined with the fully green printing fabrication, the biocompatible application potential, and the inherent biodegradability, presents a viable pathway toward closed-loop sustainability for our sensors (Fig. 5a). This integrated strategy facilitates the large-scale deployment of magnetoresistive sensors with a minimized environmental footprint.

In the IoT context, smart packaging enabled by disposable magnetoresistive sensors represents a critical application area. As a proof of concept, a printed sensor, paired with a printed sustainable magnet, is affixed to a medicine box to monitor the opening frequency (Fig. 5b, c). This is particularly valuable for tracking medication adherence of elderly individuals with memory decline, as real-time monitoring of the medicine box via an IoT system provides caregivers and healthcare providers with critical data to enable timely intervention. In a similar operational fashion, the sensor can be incorporated into a circuit involving light-emitting diodes, enabling automatic illumination triggered by the opening of a gift box (Fig. 5b). At the end of its service, the entire package can be discarded as biodegradable waste with minimal environmental impact. For practical use, the sensors exhibit reliable operational stability, retaining consistent magnetoresistance after 8000 magnetic field cycles at 100 mT (Fig. 5d). These properties unlock new opportunities for the development of next-generation disposable magnetoelectronics systems.

The validated biocompatibility of the sensor allows for direct printing onto biological objects, thereby expanding their adaptability to interactive interfaces for wearable and implantable electronics. As a representative example, an electronic interface, comprising two sensors printed on fingernails and a magnetic ring, is used for human-computer interaction (Fig. 5e–h). To ensure durability under daily usage conditions, the sensors are encapsulated in biocompatible gelatin-glycerol gel, allowing stable operation while remaining removable through routine handwashing (Fig. 5f and Supplementary Movie 4). By altering the relative sensor-magnet distance, the electrical signals change accordingly (Fig. 5g, h). Once surpassing a predefined threshold, specific actions are initiated for the digital character such as move forward and jump (Fig. 5g, h and Supplementary Movie 4).

Discussion

In summary, this work presents a comprehensive strategy that seamlessly integrates environmental sustainability with superior sensing performance across the entire lifecycle of printable magnetoresistive sensors. By employing industry-compatible screen-printing techniques and eliminating the use of harsh treatment and harmful chemicals, the fabrication process is both scalable and eco-friendly. The sensors, composed solely of naturally derived materials, inherently provide biocompatibility, biodegradability, and environmentally benign recyclability, thereby expanding their applicability to safety-critical scenarios such as food monitoring, plant/human wearables or implantables, and direct on-skin electronics. The synergistic combination of spin-dependent hopping magnetoresistance at Fe3O4 shell-to-shell grain boundaries and Fe-core-induced magnetic flux concentration and conductivity enhancement results in significantly improved low-field sensitivity, enabling practical and reliable sensor functionality. Leveraging these technical achievements, this research represents an important advancement in magnetoresistive sensor technology. Future work would benefit from a comprehensive quantitative lifecycle assessment (LCA) to further quantify cradle-to-grave impacts and guide continued optimization. Taken together, this work paves the way for disposable magnetoelectronics and sustainable IoT applications.

Methods
Materials

The Fe particles (10 μm, Sigma Aldrich; EMSURE, average 3 μm as confirmed by scanning electron microscopy (SEM) imaging, Supplementary Fig. 20) were thermally oxidized at 235 °C under a medium vacuum (0.5 mbar) for 30 min to fabricate Fe/Fe3O4 core-shell microparticles (Supplementary Figs. 21 and 22). Without particular notice, this oxidation condition was used. Various oxidation temperatures, durations and conditions were explored to optimize magnetoresistive (MR) performance (Fig. 3e, Supplementary Figs. 23 and 24). Fe particles (<60 μm, Sigma Aldrich; average 15 μm as confirmed by SEM imaging) and Fe nanoparticles (Sigma Aldrich; average 90 nm as confirmed by SEM imaging) were thermally oxidized under the same conditions as the 3-μm particles mentioned above. Sodium carboxymethyl cellulose (NaCMC) (Mw 90,000, Sigma Aldrich) and alginic acid sodium salt (Sigma Aldrich) were dissolved in hot (60 °C) water at a weight ratio of 10% to obtain solutions. Starch (soluble, from potato, Sigma Aldrich) was dissolved in boiling water for 2 h at a 10% weight ratio to obtain a solution. Egg white was obtained from food eggs, with a typical water content of approximately 88%. Vitamin C (L-ascorbic acid, Sigma Aldrich) was dissolved in water at varying concentrations. Cellulose acetate (Mn ~50,000, Sigma Aldrich) was dissolved in acetone at a 30% weight ratio to obtain a solution (RT). Glycerol, beeswax, gelatin from porcine skin (gel strength 300, Type A), Fe3O4 powders (<5 μm), strontium ferrite powders, molybdenum powder (1–5 μm) from Sigma Aldrich, and Ecoflex 00-35 (parts A and B) were used as supplied. Fe thin films were deposited via magnetron sputtering, with a thickness of approximately 1.5 μm, as confirmed by confocal laser scanning microscopy (CLSM, Zeiss).

Fabrication of biodegradable magnetoresistive inks and sensors

Fe/Fe3O4 core-shell microparticles were uniformly dispersed in a NaCMC aqueous solution at a 60% volume ratio (Fe in the final composite) to form the Fe/Fe3O4-NaCMC ink. Inks with various volume ratios from 40% to 80% and alternative binders (egg white, starch, and alginic acid sodium salt) were also prepared. Without particular notice, 60% volume ratio and NaCMC binder were used. A flat flexible cable (FFC) served as the standard substrate/electrode for testing throughout. Ink was deposited using a 100 μL pipette (VWR) and then air-dried without further treatment. The FFC featured electrode slots spaced 0.5 mm apart, with a width of 5 mm and the printed sensor piece thickness of approximately 100 μm (Supplementary Fig. 20). In addition to FFCs, inks were printed on conventional substrates (plastic, paper, ceramics) and biological-substrates (tomato, leaf, daisy petals). For large-scale printing, a commercial automatic screen-printing instrument (Kundisch GmbH & Co. KG) was used to print 5 × 8 sensor arrays on A4-sized paper sheets.

Rheology characterization

Rheological measurements were performed to evaluate the viscoelastic behavior of the inks. The MCR 302 rheometer (Anton Paar) equipped with the MRD180/1T magnetocell in a plate–plate configuration (1 mm gap) was used to determine the shear‑thinning and oscillatory behavior of the inks. All measurements were performed at 22 °C and the sample volume was constant.

Vitamin C treatment for oxide shell removal

A biocompatible acidic post-treatment was employed to remove the oxide shell of Fe/Fe3O4 core-shell particles in the printed composite, enabling investigation of its role in MR performance. A biocompatible reducing acid, Vitamin C (L-Ascorbic Acid), was dissolved in water at varying concentrations. The acid solution was then drop-cast onto the dried Fe/Fe3O4-NaCMC pattern. Post-treated samples were analyzed after drying. The MR performance of the post-treated samples with different Vitamin C concentrations is shown in Supplementary Fig. 25.

Materials characterization

XRD. X-ray diffraction studies were carried out using a Rigaku SmartLab 3kW in Bragg-Brentano geometry with Cu-Kα radiation (average wavelength: 1.542 Å) and a Ni filter. The HyPix detector was employed in 1D TDI mode with XRF reduction enabled. The PDF standard cards of α-Fe (#00-006-0696), Fe3O4 (#01-084-6684), and α-Fe2O3 (#00-0011053) were used to index the reflections.

TEM. To characterize the microstructure of the as-prepared and thermally oxidized samples, transmission electron microscopy (TEM) was performed. To this end, cross-sectional TEM lamella preparation was carried out by in situ lift-out using a Helios 5 CX focused ion beam (FIB) device (Thermo Fisher). To protect the sample surface, a carbon cap layer was deposited beginning with electron-beam-assisted and subsequently followed by Ga-FIB-assisted precursor decomposition. Afterwards, the TEM lamella was prepared using a 30-keV Ga-FIB with adapted currents. Its transfer to a 3-post copper lift-out grid (Omniprobe) was done with an EasyLift EX nanomanipulator (Thermo Fisher). To minimize sidewall damage, Ga ions with only 5-keV energy were used for final thinning of the TEM lamella to electron transparency. Bright-field and high-resolution TEM (HR-TEM) imaging were done using an image-C-corrected Titan 80-300 microscope (FEI) operated at an accelerating voltage of 300 kV. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) imaging and spectrum imaging analysis based on energy-dispersive X-ray spectroscopy (EDXS) were performed at 200 kV using a Talos F200X microscope equipped with a Super-X EDX detector system (FEI). Prior to (S)TEM analysis, each specimen mounted in a high-visibility low-background holder was placed for 8 s into a Model 1020 Plasma Cleaner (Fischione) to remove potential contaminations. Determination of the formed crystalline iron oxide phases was done by fast Fourier transform (FFT) analysis of selected cross-sectional iron oxide shell regions. In particular, potential zone axis diffractograms were calculated from the recorded HR-TEM images and compared with simulated diffraction patterns of cubic magnetite53 using the JEMS software package.

SEM. The microstructure and morphology of raw Fe powders and printed sensor pieces were observed using the backscattered electron detector of the Phenom XL Desktop SEM (Thermo Fisher Scientific, United States) with an acceleration voltage of 10 kV and a pressure of 0.1 Pa.

Raman spectroscopy: Raman signal was probed (HORIBA, LabRAM HR Evolution) using a 532 nm green laser. The incident laser is focused using a 100× objective lens with a diameter of around 1 μm. To avoid in situ oxidation of the iron powder during the measurement, the laser power is limited at 3.2 mW.

Electrical characterization

The I-V curves were recorded using a Precision Source/Measure Unit (Keysight B2900A). The temperature-dependent resistance was measured using a Tensormeter (HZDR Innovation, Germany).

Magnetoresistance measurement

The magnetoresistance ratio is defined as the magnetic field-dependent variation of the sensor’s resistance, R(H), normalized to the resistance value at zero magnetic field, R0. The expression is MR(H)=[R(H)–R0]/R0 · 100%. The sensitivity of the sensor’s response to the magnetic field is defined as the ratio of the first derivative of the sensor’s resistance with respect to the magnetic field to the resistance value, S(H)=[dR(H)/dH]/R(H). The figure of merit (FoM)24,30 is defined as the ratio of the maximum sensitivity to the magnetic field at which the maximum sensitivity occurs, FoM=Smax/Hs’max. A standard Helmholtz coil was used to generate a uniform and tunable magnetic field, and the applied magnetic fields were swept between ±100 mT. A four-probe configuration was used for the MR measurement of the printed sensors using a Tensormeter (HZDR Innovation GmbH, Germany). The drive current had a frequency of 775 Hz and an amplitude of 100 µA, with the magnetic field aligned parallel to the bias current of the sensor. To assess performance reproducibility, sensors from three independently fabricated batches were measured (batch 1-3, n=10 devices per batch; total n=30), prepared under identical conditions. All measurements were performed at room temperature.

Magnetic simulations

We perform micromagnetic simulations of ferromagnetic nano- and microspheres using OOMMF54 and Ubermag55 softwares. The geometry under consideration consists of two spheres placed along the x-axis and touching each other according to the finite difference cubic mesh. The core radius Rc and the shell thickness h are varied. We use the saturation magnetization μ0MScore=2.2 T and μ0MSshell=0.5 T for the core and shell, respectively. The exchange stiffness is set to 21 pJ everywhere. The sample is exposed to an external magnetic field with a strength of Bout=100 mT. In each simulation, the initial magnetic state is set along the field direction, then the energy minimization procedure is performed, and the stray field is calculated.

To analyze the amplification factor as a function of core radius, we considered core radii from Ri=30 nm to Ri=500 nm with a fixed shell thickness of 10 nm, and an external field is applied along the symmetry axis (x). In simulations with Ri<70 nm, the cubic mesh is of 2.5 nm size. In simulations with radii Ri>300 nm, the mesh size is 10 nm. For all other simulations, we use a mesh of 5 nm. In the case of the very small core radii below 55 nm, we found that the equilibrium state of each sphere corresponds to the 3D onion state (the magnetization has no azimuthal component with respect to the symmetry axis of the system), while for the larger spheres the equilibrium state is the whirligig one with the vortex-like curling of magnetization around the symmetry axis56. In both cases, the 3D onion and whirligig states are modified by the external field. In the following, we consider the samples with Ri>50 nm only. The gain factor is defined as,

g=μ0(Hms+Mshell)=Bout, (1)

where Hms is the mean value of the magnetic field at the interface between the spheres. Due to symmetry, the single x-component of Hms is nonvanishing. The amplification factor (gain) g increases with Ri and tends to saturate for larger radii. We repeat the same procedure to analyse the dependency of g on the shell thickness h fixing Ri=120 nm. With the growth of h from 10 nm to 50 nm, g decreases by about 40%. And finally, we calculate how g depends on the direction of the external magnetic field rotated in the x-z plane. For the fixed Ri=120 nm and h=10 nm, we perform separate energy minimization procedures for the field angles changed from 0° (along the x-axis) to 90° (along the z-axis) with a step of 15°. With the rotation of the field, the symmetry of the state reduces, giving rise to a z-component of Hms with a sequential reduction of its x-component (Supplementary Fig. 17). For the field direction of 90°, there is also a y-component of the stray field at the junction point between the two spheres.

Biodegradability characterization

The Fe/Fe3O4-NaCMC sensors printed on NaCMC substrate or on paper substrate with printed Mo contacts were immersed in water at room temperature. The dispersed Fe/Fe3O4 core-shell particles were collected and recovered by a NdFeB permanent magnet.

Recyclability and water-immersion aging tests of reclaimed Fe/Fe3O4 core-shell microparticles

1. Recycling–reprinting cycle (practical recycling condition). Printed sensors were recycled by exploiting the water solubility of the NaCMC binder. Discarded sensors were immersed in deionized (DI) water until the printed layer disintegrated and the composite dispersed. The released Fe/Fe3O4 microparticles were collected from the suspension using a permanent magnet, rinsed with DI water to remove residual NaCMC, and dried under ambient conditions (or under mild vacuum) until constant mass. The reclaimed particles were then re-mixed in a freshly prepared NaCMC aqueous solution to formulate inks following the same protocol as for the pristine ink. The ink was subsequently reprinted to fabricate new sensors using identical printing, drying, and post-treatment conditions as the initial devices. This recycling–reprinting procedure was repeated for up to three cycles. For each cycle, the residence time of the particles in water (from immersion to magnetic collection) was kept below 1 h.

2. Prolonged water-immersion (particle aging/corrosion window) experiment. To assess the effect of extended water exposure during recycling, Fe/Fe3O4 microparticles were intentionally immersed in DI water for predefined durations (1, 3, 5, 10, and 15 days) under ambient conditions. After the specified immersion time, the particles were magnetically collected, rinsed with DI water, and dried to constant mass. Inks were prepared by mixing the aged particles with NaCMC aqueous solution using the same formulation and mixing procedure as for the pristine ink. Sensors were reprinted under identical conditions, and their MR performance was evaluated as described in the MR measurement section.

Encapsulation of the printed biodegradable magnetoresistive sensors

Several biodegradable encapsulation materials were tested to protect printed biodegradable sensors and regulate their longevity. Ecoflex 00-35-part A and part B were mixed homogeneously in a 1:1 weight ratio and degassed in a vacuum chamber. Gelatin-glycerol gel was prepared by mixing glycerol with water at an 8:2 weight ratio, then dissolving gelatin powder (1:9 ratio) in the mixture, followed by heating at 70 °C under magnetic stirring until a clear viscous solution was obtained. After vacuum drying to remove water, the mixture was kept warm until use. Beeswax was heated to 90 °C for melting. Cellulose acetate was used as acetone solution by 30% weight ratio. Encapsulation materials were drop-cast onto the printed sensors on FFC to form protective layers. To evaluate the environmental stability under different storage conditions, encapsulated and bare sensors were stored under (i) ambient humidity at room temperature, 50 °C, and 80 °C, (ii) 90% relative humidity at room temperature, and (iii) immersion in water at room temperature, 50 °C, and 80 °C. After the designated storage time, the MR performance of the sensors was measured repeatedly at room temperature.

Biocompatibility characterization

Cell culture: The L929 cell line was purchased from Leibniz Institute DSMZ-German Collection of Microorganisms and Cell Cultures. L929 Cells were cultured in Dulbecco’s modified Eagle’s medium (DMEM, Gibco) containing 10% fetal bovine serum (Sigma-Aldrich), 2 mM L-glutamine (Sigma-Aldrich) and 1% penicillin/streptomycin (Biochrom). Cells were incubated under 5% CO2 at 37 °C. Cell culture medium was exchanged every 2–3 days.

MTT proliferation assay: Printed sensor pieces (Fe/Fe3O4-NaCMC) were presterilized under UV light for 4 h, and then the presterilized pieces were added into cell culture media to form a solution of 500 μg‧ml−1 for L929 cells culturing. The L929 cells were plated in 96-well plates at a density of 5 × 103 per well, and incubated with or without material samples. After 24, 48, and 72 h of culturing, the cell culture media were replaced with 90 μL of cell culture media and 10 μL of MTT solution (5 mg ml−1, Sigma-Aldrich) and then incubated for 2 h in a humidified atmosphere with 5% CO2 at 37 °C. The supernatant was replaced with 50 µl of 100% dimethyl sulfoxide (DMSO, Sigma-Aldrich), followed by shaking for 10 min. An additional 150 µl of 100% DMSO was then added and mixed thoroughly. The data were recorded using a multimodal microplate reader (Cytation 5), measuring optical density at wavelengths of both 570 nm and 690 nm. Three parallel control samples were used for each group. Cell viabilities are equal to the absorbance ratio of the experimental group and the control group.

Cell morphology and immunofluorescent staining: The F-actin and nuclei were stained with phalloidin (conjugated with Alexa Fluor 488, Thermo Fisher, 1:200) and Hoechst 33258 (Thermo Fisher, 1:10), respectively. Precisely, L929 cells were precultured with and without Fe/Fe3O4-NaCMC samples (500 μg‧ml−1) for 24, 48, and 72 h in 8-well µ-slides. After washing with PBS three times, PBS containing 4% paraformaldehyde was used to fix the cells for 10 min. Following permeabilization with 0.2% Triton X-100 for 10 min, the cells were blocked using 3% BSA for 2 h. Phalloidin and Hoechst 33258 were added for 30 min and 10 min incubation at room temperature, respectively. Finally, the antifade reagent Prolong (Thermo Fisher) was added to each well to prevent fluorescence quenching. The cells were imaged using a confocal fluorescence microscope (Olympus IX83).

Printed sustainable magnets

Glycerol was mixed with water at a 2:1 weight ratio, followed by the addition of gelatin at a 1:9 weight ratio. The mixture was heated to 70 °C under magnetic stirring until a clear viscous solution was obtained57. Biocompatible strontium ferrite powders were then added at a 7:3 weight ratio and mixed thoroughly. The resulting ink was cast into molds and cured at room temperature for 24 h to form the final sustainable magnets (Supplementary Fig. 26). The printed magnets were magnetized by a constant magnetic field (2 T) for 5 min using an electromagnet.

Application of disposable magnetoresistive sensors

(1) Smart gift box: A Fe/Fe3O4-NaCMC sensor was printed on a paper substrate and integrated into a hybrid electronic circuit (featuring an amplification cascade and a light emitting diode (LED), as detailed in our previous work21). A printed biodegradable magnet attached to the cap of the box modulated the resistance of the sensor. The variation in resistance controlled the transistor circuit in the amplifier circuit, which regulated the operation of the LED.

(2) Smart Medicine Box: A printed biodegradable magnet was affixed to the medicine box cap, while a Fe/Fe3O4-NaCMC sensor with four-point molybdenum electrodes was printed on a NaCMC substrate. Resistance changes were recorded using a Tensormeter (HZDR Innovation GmbH, Germany) with NI LabVIEW software (version 2019 SP1, National Instruments, USA).

(3) On-nail wearable electronics for interactive human-machine interface: Two Fe/Fe3O4-NaCMC sensors were printed on the fingernails of the index and middle fingers, with contacts integrated beneath the printed layer. The sensors were encapsulated with a gelatin-glycerol gel. A magnetic ring worn on the thumb provided the magnetic field source. MR variation signals were acquired using a Tensormeter and processed with NI LabVIEW software (version 2019 SP1). A custom 3D game programmed in Spline interpreted the sensor signals; when a fingernail approached the magnetic ring, the resulting MR change (exceeding a preset threshold) triggered specific actions (e.g., move forward for the index finger and jump for the middle finger).

Ethics statement

We applied a permanent magnet to a finger of a user in several studies reported in this manuscript. This magnet is not an electronic component. Furthermore, in several studies, a sensor is applied on skin of a user. These studies are done according to the ethical approval #SR-EK-459122024 from the ethics committee at the Technical University of Dresden. For this case, we have a written consent of the user (one volunteer, male, 29 years old), who was wearing this sensor. The sensor is not worn on the skin for any extended duration.

Data availability

All of the data supporting the conclusions are available within the article and the Supplementary Information. Additional data are available from the corresponding authors upon request. Source data are provided with this paper.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This is a timely and technically strong manuscript from Makarov and co-authors. The demonstration of biodegradable, recyclable magnetoresistive sensors with credible low-field performance is an important contribution to sustainable magnetoelectronics. The work is clearly of interest and should be published at Nature Communications; however, some major points require further explanation and contextualisation. Please see individual comments below:\n- Particle recovery is shown, but it is not very clear whether the reclaimed Fe/Fe3O4 retains functional quality. Even a discussion of expected reusability and potential barriers would help support the circularity claim.\n- The issue of water sensitivity is acknowledged, but the implications for storage may need further clarification. The authors should discuss the operational window e.g. humidity, temperature, and time in service and clarify how encapsulation strategies change that window.\n- The authors should explain how particle size distribution and orientation affect the effective gain factor in the printed composite.\n- How does sensitivity and figure of merit at <10 mT compare to samples from the literature?\n- Was sensor readout stable across practical bias ranges and was there an optimal operating voltage to minimize drift?\n- Finally, since many binders were used, is there any binder feature (e.g. polarity or mechanical performance) that heavily influences the magnetic or electrical coupling between Fe/Fe3O4 and the overall MR response?", "reviewer_2": "The study demonstrates clear potential for significant contributions to the field. However, several substantive issues require careful revision and clarification before this work can be considered for publication:\n1. This manuscript systematically optimizes the magnetic and electronic properties (oxidation temperature, particle size, and binder type) which is appreciative. However, the authors made a major point in using “industry-scale screen printing” (Fig. 1b, Supplementary Fig. 1) for high-throughput fabrication. This is a key claim in terms of scalability and practicality. Nonetheless, they provide no data regarding the optimization of ink to prove its printability. To that end, it is important to know the rheological profile of the ink. Rheological data (viscoelastic properties, shear-thinning behavior of the ink for screen printing, G′/G′′ behavior etc., and contact angle measurements) are critical parameters. In addition, answering the reason for selecting the 60% volume ratio would show how these choices affect the printability of the ink. The manuscript would benefit from the inclusion of such characterization of the ink and aid in the reproducibility of the work.\n2. On page 6, authors mentioned “These designs work in concert, delivering exceptional low-field response, as evidenced by a higher magnetoresistance ratio at 10 mT relative to all printed magnetoresistive sensors reported previously21–31,40 (Fig. 1h)”. Authors are requested mention the supporting supplementary table.\n3. In Figure 1h, the authors highlight the large-scale fabrication, green synthesis, biocompatibility, biodegradability, recyclability, and %MR at 10 mT to emphasize the practical significance of their sensors. However, it is unclear which specific synthesis parameter(s) was/were considered in this comparison. Based on the figure caption, it seems only the binders were compared. The authors are requested to clarify the parameters used and justify their selection to ensure that the comparison is scientifically meaningful and is not limited to a single fabrication variable.\n4. The authors use an acid wash (Vitamin C) treatment for the selective removal of the Fe₃O₄ shell and demonstrate a transition to linear current-voltage behavior, indicative of ohmic conduction, whereas the printed Fe/Fe3O4 samples exhibit nonlinear current-voltage characteristics, which they attribute to the variable-range hopping mechanism (Supplementary Fig. 5). In addition, on page 9, the authors claim that “The magnetoresistive behavior of Fe/Fe3O4 core-shell particle sensors can be attributed to spin-dependent hopping across magnetically disordered interfaces between adjacent Fe3O4 shells. Upon application of an external magnetic field, the alignment of local magnetic moments reduces spin disorder and enhances carrier hopping mobility, giving rise to negative magnetoresistance effects [Ref. 47,48].” Authors are requested to include the relevant MR curve (if possible) for a direct and robust visual demonstration of the indispensable role of the magnetically disordered interfaces between adjacent Fe₃O₄ shell in generating the magnetoresistance.\n5. The authors claimed an improved low-field sensitivity with exceptionally reliable practical functionality. However, a comparison of devices produced within the same batch and different batches would strengthen the scientific rigor of the technology. The authors are requested to provide a statistical analysis of the key performance parameters based on measurements from multiple independent sensor devices to ensure reproducibility. The Methods section should explicitly state the sample size (n) for each dataset.\n6. On page 11, the authors have successfully demonstrated the optimization of device performance by varying the core diameter and shell thickness using numerical simulations. The authors also mentioned “….. as the core diameter increases, the greater permeability contrast improves flux concentration. However, beyond a critical size, the resulting flux distribution reaches a geometric limit, no longer enhancing the field in grain boundaries.” The observed normalized MR shown in Figure 4i is related to the overall particle size. The authors are required to provide direct microstructural evidence (e.g., cross-sectional SEM/TEM/HRTEM) to quantify the final core diameter and precise shell thickness of the particles. These values should be explicitly stated in the main text and correlated with the performance data.\n7. The claim of a \"truly closed-loop sustainable life cycle\" (e.g., Page 12, Fig. 5a) should be reconsidered. This phase implies a rigorous Life Cycle Assessment (LCA) that quantitatively evaluates environmental impacts from raw material extraction to end-of-life. The authors are encouraged to reflect on the presented evidence more accurately. For instance, wording such as \"demonstrates key attributes for a sustainable life cycle\" or \"presents a viable pathway towards closed-loop sustainability\" would be more appropriate. Moreover, including a qualitative discussion acknowledging that a comprehensive quantitative LCA would be a valuable future direction could add important nuances and strengthen the environmental relevance of this study.\nMinor comments:\ni) The placement of Figure 1c in the current version may be confusing for readers. The authors are encouraged to rearrange the figure to ensure a more logical flow and clearer distinction from Figures 1d and 1e. Adding labels such as \"Fe core (conductor & flux guide)\" and \"Fe₃O₄ shell (MR-active)\" to the schematic would make the synergistic mechanism immediately clearer.\nii) In Supplementary figure 11, the colors described in the caption do not correspond to those of the respective curves in the graph, particularly the green curve in S11-a. The authors are requested to verify this inconsistency.\niii) Page 8, section “Spin-dependent hopping-mediated grain boundary …..” ─ The sentence \"…, the Fe/Fe₃O₄ sensors exhibit resistance reduction by over two orders of magnitude...\" should cite the specific supplementary table where these data are presented (apparently referring to Supplementary Tables 3). The authors are advised to verify this reference.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "We thank the Reviewers for their constructive comments, which we used to refine our manuscript. All changes are indicated in the manuscript and supporting information files.\nOur itemized responses to the remarks of the Reviewers are summarized below.\nReviewer #1 (Remarks to the Author):\nOverall Comment: This is a timely and technically strong manuscript from Makarov and co-authors.\nThe demonstration of biodegradable, recyclable magnetoresistive sensors with credible low-field\nperformance is an important contribution to sustainable magnetoelectronics. The work is clearly of\ninterest and should be published at Nature Communications; however, some major points require\nfurther explanation and contextualisation. Please see individual comments below:\nResponse: We sincerely thank the Reviewer for this positive and encouraging assessment of our\nmanuscript. We have revised the manuscript to strengthen clarity, expand the relevant discussion, and\nbetter position our results within the broader literature. We address each individual comment in detail\nbelow, and all corresponding changes have been incorporated into the revised manuscript.\nComment 1: - Particle recovery is shown, but it is not very clear whether the reclaimed Fe/Fe O microparticles retain functional quality. Even a discussion of expected reusability and potential barriers would help support the circularity claim.\nResponse: To explicitly address whether the reclaimed Fe/Fe O microparticles retain functional quality,\nwe have added a dedicated recyclability assessment of the recovered particles by re-formulating the ink\nand reprinting sensors using Fe/Fe O fillers collected after repeated recycling cycles. Under practical\nrecycling conditions, where the particle residence time in water is kept below 1 h per cycle (NaCMC\ndissolution followed by magnetic collection), the MR curves of the reprinted sensors nearly overlap with\nthose of the initial devices, and the MR ratio at 100 mT remains essentially unchanged over three\nconsecutive recycling cycles (new Supplementary Fig. 4a,b). These results demonstrate that the\nreclaimed Fe/Fe O particles maintain their functional performance and support the reusability required\nfor circular operation.\nIn addition, we now discuss potential barriers and practical constraints. Because water is used both as\nthe recycling medium and as the ink solvent, prolonged water exposure can gradually corrode/age the\nparticles and lower the MR response. We therefore performed a worst-case “extended immersion”\nexperiment, intentionally prolonging the Fe/Fe O particle immersion time during a single recycling step,\nwhich leads to a gradual decrease of the MR response, the MR ratio (at 100 mT) reaching 2.57% after\n15 days (new Supplementary Fig. 4 c,d). This identifies an operational boundary and provides guidance\nfor fabrication and recycling: the ink should be prepared on demand, and the recycling process should\nbe conducted promptly to minimize the particle residence time in water. Importantly, since the\nperformance degradation becomes evident only on a multi-day timescale, while practical recycling is\ncompleted within <1 h per cycle, we expect that a reasonable number of recycling loops will not cause\nan obvious performance loss in reprinted sensors.\nRevisions:\nSupporting Information:\nSupplementary Fig. 4. Effect of the recycling procedure on the MR performance of reprinted\nsensors. a. MR curves of sensors printed with pristine Fe/Fe O microparticles (“Initial”) and with\nparticles recovered after 1st–3rd recycling cycles. In each recycling cycle, the NaCMC binder was\ndissolved in water and the dispersed Fe/Fe O particles were collected magnetically; the particle\nresidence time in water was kept below 1 h. b. Corresponding MR ratio at 100 mT as a function of\nrecycling cycle. c. MR curves of sensors reprinted using Fe/Fe O particles exposed to water for different\nimmersion durations (particle corrosion time) during a single recycling step (1–15 days), showing\nprogressive performance degradation upon prolonged immersion. d. Corresponding change of the MR\nperformance as a function of the immersion (corrosion) time.\nThe recycling of the printed sensors relies on the water solubility of the NaCMC binder. During end-of-\nlife processing, the printed composite disintegrates in water as NaCMC dissolves, releasing Fe/Fe O\nparticles into the suspension. Owing to their intrinsic magnetism, the particles can be efficiently\ncollected using a permanent magnet, dried, and re-dispersed in a freshly prepared NaCMC aqueous\nsolution to formulate the ink for reprinting. This water-enabled dissolution–magnetic collection route\nconstitutes a key step enabling closed-loop recyclability without harsh reagents.\nImportantly, when the recycling step is performed promptly, the MR performance of reprinted sensors\nremains essentially unchanged. As shown in panels a and b, particles recovered through three\nconsecutive recycling cycles, each with a short water exposure time (< 1 h), yield reprinted sensors\nwhose MR curves nearly overlap with that of the initial device, and the MR ratio at 100 mT stays around\n3%. This indicates a good reusability of the Fe/Fe O particles under practical, time-efficient recycling\nconditions.\nIn contrast, a prolonged water immersion leads to a gradual decline in the MR performance (panels c\nand d). When Fe/Fe O particles are kept in water for extended durations during a single recycling step,\n2\nthe MR performance gradually decreases, reaching 2.57% after 15 days of immersion, due to the water\ninduced corrosion.\nThese observations provide practical guidance for both fabrication and recycling. First, because the ink\nuses water as the solvent and the particles are continuously exposed to an aqueous environment once\nmixed, prolonged storage can induce ink aging and performance loss. Therefore, the ink should be\nprepared on demand (i.e., mix NaCMC aqueous solution with Fe/Fe O particles shortly before printing).\nSecond, during recycling, the residence time of particles in water should be minimized. Notably, since\nthe performance degradation becomes evident only after multi-day immersion while typical recycling\nrequires less than 1 h per cycle, water-induced corrosion is a relatively slow process in comparison to\nthe practical recycling timescale. Consequently, a reasonable number of recycling loops is expected to\nhave no impact on the MR performance of reprinted sensors, supporting the feasibility of closed-loop\nreuse of the MR fillers.\nMain text: page 7\nadded:\nNotably, under practical recycling conditions (water exposure < 1 h per cycle), the reclaimed Fe/Fe₃O₄\nmicroparticles retain their functional quality, as evidenced by the essentially unchanged MR\nperformance of reprinted sensors over multiple recycling cycles (Supplementary Fig. 4), confirming the\nexcellent reusability of the magnetic fillers.\nMethod: Page 19\nadded:\nRecyclability and water-immersion aging tests of reclaimed Fe/Fe O microparticles\n1. Recycling–reprinting cycle (practical recycling condition). Printed sensors were recycled by\nexploiting water solubility of the NaCMC binder. Discarded sensors were immersed in deionized (DI)\nwater until the printed layer disintegrated and the composite dispersed. The released Fe/Fe O\nmicroparticles were collected from the suspension using a permanent magnet, rinsed with DI water to\nremove residual NaCMC, and dried under ambient conditions (or under mild vacuum) until constant\nmass. The reclaimed particles were then re-mixed in a freshly prepared NaCMC aqueous solution to\nformulate inks following the same protocol as for the pristine ink. The ink was subsequently reprinted\nto fabricate new sensors using identical printing, drying, and post-treatment conditions as the initial\ndevices. This recycling–reprinting procedure was repeated for up to three cycles. For each cycle, the\nresidence time of the particles in water (from immersion to magnetic collection) was kept below 1 h.\n2. Prolonged water-immersion (particle aging/corrosion window) experiment. To assess the effect of\nextended water exposure during recycling, Fe/Fe O microparticles were intentionally immersed in DI\nwater for predefined durations (1, 3, 5, 10, and 15 days) under ambient conditions. After the specified\nimmersion time, the particles were magnetically collected, rinsed with DI water, and dried to constant\nmass. Inks were prepared by mixing the aged particles with NaCMC aqueous solution using the same\nformulation and mixing procedure as for the pristine ink. Sensors were reprinted under identical\nconditions, and their MR performance was evaluated as described in the MR measurement section.\nfurther clarification. The authors should discuss the operational window e.g. humidity, temperature,\nand time in service and clarify how encapsulation strategies change that window.\nResponse: In the original manuscript, we primarily evaluated a long-term water-immersion stability at\nroom temperature (up to 90 days) to demonstrate that biodegradable encapsulation can regulate the\nwater-triggered performance degradation (Fig. 2c). To clarify practical storage/service implications, we\nhave now performed a systematic aging study under controlled humidity and temperature conditions\nand added the results as Supplementary Fig. 5.\nThe new data define the operational window as follows:\n1. Ambient humidity (room temperature to 80 °C): Bare sensors and those encapsulated with beeswax\nor ecoflex show essentially unchanged MR over 20 days, indicating that for dry/ambient environments,\nencapsulation is not required for at least 20 days even at elevated temperature (≤80 °C). Notably,\nbeeswax is not suitable for high-temperature encapsulation because it melts at ~80 °C.\n2. High humidity (95% RH, room temperature): The unencapsulated devices become non-conductive\nrapidly (within ~2 h; the first scheduled measurement already fails), whereas both beeswax and ecoflex\nencapsulation preserve stable MR for at least 20 days, demonstrating that encapsulation effectively shifts\nthe operational window to highly humid environments.\n3. Water immersion (50 °C and 80 °C): Under hot water exposure, the lifetime becomes strongly\nencapsulation-dependent. Beeswax provides only short-term protection at 50 °C (stable in the first ~5\ndays, followed by pronounced degradation and device failure by day ~15). In contrast, ecoflex offers\nthe broadest window, maintaining stable MR for at least 20 days at 50 °C in water, and for ~15 days at\n80 °C before failure at day 20.\nOverall, these results complement the original long-term room-temperature immersion data (Fig. 2c)\nand explicitly show how encapsulation expands the usable humidity/temperature regime—from dry\nambient storage to high-humidity and warm-water environments—allowing application-specific\ntailoring of device lifetime via the choice of encapsulation layer.\nRevision:\nAdded new Supplementary Fig. 5:\nFe/Fe O -NaCMC sensors. MR ratio (at 100 mT) of printed sensors without encapsulation (“Bare”)\nand with beeswax or Ecoflex encapsulation after storage under a. ambient humidity at room temperature,\nb. ambient humidity at 50°C, c. ambient humidity at 80°C, d. 95% relative humidity at room temperature,\ne. immersion in water at 50°C, and f. immersion in water at 80°C. Beeswax was not tested at 80°C due\nto melting. MR was measured at room temperature after the indicated storage time. Data points at 0%\ncorrespond to the loss of electrical conduction (device failure).\nThe printed Fe/Fe O -NaCMC composite is intrinsically moisture-sensitive because the NaCMC matrix\nis hydrophilic and water-soluble; moisture uptake can swell/soften the binder and disrupt the particle\npercolation network, leading to a rapid increase in resistance and eventual loss of conductivity. The\nsensors remain stable for at least 20 days under ambient humidity even when continuously stored at up\nto 80°C, whereas unencapsulated devices fail rapidly at 95% relative humidity (RH). The encapsulation\neffectively delays the moisture ingress and thus expands the operational window: beeswax and Ecoflex\nboth protect the device in high humidity at room temperature, while under water immersion the lifetime\nbecomes temperature and encapsulation dependent. Beeswax provides only short-term protection at\nelevated temperatures (accelerated degradation in warm water and melting at ~80°C), whereas Ecoflex\noffers the widest window (stable for ≥20 days in water at 50°C and ~15 days at 80°C). Together with\nthe long-term room-temperature immersion results in the Fig. 2c (main text), these data highlight that\nthe service lifetime can be application-specifically tuned by selecting an appropriate biodegradable\nencapsulation strategy.\nMain text: page 8\nadded a brief discussion:\nConsistent with these immersion results, accelerated aging under controlled humidity and temperature\nfurther confirms that encapsulation markedly expands the operational window from ambient conditions\nto high-humidity and warm-water environments (Supplementary Fig. 5).\nAdded:\nTo evaluate the environmental stability under different storage conditions, encapsulated and bare sensors\nwere stored under (i) ambient humidity at room temperature, 50°C, and 80°C, (ii) 90% relative humidity\nat room temperature, and (iii) immersion in water at room temperature, 50°C, and 80°C. After the\ndesignated storage time, the MR performance of the sensors was measured repeatedly at room\ntemperature. The encapsulated sensors were immersed in water at room temperature to assess stability,\nand their MR performance was measured periodically.\nComment 3: - The authors should explain how particle size distribution and orientation affect the\neffective gain factor in the printed composite.\nResponse: The gain factor is defined as the amplification of the local magnetic field at the shell–shell\ngrain-boundary junctions by the Fe core (i.e., the ratio between the locally concentrated field and the\napplied external field). In a printed composite, this amplification is determined by many neighboring-\nparticle junctions along percolation paths. Therefore, both particle size distribution (size mismatch\nbetween adjacent particles) and particle orientation (relative angle between the external field and the\npercolation path) can affect the effective gain factor.\nFollowing the reviewer’s suggestion, we performed additional simulations (external field 100 mT) to\nquantify these effects while fixing the Fe O shell thickness to 10 nm. To evaluate the influence of size\ndistribution, we considered two contacting core–shell particles, fixed the core radius of one particle at\n120 nm, and varied the core radius of the second particle from 50 to 120 nm (new Supplementary Fig.\n16). The gain factor at the junction points changes only moderately, remaining in the range of ~13–16,\nindicating that reasonable size mismatch introduces only a limited variation in local field amplification.\nThis behavior is related to the change in magnetization distribution near the junction, where the smaller\nparticle tends to be more uniformly magnetized under the applied field.\nWe also examined the influence of field orientation by rotating the external magnetic field with respect\nto the symmetry axis of the contacting particle pair (Supplementary Fig. 17 and 18). For two identical\nparticles, the gain factor is highest when the field is aligned with the interparticle axis and decreases\nprogressively with increasing tilt, reaching values of ~3 for the perpendicular orientation. A size-\nmismatched pair (core radii 120 nm and 60 nm) follows the same overall trend and shows a more\nmonotonic angular dependence (new Supplementary Fig. 18), consistent with a more homogeneous\nmagnetization of the smaller particle. It is worth noting that the gain factor is highly sensitive to the\nrelative orientation between the external magnetic field and the percolation path connecting adjacent\nparticles (Supplementary Fig. 17). As the alignment shifts from parallel to tilted, the gain factor\ndecreases progressively. Due to the random arrangement of particles within the composite, the overall\naveraged effect is expected to be lower, which is in accordance with the experimentally observed gain\nfactor of approximately 10.\nOverall, these simulations indicate that particle size distribution introduces only a modest spread in the\nlocal gain factor, whereas orientation can cause a stronger reduction at individual junctions. In a\nrandomly packed printed composite, averaging over many junctions with different orientations is\ntherefore expected to yield an effective gain factor lower than the ideal aligned-pair maximum,\nconsistent with the experimentally observed value around 10.\nRevision:\nSupplementary Fig. 16. Simulation of particle-size-mismatch effects on the local gain factor at a\ncore-shell junction. a-e. Spatial maps of the gain factor (colormap) in the axial cross-section of two\n7\ncontacting spherical Fe/Fe O core–shell particles with different core-radius ratios. The larger particle\nis kept with a constant core radius, R , of 120 nm, while the smaller particle has core radii, R , of 50 nm\n(a), 60 nm (b), 80 nm (c), 100 nm (d), and 120 nm (e). In all cases, the Fe O shell thickness is fixed at\n10 nm. (f) Gain factor evaluated at the junction as a function of the core-radius ratio (R /R ), showing\nonly a modest variation across the investigated size-mismatch range.\nSupplementary Fig. 18. Simulation of field-orientation dependence of the local gain factor in a\nsize-mismatched Fe/Fe O particle pair. a-c. Spatial maps of the local gain factor (colormap) in the\nx–z axial cross-section of two contacting spherical core-shell Fe/Fe O particles (core radii: 120 nm and\n8\n60 nm; shell thickness: 10 nm), together with the corresponding equilibrium magnetization distribution\n(arrows). An external magnetic field of 100 mT is applied with a tilt angle θ = 30° (panel a), 60° (panel\nb), and 90° (panel c) relative to the horizontal/interparticle axis. d. Gain factor at the junction as a\nfunction of θ, showing a progressive reduction with increasing tilt, consistent with the evolution of the\nequilibrium magnetic state near the junction.\nMain text: page 11\nRevised discussion:\nAdditional simulations further indicate that a reasonable size mismatch between two contacting particles\nintroduces only a modest variation in the local gain factor (Supplementary Fig. 16), whereas the gain\nfactor is highly sensitive to the relative orientation between the external magnetic field and the\npercolation path connecting adjacent particles (Supplementary Fig. 17 and 18).\nComment 4: - How does sensitivity and figure of merit at <10 mT compare to samples from the\nliterature?\nResponse: A detailed quantitative comparison is provided in Supplementary Table 1, where sensitivity\nand FoM values at ≤10 mT are compiled from representative printed magnetoresistive sensors. To\nfurther improve clarity and visibility, we additionally prepared a radar chart summarizing the sensitivity\nand FoM in the low-field regime (<10 mT) (Fig. R1). Based on this comparison, the magnetoresistance\nratio at 10 mT of our Fe/Fe O -based sensor is higher than that of all previously reported printed\nmagnetoresistive sensors. In terms of low-field sensitivity (<10 mT), our sensor outperforms the\nmajority of reported printed systems, typically by several-fold and, in some cases, approaching one order\nof magnitude. An exception is a printed Ni Fe permalloy-based sensor (DOI: 10.1038/s41467-022-\n81 19\n34235-3), which exhibits very high sensitivity due to the ultrahigh magnetic permeability and low\ncoercivity of permalloy. Notably, this Ni Fe -based sensor shows a relatively low magnetoresistance\n81 19\nratio (<1%) and saturates at magnetic fields below ~2.5 mT, thereby limiting both signal amplitude and\neffective detection range. In addition, Ni Fe relies on a high nickel content (>80%), which involves\n81 19\nhazardous and non-eco-sustainable elements. A similar trend is observed for the figure of merit at <10\nmT. Our sensor exhibits a FoM that is higher than most reported printed magnetoresistive sensors, often\nby more than an order of magnitude, with only two Ni Fe -based systems (DOI: 10.1038/s41467-022-\n81 19\n34235-3 and 10.1002/adma.202005521) showing higher values. Overall, this comparison highlights that\nthe proposed Fe/Fe O -based sensors achieve a rare combination of high low-field performance, wide\ndetection range, and intrinsic eco-sustainability.\nreported printed MR sensors. The Ref. numbers correspond to the ones in the main text.\nComment 5: - Was sensor readout stable across practical bias ranges and was there an optimal\noperating voltage to minimize drift?\nResponse: We evaluated sensor readout stability and identified a practical operating bias by combining\n(i) time-domain output stability, (ii) signal-to-noise ratio (SNR) and noise spectral density (NSD) under\ndifferent excitation currents, and (iii) bias-dependent MR characteristics (Fig. R2a–d).\nFrom the device geometry, the optimized Fe/Fe O sensor yields an electrical resistivity of ~0.6 Ω·m,\ncorresponding to a channel resistance of ~560 Ω. Accordingly, the excitation-current range in Fig. R2b\n(283 nA–286 µA) maps to a bias-voltage range of ~0.16 mV–0.16 V, with ultralow power dissipation\nof ~45 pW–46 µW, which avoids self-heating. At a representative practical operating point (≈0.16 V),\nthe time-domain output remains stable over the measurement window with no observable drift (Fig.\nR2a). The NSDs measured at room temperature show that very low excitation currents lead to an\nelevated noise floor, while increasing the excitation current suppresses the NSD and finally yields a\nsaturated and stable baseline around 0.1 V bias voltage (~133 μA excitation current) (Fig. R2b).\nConsistently, at an ultralow bias of 1 mV (≈1.8 µA for a ~560 Ω channel), the MR curve becomes noise-\ndominated and the apparent MR is limited by the poor SNR (Fig. R2c).\nFig. R2d, the MR performance is found to be stable across this bias range. It is important to note that\nhigher biases (>1 V) cause a measurable MR suppression (we observed a decrease from ~3.3% to 2.8%\nMR between 0.1 V and 5 V), consistent with the voltage-induced reduction of the hopping barrier.\nTherefore, we recommend (and used in this work) a low-bias operating point around 0.1 V combined\nwith low-noise AC (lock-in) readout, which minimizes noise spectral density while maintaining\nsensitivity near its maximum.\nFig. R2. a. Time-domain output stability. b. Noise spectral density (NSD) of the sensor at different\nexcitation currents. c. Low signal-to-noise ratio MR curve measured at 1mV bias voltage. d. Voltage-\ndependent magnetoresistance characterization.\nComment 6: - Finally, since many binders were used, is there any binder feature (e.g. polarity or\nmechanical performance) that heavily influences the magnetic or electrical coupling between Fe/Fe3O4\nand the overall MR response?\nResponse: In our experiments, we intentionally tested a diverse set of polymeric binders, including\nalginate, starch, egg white, and NaCMC, which span a wide range of chemical polarity, functional\ngroups, and mechanical characteristics (Fig. 2d and Supplementary Fig. 6). Despite these pronounced\ndifferences, the resulting sensors exhibit very similar magnetoresistance ratios (around −3%) and\nsensitivities (> 3.5 T⁻¹), without any systematic trend linked to binder chemistry or mechanics.\nThis observation indicates that no specific binder feature, such as polarity or mechanical compliance,\nheavily dominates the magnetic or electrical coupling in the composite. All tested binders are electronically\ninsulating and magnetically inert. Therefore, they do not introduce additional electronic or magnetic\ncoupling pathways. Instead, the binder primarily serves to immobilize the Fe/Fe O core-shell\nmicroparticles and stabilize the percolated microstructure. Consistent with the transport analysis\npresented in Fig. 3, the overall MR response is governed by spin-dependent hopping across Fe O grain\nboundaries and by the Fe-core-induced magnetic flux guiding effect, both of which are intrinsic to the\nFe/Fe O architecture rather than the binder. The weak dependence on binder chemistry further\nhighlights the robustness and process tolerance of the proposed sustainable sensor platform.\nOverall Comment: The study demonstrates clear potential for significant contributions to the field.\nHowever, several substantive issues require careful revision and clarification before this work can be\nconsidered for publication:\nResponse: We sincerely thank the Reviewer for their positive evaluation of our manuscript.\nComment 1: 1. This manuscript systematically optimizes the magnetic and electronic properties\n(oxidation temperature, particle size, and binder type) which is appreciative. However, the authors\nmade a major point in using “industry-scale screen printing” (Fig. 1b, Supplementary Fig. 1) for high-\nthroughput fabrication. This is a key claim in terms of scalability and practicality. Nonetheless, they\nprovide no data regarding the optimization of ink to prove its printability. To that end, it is important to\nknow the rheological profile of the ink. Rheological data (viscoelastic properties, shear-thinning\nbehavior of the ink for screen printing, 𝐺′/𝐺′′ behavior etc., and contact angle measurements) are critical\nparameters. In addition, answering the reason for selecting the 60% volume ratio would show how these\nchoices affect the printability of the ink. The manuscript would benefit from the inclusion of such\ncharacterization of the ink and aid in the reproducibility of the work.\nResponse: In the revised manuscript, we added a dedicated rheological assessment and clarified the\nrationale for selecting the 60 vol% Fe/Fe O particles formulation (Fe/Fe O particles volume fraction\nin the final dried composite).\nRheology added (viscosity window, shear-thinning, and G′/G″). We performed stepwise steady-\nshear measurements (1–100 s⁻¹) and small-amplitude oscillatory frequency sweeps for inks with varied\nNaCMC concentration (10 wt% and 15 wt% NaCMC in the aqueous binder, at 60 vol% Fe/Fe O\nparticles) and varied Fe/Fe O particles loading (30/60/90 vol% Fe/Fe O particles, at 10 wt% NaCMC).\nThe results and detailed discussion are now provided as new Supplementary Fig. 2, demonstrating\nsuitable viscosity window, pronounced shear-thinning and a tunable viscoelastic response (G′/G″) as a\nfunction of formulation, consistent with screen-printing-compatible ink behavior.\nRole of NaCMC concentration (tuning viscosity/viscoelasticity and ensuring ink stability). NaCMC\nconcentration is a key formulation parameter that simultaneously tunes the viscosity and viscoelasticity\nof the particle-laden ink, thereby governing both mesh transfer under shear and shape retention after\nprinting. In our screening, decreasing NaCMC concentration systematically reduced the low-shear\nviscosity and viscoelastic moduli (G′ and G″), weakening the polymer/particle network that stabilizes\nthe suspension. When the NaCMC concentration was too low, the ink became unstable and exhibited\nrapid sedimentation and phase separation at the same particle loading.\nRationale for selecting 60 vol% Fe/Fe O particles (printability, electrical percolation, and\nmaterial efficiency). The choice of 60 vol% Fe/Fe O particles was guided by a balanced optimization\nacross processing and device requirements. At low particle loading (e.g., 30 vol%), it is difficult to\nestablish a robust conductive percolation network after printing, whereas excessively high loading\nproduces a highly solid-like paste that can hinder mesh transfer and increase clogging risk. In addition,\nvery high particle fractions reduce the effective binder volume available for particle rearrangement and\nconsolidation during drying, which can slightly compromise magnetoresistance performance\n(Supplementary Fig. 24) while also increasing material consumption without commensurate benefits.\nAccordingly, the formulation of 60 vol% Fe/Fe O particles provides a practical compromise between\nreliable screen printing and robust electrical/magnetoresistive performance.\nRevision:\nSupplementary Fig. 2. Rheological characterization of NaCMC–Fe/Fe O inks for screen printing.\na. Stepwise steady-shear viscosity of inks containing 60 vol% Fe/Fe O particles (in the final dried\ncomposite) formulated using NaCMC aqueous binders with different NaCMC concentrations (10 wt%\nand 15 wt% NaCMC in water). The shear rate was sequentially set to 1, 10, 30, and 100 s⁻¹ (values\nindicated in the panel). b. Frequency-dependent storage modulus (G′) and loss modulus (G″) of the inks\nin panel a measured by small-amplitude oscillatory shear. c. Stepwise steady-shear viscosity of inks\nformulated with a 10 wt% NaCMC aqueous binder and different Fe/Fe O particles volume fractions\n(30, 60, and 90 vol% in the final dried composite). d. Corresponding oscillatory frequency sweeps of G′\nand G″ for the inks in c. NaCMC concentration refers to the polymer weight fraction in the aqueous\nbinder solution used for ink preparation; particles content refers to the Fe/Fe O particle volume fraction\nin the composite after solvent evaporation. All measurements were performed at 22°C using a plate–\nplate geometry (1 mm gap).\nRheological characterization was conducted to evaluate the printability window of NaCMC–Fe/Fe O\ncomposite inks by varying the NaCMC concentration in the aqueous binder and the Fe/Fe O particles\nvolume fraction in the final dried composite. First, viscosity of the ink is in the range that is suitable for\nscreen printing. The stable formulations exhibit pronounced shear-thinning behavior in stepwise steady-\nshear tests: the viscosity decreases systematically when the shear rate is increased from 1 to 100 s⁻¹,\nwhich is desirable for screen printing because the ink can flow readily through the mesh under the\nsqueegee yet recover a higher viscosity at low shear to suppress spreading after printing. Increasing the\nNaCMC concentration (10 wt% → 15 wt%, at 60 vol% Fe/Fe O particles) substantially raises the low-\nshear viscosity and the viscoelastic moduli (G′ and G″), indicating a strengthened polymer/particle\nnetwork that improves the suspension stability and shape retention. In contrast, inks formulated with a\n5 wt% NaCMC binder at 60 vol% Fe/Fe O particles were not stable (rapid sedimentation and phase\nseparation), evidencing that an insufficient binder concentration fails to provide an adequate\nyield/structural strength for printing.\nvol%) progressively elevates the viscosity and moduli. The 90 vol% Fe/Fe O particles ink shows a\nmarkedly solid-like response with high, weakly frequency-dependent G′ and G′ ≫ G″ across the\nmeasured range, consistent with a jammed/percolated particle skeleton. While such a structure can aid\nshape fidelity, it may also impede mesh transfer and increase the risk of screen clogging. By comparison,\n10 wt% NaCMC–60 vol% Fe/Fe O particles provides a balanced rheological profile—stable dispersion,\nstrong shear-thinning, and stable viscoelasticity—supporting reliable screen printing with good pattern\nfidelity and minimal slumping.\nMain text: page 5\nRheological measurements further corroborate the screen-printing suitability of the selected ink,\nfeaturing the suitable viscosity for screen printing and pronounced shear-thinning under increasing shear\nrate (Supplementary Fig. 2).\nMethod: page 15\nRheology characterization\nRheological measurements were performed to evaluate the viscoelastic behaviour of the inks. The MCR\n302 rheometer (Anton Paar) equipped with the MRD180/1T magnetocell in a plate–plate configuration\n(1 mm gap) was used to determine the shear‑thinning and oscillatory behaviour of the inks. All\nmeasurements were performed at 22°C and the sample volume was constant.\nComment 2: 2. On page 6, authors mentioned “These designs work in concert, delivering exceptional\nlow-field response, as evidenced by a higher magnetoresistance ratio at 10 mT relative to all printed\nmagnetoresistive sensors reported previously21–31,40 (Fig. 1h)”. Authors are requested mention the\nsupporting supplementary table.\nResponse: We agree that the comparison statement on page 6 should be explicitly supported by the\ncorresponding supplementary data. In the revised manuscript, we have updated the sentence to directly\nreference Supplementary Table 1, which provides a detailed quantitative comparison of printed\nmagnetoresistive sensors reported in the literature. This table underpins the comparison shown in Fig.\n1h and substantiates the statement regarding the magnetoresistance ratio at 10 mT. The revised sentence\nnow explicitly cites Supplementary Table 1 to improve clarity and transparency.\nRevision (for comment 2):\nMain text: On Pages 6\nThese designs work in concert, delivering exceptional low-field response, as evidenced by a higher\nmagnetoresistance ratio at 10 mT relative to all printed magnetoresistive sensors reported previously21–\n31,40 (Fig. 1h and Supplementary Table 1).\nComment 3: 3. In Figure 1h, the authors highlight the large-scale fabrication, green synthesis,\nbiocompatibility, biodegradability, recyclability, and %MR at 10 mT to emphasize the practical\nsignificance of their sensors. However, it is unclear which specific synthesis parameter(s) was/were\nconsidered in this comparison. Based on the figure caption, it seems only the binders were compared.\nThe authors are requested to clarify the parameters used and justify their selection to ensure that the\ncomparison is scientifically meaningful and is not limited to a single fabrication variable.\nprocessing parameters within our Fe/Fe O system, nor to isolate a single fabrication variable such as\nthe binder. Instead, Fig. 1h provides a system-level benchmark of previously reported printed\nmagnetoresistive sensors from the literature, highlighting their practical relevance by combining (i) the\nfunctional performance at low field (%MR at 10 mT) with (ii) application- and sustainability-related\nattributes, including large-scale fabrication compatibility, green processing, biocompatibility,\nbiodegradability, and recyclability.\nImportantly, the comparison in Fig. 1h is based on the complete reported sensor systems, including both\nthe magnetoresistive functional materials (e.g., [Co/Cu] multilayer microflakes, NiFe-based systems, Bi\nmicroparticles, Fe-based fillers) and the associated binder matrices/processing routes, as summarized\nquantitatively in Supplementary Table 1. We have revised the content, figure caption of Fig. 1h and the\ncorresponding text to explicitly direct readers to Supplementary Table 1, thereby improving\ntransparency and preventing the interpretation that the comparison is limited to a single fabrication\nvariable.\nBy contrast, the influence of specific synthesis and processing parameters within our system is\nsystematically investigated elsewhere in the manuscript, including oxidation temperature (Fig. 3e),\noxidation environment (Supplementary Fig. 23), oxidation time (Supplementary Fig. 24) and particle\nsize (Supplementary Fig. 15), particle volume ratio (Supplementary Fig. 24), binder type (Fig. 2d and\nSupplementary Fig. 6), and substrate type (Supplementary Figs. 7 and 8). Collectively, these data\ndemonstrate that the reported performance originates from a carefully optimized material and structural\ndesign rather than from any single fabrication parameter.\nRevision:\nOn pages 6\nThese designs work in concert, delivering exceptional low-field response, as evidenced by a higher\nmagnetoresistance ratio at 10 mT relative to all printed magnetoresistive sensors reported previously21–\n31,40 (Fig. 1h and Supplementary Table 1).\nOn the content and caption of figure 1h:\n15\nh, Comparison of different printed MR sensors in terms of the large-scale and green fabrication (non-\ntoxic solvent and energy saving), biodegradable, biocompatible, recyclable and MR ratio at 10 mT. A\ndetailed quantitative comparison of the literature-reported sensor systems (including fabrication process,\nfunctional elements, binders, and low-field metrics) is provided in Supplementary Table 1. The\ncorresponding functional fillers and binders in references: Ref.21: [Co/Cu] flakes with PMMA;\n50 50\nflakes with PSBS; Ref.25: [Co/Cu] flakes with PECH; Ref.26: [Co/Cu] flakes with PECH; NiCo\n30 50\nparticles with PECH; Ref.27: FeCoNi/Cu nanowire with PDMS; Ref.28: [Ta/Py] flakes with PSBS;\nRef.29: NiFe nanowire with PDMS; Ref.30: NiFe particles with PDMS; Ref.31: Bi particles with\nButylmethacrylate; Ref.40: Fe particles with Hexadecylamine.\nComment 4: 4. The authors use an acid wash (Vitamin C) treatment for the selective removal of the\nFe₃O₄ shell and demonstrate a transition to linear current-voltage behavior, indicative of ohmic\nconduction, whereas the printed Fe/Fe3O4 samples exhibit nonlinear current-voltage characteristics,\nwhich they attribute to the variable-range hopping mechanism (Supplementary Fig. 5). In addition, on\npage 9, the authors claim that “The magnetoresistive behavior of Fe/Fe3O4 core-shell particle sensors\ncan be attributed to spin-dependent hopping across magnetically disordered interfaces between\nadjacent Fe3O4 shells. Upon application of an external magnetic field, the alignment of local magnetic\nmoments reduces spin disorder and enhances carrier hopping mobility, giving rise to negative\nmagnetoresistance effects [Ref. 47,48].” Authors are requested to include the relevant MR curve (if\npossible) for a direct and robust visual demonstration of the indispensable role of the magnetically\ndisordered interfaces between adjacent Fe₃O₄ shell in generating the magnetoresistance.\nResponse: In our work, the magnetoresistance is attributed to spin-dependent hopping across\nmagnetically disordered interfaces between adjacent Fe O shells, as discussed in the section “Spin-\ndependent hopping-mediated grain boundary magnetoresistance …”. Consistent with this mechanism,\nthe printed Fe/Fe O composites exhibit nonlinear I–V behavior (Fig. 3a and Supplementary Fig. 9) and\nnegative temperature-dependent resistance (Fig. 3b and Supplementary Fig. 11) characteristic of\nhopping-type transport, whereas selective removal/reduction of the oxide shell by the Vitamin-C (acid\nwash) treatment leads to a transition to linear (ohmic) I–V behavior (Supplementary Fig. 9) and positive\n(metal) temperature-dependent resistance behavior (Supplementary Fig. 11), indicating that charge\ntransport becomes dominated by the metallic Fe core rather than interfacial hopping.\nImportantly, the MR response is strongly suppressed when the oxide shell is destroyed and removed:\nthe acid-washed (shell-removed) samples show only a very small low-field MR (e.g., MR at 10 mT ≈\n0.04%, Supplementary Table 2), close to the Fe-dominated baseline. Moreover, the MR decreases with\nincreasing bias voltage (Fig. 3d and Supplementary Fig. 10), which is consistent with a bias-induced\nreduction of the interfacial hopping barrier and the associated suppression of spin-dependent transport.\nTo address the Reviewer’s request for a more direct visualization, we have added a representative MR(H)\ncurve of the Vitamin-C treated (shell-removed) sample together with the sample printed with pristine\nparticles and the sample printed with optimal oxidized particles (new Supplementary Fig. 25). This\ndirect comparison clearly shows that the pronounced MR arises only when Fe O –Fe O interfaces are\npresent.\nFinally, we note that the Fe core primarily contributes to magnetic flux concentration rather than being\nthe origin of MR: after removing an average gain factor (~10), the normalized MR curve of Fe/Fe O\nclosely resembles that of the printed Fe O counterpart (Fig. 4a and Supplementary Fig. 15a), supporting\n16\nthat the MR originates from the Fe O interfacial grain-boundary network while the Fe core amplifies\nthe local field at these interfaces.\nSupplementary Fig. 25. a. MR curves of printed Fe/Fe O sensor post-treated by vitamin C solution\nwith different concentration. b. MR curves of printed Fe/Fe O sensor with optimally oxidized particles,\npristine particles (naturally oxidized) and shell removed particles.\nComment 5: 5. The authors claimed an improved low-field sensitivity with exceptionally reliable\npractical functionality. However, a comparison of devices produced within the same batch and different\nbatches would strengthen the scientific rigor of the technology. The authors are requested to provide a\nstatistical analysis of the key performance parameters based on measurements from multiple\nindependent sensor devices to ensure reproducibility. The Methods section should explicitly state the\nsample size (n) for each dataset.\nResponse: To demonstrate reproducibility, we fabricated and measured three independent batches of\nFe/Fe O sensors prepared under identical conditions, as mentioned in Methods. Each batch contains n\n= 10 independent sensors (total n = 30), and we performed a statistical analysis of the key performance\nmetrics, including MR at 10 mT, saturated MR at 100 mT, and maximum sensitivity. The results show\ngood within-batch consistency and high batch-to-batch reproducibility. Specifically, the batch-wise\naverages are:\nBatch 1 (n=10): MR@10 mT = 1.74% ± 0.14%; MR@100 mT = 3.00% ± 0.18%; Smax = 3.98 ± 0.33 T⁻¹\nBatch 2 (n=10): MR@10 mT = 1.67% ± 0.13%; MR@100 mT = 2.98% ± 0.09%; Smax = 3.82 ± 0.25 T⁻¹\nBatch 3 (n=10): MR@10 mT = 1.96% ± 0.08%; MR@100 mT = 3.21% ± 0.14%; Smax = 4.37 ± 0.19 T⁻¹\nAll devices (n=30): MR@10 mT = 1.79% ± 0.17%; MR@100 mT = 3.06% ± 0.18%; Smax = 4.05 ± 0.33 T⁻¹\nThe corresponding coefficients of variation (CV) remain low (typically ~3–10% across these metrics),\nconfirming robust reproducibility. We have summarized these statistics in a new supplementary table 4.\nand visualized the within-/between-batch distributions using statistic box plots (Supplementary Fig. 3).\nFinally, following the reviewer’s request, we have updated the Methods section to explicitly state the\nsample size (n) for each dataset and add the reproducibility discussion on page 6.\nRevision:\nAdded new Supplementary Fig. 3.\nsensors. a. Magnetoresistance at 10 mT (MR@10 mT) for three independently fabricated batches (Batch\n1–3, n = 10 devices per batch) and the entire dataset (all samples, n = 30). b. Saturated magnetoresistance\nat 100 mT (MR@100 mT) for the same samples. c. Maximum low-field sensitivity (S ) for the same\nmax\nsamples. In all panels, box plots indicate the median (center line), interquartile range (box), and 1.5×IQR\nwhiskers; individual data points represent measurements from independent samples.\nAdded new Supplementary Table 4.\nSupplementary table 4. Device-to-device and batch-to-batch reproducibility of printed Fe/Fe O sensors.\nStatistical summary of key performance parameters measured for three independently fabricated batches\n(Batch 1–3, n = 10 devices per batch; total n = 30): magnetoresistance at 10 mT (MR@10 mT), saturated\nmagnetoresistance at 100 mT (MR@100 mT), and maximum sensitivity (Smax). For each batch and for\nthe pooled dataset, the mean, standard deviation (SD), and coefficient of variation (CV) are reported.\nBatch Sample MR at 10 mT Saturated MR Max\nNumber number (at 100 mT) Sensitivity (T-\n1)\n#1 2.0% 3.2% 4.52\n#2 1.7% 2.8% 3.96\n#3 1.6% 2.9% 3.69\n#4 1.7% 2.9% 3.96\nBatch #1 #5 1.8% 2.9% 4.05\n#6 1.7% 3.1% 3.85\n#7 1.5% 2.9% 3.52\n#8 1.7% 2.9% 3.92\n#9 1.8% 3.0% 3.98\n#10 1.9% 3.4% 4.31\nMean 1.74% 3.00% 3.98\nSD 0.14% 0.18% 0.33\nCV 8.05% 6.00% 8.29%\n#1 1.6% 2.9% 3.61\n#2 1.6% 3.1% 3.55\n#3 1.6% 2.8% 3.65\n#4 1.6% 2.9% 3.72\n#5 1.9% 3.0% 4.27\nBatch #2 #6 1.8% 3.0% 4.12\n#7 1.5% 3.0% 3.57\n#8 1.8% 3.1% 4.04\n#9 1.7% 3.0% 3.88\n18\n#10 1.6% 3.0% 3.81\nMean 1.67% 2.98% 3.82\nSD 0.13% 0.09% 0.25\nCV 7.78% 3.02% 6.54%\n#1 1.9% 3.1% 4.32\n#2 1.9% 3.1% 4.22\n#3 1.9% 3.1% 4.24\n#4 1.9% 3.2% 4.18\n#5 1.9% 3.2% 4.17\nBatch #3 #6 2.1% 3.4% 4.62\n#7 2.1% 3.4% 4.75\n#8 2.0% 3.4% 4.47\n#9 2.0% 3.0% 4.39\n#10 1.9% 3.2% 4.29\nMean 1.96% 3.21% 4.37\nSD 0.08% 0.14% 0.19\nCV 4.08% 4.36% 4.35%\nMean 1.79% 3.06% 4.05\nAll SD 0.17% 0.18% 0.33\nCV 9.50% 5.88% 8.15%\nMain text: page 5:\nThe printed sensors also exhibit robust device-to-device performance reproducibility (Supplementary\nFig. 3 and Supplementary Table 4).\nMethod: In the “Magnetoresistance measurement” section. On page 18.\nAdded:\nTo assess performance reproducibility, sensors from three independently fabricated batches were\nmeasured (batch 1-3, n = 10 devices per batch; total n = 30), prepared under identical conditions.\nComment 6: 6. On page 11, the authors have successfully demonstrated the optimization of device\nperformance by varying the core diameter and shell thickness using numerical simulations. The authors\nalso mentioned “….. as the core diameter increases, the greater permeability contrast improves flux\nconcentration. However, beyond a critical size, the resulting flux distribution reaches a geometric limit,\nno longer enhancing the field in grain boundaries.” The observed normalized MR shown in Figure 4i\nis related to the overall particle size. The authors are required to provide direct microstructural\nevidence (e.g., cross-sectional SEM/TEM/HRTEM) to quantify the final core diameter and precise shell\nthickness of the particles. These values should be explicitly stated in the main text and correlated with\nthe performance data.\nResponse: We agree that quantifying and explicitly reporting the final core diameter and shell thickness,\nand relating these values to the gain-factor trend in Fig. 4i, will make the structure-performance\ninterpretation clearer and more rigorous. In Fig. 4i, we investigate how the gain factor evolves with\nparticle (core) size. Accordingly, we prepared three representative particle size classes with average\ndiameters of ~90 nm, ~3 μm, and ~15 μm, quantified by statistical size analysis (Supplementary Figs.\n19 and 20). All three size classes were oxidized under the same conditions (235 °C, medium vacuum\n0.5 mbar, 30 min) to keep the oxide-shell formation comparable across samples (mentioned in Methods).\nDirect microstructural quantification of the shell thickness under the optimized oxidation conditions\n(235 °C, medium vacuum 0.5 mbar, 30 min) is provided by cross-sectional TEM/HR-TEM of the\nrepresentative ~3 μm Fe/Fe O core–shell particles (Fig. 3f and Supplementary Fig. 22), showing a\ncontinuous Fe O shell with a thickness of about 10-20 nm. For the core-size series, the use of identical\noxidation conditions is further supported by literature indicating that, under the same oxidation\nconditions, the oxide growth kinetics (and thus shell-thickness evolution) are largely independent of\nparticle size for iron/iron-oxide core–shell formation (DOI: 10.1103/PhysRevB.68.195423). Therefore,\nthe experimentally observed evolution and saturation of the normalized MR/gain factor with increasing\nparticle size (Fig. 4i and j) provide direct experimental support for the simulation-predicted trend:\nincreasing core diameter enhances flux concentration until a geometric limit is reached.\nTo improve clarity, we have now explicitly stated the particle diameters (90 nm / 3 μm / 15 μm),\nand the unified oxidation condition (235 °C, 0.5 mbar, 30 min) in the caption of Fig. 4.\nIn addition, we separately examined shell-growth-related effects experimentally by varying oxidation\ntime at fixed temperature/vacuum (Fig. 4f, g and Supplementary Fig. 15b), which shows how thicker\nshells reduce the gain factor and modify the low-field response. Together, these results provide a clear\nand experimentally grounded link between (i) the simulated trends and (ii) the measured gain-factor\nevolution: core diameter controls the flux-guiding enhancement observed in Fig. 4i, while shell\nthickness is validated independently via controlled oxidation-time variations for particles of the same\nsize (3 μm).\nRevision:\nCaption of Figure 4.\nh, SEM images of Fe/Fe O core-shell particles with different sizes (90 nm, 3 μm and 15 μm), Scale\nbars: 500 nm, 10 μm, 100 μm from top to bottom. For the distribution of particle diameters, see\nSupplementary Figs. 13 and 14. All three size classes were oxidized under the same conditions (235 °C,\nmedium vacuum 0.5 mbar, 30 min) to keep the oxide-shell formation comparable across samples. i,\nNormalized MR curves and j, sensitivity curves of printed Fe/Fe O core-shell particles with different\nsizes.\nComment 7: 7. The claim of a \"truly closed-loop sustainable life cycle\" (e.g., Page 12, Fig. 5a) should\nbe reconsidered. This phase implies a rigorous Life Cycle Assessment (LCA) that quantitatively\nevaluates environmental impacts from raw material extraction to end-of-life. The authors are\nencouraged to reflect on the presented evidence more accurately. For instance, wording such as\n\"demonstrates key attributes for a sustainable life cycle\" or \"presents a viable pathway towards closed-\nloop sustainability\" would be more appropriate. Moreover, including a qualitative discussion\nacknowledging that a comprehensive quantitative LCA would be a valuable future direction could add\nimportant nuances and strengthen the environmental relevance of this study.\nResponse: We have carefully reconsidered and refined our wording to ensure that the environmental\nclaims are aligned with the evidence presented in this study, and we fully agree that a comprehensive\nquantitative life cycle assessment (LCA) would be a valuable future direction to rigorously evaluate\ncradle-to-grave environmental impacts.\nWe have therefore revised the wording throughout the manuscript (Abstract, Introduction, Application\nsection, Discussion, and the Fig. 5 caption) to more accurately reflect the evidence presented in this\n20\nwork. In addition, following the reviewer’s suggestion, we have added a qualitative outlook in the\nDiscussion explicitly stating that future work would benefit from a comprehensive quantitative LCA to\nquantify cradle-to-grave impacts and guide continued optimization.\nRevision (for comment 7):\n1. Abstract. On page 2.\n“These properties collectively ensure full-lifecycle eco-sustainability.”\nchanged to\n“These properties collectively demonstrate key attributes for a sustainable life cycle.”\n2. Introduction. On page 4.\n“In this work, we successfully incorporate environmental sustainability into the entire lifecycle of\nprintable magnetoresistive sensors while equipping them with enhanced low-field sensing performance.”\nchanged to\n“In this work, we integrate environmental sustainability considerations across key lifecycle stages of\nprintable magnetoresistive sensors while equipping them with enhanced low-field sensing performance.”\n3. Application section. On page 12.\n“enables a truly closed-loop sustainable life cycle”\nchanged to\n“presents a viable pathway toward closed-loop sustainability”\n4. Fig. 5 caption.\n“Conceptual illustration showing the closed-loop eco-sustainability of the biodegradable MR sensors.”\nchanged to\n“Conceptual illustration showing the pathway toward closed-loop eco-sustainability of the\nbiodegradable MR sensors.”\n5. Discussion\nWe add “Future work would benefit from a comprehensive quantitative life cycle assessment (LCA) to\nfurther quantify cradle-to-grave impacts and guide continued optimization.”\nMinor comment 1: i) The placement of Figure 1c in the current version may be confusing for readers.\nThe authors are encouraged to rearrange the figure to ensure a more logical flow and clearer distinction\nfrom Figures 1d and 1e. Adding labels such as \"Fe core (conductor & flux guide)\" and \"Fe₃O₄ shell\n(MR-active)\" to the schematic would make the synergistic mechanism immediately clearer.\nResponse: We have revised the layout and labeling of Fig. 1 accordingly.\nRevision:\ncorrespond to those of the respective curves in the graph, particularly the green curve in S11-a. The\nauthors are requested to verify this inconsistency.\nResponse: We have verified the issue and corrected the color descriptions in the caption of\nSupplementary Fig. 11 (new Supplementary Fig. 15) so that they now match the corresponding curves.\nIn addition, we also updated the related color references in Fig. 4 accordingly.\nRevision: New Supplementary Fig. 15 caption.\nSupplementary Fig. 15. MR curve comparison. a, MR curves of printed Fe/Fe O core-shell particles\n(cyan curve), with which removed 10 gain factor (purple curve) and printed Fe O particles (red curve).\n22\nb, MR curves of printed Fe/Fe O core-shell particles with different time (30 min, 60 min, 90 min, and\n120 min). c, MR curves of printed Fe/Fe O core-shell particles with different size.\nFig. 4 caption.\na, Normalized MR curves and b, sensitivity curves comparison of printed Fe/Fe O core-shell particles\n(cyan curve), with which removed 10 gain factor (purple dashed line curve) and printed Fe O particles\n(red curve).\nMinor comment 3: iii) Page 8, section “Spin-dependent hopping-mediated grain boundary …..” ─ The\nsentence \"…, the Fe/Fe₃O₄ sensors exhibit resistance reduction by over two orders of magnitude...\"\nshould cite the specific supplementary table where these data are presented (apparently referring to\nSupplementary Tables 3). The authors are advised to verify this reference.\nResponse: We have verified the sentence to explicitly reference Supplementary Table 3, which contains\nthe resistance values supporting this statement.\nRevision:\nMain text: On page 9.\nCompared with composites printed with Fe O microparticles, the Fe/Fe O sensors exhibit resistance\nreduction by over two orders of magnitude (Supplementary Table 3), rendering them suitable for\npractical electronic applications.\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of\nthe Nature Communications initiative to facilitate training in peer review and to provide appropriate\nrecognition for Early Career Researchers who co-review manuscripts.\nResponse: We sincerely thank Reviewer #3 for co-reviewing our manuscript as part of the Nature\nCommunications initiative to support peer-review training and to recognize Early Career Researchers.\n24"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have successfully addressed all of my queries, and I find the current version suitable for publication in Nature Communications.", "reviewer_2": "I thank the authors for their careful revision of the manuscript and for the detailed responses to the reviewers’ comments. The concerns raised during the previous round of review have been satisfactorily addressed, and I have no further suggestions.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": ""}]

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