Introduction

Sensing technology is an important aspect of information processing, which holds a crucial position in modern science and technology1,2,3. Magnetic pressure sensors offer significant prospects in human-computer interaction, wearable health monitoring, and robotics due to their simple design, rapid response, wireless interaction, and resilience to interference from sweat or water4,5,6,7,8,9. With the advancement of flexible electronics and related technologies, magnetic pressure sensors are evolving towards miniaturization, multifunctionality, and high performance10,11. It has been demonstrated that the unique epidermal architecture of human skin enables the perception of both subtle pressures (1–2 Pa) and significant external forces (100–300 kPa)12. To mimic—or even surpass—this pressure-sensing capability, artificial systems such as robotic skin and smart wearables need to be able to handle a complex surrounding pressure environment in practical applications. High sensitivity facilitates notable output signal variations, achieving lower detection limits13,14,15. Microstructure engineering such as micro-pyramid and micro-crack structures is an effective strategy for enhancing sensitivity, enabling them to respond sensitively to subtle stresses16,17. However, the low stiffness and modulus of these microstructures, along with brittle nature, make them highly prone to reaching saturation under force, hence hindering further stress perception. Conversely, while materials or structures with high modulus can still generate sufficient deformation and output stimulus under high pressure, their ability to sense minor pressure changes is inadequate. Therefore, ensuring both low detection limits and a wide sensing range in magnetic pressure sensors is one of its significant challenges18,19,20.

Recently, innovative strategies using tunable materials have emerged to address this fundamental trade-off. For example, phase-change gels (PC-gels) enable modality-switchable sensors, shifting between high-sensitivity and broad-range modes via thermal control of their modulus21. The phase transition in liquid metals also facilitates tunable pressure sensors by generating a pronounced modulus change22,23,24. A notable example is the gallium microgranule-based sensor (GM-TPS), which achieves a high sensitivity of 16.97 kPa−1 in its soft (liquid) state and a broad detection range of ~1.45 MPa in its rigid (solid) state, exceeding the sensing capability of human skin25. Despite their impressive adaptability, these actively tunable sensors fundamentally rely on integrated thermal management systems for mode conversion, which complicates system integration and incurs response latency. In contrast to these active tuning paradigms, a structural design that enables autonomous magnetic field regulation provides a direct route to wide-range pressure sensing without external controls.

The magnetic pressure sensor is mainly composed of three parts: the force-to-magnetic conversion unit (FMCU), the elastic medium unit (EMU), and the magnetic sensing unit (MSU). The sensor operates by converting applied pressure into changes in the magnetic field through the magnetoelastic effect of the magneto-elastomer in FMCU, which are then detected by the MCU containing magneto-sensitive materials, ultimately allowing for the indirect detection of pressure26,27,28. Therefore, the force-to-magnetic conversion efficiency of the magneto-elastomer and the magnetic sensitivity of the magneto-sensitive materials determine the sensing performance of the sensors, including detection limits, sensitivity, and sensing range. Magneto-elastomers are mainly composed of micro-magnetic particles and a polymer elastic matrix composite to form magnetically composite films or magnetically composite fibers. Under small pressures, fibrous magneto-elastomers undergo large deformations due to their low stiffness and modulus, thus providing significant variation in the magnetic field. However, their small stiffness also makes them highly prone to attain the state of force saturation, which prevents them from providing further magnetic field changes at higher pressures. As a result, magnetic pressure sensors based on fibrous magneto-elastomers have high sensitivity and low detection limits, but cannot combine this with a wide sensing range29,30,31. Man et al. obtained magnetic cilia with large aspect ratios by metal tube stamping, and together with the Hall effect, achieved accurate force detection down to 2.1 μN. But the low stiffness and modulus of the cilia resulted in a maximum stress detection of 60 μN29. Similarly, Wu et al. prepared fibrous conductive coils by imitating the hair structure of spiders, and then achieved self-powered sensing of breezes as low as 1.2 m/s based on Faraday’s principle of electromagnetic induction30. Conversely, thin-film magneto-elastomers with higher modulus and stiffness could provide sufficient deformation and force-to-magnetic conversion efficiency at higher pressures, eventually allowing for a larger sensing range. However, it does not provide enough magnetic variation at low pressures32,33,34. For example, Ge et al. fabricated thin-film magneto-elastomers to realize pressure sensing in the range of 79 Pa–55 kPa based on the magneto-resistive effect32. Zhang et al. combined a thin-film magneto-elastomer and a Cu coil to achieve self-powered monitoring of pressure within hundreds of kPa, but there is still a need to improve tiny pressure sensing ability33. In conclusion, it remains a challenge to develop a magnetic pressure sensor with both low detection limits and wide sensing ranges by proper design of the magneto-elastomer structure.

In addition, the performance of the magnetic pressure sensor is also closely related to the magneto-sensitive materials in the MSU. Via utilizing the different magnetic effects of magneto-sensitive materials, it is possible to achieve magnetic field detection over various ranges, thereby enabling pressure sensing across different ranges. Magnetic effect of the flexible magneto-sensitive materials typically involves the magneto-resistive, magneto-impedance, and Hall effects35,36,37,38,39,40. Denys et al. deposited a spin valve sensor with a [Py/CoFe]/Cu/[CoFe/Py]/IrMn heterostructure on a polyimide substrate. Utilizing the giant magnetoresistance effect (GMR), they obtained sensitive magnetic field detection within the range of 2-40 mT35. Moreover, they also deposited a Permalloy/Ta composite on a PET substrate, which effectively widened the range of magnetic field sensing to 0.06–400 mT based on the anisotropic magnetoresistance effect (AMR)36. Dai and colleagues developed a 3D heterogeneous integration process for graphene Hall elements and silicon-based CMOS integrated circuits, producing high-performance integrated Hall sensors. With the Hall effect, they obtained magnetic field sensing in the range of 0.02–400 mT37. Magnetic field sensing is also possible through altering conductive paths in magnetoelectric composites under different magnetic fields. Based on this principle, Ding et al. achieved sensing in the range of 86–150 mT38. To sum up, the above magneto-sensitive materials offer a wide magnetic sensing range but struggle to detect tiny magnetic fields, such as those in the nanotesla or picotesla range. Consequently, when used in magnetic pressure sensors, they can achieve a broad pressure sensing range but have difficulty detecting minute pressures. Magnetic amorphous wires exhibit a giant magneto-impedance (GMI) effect due to their unique structure of circumferential domains on the surface and axial domains in the interior, allowing for sensitive detection of weak magnetic fields41,42. Li and colleagues designed a magnetic amorphous wire-based magnetic sensor with a cantilever beam structure, which has a detection range of seven orders of magnitude and could detect magnetic fields from 22 nT to 400 mT43. Therefore, compared to other magneto-sensitive materials, magnetic amorphous wires are one of the ideal sensitive materials for the design and fabrication of magnetic pressure sensors with low detection limits and wide sensing ranges.

Herein, magnetic amorphous wires were selected as magneto-sensitive material to design a magnetic pressure sensor. The resulting magnetic amorphous wire-based pressure sensor (MAWPS), featuring a multilayer structure, leverages both the GMI effect of magnetic amorphous wire and the magneto-elastic effect of composite magneto-elastomers. The composite magneto-elastomer within the FMCU comprises cilia-type and film-type components with opposing magnetization directions. Magnetic cilia, characterized by low stiffness and low modulus, are responsible for sensing subtle pressures, while the magnetic films, possessing higher modulus, modulate the magnitude and orientation of the magnetic field under stronger pressures. This synergistic configuration maintains the magnetic field within the sensitivity range of the amorphous wire, thereby achieving both a low detection limit and an extended sensing range. The MAWPS achieves a detection limit as low as 2.4 Pa, a sensing range exceeding 300 kPa, fast response time of approximately 0.25 s, and good cycling stability. In addition, when the magnetic amorphous wire is assembled in a biased position, the MAWPS gains the ability to recognize the direction of shear force. The proposed sensing platform is relevant for the monitor continuously breathing, object grasping, object morphology recognition, and stress direction identification. Our sensor technology is applicable to smart wearables for health monitoring and human-machine interaction, as well as to smart prosthetics and the development of intelligent soft robots44,45,46.

Results

Design principle and fabrication process of MAWPS

For aiming to achieve both a low detection limit and a broad sensing range, drawing inspiration from the structure of human skin and subcutaneous tissue is an effective strategy. The epidermal ciliary structure and subcutaneous tissue structure (Fig. 1a) enable the human body to sense pressures ranging from minute forces of a few Pa to pressures in the thousands Pa. Inspired by this, the biomimetic multilayer structure of the as-designed flexible MAWPS is illustrated in Fig. 1b. To realize the pressure sensing, we designed a force-to-magnetic induction conversion unit (FMCU) benefiting from the giant magnetoelastic effect (GME) in a magnetic composite elastomer. Here, the FMCU is composed of cilia-type and film-type magneto-elastomers, formed by compounding NdFeB particles with a PDMS matrix (Fig. 1c, d). Another component of MAWPS is the magnetic sensing unit (MSU) consisting of PDMS matrix and coiled magnetic amorphous wires. Based on the GMI effect, the impedance of the magnetic amorphous wire is closely related to external magnetic field changes. This allows the MAWPS to indirectly monitor pressure variations through the GME of the magneto-elastomer. The sensing mechanism of as-designed MAWPS are illustrated in Fig. 1e–l. The real-time optical images capturing the magnetic cilia movement under increasing pressure are shown in Supplementary Fig. 1. When subjected to a weak pressure (i.e., stage Ⅰ), the magnetic cilia with low stiffness and low modulus in FMCU deform first and induce sufficient magnetic field changes, which are then detected by the magnetic amorphous wires in the MSU (Fig. 1f). As the pressure continues increasing to reach force saturation in the magnetic cilia, the magnetic film and PDMS film with higher stiffness and modulus begins to deform (i.e., stage ⅠⅠ), providing force-magnetic conversion and pressure sensing over a wider range of pressures (Fig. 1g). The magnetic field variation provided by the magnetic cilia during bending is closely related to the detection limit, so the magnetic field variation process of the magnetic cilia bending process is simulated and shown in Fig. 1h. The angle between the pressurized bending state of the magnetic cilia and the initial position is defined as θ. According to simulation results, the magnetic field in the MSU region shows a significantly increasing trend as θ increases from 0 to 90°. Compared to the uniform distribution at θ = 0°, a gradient distribution is observed at θ = 90° (Supplementary Fig. 2). Along the bending direction, the field initially increases and then decreases (more detailed discussions are shown in Fig. 4). As reported, the GME of magneto-elastomers is significantly influenced by different magnetization directions47,48. After axial magnetization, the internal magnetic moments of magnetic cilia align along the axis, creating a magnetic field in the same direction. Compared to axial magnetization, the magnetic field distribution of magnetic cilia in the MSU region shows subtle changes between θ = 0° and θ = 90° (Supplementary Fig. 3). Similarly, the cilia magnetized perpendicularly provides a minor variation in magnetic field with the θ increases from 0 to 90° (Supplementary Fig. 4), which hinders achieving low detection limits and high sensitivity in sensors. Furthermore, although magnetic amorphous wires exhibit high magnetic sensitivity, they are also highly prone to attaining magnetic saturation. Hence, the magnetic cilia and the magnetic film are designed with opposite magnetization directions, ensuring that the magnetic field amplitude always varies within the magnetic sensitive interval of the amorphous wire through regulating the orientation of the composite magnetic field. In this case, the superimposed magnetic field presents a trend of increasing, followed by decreasing and then increasing in the reverse direction. In contrast, during the compression process from stage Ⅰ to stage ⅠⅠ for the MAWPS without the oppositely magnetized magnetic film assembled (Fig. 1i–k), the direction of the magnetic field perceived by the magnetic amorphous wire remains constant, while its magnitude increases progressively until magnetic saturation is reached (Fig. 1l). Therefore, the integration of cilia-type and film-type components with opposing magnetization orientations gives rise to a tunable magnetic field architecture, enabling the MAWPS to simultaneously achieve ultra-low detection limits and an extended sensing range.

Fig. 1: Characterization and mechanism of MAWPS.
Fig. 1: Characterization and mechanism of MAWPS.The alternative text for this image may have been generated using AI.
Full size image

a Schematic diagram of epidermal structure and subcutaneous tissue. b Schematics revealing the structure of MAWPS, FMCU refers to the force-to-magnetic conversion unit, MSU refers to the magnetic sensing unit. c, d Enlarged local structures of magnetic cilia and magnetic film. Schematic illustration of the magnetic field sensed by the coiled magnetic amorphous wire e in the uncompressed state, f under an initial compressed state (stage Ⅰ, only the magnetic cilia are compressed), g under further compressed state (stage ⅠⅠ, both the magnetic cilia and the PDMS film are compressed) of the MAWPS. Here, the direction of the blue-to-red gradient arrows indicates the orientation of the composite magnetic field sensed by the magnetic amorphous wire assembly area, while the amplitude of the arrows represents the magnitude of the composite magnetic field. h Simulation of magnetic field variations during bending of the axial magnetized cilia to 0–90°, shown in the bottom-right inset is the schematic diagram of magnetic cilia at bending state under pressure, θ refers to the bending angle. Schematic illustration of the magnetic field sensed by the coiled magnetic amorphous wire i in the uncompressed state, j under an initial compressed state (stage Ⅰ), k under further compressed state (stage ⅠⅠ) of the MAWPS without magnetic film. l Schematic comparison of the variation in the superimposed magnetic field sensed by the MSU during compression for MAWPS with and without magnetic films. m SEM image of the magnetic cilia. n Magnified SEM image of a single cilia. Optical micrographs showing the MAWPS o without and p with assembled magnetic films.

As shown in Supplementary Fig. 5, the fabrication process of MAWPS primarily involves the sequential preparation of the FMCU and MSU components. Magnetic amorphous wires with a diameter of about 120 μm (Supplementary Fig. 6) possessing a smooth glass fiber package, high saturation magnetization (about 0.62 T, Supplementary Fig. 7), high magnetic permeability (8000 at 1 kHz, Supplementary Fig. 8), and magnetic permeability changes (up to 300%) with increasing magnetic field are selected as magneto-sensitive material. Subsequently, the Cu coils are wound around them and placed in custom PTFE molds, followed by pouring PDMS and curing to obtain the MSU. A porous mold is then used to grow cilia-type magneto-elastomers on top of the MSU. The magneto-elastomers were fabricated by mixing NdFeB particles with PDMS. Here, a series of magnetic cilia with varying diameters and heights can be grown by adjusting the aperture and depth of the mold (Supplementary Fig. 9). Figure 1m and n depicts SEM image and corresponding magnified image of a magnetic cilia with a length of 2 mm. It can be observed that the magnetic cilia in the array exhibit excellent consistency, and the magnetic particles are evenly dispersed within the PDMS matrix. Then the magnetic cilia are magnetized with an impulse field of 50 kOe that reorients NdFeB micromagnets in the soft polymer matrix. The final step of the MAWPS fabrication is the growing and the magnetization process of the film-type magneto-elastomers below the MSU. The magnetized direction of the magnetic film is opposite to that of the magnetic cilia, offering an inverse magnetic field. The optical micrographs of the MAWPS with or without assembled magnetic films are shown in Fig. 1o, p, indicating that the MAWPS exhibits good flexibility.

Investigation of the factors that affect pressure sensing performance

The pressure sensing mechanism of the MAWPS is based on the measurement of electric impedance of the coil-wound magnetic amorphous wires in the MSU upon deformation of the magneto-elastomer in the FMCU. According to the GME, the deformations lead to the change of the magnetic field in the magneto-elastomer. Hence, the force-to-magnetic conversion efficiency of the magneto-elastomer and the magnetic sensitivity of the magneto-sensitive materials determine the sensing performance of the sensors, including detection limits, sensitivity, and sensing range. Here, we studied the factors affecting the impedance of the coil-wound magnetic amorphous wire and the force-to-magnetic conversion efficiency of the magneto-elastomer.

The electric impedance Z of the coil-wound magnetic amorphous wires can be written as follows,

$$Z=R+{\rm{i}}({\rm{\omega }}{L}_{i}-1/({\rm{\omega }}{C}_{i}))$$
(1)

where R is the circuit resistance, ω is the angular frequency, Ci is the capacitance provided by the impedance analyzer. Li is the inductance of a solenoid, which can be described as follows,

$${L}_{i}=\mu \times {{\rm{A}}}_{{\rm{e}}}\times {M}^{2}/{l}_{{\rm{m}}}$$
(2)

where μ is the permeability of the magnetic core (i.e., magnetic amorphous wires), M is the number of turns of the coil, Ae and lm are the cross-sectional area of the solenoid and the length of magnetic core, respectively. According to Eqs. (1) and (2), impedance is closely related to the magnetic permeability of the core. Essentially, higher magnetic permeability enhances the skin effect, leading to greater impedance variation. Compared to other magnetic core materials, the Co-based magnetic amorphous wire we selected possesses high magnetic permeability. Additionally, the number of coil turns M, and the measurement frequency f directly affects impedance variation. The factors influencing force-to-magnetic conversion primarily include the magnetic particle content λ in the magnetic cilia and magnetic film, the length L of the magnetic cilia, the array density N of the magnetic cilia, the distance A between the magnetic amorphous wire and the cilia, and the distance C from the magnetic amorphous wire to the magnetic film (Fig. 2a). Specifically, λ and L determine the total magnetic moment, which serves as the source of the magnetic field. N determines the number of active magnetic dipoles, leading to a vector superposition of their individual magnetic fields at the position of magnetic wire. The magnetic field produced by the magnetic cilia and magnetic film decays with distance, the distance A and C collectively determine the magnitude and direction of the net magnetic field perceived by the amorphous wire. The purpose of regulating all parameters is to make the superimposed magnetic field provided by the cilia-type and film-type magnetic composite match the magnetic sensitivity interval corresponding to the maximum impedance variation of the magnetic amorphous wire (Fig. 2b). During the stage Ⅰ stage ⅠⅠ, the impedance of the magnetic amorphous wire exhibits a trend of first decreasing, then increasing, and decreasing again within the sensitive range, thus extending the pressure sensing range of MAWPS.

Fig. 2: Tailoring the pressure sensing performance of MAWPS architectures.
Fig. 2: Tailoring the pressure sensing performance of MAWPS architectures.The alternative text for this image may have been generated using AI.
Full size image

a Schematics revealing the regulating parameters of MAWPS. The distance between the bottom of the magnetic cilia and the magnetic amorphous wire wound with Cu coils is characterized by the parameter A. The distance between the magnetic film and the magnetic amorphous wire is characterized by the parameter C. The number of cilia is N. The length of the magnetic cilia is characterized by the parameter L. The content of magnetic powder in the cilia-type and film-type magneto-elastomers is characterized by the parameter λ1 and λ2. The number of windings in Cu coil is M. b The change of the electrical impedance of the only magnetic amorphous wire in an applied external magnetic field taken at optimal number of coil turns and optimal measurement frequency. During the stage Ⅰ and stage ⅠⅠ, the magnetic field generated by the cilia-type and film-type magneto-elastomers first increases, then decreases, and increases again, ensuring that the magnetic amorphous wire remains within the magnetic field interval where its impedance is most sensitive to respond. c The sensitivity factor ρ1 changes with applied external magnetic field of magnetic amorphous wire containing Cu coils with different turns, the impedance is measured at different frequency and optimum external magnetic field. d The sensitivity factor ρ2 as function of relevant parameters characterizing the MAWPS architecture: A, L, N, λ1. e The sensitivity factor ρ2 and ρ2 as function of relevant parameters characterizing the MAWPS architecture: C, λ2. f Schematic illustration showing the states of the sensor before and after pressure is applied. Here, displacement B reveals the displacement magnitude of the top of the magnetic cilia with increasing pressure. g Relative impedance changes of the MAWPS with the displacement B increasing, here, the parameter of MAWPS was selected as optimal value.

First, we evaluated the magnetic sensitivity characteristics of the Co-based magnetic amorphous wire by testing the relative change rate of its impedance. The relative change of the impedance with pressure or magnetic field represented in percents is defined as follows,

$$\frac{\Delta Z}{{Z}_{0}}( \% )=\left(\frac{Z}{{Z}_{0}}-1\right)\times 100 \%$$
(3)

where Z0 and Z are impedance values without and with the external magnetic field or pressure, respectively. Here, the relative change of the impedance is caused by the external magnetic field applied through the Helmholtz coil. To monitor the variation of ΔZ/Z0, it is instructive to introduce the factor ρ1, which is defined as follows:

$${{\rm{\rho }}}_{1}={(\varDelta {\rm{Z}}/{{\rm{Z}}}_{0})}_{\max }$$
(4)

It can be noticed from Fig. 2c that the ρ1 initially increases and then decreases with increasing frequency at the same M. As the M increases from 50 to 200, the ρ1 monotonically increases, rising significantly from 200 to approximately 2800%. A larger ρ1 benefits the subsequent MAWPS in achieving a lower detection limit.

Magnetic cilia with low stiffness and low modulus provide the capability for detecting weak pressures. The distance (A) between the magnetic amorphous wire and the cilia directly determines the magnitude of the detected magnetic field changes. Simulation results indicate that the change in the magnetic field during the cilia bending process first increases and then decreases as the A increases (Supplementary Fig. 10). Here, even the modest magnetic field change (~0.2 mT) induced by initial cilia bending falls within the 1-5 Oe range of peak sensitivity for the magnetic amorphous wire, as confirmed by our prior characterization41. This favorable matching is enabled by the remarkable giant magnetoimpedance (GMI) effect and high magnetic sensitivity of the wire49,50. Similarly, the ΔZ/Z0 shown in Supplementary Fig. 11 exhibits a comparable trend. As A increases from 1.2 mm to 2 mm, the ΔZ/Z0 of the sensor first increases and then decreases, reaching its peak at A = 1.6 mm. The magnetic particle content λ1 in the cilia has a significant effect on the magnetic field magnitude. The coercivity keeps almost constant in the magneto-elastomer and the magnetic moment increases as λ1 increases (Supplementary Fig. 12). We observe that the ΔZ/Z0 increases monotonically with λ1 and reaches a maximum at λ1 = 50%, which is used in the following experiments (Supplementary Fig. 13). The reason for not continuing to increase the magnetic powder content is that additional particles would reduce the elongation at break51, making the cilia more difficult to demold. Moreover, increased magnetic particle content would excessively raise the modulus of the magnetic cilia, worsening their ability to achieve a low detection limit. In addition, the ρ2 with value of −28.1% and −29.3% are achieved at L = 2 mm and L = 3 mm, respectively (Supplementary Fig. 14). Considering the difficulty of demolding longer cilia and the marginal difference in maximum ΔZ/Z0 during the pressure process, a length of L = 2 mm was chosen. The array density of cilia is another crucial parameter affecting magnetic field variation (Supplementary Fig. 15). As the cilia density increases, the value of ΔZ/Z0 also increases and reach largest value at array@25*25 (i.e., N = 625). Here, we introduce another factor ρ2, which is defined as follows:

$${{\rm{\rho }}}_{2}=-{|\varDelta {\rm{Z}}/{{\rm{Z}}}_{0}|}_{\max }$$
(5)

The difference between ρ1 and ρ2 lies in the fact that specific parameters increase impedance, resulting in a positive ρ1 value, while others reduce impedance, leading to a negative ρ2 value. The value of ρ2 reaches extremum of −28.1% at A = 1.6 mm, L = 2 mm, λ1 = 50%, and N = 625 (Fig. 2c).

Although magnetic cilia exhibit low stiffness and modulus, allowing them to provide significant magnetic field changes under small pressures and achieve a low detection limit, they are also prone to reaching force saturation. As shown in Supplementary Fig. 16, the magnetic cilia with a length of 2 mm bent to 90° could withstand a maximum pressure of only 2.5 kPa. To ensure that the FMCU continues to provide magnetic field variations even after the cilia reaches force saturation, we have incorporated a magnetic film with an opposite magnetic field direction beneath the MSU. During continued compression, the magnetic field in the MSU region first decreases and then increases in the reverse direction. The distance C and magnetic powder content λ2 in magnetic film were regulated as shown in the Supplementary Fig. 17. The value of ΔZ/Z0 also exhibits a trend of initially increasing, then decreasing, and finally increasing in the opposite direction. At the optimal C-value of 1.2 mm, and λ2 = 33% in the magnetic film, the MAWPS demonstrates the best comprehensive pressure sensing performance, characterized with minimum value of ρ1 at minor pressure and acceptable value of ρ2 at high pressure (Fig. 2e). In summary, we obtain MAWPS architectures with optimal parameter, including M = 200 turns, f = 300 kHz, A = 1.6 mm, L = 2 mm, N = 625, λ1 = 50% in the magnetic cilia, λ2 = 33% in the magnetic film, C = 1.2 mm, respectively, which were also used as the parameters for the subsequent measurements. We assessed the pressure sensing performance of the MAWPS by investigating the magnitude of the relative impedance changes with the displacement B of the top of the cilia (Fig. 2f).

Electromechanical characterization of the MAWPS

The pressure sensing characterization of the MAWPS under optimal parameters were carried out and depicted in Fig. 3. The MAWPS exhibits sensitive detection of pressure changes within a range of 300 kPa. As pressure increases, the ΔZ/Z0 first decreases rapidly and then rises, with the rate of increase exhibiting a trend of initially being slow, followed by a quick acceleration, and then slowing down again. The pressure sensitivity of the sensor, denoted as the gauge factor (GF), can be used to describe the rate of ΔZ/Z0 change and defined by the following formula,

$${\rm{GF}}=\Delta \left(\frac{\Delta Z}{{Z}_{0}}\right)/\Delta P$$
(6)

Where ΔZ/Z0 represents the rate of relative impedance change, and ΔP represents the applied pressure. According to Eq. (4), as pressure increases, the GF value of MAWPS follows the same trend as the change in ΔZ/Z0 (Fig. 3a). While at small pressure values of 0–3.2 kPa the MAWPS is characterized by GF of 3.1% kPa−1, then the MAWPS exhibits GF of 0.07% kPa−1, 0.4% kPa−1, and 0.015% kPa−1 with the pressure grow to 3.52–117.04 kPa, 117.04–156.03 kPa, 156.03–300 kPa, respectively, indicating that the MAWPS has a broad pressure sensing range. The detection limit of the MAWPS is studied in Fig. 3b. After placing and then removing a foam sheet with a size comparable to the MAWPS and a gravity force of 2.4 Pa on the cilia surface, the ΔZ/Z0 of the MAWPS first increases from 0 to −0.04%, then decreases back to 0, revealing that the detection limit of MAWPS is as low as 2.4 Pa. Figure 3c demonstrates a distinctive step increase of the ΔZ/Z0 with applied pressure for the MAWPS. The response time during rapid loading and unloading is another crucial parameter for the application of stretchable pressure sensors. As shown in Fig. 3d, the MAWPS exhibits a rapid response time of 0.25 s and a relaxation time of 0.25 s. Moreover, the MAWPS demonstrates excellent stability over 100 loading and unloading cycles from B = 0 mm to B = 0.5 mm as shown in Fig. 3e. A comparative analysis of sensing performance between sensors based on the giant magnetoelastic (GME) effect and those based on the giant magnetoresistance (GMR) effect shows that MAWPS has a lower pressure detection limit, as well as further extending the sensing range in magnetic pressure sensors relying on the giant magneto-impedance (GMI) effect (Fig. 3f)32,33,34,49,52.

Fig. 3: Pressure sensing performance of the MAWPS with axial magnetized cilia.
Fig. 3: Pressure sensing performance of the MAWPS with axial magnetized cilia.The alternative text for this image may have been generated using AI.
Full size image

a The change in relative impedance with increasing pressure under optimal parameters of the MAWPS. Here, the green circles represent the actual measured data points, and the red dashed line corresponds to the associated linear fitting curve, with the slope of the fitted curve explicitly annotated adjacent to the line. b Impedance changes as function of applied pressure of 2.4 Pa during the loading and unloading process. c Relative impedance changes of the MAWPS under the loading with different amplitudes of the applied small pressure. d Measurement of the response time of the MAWPS at a fast loading and unloading cycle. e Relative impedance changes of the MAWPS architecture over 100 loading and unloading cycles at B-value from 0 to 0.5 mm. f Performance comparison of the MAWPS with other magnetic pressure sensors. Here, the parameter of MAWPS was selected as optimal value.

In addition to its low-pressure detection limit and wide sensing range, MAWPS also presents the capability to detect the direction of shear forces. The variations in the magnetic field generated by the bending process of the magnetic cilia in the FMCU are perceived differently at various locations within the MSU. Here, we use the term “point +number” to represent different regions within the MSU (Fig. 4a). In addition, the parameter a represents the different distances between the axis of the magnetic amorphous wire and the central axis of the MSU in the y-axis direction along the bending direction of the magnetic cilia (x+ direction). The parameter b denotes the distance from the center of the magnetic amorphous wire to the midline of the MSU in the x-direction (Fig. 4b). For the same a-value, as the bending angle of the axial magnetized cilia increases from 0 to 90°, the magnetic field variations perceived at points “1”, “2” and “3” remain largely consistent (Fig. 4c). Similar results can be obtained at different positions with the same a-value (Supplementary Fig. 18). In the case of the axial magnetized cilia bending to the x+ direction, the change in the magnetic field initially increases and then decreases with an increase in the a-value (Fig. 4d). This trend is determined by the effective number of magnetic cilia providing the magnetic field in the amorphous wire assembly region. At smaller a-values, the number of effective cilia is limited. Conversely, at the larger a-values, most magnetic cilia in the x- direction are too distant to contribute significantly to the change in the magnetic field. Moreover, compared to axially magnetized cilia, vertically magnetized cilia exhibit a similar pattern of magnetic field variation during the bending process, although the amplitudes are smaller (Supplementary Fig. 19), which aligns with the simulation results shown in Fig. 1j and k and Supplementary Fig. 3. According to the simulation results, the magnetic field variation at points perpendicular to the bending direction is identical for the same a-value. Therefore, the amorphous wire is assembled with its axis vertically to the bending direction of the magnetic cilia. The fabrication process for the MAWPS architecture with the magnetic amorphous wire in a biased position is largely consistent with the procedure illustrated in Supplementary Fig. 5. The key distinction lies in the placement of the Cu coil-wound magnetic amorphous wire, which is deliberately positioned off-center. Samples with different wire assembly configurations were systematically obtained by controlling the positional parameters a and b. Figure 4e shows the ΔZ/Z0 changes of the MAWPS architecture with different a-values under the same shear force and b-value. Here, the applied shear force in this direction is defined as Fx+ when the cilia bend toward the x+ direction. As the a-value increases from 2.5 to 10 mm, the ΔZ/Z0 shows a trend of first increasing and then decreasing, reaching a peak of approximately 7% at a = 5 mm. This trend is consistent with the simulation results, where the magnetic field increment exhibits a comparable pattern of initial increase followed by a decrease. At the optimal a-value, the shear force Fx+ induces the maximum change in relative impedance, while the corresponding change from Fx+ is nearly zero. In this case, when subjected to shear forces in the vertical direction (y-direction), adjusting the positional parameter b of the magnetic amorphous wire could produce magnetic variations similar to those in the x-direction, enabling the detection of shear forces in the y+ and y- direction. As shown in Fig. 4f, the MAWPS exhibits a clear directional sensitivity. In the case of the parameter a = 5 mm and b = 5 mm, the relative impedance change induced by Fx+ is the largest, followed by Fy+ and Fy- in decreasing order, while Fx- results in the smallest change. Moreover, the relative impedance variation of the MAWPS with vertically magnetized cilia in response to the different shear force direction are shown in Supplementary Fig. 20. Compared to axial magnetization, the MAWPS with vertically magnetized cilia provides minor changes in relative impedance variation.

Fig. 4: Characterization of the force direction recognition performance of the MAWPS with axial magnetized cilia.
Fig. 4: Characterization of the force direction recognition performance of the MAWPS with axial magnetized cilia.The alternative text for this image may have been generated using AI.
Full size image

a Schematic diagram showing the bending of magnetic cilia in MAWPS. Here, different numbers represent various positions of the MSU. b Schematic diagram of different assembly positions of coiled magnetic amorphous wires in the MSU. a and b represent the distances of the amorphous wires from the centerline of the MSU in the x and y directions, respectively. c Simulation of magnetic field variations in different regions during bending of the axial magnetized cilia at the same a-value. d Simulation of magnetic field variations in different regions during bending of the axial magnetized cilia at the same b-value. e Relative impedance changes of the MAWPS architecture with different a-value under the same shear force and b-value. f Relative impedance variation of the different shear force direction at optimum a- and b-value. Here, we kept the magnitude of the force constant while only changing its direction.

Pressure sensing applications of the MAWPS

The MAWPS with low-pressure detection limit and wide sensing range could act as ideal wearable pressure sensors. To demonstrate the capability of the MAWPS with low detection limits, we mounted the MAWPS on a mask with cotton yarn, the exhaled airflow from breathing causes the low-stiffness magnetic cilia to deform, leading to an approximately 0.06% reduction in output relative impedance changes, enabling real-time continuous monitoring of respiration (Fig. 5a). Additionally, the high magnetic field sensitivity of the magnetic amorphous wires allows for the distinction between normal and weak breathing, providing a reference for future diagnosis of respiratory-related diseases53,54. Figure 5b demonstrates that the cilia-based MAWPS possesses the ability to distinguish surface roughness. We selected two materials with different surface roughness for measurement, namely A4 paper with a roughness of 6.855 μm and 50-grit sandpaper with a roughness of 20.877 μm (Supplementary Fig. 21). When the MAWPS is mounted on the hand and used to slide across these surfaces under consistent force and speed, while the output impedance amplitude remains largely unchanged, the recovery time for the ΔZ/Z₀ signal to return to its baseline is significantly longer on the rougher sandpaper (tᵣ) compared to the smoother A4 paper (ts). Figure 5c illustrates the real-time and continuous monitoring of pressure by the MAWPS mounted on the glove. As the plastic ball is grasped and released, the relative impedance changes of MAWPS initially decrease and remain around −5%, then increases back to 0. In addition, in the case of the optimum a- and b-value shown in Fig. 4b, the MAWPS is capable of detecting wind direction (Fig. 5d). The ability to distinguish between different directions primarily arises from the variation in magnetic fields perceived by the magnetic amorphous wire placed asymmetrically, as the cilia bend in different directions (inset of Fig. 5d). Here, the wind is provided by a small electric fan, with the fan set to the same speed to ensure consistent force amplitude. The relative impedance change induced by the wind in the x+ direction is the largest, followed by y+ and y- direction in decreasing order, while x- direction results in the smallest change.

Fig. 5: In situ pressure monitoring using the MAWPS.
Fig. 5: In situ pressure monitoring using the MAWPS.The alternative text for this image may have been generated using AI.
Full size image

a Relative impedance changes response of the MAWPS mounted on the mask for breath monitoring. b Relative impedance changes response of the MAWPS for perception of object surface roughness. c Real-time output relative impedance changes of the MAWPS corresponding to the process of grasping and releasing a plastic ball. d The relative impedance changes of the MAWPS in response to the different wind directions.

Discussion

In summary, we demonstrate a magnetic amorphous wire-based pressure sensor (MAWPS) with multilayer structure, enabling both a low detection limit and a wide sensing range through a tunable magnetic field configuration. Our sensing element consists of two key components: (i) a force-to-magnetic conversion unit (FMCU), and (ii) a magnetic sensing unit (MSU). The composite magneto-elastomer within the FMCU integrates cilia-type and film-type magneto-elastomers with opposing magnetization orientations. The low-stiffness, low-modulus magnetic cilia facilitate the detection of subtle pressures, while the higher-modulus magnetic films modulate the magnitude and direction of the magnetic field under elevated pressures. This design ensures that the magnetic field remains within the sensitive range of the magnetic amorphous wires, thereby enabling the MAWPS to preserve low detection limits while significantly broadening its sensing range. The MAWPS also exhibits a low detection limit of 2.4 Pa, sensing range greater than 300 kPa, high response time about 0.25 s, and good cycling stability. In addition, when the magnetic amorphous wire is assembled in a biased position, the MAWPS gains the ability to recognize the direction of shear force. We demonstrate the use of MAWPS in smart wearables to monitor continuous breathing, object grasping, object morphology recognition, and stress direction identification. Furthermore, we envision broad applicability of the MAWPS for prosthetics and also for robotic applications44,45,46.

Methods

Fabrication of the MAWPS

The fabrication process of MAWPS primarily involves the preparation of the magnetic sensing unit (MSU) and the force-magnetic conversion unit (FMCU). Firstly, the Cu wires (diameter of 80 μm) are wound around the magnetic amorphous wire (diameter of 120 μm, composition of the alloy is Co69Fe4(B, C)16Si7Cr4, Aichi-steel, Japan) by using a winding machine, forming a tight inductance coil with tunable number of windings (50-200 turns). The wound amorphous wire is then placed into a PTFE mold (10 mm × 10 mm) with a grooved structure, and PDMS (including pre-polymer and its curing agent; Sylgard 184, Dow Corning, USA) is cast and cured to form the MSU. The FMCU consists of cilia-type and film-type magneto-elastomers with opposing magnetization orientations. A porous PTFE mold (pore diameter is 200 μm, depth of the pore is 2 mm) then used to grow cilia-type magneto-elastomers on top of the MSU. The magneto-elastomers were fabricated by mixing NdFeB particles (particle size ~5 μm, XND Co. PRC) and PDMS with different mass ratios. Here, the cilia are grown on the surface of partially cured PDMS to enhance the adhesion between the cilia and the MSU. Then the magnetic cilia are magnetized with impulse field of 50 kOe using magnaflux generator (SCH-3540MD Pulse magnetizer, Shanghai Pingye Co Ltd, China). The final step of the MAWPS fabrication is the growing and the magnetization process of the film-type magneto-elastomers below the MSU. The magnetized direction of the magnetic film is opposite to that of the magnetic cilia, offering an inverse magnetic field. In the fabrication process, after removing air bubbles through a vacuum extraction device, the so-formed MSU and FMCU were cured sequentially in a vacuum oven at 60 °C for 4 h.

Microscopy characterization

SEM imaging of magnetic cilia and amorphous wires were obtained by a microscope (Sirion200, FEI, USA). Photographs of the MAWPS were taken by a digital camera.

Magnetic characterization

The magnetic field for testing impedance of magnetic amorphous wires was provided by a Helmholtz coil setup. The required current is provided by a current source device (Keithley 237, Keithley Instruments, USA). The magnetic field is measured by a Gauss meter (AFG 3101 C, Tektronix, USA). The hysteresis loop of magnetic amorphous wires was taken by a vibrating sample magnetometer (Lakeshore7410, Lakeshore, USA). The permeability analysis was carried out by an impedance analyzer (Agilent 4294 A, USA). The impedance of magnetic amorphous wires and the MAWPS were measured using an impedance analyzer (Hioki IM3570, Japan). The magnetic field simulation is obtained through finite element analysis using COMSOL Multiphysics.

Pressure measurement

Pressure measurement and cycle testing was performed by a computer controlled material testing machine (Instron 5943, USA).

Device characterization

The output impedance date reading of MAWPS is controlled by a program written in LabVIEW (National Instruments, USA). The masks and gloves used for MAWPS integration are sourced from commercially available KN95 masks and rubber gloves. The wind is provided by an adjustable handheld fan.