Introduction

Addressing the energy and environmental crisis requires immediate and significant improvements in energy and resource utilization efficiency1,2. This pressing challenge is creating an urgent demand for materials with multiple superior and often unconventional properties2,3,4,5,6. For instance, there are strong requirements for flexible, high-performance thermoelectric materials for wearable power generation devices7, ductile ceramics with high transparency for self-energy-harvesting robots8, and thermally stable metallic magnetic materials with high electrical resistivity for high-energy-efficiency electric aircraft9. However, these unprecedented properties remain unattainable due to inherent physical constraints. As for semiconducting thermoelectric materials, electrons inevitably conduct heat, preventing the simultaneous achievement of high electrical conductivity and low thermal conductivity10, while their directional covalent bonding hinders the realization of flexibility7. In ceramics, they are unable to exhibit excellent plasticity due to lack of dislocations11, and they also struggle to achieve high transparency due to the scatter and absorption of light caused by grain boundaries and defects8. And in metallic magnetic materials, the high density of free electrons restricts the achievement of high electrical resistivity, while the inherently metastable magnetized state inhibits great thermal stability9,12,13. Although traditional strategies based on compositional design can typically address a single physical constraint, they often fall short when faced with the challenge of simultaneously overcoming multiple physical barriers, ultimately failing to achieve the desired material properties needed for advanced applications14,15.

In contrast, bio-materials simultaneously achieve multiple excellent properties through ingenious ordered structural design16,17. For example, teeth exhibit superior hardness and corrosion resistance far exceeding those of the constituent apatite attributed to the surface brick-and-mortar structure, while they also demonstrate excellent toughness derived from their internal layered fiber structure18,19,20. Inspired by bio-materials, we propose a multi-level ordered structure (MOS) strategy to concurrently unlock multiple physical constraints underlying conventional material performance bottlenecks. This strategy constructs multiple ordered characteristics across diverse structural levels to manipulate the behaviors of particles (e.g. electron scattering and ion migration) and functional units (e.g. domain wall movement and dislocation evolution), which gives rise to physical mechanisms and functional processes that differ from traditional ones, effectively breaking the conventional physical constraints.

As a proof of concept for the MOS strategy, we use magnetic materials as an example. State-of-the-art magnetic materials, such as metallic NdFeB, SmCo, and FeSi21,22, face longstanding challenges of low electrical resistivity ρ and poor thermal stability, which severely limit their energy efficiency and precision, thereby hindering the realization of future magnetic levitation transport systems, electric aircraft, and 6 G networks. However, according to traditional views, the high density of free electrons in metals inherently leads to low ρ, while the magnetized state, characterized by aligned atomic magnetic moments and higher magnetostatic energy, is metastable and highly susceptible to thermal disturbances, inevitably resulting in poor thermal stability12,23. It thus seems impossible to transform highly conductive metals into resistive materials while simultaneously stabilizing the inherent metastable state.

Here, using the MOS strategy, we demonstrate a resistive magnetic metal with great thermal stability, which features various ordered characteristics across surface and internal bulk levels. Fabricated through field-assisted self-assembly (FASA) of Fe and NdFeB nanograins, the resulting MOS surpasses the ρ of its constituents Fe and NdFeB by 2600% and ~100–300%, respectively, defying the Vegard’s mixture law. Meanwhile, its thermal stability of coercivity outperforms that of the state-of-the-art commercial performance by more than 100%. Moreover, the MOS not only breaks the trade-off between remanent magnetization Br and coercivity Hc, achieving a good combination of both, but also exhibits great corrosion resistance and high stiffness. The MOS strategy introduces abundant heterogeneous interfaces across various structural levels, forming ordered scattering networks that effectively achieve high resistivity through strong electron scattering, despite the presence of numerous free electrons. In addition, its multi-dimensional pinning traps more efficiently suppress the growth of reverse domains compared to traditional structures, greatly enhancing magnetic stability. Together, these mechanisms effectively overcome conventional physical constraints, breaking through performance bottlenecks. The MOS strategy provides a general paradigm for simultaneously controlling the behaviors of particles and functional units by reshaping thermodynamic energy profiles and kinetic processes, which can be extended to other material systems to explore diverse superior performances.

There are several previous reports on gradient structures, such as grain size gradient and composition gradient, which have been explored in mechanical, shape-memory and magnetic materials24,25,26,27,28,29. While these studies have demonstrated the potential of gradient structures for improving material performance, the conventional gradient structures, synthesized by mechanical deformation and traditional melt spinning, typically exhibit single-level ordering and address only one property bottleneck. In contrast, our MOS, fabricated using the FASA technique, has multi-level structural ordering, featuring a surface sandwich core-shell structure and an internal grain size gradient (Fig. 1a), and enables the simultaneous overcoming of multiple physical constraints. This is achieved by pre-introducing cluster structures with low nucleation barriers in alloy melt to modify its crystallization kinetics, a feature not commonly found in traditional melt spinning technique. The sandwich core-shell structure significantly enhances electron scattering through ordered scattering networks formed by multiple heterogeneous interfaces and serves as domain wall traps to block domain wall movement30,31, resulting in high ρ and strengthening Hc. Meanwhile, the grain size gradient, with its increasing pinning sites, facilitates progressively stronger multi-step domain wall pinning (Fig. 1b). These unique pinning mechanisms lead to multi-dimensional pinning traps, greatly enhancing Hc and overcoming the Br-Hc trade-off that traditional approaches fail to address32,33. Moreover, the gradient structure contains numerous nanograins with a high density of grain boundaries, which effectively suppress the nucleation and growth of reverse domains34,35, leading to a high magnetic thermal stability.

Fig. 1: Resistive metallic MOS with high thermal stability.
figure 1

a Schematic of the MOS and the breakthroughs in electrical resistivity and magnetic thermal stability. The superior electrical resistivity and magnetic thermal stability are attributed to increased electrons scattering and suppressed reverse domains. b The MOS breaks the trade-off between remanent magnetization and coercivity through enhancing domain wall pinning field compared to the homo-structure counterpart. The simultaneous improvements in electrical resistivity and magnetic thermal stability have been achieved without compromising magnetic performance.

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Results and discussion

Construction of the MOS material and microstructural analysis

To construct the complex sandwich core-shell structure, we selected Ti and Nb as key elements, guided by the density functional theory (DFT) calculations (Supplementary Fig. 1 and Supplementary Table 1). The DFT results show that both Ti and Nb have very low solubilities in α-Fe and Nd2Fe14B, leading to the formation of a TiNb layer between α-Fe and Nd2Fe14B grains, thereby yielding the sandwich structure. By combining this approach with the FASA technique (for fabricating gradient structures), the desired MOS structure can be created (Fig. 1a). By pre-introducing NdFeB cluster structures with low nucleation barriers33,36, the target Nd2Fe14B preferentially precipitated and caused the element enrichment in surrounding residual melt to induce sequential precipitations of α-Fe and TiNb phases, forming the sandwich core-shell structure, while the temperature gradient resulted in a grain-size gradient structure (Fig. 2a and Supplementary Figs. 2 and 3). More details can be found in Supplementary Note 1. Transmission electron microscopy (TEM) and X-ray diffraction (XRD) were applied to characterize the resulting MOS. The MOS features a pronounced grain size gradient along the temperature gradient (Fig. 2b−e) and the XRD refinement analysis reveals that the MOS consists of α-Fe (21.1 vol.%) and Nd2Fe14B phases (Fig. 2f and Supplementary Fig. 4). Statistical analysis of the grain size in Bright-field TEM images shows that the average size of α-Fe grains changes from 9.3 nm to 23.4 nm along the gradient, while the average size of Nd2Fe14B grains increases from 16.5 nm to 127.7 nm (Fig. 2e and Supplementary Fig. 5). The studies of scanning transmission electron microscopy (STEM) equipped with energy dispersive spectroscopy (EDS) and high-resolution transmission electron microscopy (HRTEM) with corresponding fast Fourier transformation (FFT) show that, in the MOS surface layer, the large Nd2Fe14B grains are encased by small α-Fe grains (Fig. 2g−j). Moreover, HRTEM with corresponding FFT, high-magnification STEM-EDS mapping and composition line profile indicate that an amorphous TiNb layer is sandwiched between the Nd2Fe14B and α-Fe (see Fig. 2g−m), represented as MOS sandwich core-shell (MOS-S), which is further revealed in Supplementary Fig. 6. This MOS-S structure is helpful to manipulate the behavior of electrons and domain walls in the material.

Fig. 2: Construction and microstructural characterization of the MOS.
figure 2

a Schematic of the field-assisted self-assembly technique (FASA) to construct MOS. The initial melt temperature is precisely controlled to pre-generate ordered NdFeB cluster structures, and then a temperature gradient field is applied to create a gradient in undercooling. Secondly, the NdFeB cluster structures with low nucleation barriers can crystallize into Nd2Fe14B grains and maintain a high growth rate at low undercooling, while high undercooling induces extensive nucleation. Thirdly, the continuous growth of Nd2Fe14B grains causes the residual melt to be Fe-rich, resulting in the precipitation of α-Fe grains around the Nd2Fe14B grains. Fourthly, the further element enrichment of the residual melt leads to the formation of TiNb between the α-Fe and Nd2Fe14B grains. b–d Bright-field TEM images of the grain size gradient, with a sandwich core-shell structure at the surface layer. e Grain size statistics along the thickness (t) of the ribbon materials. Error bars represent the standard deviation from the independent measurements of at least 1000 grains. f XRD patterns of the MOS, which exhibit diffraction peaks of both α-Fe and Nd2Fe14B crystals. g Energy dispersive spectroscopy mapping in region (b) yielded by a scanning transmission electron microscopy (STEM-EDS). h HRTEM images of MOS. i, j Fast Fourier transform (FFT) images corresponding to the blue and red regions in (h). k The enlarged view of the orange region in (h), showing an amorphous characteristic. l STEM-EDS mapping of sandwich core-shell structure. m STEM-EDS composition line profile in (l).

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Functionalities of the MOS material

The engineered MOS shows an exceptional combination of large ρ and high thermal stability, effectively suppressing eddy-current energy loss and preventing thermal failure. Since the eddy current concentrates at the material surface due to the skin effect21, the ρ of the surface MOS-S is the most critical and reaches 262.3 μΩ·cm (Fig. 3a and Supplementary Fig. 7). This value significantly exceeds those of its constituents, α-Fe and Nd2Fe14B, with enhancements of 2600% and ~100–300%, respectively, breaking the Vegard’s mixture law (Fig. 3a). Compared to the homo-structure (HS) with the same composition and similar grain size, the MOS-S exhibits an increase of over 100% in ρ (Fig. 3b and Supplementary Fig. 8). Furthermore, the MOS-S also exhibits larger ρ compared to gradient structures (GS), such as GS Nd2Fe14B/α-Fe and GS Nd2Fe14B with compositions of Nd9.28Fe83.51B7.22 and Nd11.8Fe82.2B, respectively, all synthesized using the same method. (see Methods and Supplementary Figs. 9 and 10). This result highlights the contribution of the sandwich core-shell structure to the performance. Additionally, our MOS-S outperforms the state-of-the-art commercial SmCo5, Sm2Co17 and NdFeB, showing improvements in ρ ranging from ~81% to ~441% (Fig. 3b). Moreover, the MOS achieves good thermal stability with a temperature coefficient of Hc (β = −0.268%/°C), exceeding that of commercial NdFeB (β = −0.620%/°C) by over 100% (Fig. 3c), attributed to the suppression of reverse magnetic domains by high-density grain boundaries due to the small grain size34,35. Compared to the NdFeB fabricated by different methods, including alloying and grain boundary diffusion process (GBDP), the MOS exhibits the highest thermal stability of coercivity (represented as 1/|β|). Ultimately, our MOS achieves an excellent combination of high ρ and large 1/|β|, which transcends those of the state-of-the-art commercial NdFeB, SmCo5 and Sm2Co17 (Fig. 3d).

Fig. 3: Electrical resistivity, thermal stability, and magnetic properties of the MOS.
figure 3

a The electrical resistivity (ρ) of the MOS-S compared to its constituents α-Fe and Nd2Fe14B. Error bars represent the range of ρ. b Comparison of the ρ of the MOS-S, homo-structure (HS) with the same composition, gradient structures (GS) Nd2Fe14B, GS Nd2Fe14B/α-Fe (both without the sandwich core-shell structure), single crystal (S.C.) NdFeB, commercial (Comm.) SmCo5, Sm2Co17 and NdFeB. Error bars represent the range of ρ. c Comparison of the thermal stability of Hc among the MOS, commercial NdFeB, untreated NdFeB, and NdFeB treated by grain boundary diffusion process (GBDP) and alloying. The thermal stability of Hc is designated as 1/|β|, where β is the temperature coefficient of Hc. d Comparison of the ρ and 1/|β| of the MOS and the state-of-the-art commercial performances, including SmCo5, Sm2Co17 and NdFeB. Error bars represent the range of ρ and 1/|β|. e Plot of Br and Hc of the MOS, GS Nd2Fe14B, GS Nd2Fe14B/α-Fe and NdFeB based nanocomposite magnets prepared by various methods, including melt spinning (MS), high-pressure torsion deformation (HPTD) and amorphous alloys annealing (ANN). f The changes in (BH)max and ρ in the MOS fabricated using the FASA method compared to NdFeB magnets prepared by GBDP and NdFeB composite magnets with Dy2O3, NdF3, CaF2 and SiO2. The data for comparison are derived from literature, see Supplementary Tables 3−7.

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Importantly, while achieving superior ρ and thermal stability, our MOS also enhances the magnetic performance. Compared to the HS (Hc = 3.0 kOe), the MOS demonstrates a nearly 200% improvement in Hc, reaching approximately 9.0 kOe with simultaneously enhanced Br (Supplementary Figs. 8 and 11). Such a high Hc of the MOS exceeds those of conventional high-Fe-content nanocomposite magnets (α-Fe > 20 vol.%) by over 50% (Supplementary Fig. 12). Consequently, the MOS breaks the long-standing Br-Hc trade-off and achieves a great combination of Br and Hc, which cannot be attained in existing nanocomposite magnets prepared by melt spinning (MS), high-pressure torsion deformation (HPTD) and amorphous alloys annealing (ANN) (Fig. 3e). A high energy density is thus realized in the MOS, which surpasses HS by 121%. Additionally, the MOS also exhibits higher energy density compared to GS Nd2Fe14B and GS Nd2Fe14B/α-Fe (Supplementary Figs. 9−11). Furthermore, the FASA technology simultaneously improves both ρ and energy density (BH)max, unlike traditional methods such as GBDP and compositing, which often increase resistivity at the expense of magnetic performance by introducing insulating but non-magnetic components (Fig. 3f). As a result, the MOS demonstrates simultaneous enhancement in energy density, resistivity and temperature coefficient of coercivity—a feat that traditional composition-design-based methods cannot attain, as shown in Supplementary Table 2.

In addition, the MOS also demonstrates superior corrosion resistance and stiffness. Electrochemical measurements reveal that the MOS exhibits significantly stronger corrosion resistance than commercial NdFeB, melt spinning (MS) NdFeB, and HS (Fig. 4a, b), with over 12 times lower corrosion current compared to the state-of-the-art commercial NdFeB, as well as a more favorable corrosion potential. Similar trends are observed in the electrochemical impedance spectroscopy (EIS) measurements, where the MOS demonstrates the largest corrosion impedance (Supplementary Fig. 13). The high corrosion resistance results from the α-Fe shells with high corrosion potential37, which suppress the normally severe grain boundary corrosion in commercial NdFeB38. Furthermore, nanoindentation tests show that our MOS has a reduced modulus which is 51% higher than that of commercial NdFeB, making it more resistant to vibrations and impacts during device operation39. The large stiffness of the MOS may result from the good intrinsic mechanical properties of the α-Fe phase40,41 and the effective stress transfer at the α-Fe/NdFeB heterointerfaces42,43.

Fig. 4: Electrochemical corrosion and mechanical properties of the MOS.
figure 4

Potential dynamic polarization curves (a) and comparison of corrosion current and potential (b) for the MOS, HS, MS NdFeB and Comm. NdFeB. Nanoindentation load-depth curves (c) and comparison of reduced modulus (d) for the MOS, HS, MS NdFeB and Comm. NdFeB. Error bars represent the standard deviation from at least 100 independent measurements.

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Mechanisms of electrical and magnetic performance in the MOS

Our MOS demonstrates the lowest temperature rise under an alternating magnetic field compared to the HS and state-of-the-art commercial SmCo5, Sm2Co17, and NdFeB, which is attributed to the high ρ of surface MOS-S, effectively suppressing the eddy currents (Fig. 5a). To reveal the underlying mechanisms of the resistive metallic MOS, we measured ρ at different temperatures. The experimental data of temperature-dependent ρ of the MOS aligns well with the typical metallic model, where the increasing ρ with temperature rise is due to stronger lattice scattering (Fig. 5b and Supplementary Fig. 14). To further elucidate the critical role of the sandwich core-shell structure in enhancing ρ, we gradually removed the material from bulk to surface to measure ρ at various thickness. The ρ increases rapidly as it approaches the surface MOS-S, whereas the ρ of the HS remains constant, suggesting that the strong electron scattering of sandwich core-shell structure on the surface is crucial for the large ρ (Fig. 5c and Supplementary Fig. 15). This viewpoint is further supported by the anisotropic resistivity of the MOS, where the surface resistivity is larger than that of gradient direction perpendicular to surface, as shown in Supplementary Fig. 16. Then we conducted finite element simulations to assess the impact of structural ordering on ρ, as shown in Fig. 5d. The simulation results demonstrate that the ρ of the sandwich core-shell model exceeds those of the other models, including single phase (SP), composite (COM) and core-shell (CS), notably surpassing single-phase NdFeB by more than 100% (Fig. 5e). Therefore, these results suggest that the sandwich core-shell structure can enhance electron scattering and disrupt conductive paths through the abundant heterogeneous interfaces between α-Fe, TiNb and Nd2Fe14B to increase ρ. The consistent trends between the simulation and experimental results (Fig. 5e) further support our conclusion.

Fig. 5: Electron transport and magnetization reversal of the MOS.
figure 5

a Experimental temperature rise curves (left) and temperature distribution images (right) of the MOS, HS, and the state-of-the-art commercial SmCo5, Sm2Co17, and NdFeB in an alternating magnetic field. b Experimental data and model fitting of temperature-dependent electrical resistivity of the MOS. c Electrical resistivity enhancement along gradient direction of the MOS. d Four models in the simulations represent single-phase NdFeB (SP), NdFeB/α-Fe composite (COM), NdFeB/α-Fe composite with core-shell (CS) structure, and MOS sandwich core-shell (SCS) structure. e Electrical resistivity calculated by simulations with different models, as well as the corresponding resistivity measured in single-phase NdFeB (represents SP), Nd2Fe14B/α-Fe prepared by melt spinning (represents COM), surface of the GS Nd2Fe14B/α-Fe with a core-shell structure (represents CS), and surface of the MOS (represents SCS). f Initial magnetization curves (left) and their corresponding differential curves (right) of the MOS and HS. g Applied field dependence of Hc (left) for the MOS and HS, along with their corresponding differential curves (right) of the MOS and HS. The primary pinning field Hp is indicated in (f) and (g).

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To reveal the coercivity mechanism of the MOS, we measured the initial magnetization curves and the applied field dependence of Hc. We found an enhanced pinning field (Hp) in the MOS, distinct from the weak pinning in HS (Fig. 5f, g). The domain wall pinning strength depends on the pinning site density and difference in domain wall energy, according to the formula below44,

$${H}_{\tt p}\cong f\cdot \frac{\Delta \gamma }{2\delta {M}_{\tt s}}$$
(1)

where f is the pinning site density, Δγ is the variation in domain wall energy between the pinning sites and matrix phases, δ is the domain wall thickness, and Ms is saturation magnetization. The domain wall energy is expressed as below13,

$$\gamma=4{(AK)}^{\frac{1}{2}}$$
(2)

where A is exchange stiffness coefficient and K is magnetocrystalline anisotropy constant. Due to the progressively increasing pinning site density f (grain boundaries), the pinning field of gradient structure can be enhanced, which is proved by the observed enlarged Hp compared to that of HS with large grain size (Supplementary Fig. 17a, b). Furthermore, as the TiNb layer of the sandwich core-shell structure has smaller K than matrix phases because of its amorphous characteristic, it acts as a low-energy trap, further enhancing the pinning field (Supplementary Fig. 17c, d)30,31.

Therefore, the MOS can break the trade-off between Hc and Br because the enhancement of Hc primarily relies on structural design without sacrificing magnetization (Fig. 3e). Meanwhile, our FASA technique has demonstrated good tunability of grain size (up to 500 nm) and morphology of sandwich core-shell structure (see Supplementary Figs. 18 and 19). Although the obtained energy density of MOS outperforms those of most existing nanocomposite magnets (Fig. 3e), further enhancement of the energy density requires well-oriented nanograins. In future work, it could potentially be achieved by adding an additional magnetic field to the FASA process, where the coupled temperature gradient and magnetic field can induce oriented nucleation and facilitate the directional growth of aligned nanograins45,46,47. Similar multi-field coupling technologies have been demonstrated to be feasible in achieving well-oriented nanograins32,47,48,49. Adding other physical fields, such as stress or electric fields, could further improve grain morphology control.

This study reports a general multi-level ordered structure strategy to simultaneously overcome multiple physical constraints in materials. We exemplify its power by fabricating a resistive magnetic metal with excellent thermal stability, an achievement traditionally seemed impossible due to high density of free electrons and inherent instability of the magnetized state. The MOS also breaks the long-standing trade-off between magnetization and coercivity and exhibits good corrosion resistance and stiffness.

This structure-based strategy introduces a broad design paradigm for diverse fields to overcome conventional physical constraints that underlie material performance bottlenecks. By reshaping thermodynamic energy profiles and kinetic processes, it controls the transport of particles (e.g., electrons, phonons, ions) and the evolution of functional units (e.g., domain walls, dislocations). Constructing structural ordering at multiple levels holds significant potential for simultaneously overcoming various physical constraints and achieving breakthroughs in a range of properties across thermoelectric, catalytic, battery, and biomedical materials.

Methods

Materials preparation

The magnetic metal featuring multi-level ordered structure (MOS) was constructed by a field-assisted self-assembly (FASA) technique with a gradient temperature field. Firstly, a uniform ingot was prepared by arc-melting commercial pure metals (purity higher than 99.5 wt.%) in a vacuum induction furnace (p < 10−3 Pa). The initial composition of the ingot was Nd9FebalB6.5Ti0.8Nb0.8. Then, the raw ingot was heated to 1200 °C and held for 15 s in a quartz tube with Ar atmosphere until it became a uniform melt, followed by cooling to 1150 °C and holding for 10 s to enhance the nucleation tendency of the melt but without activating initiating nucleation. The induced structural and compositional fluctuations in the melt could lead to the formation of numerous cluster structures33,36. Thirdly, we applied a gradient temperature field to the melt by jetting (p = 0.06 MPa) it onto a rotating copper wheel (14 m/s). This gradient temperature field within the melt was achieved through nearly unidirectional heat transfer, as the superior thermal conductivity of copper ensures that heat transfer from the melt to the copper significantly surpasses the thermal radiation to the Ar environment. The gradient temperature field (average gradient = ΔT/thickness) can be adjusted by changing the rotational speed. We selected a rotational speed of 14 m/s to achieve an appropriate temperature gradient, which provided the necessary undercooling at high-temperature regions of the melt to induce the self-assembly process through sequential precipitation.

The choice of Ti and Nb elements is guided by DFT calculations (Supplementary Fig. 1 and Supplementary Table 1), which indicate their low solubility in α-Fe and Nd2Fe14B phases. This characteristic promotes segregation of Ti and Nb at the interface between Nd2Fe14B and α-Fe and supports the formation of the targeted MOS. Firstly Nd2Fe14B precipitates preferentially due to the pre-introduced cluster structures with low nucleation barriers. Then, the residual melt becomes enriched with Fe, which induces the precipitation of α-Fe50,51. Finally, the remaining melt, which has further enrichment of Ti and Nb, solidifies into a TiNb mid layer between Nd2Fe14B (core) and α-Fe (shell) grains. Due to the internal high-density grain boundaries and excessively rapid cooling rate, complete sandwich TiNb layer tends to form at the surface. More details can be found in Supplementary Note 1.

To verify the successful introduction of cluster structures, we quenched the melt at 1150 °C and characterized their microstructures. Meanwhile, we also quenched the melt at higher temperature (1300 °C) to demonstrate that the introduction of cluster structures relies on precise control of the initial temperature. Additionally, to evaluate the impact of the unique MOS structure on electrical, thermal, magnetic, corrosion-resistant and mechanical performance, we prepared homo-structure (HS), gradient structure counterparts with the same composition for comparison. A uniform amorphous precursor was synthesized by adjusting the rotational speed to 32 m/s and the melt temperature to 1150 °C, preventing the development of the MOS. Then, by annealing (750 °C for 1 min) the precursor, the uniform HS without multi-level ordered structure was obtained. The gradient structure Nd2Fe14B/α-Fe (GS Nd2Fe14B/α-Fe) with a composition of Nd9.28Fe83.51B7.22 and the gradient structure Nd2Fe14B (GS Nd2Fe14B) with a composition of Nd11.8Fe82.2B were fabricated using the same processing conditions as MOS. To verify the tunability of the FASA process, we used a lower wheel speed (10–11 m/s) to prepare MOS with larger grains (MOS-L), and modified the material composition to fabricate MOS with a thicker TiNb layer (MOS-T).

Microstructure characterization

The microstructures of samples were examined using a transmission electron microscopy (TEM, JEOL JEM-2100 Plus), while the chemical composition and distribution were analyzed by energy dispersive spectroscopy (EDS) integrated with a scanning transmission electron microscopy (STEM, JEOL JEM-F200). The grain size distribution study was carried out by using digital micrograph-analysis software (Gatan, Inc., USA) to analyze TEM images obtained from various regions of the samples, where over 1000 grains were collected from each region for statistical analysis. The TEM and STEM specimens were prepared using focused ion beam technology at various thicknesses52.

The phase composition of the synthesized materials was investigated by X-ray diffraction (XRD, PANalytical) with Co Kα radiation. By using HighScore Plus software (PANalytical B.V., Inc.) to process the Rietveld refinement53, the volume fractions of the constituent phases were investigated, where the results were obtained with acceptable goodness of fit (GOF) σ = 1.66 (<2), R profile (Rp) = 1.76 (<10) and weighted R profile (Rwp) = 2.46 (<10).

Electrical resistivity measurements

The electrical resistivity of the MOS material, along with HS, GS Nd2Fe14B, GS Nd2Fe14B/α-Fe, and commercial NdFeB, was measured using the Kelvin method along the length of samples54 (Supplementary Fig. 20). Furthermore, the electrical resistivity at various thickness was measured by removing the material from bulk to surface perpendicular to the tested direction. These measurements were performed on an XTM-600 micromanipulator probe station. For precise current input and voltage output, a Keithley 2636B was employed, and ultra-low noise triaxial cables were used to minimize potential interference. The entire measurement process was meticulously controlled via LabVIEW programs. To further mitigate noise from vibrations and prevent the oxidation of the samples during testing, the probe station was placed in MT-C002 glove box under a nitrogen atmosphere and on a DVT-2000 vibration isolation table. Every sample was measured three times to get a mean value. To measure the resistivity at different thickness, the sample was progressively ground from the small-grain side using 3000-grit SiC sandpaper, reducing its thickness. The resistivity was then measured at each stage, and the thickness was determined using a micrometer. The change in thickness, Δt, was defined as the difference between the initial thickness, t0, and the current thickness, t.

Magnetic property measurements

Magnetic properties of the synthesized materials were tested at ambient temperature along the length of samples using a vibrating sample magnetometer (VSM). Before magnetic measurement, the samples were magnetized using an external magnetic field of 10 T47. The magnetization reversal behaviors were analyzed through the initial magnetization curves and the minor hysteresis loops, which were achieved by using the VSM (Lakeshore 7410, 3T). To assess the magnetic thermal stability, the coercivity temperature coefficient (β) was measured from ambient temperature to 220 °C with the VSM (Lakeshore 7407, 1.6 T). Given that the thickness (15–42 μm) is much smaller than the length (5.5 mm) and width (0.5–2 mm), the self-demagnetization effect along the length was negligible. To ensure the reliability of the obtained results, at least three samples were measured for each experimental condition.

Electrochemical corrosion measurements

Electrochemical corrosion resistance of the MOS and HS material, GS NdFeB, Comm. NdFeB was measured using standard three-electrode cell (CHI660e workstation) in 3.5 wt.% NaCl aqueous solution. The samples were used as the working electrode, a Pt wire served as the counter electrode and Ag/AgCl acted as the reference electrode. All polarization curves were recorded from −1.2 V to −0.4 V at a scan rate of 5.0 mV/s after the open circuit potential reached steady state. Electrochemical impedance spectroscopy (EIS) was performed by a sinusoidal potential perturbation of 20 mV. The working electrodes were embedded in resin, polished sequentially with 3000- to 5000-grit SiC paper, rinsed with ethanol, and air-dried to ensure optimal surface preparation55. The thickness loss during polishing is less than 1 μm to ensure that the sandwich core-shell structure on the surface layer remains intact.

Stiffness measurements

The stiffness of the MOS and HS, GS NdFeB, Comm. NdFeB was measured using a nanomechanical testing system (FT-I04 Femto-Indenter) under continuous stiffness measurement (CSM) mode at a constant indentation depth of 200 nm with a step size of 1 μm. For each sample, more than one hundred points were measured, yielding a mean value. The specimens tested were ground using 5000-grit SiC paper and subsequently polished with a 0.05–3 μm diamond suspension solution on a UNIPOL-830 polishing machine, achieving a surface roughness of Sa ≤ 50 nm56. The thickness loss during polishing is less than 1 μm to ensure that the sandwich core-shell structure on the surface remains intact.

Temperature rise measurements

To study the temperature rise of MOS under an alternating magnetic field, the MOS material, as well as HS material and Comm. NdFeB, SmCo5, Sm2Co17 magnets were exposed to a magnetic field of 0.2 mT and 220 kHz to generate eddy-current heating. The temperature rise of the materials during the experiment was measured using a FOTRIC 225 s infrared camera. Each sample was subjected to the alternating magnetic field for more than 180 s to ensure the temperature stabilized.

First principle computational method

The heat of formations for the reaction between Nb/Ti and Fe/Nd8Fe56B4 are calculated by the first principle computational method. Firstly, the crystal structures for α-Fe, Nb, Nd, Ti, B, Nd8Fe56B4, and Nb/Ti-doped Fe/Nd8Fe56B4 solution are constructed. To meet the requirements of solid solubility, a 3 × 3 × 3 supercell for α-Fe is built, and a unit cell for the other crystals is used. Secondly, the energies for these structures are calculated within the framework of density functional theory (DFT) in the VASP software57. During the calculations, the exchange-correlation interaction was described by using the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof parameterization58. The ion-electron interaction has been described by the projector-augmented wave (PAW) potentials59. The cutoff energy for the plane wave basis set is set to 300 eV, and the k-point separation in the reciprocal space of the Brillouin zone is 0.04 nm−1. Finally, the heat of formation per atom Ef for these reactions can be calculated by using the following formula,

$${E}_{\tt f}=\frac{{E}_{\tt p}-{E}_{\tt r}}{m}$$
(3)

where Ep is the energy for the product, Er is the energy for the reactant, and m is the total number of atoms in the reactants.

The calculated heat of formation per atom is summarized in Supplementary Table 1. The heat of formation for Nb/Ti-doped Nd8Fe56B4 solution is positive in our studied concentration range, this indicates that the Nb/Ti-doped Nd8Fe56B4 solution is unstable. For the Nb/Ti-doped Fe solution, when the dope concentration reaches a critical value, the heat of formation becomes positive, this indicates that the solid solubility for these solutions is limited.

Electrical resistivity simulations

To reveal the impact of the MOS-S, we conducted the simulations of electrical resistivity using the COMSOL Multiphysics software. We established four models, including single phase NdFeB (SP), Fe/NdFeB composite (COM), Fe/NdFeB composite with core-shell (CS) structure, and the sandwich core-shell (SCS) with abundant heterogeneous interfaces cutting off the conductive paths. These models exhibit the grain boundaries of NdFeB and Fe. As the TiNb layer is amorphous, its grain boundaries are not indicated. The influence of grain boundaries in resistivity was simulated using the Mayadas-Shatzkes model (MS model)60. We estimated the resistivity of amorphous TiNb layer based on the MS model and previous studies61,62. In the simulation, we grounded the bottom end and applied a current of 0.1 A to the top end, thereby obtaining a potential distribution. Based on the simulation results, we calculated the electrical resistivity values for these four different models.