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. 2026 Feb 19;16:9885. doi: 10.1038/s41598-026-40891-y

Reversible magnetic behavior in amorphous wires for precision sensing applications

T-A Óvári 1, M Lostun 1, S Corodeanu 1, G Ababei 1, H Chiriac 1, N Lupu 1,✉
PMCID: PMC13018552  PMID: 41714447

Abstract

Amorphous magnetic wires based on Co-Fe alloys exhibit exceptionally soft magnetic behavior, making them attractive for advanced sensing technologies. Their magnetic performance is governed primarily by internal stresses, magnetoelastic interactions, and induced anisotropies. We demonstrate that helical magnetic anisotropy induced by stress annealing is fully reversible upon thermal relaxation, a mechanism not previously demonstrated for resetting the magnetic state in these wires. Magneto-optical Kerr effect imaging reveals corresponding changes in surface domain structures, confirming the reversible nature of magnetization processes at the microscale. We attribute this behavior to anelastic rearrangements and orientational ordering of nanoscale clusters within the amorphous matrix, which modulate magnetoelastic energy and produce the induced anisotropy. The demonstrated reversibility provides a mechanism for resettable or tunable magnetic responses in wire-based magnetic sensors and other precision electromagnetic devices.

Keywords: Reversible magnetic anisotropy, Stress annealing, Amorphous magnetic wires, Magnetostriction, Magneto-optical Kerr effect (MOKE), Magnetic sensing

Subject terms: Materials science, Nanoscience and technology, Physics

Introduction

Amorphous magnetic wires represent a technologically important class of materials, valued for their cylindrical symmetry, ultralow coercivity, high magnetic permeability, and tunable magnetoelastic and overall magnetic properties1,2. Their behavior is governed by a delicate balance between internal stresses, structural disorder, and magnetostriction, enabling an array of sensing applications spanning fields from automotive engineering to biomedical diagnostics3,4.

In Co-Fe-based amorphous wires, the intrinsic magnetostriction is near zero, producing nearly bistable or gently sloped longitudinal magnetization curves, depending on fabrication conditions5,6. However, many sensing applications, such as low-frequency magnetic field detection, displacement sensing, and magneto-impedance-based devices, require stable and well-controlled magnetic permeability over a wide field range. Achieving such control relies heavily on tailoring magnetic anisotropy through various annealing processes, and, most effectively, stress annealing7.

While stress annealing is known to induce helical magnetic anisotropy with an important transverse component8, a key unresolved question concerns the reversibility of the induced magnetic state. In particular, it is unclear whether anisotropy induced by stress annealing, which is often attributed to microstructural evolution, can be undone without degrading the material.

In this work, we demonstrate experimentally that magnetic anisotropy induced in Co-Fe-based amorphous wires via controlled stress annealing is fully reversible. By combining B-H loop measurements, magnetostriction analysis, magneto-optical Kerr effect (MOKE) investigations, ultra-high resolution transmission electron microscopy (UHR-TEM), selected area electron diffraction (SAED), and differential scanning calorimetry (DSC) we show that:

  • i.

    Stress annealing induces a strong helical anisotropy with a significant perpendicular component, modifying magnetization reversal behavior in comparison with the as-cast state.

  • ii.

    Magnetostriction changes sign, indicating changes in the intrinsic magnetoelastic energy.

  • iii.

    Subsequent structural relaxation restores the as-cast magnetic behavior, including the characteristic magnetization curves.

  • iv.

    The underlying mechanism is anelastic and microstructural, involving reversible ordering/disordering of nanoscale clusters.

This reversible cycle of anisotropy control opens the door to new device concepts that require tunability or periodic recalibration, demonstrating significant potential for precision sensing applications.

Results

As-cast amorphous wires exhibit inclined longitudinal hysteresis loops with low coercivity and modest remanence, as shown in Fig. 1. MOKE imaging reveals that surface domains are predominantly longitudinal, with magnetization rotation preceding domain wall motion (insets in Fig. 1b). The negative magnetostriction of the as-cast amorphous wires is consistent with a predominantly longitudinal easy axis in the inner core and a thin circumferential outer shell, resulting from the internal frozen-in stresses of rapid solidification in combination with the shape anisotropy of magnetic cylinders having a large aspect ratio.

Fig. 1.

Fig. 1

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Hysteresis loops (a) and magnetization curves (b) for as-cast, stress-annealed (545 °C, 18 s, 45 MPa), and relaxation-treated Co68.15Fe4.35Si12.5B15 amorphous wires, alongside representative MOKE surface domain images (insets in Fig. 1b).

Stress annealing at 545 °C for 18 s and an applied tensile stress of 45 MPa produces substantial modifications in the magnetization behavior, as shown in Fig. 1. Increased inclination in the B-H curves and reduced magnetic permeability at low applied fields confirm the development of a helical magnetic anisotropy within the stress-annealed magnetic wire. MOKE characterization confirms this shift, showing that surface domains adopt helical configurations with enhanced transverse components9. The duration of the stress annealing was found to be optimal at 18 s, as shorter duration did not result in sufficient changes and longer duration deteriorates the magnetic properties.

In order to investigate the reversibility of the magnetic behavior, a subsequent relaxation treatment at 400 °C for 30 min. was applied to the stress-annealed wires. The lower temperature for the relaxation treatment was chosen to avoid irreversible microstructural changes, while the longer duration was necessary to allow a substantial relaxation of the stress-annealed wires. Figure 1 illustrates the progressive evolution of the magnetic response across the as-cast, stress-annealed, and relaxed states. The stress-annealed curves exhibit the strongest perpendicular anisotropy, whereas the relaxation treatment nearly restores the original magnetic behavior.

Stress annealing causes the effective magnetostriction coefficient to shift from slightly negative values to slightly positive values (Fig. 2). This transition reflects rebalancing of magnetoelastic energy due to microstructural rearrangements, as also supported by UHR-TEM images and differential scanning calorimetry (DSC) curves (Fig. 3). After relaxation, λₛ decreases significantly towards its initial value, although it does not completely shift back to the initial negative values, most likely due to the alteration of the intrinsic internal stresses arising from the rapid solidification fabrication process. This is also the reason behind the increased remanence and implicitly of the squareness of the hysteresis loop in case of the relaxed samples.

Fig. 2.

Fig. 2

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Magnetostriction evolution for the as-cast (a) and the stress-annealed and relaxed samples (b), demonstrating a clear trend consistent with the observed changes in magnetic anisotropy induced by annealing.

Fig. 3.

Fig. 3

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DSC curves of as-cast, stress-annealed and relaxed Co68.15Fe4.35Si12.5B15 amorphous wires.

The stress-annealing temperature is slightly below the crystallization temperature, Tx ∼ 549 °C. Owing to the Co-based amorphous nature of the alloy, the microstructure is more stable than in conventional Fe-based nanocrystalline materials, which typically exhibit two-stage crystallization, with α-Fe formation in the first stage10. In contrast, the present Co-Fe-based wires show a single-stage crystallization process, as evidenced by the presence of the single exothermic peak in Fig. 3.

MOKE measurements in longitudinal (LMOKE) and in transverse (TMOKE) configurations, respectively, confirm the changes in magnetization reversal mechanisms, as observed in Figs. 4 and 5.

Fig. 4.

Fig. 4

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MOKE domain image (a) and surface loops (b) for as-cast amorphous wires. The numbered markers in the MOKE domain image (a) indicate representative positions along the wire at which hysteresis loops (b) were recorded.

Fig. 5.

Fig. 5

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MOKE surface loops and domain image (inset) for stress-annealed amorphous wires at 545 °C, for 18 s and 45 MPa.

As-cast samples show rotational processes accompanied by localized domain wall motion. In contrast, stress-annealed samples exhibit discrete jumps and domain redistributions characteristic of helical anisotropy. These features disappeared after relaxation.

Figure 6 provides a schematic representation of the inferred microstructural mechanism. Stress annealing promotes orientational ordering of small (~ 1–5 nm) α-(Fe, Co) nanoclusters within the amorphous matrix. Overall, the amorphicity of the samples is maintained as shown by the SAED images (insets in Fig. 6a,b). This reorientation introduces anelastic strains perpendicular to the applied stress, generating transverse anisotropy.

Fig. 6.

Fig. 6

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UHR-TEM microstructure imaging of the as-cast (a) and stress-annealed (545 °C, 18 s, 45 MPa) (b) amorphous wires, illustrating the reversible cluster-orientation mechanism responsible for the anisotropy induced by stress annealing and the associated anelastic strain development.

During relaxation, these clusters gradually lose their orientational bias, restoring the as-cast internal structure and thus the original anisotropy, while the magnetostriction also follows this trend, decreasing towards zero, but without reaching back into the initial range of negative values (Fig. 2).

Discussion

The induced anisotropy in the as-cast state has a magnetoelastic origin, due to the coupling between the intrinsic large internal stresses induced during the rapid solidification process and magnetostriction11. Even though magnetostriction is quite small, the large internal stresses will compensate and still give rise to important magnetoelastic contributions12. Under tensile load and elevated temperature, nanoclusters undergo directional reorganization, producing local anelastic strain fields, as illustrated schematically in Fig. 6b. This mechanism is energetically favorable because the amorphous structure lacks long-range order (Fig. 6a) and can accommodate reversible rearrangements. It is similar to the mechanism described in13,14.

The most striking result of this study is the extent of reversibility. Both magnetization curves and magnetostriction nearly return to their as-cast values. This suggests that no significant irreversible structural relaxation or nanocrystallization occurs, as confirmed by the SAED patterns. Moreover, cluster orientations remain metastable and can re-randomize under mild thermal activation, such as the relaxation treatment performed in this case. Also, reversible cycling is made possible by the reduced energy associated with cluster alignment.

Prior studies on Fe-based amorphous wires have documented induced anisotropies, but reversibility is rarely reported and often incomplete15,16. The present results are unique in demonstrating a complete reversible cycle involving both magnetic and magnetoelastic properties in Co-Fe-based amorphous wires.

The ability to tune and reset magnetic anisotropy would enable: (i) reconfigurable sensor operation modes; (ii) drift compensation through periodic thermal cycling; (iii) tailored sensitivity windows for magnetic field, stress, or position sensing; and (iv) enhanced long-term stability for devices requiring recalibration.

Such functionalities are increasingly important in precision metrology, medical sensing, and advanced automotive applications.

Methods

The amorphous magnetic wires with the nominal composition Co68.15Fe4.35Si12.5B15 were produced using the in-rotating-water quenching technique17,18 at the National Institute of Research and Development for Technical Physics, Iași, Romania. The actual samples employed in our investigation were 120 μm in diameter.

The as-cast wires exhibit a saturation magnetization, µ0MS, of 0.68 T, measured by means of vibrating sample magnetometry (VSM). By measuring the inductive hysteresis loops along the wire axis, we determined the low field coercivities, HC, to be smaller than 8 A/m, and the corresponding relative magnetic permeability, µr, between 2 ⋅ 105 and 3 ⋅ 105.

The magnetostriction coefficient was determined using the small-angle magnetization rotation (SAMR) method, based on the stress dependence of the anisotropy field19,20. Magnetostriction has been found to vary between − 0.67 ⋅ 10− 7 and − 0.66 ⋅ 10− 7 in the as-cast state, which is consistent with the nearly zero magnetostrictive character expected for amorphous wires with this composition.

Surface magnetization has been investigated by means of magneto-optical Kerr effect (MOKE) measurements performed in either longitudinal (LMOKE) or transverse (TMOKE) configurations, using a NanoMOKE2 magnetometer having a built-in optical microscope. Due to the small probed surface area relative to wire length, MOKE is particularly sensitive to local magnetization rearrangements. Using this method, we have studied both local surface hysteresis loops and domain images in maximum applied fields up to 20 kA/m.

Microstructure has been investigated by means of ultra-high resolution transmission electron microscopy (UHR-TEM), using a Carl Zeiss LIBRA 200MC UHR-TEM, while the thermal stability has been studied by using a SETARAM LABSYS system at heating rates of 20 K/min.

As-cast amorphous wires were subjected to controlled heat treatments under longitudinally applied tensile stress, with applied stresses ranging from 4 to 90 MPa at temperatures of 540–545 °C for 18 s. A separate relaxation heat treatment, performed without applied tensile stress at 400 °C for 30 min. was used to assess reversibility of the induced anisotropy.

Conclusions

We have demonstrated controllable and fully reversible magnetic anisotropy in Co-Fe-based amorphous wires through stress annealing and subsequent structural relaxation. Key findings include the helical magnetic anisotropy, with a strong perpendicular component, induced because of stress annealing, and the accompanying change in sign of the magnetostriction, associated with a modification of the intrinsic magnetoelastic energy. More importantly, a relaxation treatment restores the as-cast magnetic state and the corresponding magnetic behavior, which includes the domain structure and magnetization reversal mechanism.

The described reversibility of the magnetic anisotropy and behavior is consistent with a reversible, anelastic ordering of nanoscale clusters.

These results enable resettable and tunable magnetic responses, offering novel possibilities for precision sensing technologies that rely on Co-Fe-based amorphous wires capable of detecting extremely low magnetic fields (pT down to fT), where precise control of their macroscopic magnetic properties is essential.

Author contributions

HC and NL conceived the approach, designed the research, and supervised the work. SC prepared the amorphous and annealed samples and performed the magnetic measurements – hysteresis and magnetization curves. ML performed the magneto-optical Kerr effect and magnetostriction measurements. GA performed the UHR-TEM investigations. NL, HC and TAÓ analyzed and interpreted the results and wrote the manuscript. All authors reviewed the manuscript.

Funding

Work supported by the Romanian Executive Agency for Higher Education, Research, Development and Innovation Funding (UEFISCDI) under project PN-IV-P1-PCE-2023-1896 - Contract no. 12PCE/03.01.2025 and by the Nucleu Program (Project PN 23 11 01 01) financed by the Romanian Ministry of Education and Research.

Data availability

Data underlying the results presented in this paper are available from the corresponding author (nicole@phys-iasi.ro) upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

Data underlying the results presented in this paper are available from the corresponding author (nicole@phys-iasi.ro) upon reasonable request.

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