Key Takeaways & Executive Findings
- •• • TSA induces a sharp increase in uniaxial anisotropy constant (Ku) from 22.5 to 665 J/m3 across 0–300 MPa stress, while maintaining ultrafine grain size (≤11 nm), enabling precise tuning of magnetic anisotropy without compromising nanocrystalline structure. • • Domain width is refined from 110 to 36 μm with increasing stress, shifting magnetization mechanism from domain-wall displacement to rotation-dominated reversal, which is critical for achieving stable permeability at high frequencies. • • At 50 MPa, effective permeability (μe) of ~2330 is maintained up to 1 MHz, while at 300 MPa, μe of ~585 remains constant from 1 kHz to 10 MHz, demonstrating exceptional frequency stability for MHz-class power electronics. • • The quantitative correlation between Ku, domain structure, and μe provides a design framework for optimizing stress-annealing parameters to meet specific high-frequency application requirements, such as precision current transformers and EMC filters.
Abstract
Tensile stress annealing (TSA) is an effective strategy for tailoring magnetic anisotropy and high-frequency performance in nanocrystalline soft magnetic alloys. Here, we systematically investigate the influence of TSA on the microstructure, magnetic domain evolution, and permeability stability of Fe69.5Co3Nb2Mo1.5Si14B9Cu1 nanocrystalline alloys. Across all applied stresses (0–300 MPa), the alloys retain an ultrafine grain size (≤11 nm), yet the induced uniaxial anisotropy constant (Ku) rises sharply from 22.5 to 665 J/m3. This increase in Ku refines the magnetic domain structure, reducing average domain width from 110 to 36 μm, and shifts the magnetization mechanism from domain-wall displacement to rotation-dominated reversal. Quantitative correlation between Ku, domain structure, and effective permeability (μe) reveals that higher stress suppresses μe at low frequencies but yields exceptional frequency stability: μe ≈ 2330 is maintained up to 1 MHz at 50 MPa, and μe ≈ 585 remains constant from 1 kHz to 10 MHz at 300 MPa. These findings demonstrate that stress-induced anisotropy is a decisive factor in governing high-frequency magnetic response, offering both mechanistic insight and a practical framework for designing next-generation soft magnetic materials for precision current transformers, EMC filters, and MHz-class power electronics.
1. Introduction
The rapid evolution of power electronics has intensified the demand for magnetic components capable of operating efficiently at high frequencies, often in the MHz range. Devices such as current transformers, DC-DC power converters, and electromagnetic compatibility (EMC) filters are integral to smart grids, electric vehicles, renewable energy systems, and high-speed communication infrastructure. However, the proliferation of rectifiers, inverters, and high-frequency switching circuits introduces substantial DC and harmonic components into the power grid. These effects induce nonlinear magnetic behavior and permeability degradation in transformer cores, ultimately compromising measurement accuracy and efficiency. Achieving low, stable effective permeability (μe) under high-frequency excitation and DC-bias is therefore critical for suppressing electromagnetic interference and ensuring reliable performance in next-generation power systems.
Fe-based nanocrystalline alloys are a prime candidate for such applications due to their unique amorphous-nanocrystalline dual-phase structure, which combines high saturation magnetic flux density (Bs), high μe, low coercivity (Hc), and low core loss (Pcv). Yet under DC-bias, these alloys are prone to saturation, where μe declines sharply even at relatively low DC-bias fields, severely restricting their usable frequency range. Conventional strategies, such as Ni alloying or magnetic field annealing, are commonly employed to modulate Ku to mitigate this effect. However, their effectiveness is often limited by intrinsic trade-offs. While Ni alloying can tune μe to a certain degree, it adversely affects frequency stability. Additionally, magnetic field annealing results in mediocre permeability linearity and inadequate DC-bias tolerance. This study systematically investigates tensile stress annealing (TSA) as an alternative to overcome these bottlenecks, demonstrating that stress-induced anisotropy can achieve both high μe and exceptional frequency stability, offering a practical pathway for next-generation soft magnetic materials.
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Zhijun Guo, Jifeng Zhou, Qianqian Liu, Mingjuan Cai, Yanzhou Fan, Qiang Luo, Baolong Shen (2026). Stress-Induced Anisotropy for MHz-Stable Permeability in Fe-Based Nanocrystalline Alloys. SCIENCE CHINA Materials. https://doi.org/10.1007/s40843-025-3883-2
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Frequently Asked Questions
What is the maximum tensile stress that can be applied without causing significant grain growth or degradation of soft magnetic properties?
Across all applied stresses up to 300 MPa, the alloys retain an ultrafine grain size of ≤11 nm, indicating that TSA does not induce significant grain growth. The induced uniaxial anisotropy constant (Ku) increases sharply from 22.5 to 665 J/m3, which is beneficial for high-frequency stability, but at the cost of reduced low-frequency permeability.
How does the stress-induced anisotropy affect the magnetization mechanism and domain structure?
Increasing stress refines the magnetic domain structure, reducing average domain width from 110 to 36 μm. This refinement shifts the magnetization mechanism from domain-wall displacement to rotation-dominated reversal, which is key to achieving stable permeability at high frequencies.
What are the specific permeability values and frequency ranges achieved at different stress levels?
At 50 MPa, μe ≈ 2330 is maintained up to 1 MHz. At 300 MPa, μe ≈ 585 remains constant from 1 kHz to 10 MHz. These values demonstrate that TSA can tailor permeability for specific frequency ranges, making it suitable for MHz-class power electronics.
How does TSA compare to conventional magnetic field annealing in terms of permeability stability and DC-bias tolerance?
TSA provides superior frequency stability compared to magnetic field annealing, which often results in mediocre permeability linearity and inadequate DC-bias tolerance. The quantitative correlation between Ku, domain structure, and μe in TSA allows precise control over high-frequency response, addressing the limitations of conventional methods.
What are the potential industrial applications of these stress-annealed Fe-based nanocrystalline alloys?
The exceptional frequency stability and tunable permeability make these alloys ideal for precision current transformers, EMC filters, and MHz-class power electronics, where stable performance under high-frequency excitation and DC-bias is critical.
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