France



I. INTRODUCTION&lt;br/&gt;With the rapid development of the power electronics industry, electrical equipment is tending towards high-power, high-frequency, and miniaturization, in particular for the inductors, chokes, and transformers &lt;sup&gt;[1]&lt;/sup&gt;. The magnetic material becomes a hinder to improve the device performance further&lt;sup&gt; [2]&lt;/sup&gt;.&lt;br/&gt;At present, soft magnetic ferrite is widely used in high frequency applications due to the lower conductivity and core loss at the high operating frequency. However, the saturation flux density of ferrite is usually less than 0.5 T, which is much lower than that of alloy soft magnetic materials&lt;sup&gt; [3]&lt;/sup&gt;. Nanocrystalline and amorphous alloys have excellent magnetic properties, such as low coercive force, high permeability, and saturation flux density, but these materials have high conductivity which causes great eddy current loss &lt;i&gt;P&lt;sub&gt;ed&lt;/sub&gt;&lt;/i&gt;. Magnetic cores fabricated by amorphous and nanocrystalline alloy powders can effectively reduce the &lt;i&gt;P&lt;sub&gt;ed&lt;/sub&gt;&lt;/i&gt; due to their lowered conductivity &lt;sup&gt;[4]&lt;/sup&gt;. Consequently, these powder cores are gradually used in high-frequency and high-power applications. In fact, it is inevitable that the core and winding losses will lead to the temperature increase of the core, in particular, at high frequency &lt;sup&gt;[5]&lt;/sup&gt;. Therefore, it is significant to study the temperature dependence of the magnetic properties of powder cores at high frequency. The results can be used to optimize the performance of electrical devices.&lt;br/&gt;II. MEASUREMENT PRINCIPLE AND SYSTEM&lt;br/&gt;In this article, the magnetic properties and loss characteristics of nanocrystalline powder core, amorphous powder core, ferrite, X-Flux (Fe-Si), and Kool-Mµ (Fe-Si-Al) are measured and analyzed in the range of 25 °C to 125 °C from 20 kHz to 100 kHz. The magnetic properties measurement system for the toroidal powder core sample is constructed, as shown in Fig.1. The toroidal powder core is placed in a thermotank for heating, and the internal temperature in the thermotank can be controlled by PID adjustment. The magnetic field intensity &lt;i&gt;H&lt;/i&gt; and the magnetic flux density &lt;i&gt;B&lt;/i&gt; are calculated by Ampere law and Faraday’s law of induction, respectively. The core loss is calculated by the Poynting equation and analyzed by the Steinmetz equation.&lt;br/&gt;III. EXPERIMENTAL RESULTS OF POWDER CORES&lt;br/&gt;The magnetic properties of the above materials as a function of temperature are investigated, such as coercive force, remanence, complex permeability, inductance factor, saturation flux density, and core loss. The properties are discussed using the micro-magnetism theory. Meanwhile, the material properties of the above materials are compared and summarized.&lt;br/&gt;A. Magnetic properties at different conditions&lt;br/&gt;The inductance factor, &lt;i&gt;AL&lt;/i&gt;, of Kool-Mµ decreases with the increasing temperature. When the temperature rises from 25 °C to 50 °C, the &lt;i&gt;AL&lt;/i&gt; of Kool-Mµ only changed by 0.383% from 156.7 nH/N&lt;sup&gt;2&lt;/sup&gt; to 156.1 nH/N&lt;sup&gt;2&lt;/sup&gt; at 100 kHz, 30 mT, which is a very little variation. But it decreased by 7.367% from 156.1 nH/N&lt;sup&gt;2&lt;/sup&gt; to 144.6 nH/N&lt;sup&gt;2&lt;/sup&gt; with the temperature rising from 50 °C to 125 °C.&lt;br/&gt;The saturation flux density &lt;i&gt;B&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt; of the ferrite is also affected by temperature and frequency. The saturation flux density presents a downward trend with the increasing temperature or frequency, as shown in Fig.2 (a). The experimental results indicate that the saturation flux density of ferrite decreased from 0.479 T to 0.453 T while the operating frequency is from 20 kHz to 100 kHz at room temperature, which decreased by 5.428%. From 25 °C to 125 °C, the saturation flux density of ferrite decreased from 0.453 T to 0.319 T at 100 kHz, which decreased by 29.581%.&lt;br/&gt;B. Core loss analysis at different conditions&lt;br/&gt;When the temperature is increased from 25 °C to 125 °C, the loss of Kool-Mµ increases from 48.68 W/kg to 75.368 W/kg by 54.823% at operating frequency &lt;i&gt;f &lt;/i&gt;= 100 kHz, and magnetic flux density &lt;i&gt;B&lt;/i&gt; = 80 mT. However, the core loss of X-Flux and amorphous powder cores shows a decrease with increasing temperatures. The loss of X-Flux decreases from 199.708 W/kg at 25 °C to 175.805 W/kg at 125 °C by 11.969% while the loss of amorphous powder cores decreases from 118.165 W/kg at 25 °C to 107.127 W/kg at 125 °C. It is found that the amorphous powder cores have better temperature stability, as shown in Fig.2 (b). The nanocrystalline powder core shows the relative temperature stability compared with other samples since the loss values are similar at the experimental temperatures. On the other hand, the Kool-Mµ shows clearly temperature dependent loss property among the five samples. In addition, the core loss of the X-Flux is the largest, then followed by amorphous powder core, Kool-Mµ, nanocrystalline powder core, and ferrite at different frequencies over the experimental temperature range.&lt;br/&gt;In summary, the magnetic properties of five samples of different materials are measured at high frequencies over the temperature range from 25 °C to 125 °C. The physical characteristic of different materials exhibits an opposite trend with increasing temperature. The detailed comparison of results for five powder core materials will be shown in the full paper.

**References:**

[1] C. Jiang, X. Li, S. Ghosh, IEEE Transactions on Power Electronics., Vol. 35, p.10821-10830 (2020)&lt;br/&gt;[2] J. Millan, P. Godignon, X. Perpina, IEEE Transactions on Power Electronics., Vol. 29, p.2155-2163 (2014)&lt;br/&gt;[3] M. Yang, Y. Li, Q. Yang, IEEE Transactions on Applied Superconductivity., Vol. 30, p.1-5 (2020)&lt;br/&gt;[4] T. Suzuki, P. Sharma, L. Jiang, IEEE Transactions on Magnetics., Vol. 54, p.1-5 (2018)&lt;br/&gt;[5] N. Takahashi, M. Morishita, D. Miyagi, IEEE Transactions on Magnetics., Vol. 46, p.548-551 (2010)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d2b5dd3ec3b4878edd704526e47b46a8.jpg)
Fig. 1 Schematic diagram of experimental system for magnetic properties measurement with the effect of temperature.

![](https://assets.underline.io/uploads/markdown_image/1/image/20e4974e919b4bd9fa16021bb94c5041.jpg)
Fig. 2 The fundamental magnetization curve of TDK PC95 at different temperature (a), and core loss characteristic curves of amorphous (AM) and X-Flux powder cores at 100 kHz and different temperatures (b).

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 Temperature Dependence of Powder Cores Magnetic Properties for High Frequency Applications

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I. INTRODUCTION With the rapid development of the power electronics industry, electrical equipment is tending towards high-power, high-frequency, and miniaturization, in particular for the inductors, chokes, and transformers [1]. The magnetic material becomes a hinder to improve the device performance further [2]. At present, soft magnetic ferrite is widely used in high frequency applications due to the lower conductivity and core loss at the high operating frequency. However, the saturation flux density of ferrite is usually less than 0.5 T, which is much lower than that of alloy soft magnetic materials [3]. Nanocrystalline and amorphous alloys have excellent magnetic properties, such as low coercive force, high permeability, and saturation flux density, but these materials have high conductivity which causes great eddy current loss Ped. Magnetic cores fabricated by amorphous and nanocrystalline alloy powders can effectively reduce the Ped due to their lowered conductivity [4]. Consequently, these powder cores are gradually used in high-frequency and high-power applications. In fact, it is inevitable that the core and winding losses will lead to the temperature increase of the core, in particular, at high frequency [5]. Therefore, it is significant to study the temperature dependence of the magnetic properties of powder cores at high frequency. The results can be used to optimize the performance of electrical devices. II. MEASUREMENT PRINCIPLE AND SYSTEM In this article, the magnetic properties and loss characteristics of nanocrystalline powder core, amorphous powder core, ferrite, X-Flux (Fe-Si), and Kool-Mµ (Fe-Si-Al) are measured and analyzed in the range of 25 °C to 125 °C from 20 kHz to 100 kHz. The magnetic properties measurement system for the toroidal powder core sample is constructed, as shown in Fig.1. The toroidal powder core is placed in a thermotank for heating, and the internal temperature in the thermotank can be controlled by PID adjustment. The magnetic field intensity H and the magnetic flux density B are calculated by Ampere law and Faraday’s law of induction, respectively. The core loss is calculated by the Poynting equation and analyzed by the Steinmetz equation. III. EXPERIMENTAL RESULTS OF POWDER CORES The magnetic properties of the above materials as a function of temperature are investigated, such as coercive force, remanence, complex permeability, inductance factor, saturation flux density, and core loss. The properties are discussed using the micro-magnetism theory. Meanwhile, the material properties of the above materials are compared and summarized. A. Magnetic properties at different conditions The inductance factor, AL, of Kool-Mµ decreases with the increasing temperature. When the temperature rises from 25 °C to 50 °C, the AL of Kool-Mµ only changed by 0.383% from 156.7 nH/N2 to 156.1 nH/N2 at 100 kHz, 30 mT, which is a very little variation. But it decreased by 7.367% from 156.1 nH/N2 to 144.6 nH/N2 with the temperature rising from 50 °C to 125 °C. The saturation flux density Bs of the ferrite is also affected by temperature and frequency. The saturation flux density presents a downward trend with the increasing temperature or frequency, as shown in Fig.2 (a). The experimental results indicate that the saturation flux density of ferrite decreased from 0.479 T to 0.453 T while the operating frequency is from 20 kHz to 100 kHz at room temperature, which decreased by 5.428%. From 25 °C to 125 °C, the saturation flux density of ferrite decreased from 0.453 T to 0.319 T at 100 kHz, which decreased by 29.581%. B. Core loss analysis at different conditions When the temperature is increased from 25 °C to 125 °C, the loss of Kool-Mµ increases from 48.68 W/kg to 75.368 W/kg by 54.823% at operating frequency f = 100 kHz, and magnetic flux density B = 80 mT. However, the core loss of X-Flux and amorphous powder cores shows a decrease with increasing temperatures. The loss of X-Flux decreases from 199.708 W/kg at 25 °C to 175.805 W/kg at 125 °C by 11.969% while the loss of amorphous powder cores decreases from 118.165 W/kg at 25 °C to 107.127 W/kg at 125 °C. It is found that the amorphous powder cores have better temperature stability, as shown in Fig.2 (b). The nanocrystalline powder core shows the relative temperature stability compared with other samples since the loss values are similar at the experimental temperatures. On the other hand, the Kool-Mµ shows clearly temperature dependent loss property among the five samples. In addition, the core loss of the X-Flux is the largest, then followed by amorphous powder core, Kool-Mµ, nanocrystalline powder core, and ferrite at different frequencies over the experimental temperature range. In summary, the magnetic properties of five samples of different materials are measured at high frequencies over the temperature range from 25 °C to 125 °C. The physical characteristic of different materials exhibits an opposite trend with increasing temperature. The detailed comparison of results for five powder core materials will be shown in the full paper.

**References:**

[1] C. Jiang, X. Li, S. Ghosh, IEEE Transactions on Power Electronics., Vol. 35, p.10821-10830 (2020) [2] J. Millan, P. Godignon, X. Perpina, IEEE Transactions on Power Electronics., Vol. 29, p.2155-2163 (2014) [3] M. Yang, Y. Li, Q. Yang, IEEE Transactions on Applied Superconductivity., Vol. 30, p.1-5 (2020) [4] T. Suzuki, P. Sharma, L. Jiang, IEEE Transactions on Magnetics., Vol. 54, p.1-5 (2018) [5] N. Takahashi, M. Morishita, D. Miyagi, IEEE Transactions on Magnetics., Vol. 46, p.548-551 (2010)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d2b5dd3ec3b4878edd704526e47b46a8.jpg)
Fig. 1 Schematic diagram of experimental system for magnetic properties measurement with the effect of temperature.

![](https://assets.underline.io/uploads/markdown_image/1/image/20e4974e919b4bd9fa16021bb94c5041.jpg)
Fig. 2 The fundamental magnetization curve of TDK PC95 at different temperature (a), and core loss characteristic curves of amorphous (AM) and X-Flux powder cores at 100 kHz and different temperatures (b).

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Thin magnetic cylindrical wires attract considerable attention due to interesting features of a domain wall motion like absence of the Walker breakdown that prevents fast domain wall dynamics [1]. Amorphous glass-coated microwires are composite material, in which very high domain wall velocities have been observed [2-3]. Owing to the amorphous state of wires, the magnetocrystalline anisotropy vanishes. Recently, it was shown that the axial magnetic anisotropy resulting from rapid quenching has comparable strength, leading to a tilted domain wall orientation [4]. It is an open question of how the tilted domain wall in cylindrical wires moves at high velocities and the origin of the so-called unidirectional effect [5]. An essential prerequisite for understanding the magnetic domain walls dynamics is a detailed knowledge of its spin structure in static. While several experimental techniques allow for well controllable deposition of magnetic structures with complex geometries [6], a reliable determination of a surface magnetization usually meets several obstacles in case of sample with curved surface. In the first part, we extend our analytical model of the Magneto-Optical Kerr Effect (MOKE) contrast [7] for cylinders with reduced diameter. Understanding the underlying mechanisms allows devising a new approach for interpretation of magneto-optical observations of thin magnetic cylinders. It is shown that the cylindrical shape of sample surface gives rise to a spatial distribution of the planes of incidence that are all tilted each to other. Phase diagrams of a magneto-optical contrast are calculated for various angles of incidence, extinction angles between polarizer and analyzer and as a function of thickness of a glass coat. In particular, it is shown that additional layer of a glass coat changes remarkably the circumferential dependence of light intensities. Our framework is used to optimize the LASER MOKE setup for direct visualization of a surface shape of domain wall in thin magnetic cylinders [4]. Stabilization of a domain wall is achieved by two opposite magnetic fields, resulting in effective one-dimensional potential well. Periodic back-and-forth motion of the well is used to synchronize the domain wall position with MOKE imaging and direct time-resolved images of a surface magnetism are performed. In contrary to previous measurements, a small pick-up coil is wounded around a thin glass capillary in order to detect spin dynamics inside the wire (Fig. 1). A direct comparison between surface domain wall position detected by MOKE and a signal from pick-up coils is given. It is shown that the voltage induced in pick-up coil has two sources: a, the voltage from spatially dependant magnetic field controlling the domain wall position and b, the signal from the domain wall. Employing simulations based on finite element method, the shape of a magnetic potential well is calculated. The profile of the magnetic domain wall potential well is then used to calculate the contribution from domain wall. At slow motion of a domain wall potential well, the signal from pick-up coils is well synchronized with a surface domain wall motion. The result implies almost planar structure of a domain wall. At high domain wall velocities, the signal in pick-up coil is induced earlier than surface boundary arrives to the position of a pick-up coil. The findings show that the tilted domain wall in microwires is not planar during the propagation. Our time-resolved observations of a domain wall depinning process show domain wall strongly distorts at pinning centres (Fig. 2). The finding is important for correct interpretation of a domain wall velocities measured by Sixtus-Tonks method. Finally, we propose a single scheme for wireless magneto-optical sensor based on domain wall motion in thin magnetic cylinders.

**References:**

[1] M. Yan, A. Kákay, S. Gliga, et al., Phys. Rev. Lett., Vol 104, p.057201 (2010) [2] P. Klein, R. Varga, M Vázquez, J. Alloy. Compd., Vol 550, p.31 (2013) [3] R. Varga, K. L. Garcia, M. Vazquez, P. Vojtanik, Phys. Rev. Lett., Vol 94, p.017201 (2005) [4] K. Richter, A. Thiaville, R. Varga, J. McCord, J. Appl. Phys., Vol. 127, p.193905 (2020) [5] J. Onufer, J Ziman, M. Kladivova, J. Magn. Magn. Mater., Vol 396, p.313 (2015) [6] A. Fernandez-Paecho, et al., Sci. Rep., Vol 3, p.1492 (2013) [7] K. Richter, A. Thiaville, and R. Varga, Phys. Rev. B, Vol. 96, p.064421 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a9c31b25e237279d8a20cbb60d77e613.jpg)
Fig. 1 Stabilization of a domain wall by potential well. Microwire (M) is places between coils. Pair of driving coils (C1 and C2) generates opposite magnetic fields H1 and H2. The domain wall is moved back-and-fforth by ramping the current in one coil. Surface magnetization is detected by two LASER spots (red lines). Inner magnetization dynamics is sensed by pick-up coil (P).

![](https://assets.underline.io/uploads/markdown_image/1/image/1264f9eaa0f431b2bb7352ea0cd982ce.jpg)
Fig. 2 Time-resolved observation of a domain wall depinning proces in amorphous glass-coated microwire. Images are perfomed by time-rsolved MOKE microscopy.

 Time-resolved observation of a domain wall motion in microwires with positive magnetostriction

—The idea of the present work is devoted to improving the SOLT calibration standard by specially designed microstrip cells as a PCB SOLT standard for VNA calibration and measuring the high-frequency magnetoimpedance (MI) for the development of various high-performance micro-sensor devices. The high-frequency sensitivity of MI was enhanced by the current annealing of partially crystalline wires. In the past few years, soft ferromagnetic amorphous wires have attracted growing attention in research due to their miniature dimensions, excellent soft magnetic properties, and giant-magnetoimpedance (MI) effect [1,2]. The MI effect which is referred to as a large and sensitive change in the complex-valued impedance of a magnetic conductor in the presence of an external magnetic field and/or mechanical stress is of particular interest for the development of various high-performance micro-sensor devices [3]. To optimize sensing operation regimes, it is important to measure the impedance characteristics of the individual wire which may present considerable problems at higher frequencies in the GHz range. This is related to uncertainties occurring due to the calibration of measuring devices (Network Analyzer). In the present work, we suggest an application-specific calibration technique with a specially designed microstrip cell for the impedance measurement for frequencies up to 6 GHz. We also demonstrate that the MI plots change their shape with increasing frequency and high sensitivity range caused by the directional change in the dc magnetization vanishes at frequencies of about 2 GHz for Co-rich wires with a circumferential anisotropy. The frequency range of high MI sensitivity can be enhanced by inducing a surface anisotropy in partially crystallized wires. Coaxial and microstrip transmission lines are widely used as sample holders, however, in the case of the impedance measurements when the sample is subjected to mechanical stress, coaxial lines are not convenient. Here we discuss the calibration procedures for microstrip lines. In the microwave de-embedding methods, the electrical reference planes are shifted to the sample location. This requires the use of dummy sample holders with specific terminations, for example, three reflection standards (open, short, and match load) and two ports connected together (thru). This calibration procedure is known by its name as short-open-load-thru (SOLT) or thru-open-short-match (TOSM). Accurate calibration standards can be fabricated on customized PCB, then, the complex impedance Z is calculated from the S21–parameter using a simple formula without solving any equations. Fig. 1 shows the MI characteristics at different frequencies of amorphous Co66.6Fe4.28B11.51Si14.48Ni14.4Mo1.69 microwires in an as-prepared state (total diameter D=25.8 µm metal core diameter d=25 µm and d=14.2 µm). The wire has a well-defined circular anisotropy with an anisotropy field of about 7.5 Oe. The wires of this composition are of particular interest due to low Curie temperature, so they can be used as embedded temperature sensors. It is seen that the high sensitivity of MI due to the dc magnetization re-orientation is preserved for frequencies below 2 GHz. When the dc magnetization is along the wire and does not change by the field, only the permeability parameter determines the field behavior of the impedance: for high frequencies, it increases with a much lower slope: the sensitivity of the impedance change is about few present per Oe. In the case of wires with partial crystallization, the current annealing establishes a stronger surface anisotropy which improves the MI behavior at higher frequencies. Moreover, it is possible to realize a strong stress dependence of MI at zero fields as demonstrated in Fig. 2. Acknowledgment: This work was supported by the Russian Foundation for Basic Research (RFBR 19-32-90129) and the part from the Ministry of Education and Science of the Russian Federation in the framework of the Increase Competitiveness Program of MISiS.

**References:**

 [1] L. V. Panina, K. Mohri, T. Uchiyama, Giant Magneto-Impedance in Co-Rich Amorphous Wires and Films, IEEE Trans. Magn. Vol. 31, p. 1249-1260 (1995). [2] M. Vázquez, Soft magnetic wires, in: Phys. B Condens. Matter. Vol 299, p. 302-313 (2001). [3] J. Alam, C. Bran, H. Chiriac, et al, Cylindrical micro and nanowires: Fabrication, properties and applications, J. Magn and Magnetic Mater. Vol. 513 (2020) 167074.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0925a8b841221cb3b8ae375e66205925.jpg)
Fig. 1: MI vs magnetic field of amorphous Co66.6Fe4.28B11.51Si14.48Ni14.4Mo1.69 microwires in as-prepared state at GHz frequency range a) 0.1 GHz to 0.9 GHz and b) 1.5 GHz to 2.5 GHz

![](https://assets.underline.io/uploads/markdown_image/1/image/37529af52350f8e5679fc02dc7919582.jpg)
Fig. 2: Effect of tensile stress on the MI vs. magnetic field of Co71Fe5B11Si10Cr3 (total diameter, a metal core diameter, partially crystalline) microwires after DC current annealing at 50 mA for 30 minutes. The frequency is 2.1 GHz.

 Magneto-Impedance Behavior of Soft Ferromagnetic Microwires at Ghz-Frequency for The Application of High-Performance Magnetic Sensory Devices

Thermal treatments of amorphous alloys are known to cause structural relaxation which is followed by an evaluation of the magnetic anisotropy and saturation magnetostriction. In this work we investigated the effect of annealing with a temperature close to the onset of the crystallization on the magnetic hysteresis properties of glass-coated amorphous microwires of Co-rich compositions with a nearly zero magnetostriction. The annealing process was performed on the wires by two methods: dc current annealing and conventional annealing in finance (at 475-490 oC for 30 min). The current intensities were chosen such to ensure similar annealing conditions. The annealing temperatures were higher than the Curie temperature (~360 oC) and slightly lower than the primary crystallization temperature (510 oC). We have demonstrated a sharp change in the shape of the magnetic hysteresis after annealing which is caused by the change in the magnetostriction. Typically, amorphous microwires of Co-rich compositions with negative magnetiostriction are regarded as excellent soft magnetic materials suitable for large and sensitive magnetoimpedance (MI) [1]. A well-defined circumferential anisotropy could be established in these wires by a proper choice of composition, geometry and annealing treatments, which increases the MI ratio up to hundred percent in characteristic fields of few Oersted [2]. The high sensitivity of impedance to low magnetic fields makes amorphous ferromagnetic microwires a promising material for the construction of different sensor systems. In the present work, the transformation of the sign of magnetostriction in amorphous microwires of composition: Co71Fe5B11Si10Cr3 (diameter: D/d = 29/25 µm) and Co66.6Fe4.28B11.51Si14.48Ni1.44Mo1.69 (diameter: D/d = 35/25 µm) was established after annealing in a narrow temperature range near the crystallization onset. This restores soft magnetic properties and ensures high temperature stability of all magnetic parameters. The wires under the study were produced by quenching and drawing technique (also referred to as modified Taylor-Ulitovskiy method). The choice of composition is justified by specific magnetoelastic properties with near zero magnetostriction of the order . It is known that annealing without applied stress can produce short-range order relaxation and consequently releases some frozen-in stresses and improves soft magnetic properties. In the present paper, we propose current and conventional annealing at relatively high temperatures slightly lower than the primary crystallization temperature. This causes nano crystallization and sharp change in the saturation magnetostriction. Therefore, we proposed a method of controllable change in magnetic anisotropy by changing the sign of magnetostriction. In particular, this results in a change in the shape of magnetic hysteresis and enhances the sensitivity of MI at microwave frequencies. The hysteresis loop of samples annealed by dc current and by conventional annealing are shown in Figures 1, 2. The annealing at temperatures higher than the Curie temperature increases the saturation magnetostriction and induces an axial easy anisotropy. A sharp change in the behavior of the hysteresis loops occurs after annealing with temperatures near the crystallization point, which can be explained by a change in the sign of the magnetostriction constant from small positive to large negative. Acknowledgment: This work was supported by the Russian Foundation for Basic Research (RFBR: 19-32-50097; 20-32-90145)

**References:**

[1] M. G. Nematov, I. Baraban, N.A. Yudanov at all, Journal of Alloys and Compounds, 837, 155584 (2020) [2] A. Zhukov and V. Zhukova, Nova Science Publishers, New York (2009)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2bbc7c20b4da82c458e9605dc6b74369.jpg)
Fig. 1. Hysteresis loops of amorphous Co71Fe5B11Si10Cr3 (diameter: D/d = 29/25 µm)microwires after dc current of which approximately corresponds to 490oC.

![](https://assets.underline.io/uploads/markdown_image/1/image/021e6e0bc8a907964c76b7edc22e8cfa.jpg)
Fig. 2. Hysteresis loops of amorphous Co71Fe5B11Si10Cr3 (diameter: D/d = 29/25 µm) microwires after annealing at furnace (475oC, 485oC, 490oC)

 Transformation of the Magnetostriction of Amorphous Microwires by Heat Treatment

Submicron and nanosized cylindrical amorphous Fe77.5Si7.5B15 and (Co0.94Fe0.06)72.5Si12.5B15 wires with diameters between 100 and 900 nm have been successfully cast by means of an upgraded variant of the glass-coated melt spinning technique [1]. Amorphous samples with both compositions show a magnetically bistable behavior, i.e., a single step axial magnetization reversal with a characteristic rectangular hysteresis loop. This reversal consists in the displacement of a 180-degree domain wall along the wire axis when the applied field is equal to or larger than the switching field. The values of the switching field are significantly different, with the positive magnetostrictive amorphous submicron wires (Fe77.5Si7.5B15) displaying one to two orders of magnitude larger values than the nearly zero magnetostrictive (Co0.94Fe0.06)72.5Si12.5B15 ones. This emphasizes the importance of the types and magnitudes of the intrinsic magnetic anisotropies. Here we report on the study of structural relaxation within the amorphous submicron wires using measurements of the 180-degree domain wall velocity, in order to gain deeper insights into the roles played by the various types of magnetic anisotropy in amorphous submicron wires with different magnetostriction, such as Fe77.5Si7.5B15 with the magnetostriction constant of 25 × 10-6 and (Co0.94Fe0.06)72.5Si12.5B15 with the magnetostriction constant of -1 × 10-7, respectively. The samples have been furnace annealed in vacuum at 200°C and 350°C for 1h, in order to induce structural relaxation phenomena in the amorphous phase without crystallization. Domain wall velocity measurements have been performed on as-cast and annealed samples with both compositions and different diameters, using a method developed specifically for such ultrathin cylindrical wires [2]. Fig. 1 shows the dependence of the domain wall velocity on the annealing temperature for highly magnetostrictive amorphous Fe77.5Si7.5B15 samples with diameters between 230 and 850 nm. Fig. 2 illustrates the same dependence in the case of nearly zero magnetostrictive (Co0.94Fe0.06)72.5Si12.5B15 samples with 300 and 770 nm in diameter, respectively. The domain wall velocity increases monotonically with the annealing temperature for all the highly magnetostrictive samples. The slope of the curves decreases with the increase in the wire diameter. This behavior originates in the stress relief that accompanies the structural relaxation and shows the important role played by the magnetoelastic anisotropy in the Fe77.5Si7.5B15 samples. The effect is more pronounced in the thinner samples, due to their stronger intrinsic magnetoelastic interaction. A completely different behavior has been observed in the nearly zero (Co0.94Fe0.06)72.5Si12.5B15 samples. For a wire with 770 nm in diameter, a monotonic decrease of the domain wall velocity with the annealing temperature was observed. For a thinner one, with 300 nm in diameter, a change of slope was observed: the wall velocity slightly increases after annealing at 200°C, and then drops below the value of as-cast sample after annealing at 350°C. This behavior is consistent with a diminished role of the magnetoelastic anisotropy and a more prevalent role of the shape anisotropy. Only the latter is important in the thicker sample. In the thinner one, the magnetoelastic anisotropy contributes to the magnetic behavior until a sufficiently large annealing temperature is used, so that the residual stresses are decreased. The results show that measuring the domain wall velocity of amorphous submicron wires with different magnetostriction constants can provide essential information on the structural relaxation effects by means of the dominant magnetic anisotropy type and its changes triggered by the low temperature annealing process. This analysis is important for the future application of cylindrical amorphous submicron wires. Acknowledgements - Work supported by the Romanian Executive Agency for Higher Education, Research, Development and Innovation Funding (UEFISCDI) under contract no. 511PED/2020 (project PN-III-P2-2.1-PED-2019-0586/NanoCyliCon).

**References:**

[1] T.-A. Óvári, N. Lupu, and H. Chiriac, Recent trends in magnetic nanowires and submicron wires prepared by the quenching and drawing technique, in Magnetic Nano- and Microwires (Second Edition), edited by M. Vázquez (Woodhead Publishing, Cambridge, 2020), pp. 221-253. [2] S. Corodeanu, H. Chiriac, and T.-A. Óvári, Accurate measurement of domain wall velocity in amorphous microwires, submicron wires and nanowires, Rev. Sci. Instrum. 82 (2011) 094701.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d460a15c063e392de7c341532897f628.jpg)
Fig. 1. Domain wall velocity vs. annealing temperature for highly magnetostrictive amorphous Fe77.5Si7.5B15 glass-coated submicron wires.

![](https://assets.underline.io/uploads/markdown_image/1/image/2b1a79db360ef8ca5113605e7160f667.jpg)
Fig. 2. Domain wall velocity vs. annealing temperature for nearly zero magnetostrictive amorphous (Co0.94Fe0.06)72.5Si12.5B15 glass-coated submicron wires.

 Correlation between Structural Relaxation and Magnetic Behavior in Amorphous Submicron Magnetic Wires

I. INTRODUCTION With the rapid development of new, ultra-low power spin-based devices such as magnetic random access memory (MRAM), spin logic, and so on, the magnetization dynamics in amorphous Co-Fe-B thin films has been studied intensively both from the fundamental and application points of view. In particular, a Gilbert damping constant (α), which describes the strength of damping torque, is one of the most important parameters to understand the dynamics. Until now, other groups reported α of amorphous Co-Fe-B thin films with various thicknesses and B compositions [1],[2], while details about the effect of Co compositions on α of these films have not been understood fully. In addition, the correlation between α and other magnetic parameters such as magnetic anisotropy, magnetostriction and so on still remains unclear. Herein, we evaluate the soft and high-frequency magnetic properties of Co–Fe–B thin films with various Co compositions, and discuss in detail the effect of Co composition on these magnetic properties of these films. III. EXPERIMENTAL PROCEDURES 10-nm thick CoxFe80-xB20 (Co–Fe–B) thin films (0 ≤ x ≤ 80) were fabricated by RF sputtering onto glass substrates. Co composition (x) was determined by energy dispersive x-ray spectroscopy (EDX) and the saturation magnetization estimated from VSM. The identification of the crystallographic structure of Co–Fe–B films was performed using the high-angle XRD analysis and TEM observation. These analyses indicated that every film structure is amorphous regardless of Co composition. The soft magnetic properties of Co–Fe–B films and the in-plane M–H curves were measured by VSM. The measurement of magnetostriction was performed using a thin-film magnetostriction measurement system (Toei Scientific Industrial Co., Ltd), which used an optical-cantilever method to detect sample deflection caused by magnetostrictive effect. The saturation magnetostriction (λs) of these films was evaluated using this system in an external magnetic field of 0.0 - +13.5 kA/m, which was sufficiently strong to magnetically saturate the films. The high-frequency magnetic properties were evaluated using a broadband ferromagnetic resonance (B-FMR) measurement technique with a coplanar waveguide (CPW) and a vector network analyzer (VNA). These measurements were performed at room temperature. III. RESULTS AND DISCUSSION Figure 1(a) shows the dependence of saturation magnetostriction (λs) on Co composition (x) for Co–Fe–B thin films. λs increased when Co composition increased up to 15 at.%, kept constant when Co composition was 15–40 at.%, and further decreased markedly when Co composition was above 40 at.%. This feature was almost similar to that of the Co-Fe–B bulk alloy, while their values were higher than those of these alloys [3]. The reason for this may be attributed to the compressive stress induced in the film plane during the film deposition. To understand the high-frequency magnetic properties of Co–Fe–B thin films, the parameters related to these properties [e.g., effective in-plane damping constant (α//) and magnetic inhomogeneous broadening at zero frequency (ΔH(0))] were estimated and are summarized in Fig. 1(b) as a function of Co composition (x). α// decreased to a minimum at the Co composition of 15 at.%, increased to approximately 0.0096 when Co composition was increased up to 30 at.%, again decreased to approximately 0.0062 for the Co composition between 40–50 at.%, and further markedly increased to a maximum at 80 at.%. The α// values for the Co composition of 30 and 80 at.% were twice or three times as high as those for other Co compositions, respectively. On the other hand, for ΔH(0), the trend was almost similar to that of α//. The values for the Co compositions of 30 and 80 at.% were much higher than those for other Co compositions. Therefore, these results suggest that the magnetic inhohmogeneities such as the anisotropic dispersion, two-magnon scattering, and so on mainly influences on the high-frequency magnetic properties of Co–Fe–B thin films. ACKNOWLEDGEMENT The authors thank Prof. Satoshi Okamoto, and Associate Prof. Nobuaki Kikuchi at Tohoku University for performing the photo lithography and measuring XRD diffraction patterns, and Mr. Osamu Mori, Mr. Takashi Oizumi, Mr. Shigeyuki Sato, and Mr. Ryoichi Utsumi of Toei Scientific Industrial Corporation for measuring magnetostriction. This work was supported in part by KAKENHI (JP17H03226) from MEXT, Japan. This work was supported in part by CSIS, CSRN, and CIES, Tohoku University. This work was also supported in part by the ASRC in Japan.

**References:**

[1] M. Oogane et al., Jpn. J. Appl. Phys. 45, 3889 (2006). [2] X. Liu et al., J. Appl. Phys. 110, 033910 (2011). [3] R.C. O’Handley, Solid State Comm. 21, 1119 (1977).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/61c7e0f4781eb9c38d8e77db3d1af2e9.jpg)
Fig. 1. (a) Dependence of saturation magnetostriction (λs) on Co composition (x) for Co–Fe–B thin films. The dotted line shows λs of the Co-Fe–B bulk alloy reported in Ref.[3]. (b) Change in the effective in-plane damping constant (α//) and magnetic inhomogeneous broadening at zero frequency (ΔH(0)) of Co–Fe–B thin films with Co composition (x).

 Study on the soft and high-frequency magnetic properties of amorphous Co-Fe-B thin films with various Co compositions

The magnetostrictive materials in the form of thin films have become increasingly vital in the development of actuators and sensors. Applying a strain to the magnetostrictive ferromagnet offers a degree of control over the material's magnetic anisotropy energy. In the recent past, there has been continued interest in having control of perpendicular magnetic anisotropy in the thin films through stain from piezoelectric material [1-4]. The induction of stain during the measurement allows the introduction of various strains. In addition, the measurement of the ensuing magnetic anisotropy changes permits an accurate calculation of magnetostriction. The magnetostriction constant λ is calculated from the changes of the magnetic anisotropy field induced by strain with applied stress. We report on our study of multilayers of Ta(3)/[Pt(2.3)/Co68Fe22B10(0.7)/Ir(0.5)]n/Pt(2.3) and Ta(3)/[Pt(2.3)/Co68B32(0.8)/Ir(0.5)]n/Pt(2.3) with perpendicular magnetic anisotropy deposited by dc magnetron sputtering onto a glass substrate. Here, the layer thicknesses are displayed in nm and ‘n’ is the number of Pt/CoFeB/Ir or Pt/CoB/Ir trilayer. The polar MOKE was used in the characterisation of all the samples to display perpendicular magnetic anisotropy due to a large interface contribution Fig.1.(a). Also, we measure the magnetic anisotropy using a technique based on the Anomalous Hall Effect. The anisotropy measurement was done under strain applied perpendicular to plane using a biaxial piezoelectric transducer. A voltage of 150 V applied to the transducer generates a maximum strain of ~0.1%. This results in a decrease of the perpendicular anisotropy field in the films up to 12 mT as shown in Fig.1.(b). The Pt/CoFeB/Ir and Pt/CoB/Ir magnetostriction constant is found from a least-squares fit of the change in anisotropy field as shown in Fig 1.(c).

**References:**

[1] Lee J-W et al., Appl. Phys. Lett. 82 2458 (2003). [2] Kim J-H et al., Appl. Phys. Lett. 97 252508 (2010). [3] Lei N et al., Phys. Rev. B 84 012404 (2011). [4] De Ranieri E et al., Nat. Mater. 12 808–14 (2013).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b52b61b3e21d63c56539635c9b5361a9.jpg)
Fig.1.(a) Polar MOKE measurement for [Pt/CoFeB/Ir]n and [Pt/CoB/Ir]n multilayers on glass substrates. (b) The change in the anisotropy field of Pt/CoFeB/Ir and Pt/CoB/Ir with different repeats is due to out-of-plane strain εz and the solid line is a fit of the data. (c) Magnetostriction constant of Pt/CoFeB/Ir and Pt/CoB/Ir with different repeats.

 Anisotropy field change with piezoelectric strain in ultrathin Pt/Co(Fe)B/Ir films

The giant magnetoimpedance (GMI) effect is the change of the total impedance under the application of an external DC field when alternating current flows through the ferromagnetic conductor. The three-layered film structure with a non-magnetic conductive center layer seems to be promising for future GMI sensor applications. Furthermore, it was reported that the meander structure allows one to improve the GMI effect of the sensor [1], and also can enhance the spatial resolution of the sensor [2]. However, the experimental and theoretical research concerning the influence of the meander structure on the GMI behavior in three-layered film is very limited, which needs further study. In this work, the three-dimensional physical models for NiFe/Cu/NiFe films with two different structures which are linear and meander are developed (as shown in Fig.1). Firstly, the magnetization process of the soft magnetic film of these structures is simulated by the Landau–Lifshitz equation for the magnetization motion. And then the electromagnetic distribution of these structures is calculated in the presented simulation model. Finally, we obtained the relationship between the impedance of the film and the applied magnetic field or excitation frequency. The influence of geometric parameters and structures of the films on the GMI is also analyzed. As shown in Fig.2(a), the GMI effect in meander structures appears to be much stronger compared with that in linear structure films, and the maximum values of the GMI ratio are more than 150% within the frequency range from 100MHz to 250MHz. For further analysis, Fig.2(b) shows the frequency dependence of the imaginary part of impedance (Im(Z)) with different values of the external magnetic field (Hext). It presents that the mutual inductance of each parallel line in the meander structure will reduce the total inductance and decrease frequency response. The results obtained could be useful both for a better understanding of the GMI effect of the meander structure film and for designing a high-sensitivity magnetic field sensor.

**References:**

[1] Rivero M A, Maicas M, Lopez E, et al. Influence of the sensor shape on permalloy/Cu/permalloy magnetoimpedance[J]. Journal of magnetism and magnetic materials, 2003, 254: 636-638. [2] Kikuchi H, Tanii M, Umezaki T. Effects of parallel and meander configuration on thin-film magnetoimpedance element[J]. AIP Advances, 2020, 10(1): 015334.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7c7c197018fb325bd7040721145b48bb.jpg)
Fig. 1 Schematic description of linear structure and meander structure FeNi/Cu/FeNi films.

![](https://assets.underline.io/uploads/markdown_image/1/image/87e34e1ac83aad278bdad7af5f00e35e.jpg)
Fig. 2 (a) The GMI ratio for linear and meander FeNi/Cu/FeNi films. (b) Frequency dependence of the imaginary part of impedance.

 Effect of Meander Structure on Magnetoimpedance Characteristics in FeNi/Cu/FeNi Films

Nanocrystalline materials are soft magnetic materials discovered by the Yoshizawa teamwork in 1988[1]. These materials are amorphous alloys which have been partially crystallized using rapid cooling technique. Their interesting magnetic high characteristics, such as high saturation flux density (Bs&gt;1.25 T), low coercivity (Hc &lt;10 A/m) and low dynamic losses, are owing to their two-phase nature nanosize randomly oriented Fe(Si) crystals in the amorphous matrix [2][3]. Ultra soft magnetic characteristics can be reached by applying a magnetic field during their thermal annealing which induces a field uniaxial anisotropy that allows controlling hysteresis loop shape [4][5]. A round hysteresis loop (R type) is obtained by applying a thermal annealing in the temperature range of 500-600°C, a flat B–H curve (F type) can be obtained by applying a transverse magnetic field during the thermal annealing, whereas a longitudinal magnetic field allows having a square hysteresis loop (Z type). The variety of B-H hysteresis loops makes these materials suitable for many applications operating whether with high permeability materials like transformers, current sensors, CEM filter and magnetic shielding or with low permeability like smoothing inductance and current transformers. In aircraft applications and electric vehicles industry, the compactness of electrical systems is very important to increase energy efficiency but this reduction of masse and volume exposes magnetic components to high temperatures and decreases their magnetic properties over time. There are several works deal with studying magnetic materials behavior under high temperature but few of them discuss the magnetic ageing (temperature+time) which is a very serious issue concerns many industries. The study presented in [6] is based on monitoring magnetic characteristics evolution under thermal ageing of two nanocrystalline nuances: µ30 000 (F type) and µ500 000 (R type). Many measurements have been done which proved that there were no microstructures changes to make correlation with the noticed ageing in both nuances. However, some of these measurements proved that the total anisotropic energy in the material has increased which lead to the following hypothesis; a new anisotropic energy was introduced during ageing process which disturbs the domain walls displacement and magnetic domains rotation[7]. The current work is based on studying nanocrystalline FeSiCuNbB magnetic behavior during thermal ageing at four temperatures (-55, 110, 150 and 200°C). The ageing study has been performed on high permeability µ1000 000 (Z type) toroidal wound cores where the magnetization process is determined by domain walls displacement. To monitor ageing evolution, quasi-static B-H loops were measured with applying a 300 mHz sinusoidal magnetic field. All the following characteristics were measured: coercive force Hc, maximal permeability µmax, saturation flux density Bs, hysteresis losses Phys and Ek the total anisotropic energy developed during the magnetization process. Finally, a comparison between nanocrystalline (Z type) ageing evolution and other nuances presented in work [6] will be analysed and discussed in paper.

**References:**

[1] Y. Yoshizawa, S. Oguma, and K. Yamauchi, “New Fe-based soft magnetic alloys composed of ultrafine grain structure,” J. Appl. Phys., vol. 64, no. 10, pp. 6044–6046 (1988). [2] G. Herzer, “Grain structure and magnetism of nanocrystalline ferromagnets,” IEEE Trans. Magn., vol. 25, no. 5, pp. 3327–3329 (1989). [3] S. Flohrer, R. Schäfer, and G. Herzer, “Magnetic microstructure of nanocrystalline FeCuNbSiB soft magnets,” J. Non. Cryst. Solids, vol. 354, no. 47–51, pp. 5097–5100 (2008). [4] K. Yoshizawa, Y. Yamauchi, “Effect of magnetic field annealing on magnetic properties in ultrafine crystalline Fe-Cu-Nb-Si-B Alloys,” IEEE Trans. Magn., vol. 25, no. 5, pp. 3324–3326 (1989). [5] Y. Yoshizawa and K. Yamauchi, “Induced Magnetic Anisotropy and Thickness Dependence of Magnetic Properties in Nanocrystalline Alloy ‘Finemet,’” IEEE Transl. J. Magn. Japan, vol. 5, no. 11, pp. 1070–1076 (1990). [6] A. Lekdim, L. Morel, and M. Raulet, “Magnetic ageing study of high and medium permeability nanocrystalline FeSiCuNbB alloys,” J. Magn. Magn. Mater., vol. 428, no. December 2016, pp. 260–268 (2017). [7] A. Lekdim, L. Morel, and M. A. Raulet, “Magnetic properties evolution of a high permeability nanocrystalline FeCuNbSiB during thermal ageing,” EPJ Appl. Phys., vol. 79, no. 2 (2017).

**Images:**

 Magnetic Properties Evolution During Thermal Ageing of High Permeability Nanocrystalline FeSiCuNbB Alloys Annealed with Longitudinal Field

Fe-based soft magnetic materials have been widely used in electrical devices, such as motors, transformers, and inductors, due to their high saturation magnetic flux density. These Fe-based materials generally have a cubic crystal structure with the &lt;100&gt; easy axis of magnetization and fairly high intrinsic crystalline anisotropy constants. Thus, in order to improve their soft magnetic properties, nano-crystalline Fe-based alloy ribbons have been fabricated by rapid solidification and subsequent annealing processes. Because nano-crystalline grains with isotropic and homogeneous microstructures are known to reduce the coercivity (HC) effectively. However, the saturation magnetization (MS) of nano-crystalline alloy ribbons is reduced by adding glass forming elements. Thus it is always required to increase the Ms of the Fe-based alloy ribbons without deteriorating their coercivity. Our previous study showed that Fe84.3B13.7C1Cu1 amorphous ribbons could be fabricated by the rapid solidification process (RSP) and their crystallization procedures during the subsequent annealing process were discussed in terms of the nucleation and crystal growth of a-Fe grains [1]. In these ribbons, square shaped Fe grains were found to be formed and the growth rate of them were shown to be too fast to control the grain size below the exchange length of Fe [2]. Thus, despite their high Fe concentration, the permeability of the ribbons was limited by their HC. This means that it is required to develop the method for inhibiting the grain growth rate and controlling the morphology of annealed Fe grains. In this paper, Fe82.3B13.7C1Cu1Nb2 as-quenched ribbons were fabricated and annealed to understand the effect of Nb addition on the magnetic properties and microstructures during the annealing process. In this experiment, the ingots of Fe82.3B13.7C1Cu1Nb2 alloy were prepared by an arc melt process. As-quenched alloy ribbons were fabricated by the RSP under Ar atmosphere. The thermal properties of the as-quenched ribbons were analyzed by a differential thermogravimetric analyzer (DTA, TG-DTA2000SA) at a heating rate of 10 oC/min under Ar atmosphere. The annealing process was conducted using a rapid thermal process (RTP, IA-1240) equipment. During RTP, the ribbons were heated at a heating rate of 80 oC/min under Ar atmosphere. The MS and HC were measured by a vibrating sample magnetometer (VSM, LakeShore 7410). The microstructures of samples were analyzed by X-ray diffractometer (XRD, D/MAX-2500/PC) with CuKa radiation and atom probe tomography (APT, LEAP 4000X HR) analysis. The APT samples were prepared in the form of needles of 6060200 nm using a focused ion beam (FIB, Helios nanolab G3 UC). The XRD and compositional analysis of as-quenched ribbons confirmed the successful fabrication of Fe82.3B13.7C1Cu1Nb2 amorphous ribbons with a thickness of 21 μm and a width of 2 mm. The average MS and HC of the amorphous ribbons, measured at 10 kG, were 150.2 emu/g and 0.42 Oe, respectively. The DSC analysis of the amorphous ribbons showed that the first exothermic peak (Tx1) started at 400 oC and its maximum peak intensity appeared at 420 oC. In addition, the secondary crystallization temperature of the ribbons was increased up to 550 oC. Compared to Fe84.3B13.7C1Cu1 amorphous alloy, the higher peak temperatures indicate that the addition of Nb element improved the thermal stability of the ribbons. Figure 1 shows changes in the magnetic properties of Fe84.3B13.7C1Cu1 and Fe82.3B13.7C1Cu1Nb2 as-quenched ribbons annealed at their own Tx1 with increasing the annealing time. As shown in the figure, the low Ms of Fe-B-C-Cu-Nb as-quenched ribbon confirms that the Nb addition effectively stabilize the thermal stability of the Fe-B-C-Cu ribbon. Despite the high thermal stability, the MS and HC values of the Fe-B-C-Cu-Nb ribbon are shown to be sharply increased after annealing for 60 seconds. However, as the annealing time increased further, the increasing rate of the HC sharply drops, which is much lower than that of the Fe-B-C-Cu ribbon. These changes in magnetic properties should be caused by that the Nb addition changes the crystal nucleation and growth rate of the as-quenched ribbon and the crystalline shape of Fe grains during the annealing. In order to understand the microstructural effect of the Nb addition, the compositional changes at the interfaces of amorphous/crystalline grain during the annealing were measured by APT and their elemental distributions with the annealing time are shown in Figure 2. These figures confirm that B and C atoms, known as amorphous forming elements, were continuously pushed out of the a-Fe grain with increasing the annealing time. On the other hand, Cu atoms are known to act as nucleation sites of nanocrystals but evenly distributed in the a-Fe grain and the amorphous matrix. However, the diffusion of Nb atoms into the matrix is clearly observed when the annealing time is longer than 300 sec. This Nb diffusion behavior in the annealing time is in well accord with the coercivity change of the Fe82.3B13.7C1Cu1Nb2 ribbon. The change in the morphology of the a-Fe grain behavior was also confirmed by TEM. These results clearly show the role of Nb atoms in the fabrication of nanocrystalline a-Fe grains and more detailed analysis results will be presented.

**References:**

[1] K. Lee, M. Choi, G. Lee, M. Kim, and J. Kim, "Changes in Microstructure and Magnetic Properties of Fe–B–Cu–C Ribbons According to Annealing Conditions," IEEE Transactions on Magnetics, vol. 55, no. 2, pp. 1-4, 2019. [2] H. Lashgari, D. Chu, S. Xie, H. Sun, M. Ferry, and S. Li, "Composition dependence of the microstructure and soft magnetic properties of Fe-based amorphous/nanocrystalline alloys: a review study," Journal of Non-Crystalline Solids, vol. 391, pp. 61-82, 2014.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6425dde224148ea7d23da2b73129c173.jpg)
Fig 1. Changes in the magnetic properties of Fe84.3B13.7C1Cu1 and Fe82.3B13.7C1Cu1Nb2 ribbons annealed at Tx1 for different annealing times

![](https://assets.underline.io/uploads/markdown_image/1/image/f44f6206d6b4f04273996415b8606716.jpg)
Fig 2. Changes in element distributions of the Fe82.3B13.7C1Cu1Nb2 ribbon at the interface during annealing

 Nb effects on the magnetic and microstructural properties of Fe-based nano-crystalline alloys

Due to high permeability, low coercivity, high resistivity, and low eddy current loss, amorphous and nanocrystalline materials with their excellent magnetic properties are attractive for high-frequency high-power applications, such as transformers, reactors and inverters to achieve high power density transmission. However, some electrical applications include inductors and transformers for multi-kilowatt power converters often necessary to add air gap in the magnetic core. The reasons are as follow: (a) reducing the equivalent permeability μre of the core, (b) increasing the excitation current for saturation, (c) effectively improve the anti-saturation ability of the core, (d) improve the capacity of the energy storage of magnetic components. The desired functions achieved from magnetic characteristic changes due to the air gap including: maintaining the stability of the inductance value of the reactor, increasing the power density of the inductor and the optimized design of the high frequency transformer, etc. Moreover, air gap may also increase the core loss. It is of great significance to study the magnetic properties of the cores with different air gaps. In this paper, dynamic magnetic properties of C-type amorphous (AMCC025) and nanocrystalline (F3CC0125) cores are measured with different air gap lengths (0-6mm) and frequencies (5-20 kHz) based on a novel designed magnetic tester. The tester can restrain the C-type core from six directions to ensure the stability of the testing sample. The air gap between the two cores can be accurately adjusted by the screw fixed on the precision displacement stage. The minimize air gap length can be fixed on 0.01mm. The effect of air gap length and frequency on the magnetic properties of different materials are compared. Moreover, the corresponding core losses of the samples in a wide range of frequency are analyzed. The traditional Steinmetz empirical formula is revised, and the core loss is calculated in sections according to the air gap length, and compared with experimental values. The hysteresis loops of the amorphous and nanocrystalline alloy cores at the same frequency of 20 kHz, different magnetic densities and different air gap lengths are shown in Fig. 1. As the air gap length increases, the slope of the B-H loops is reduced more and the slope of inclination is smaller slowly. Moreover, the effect of the air gap on the magnetic properties of nanocrystalline cores is more obvious than that of amorphous cores. It can be found that the nanocrystalline alloy is more sensitive to air gap than amorphous alloy due to its ultra-high relative permeability. According to the intensity of the fringing effect caused by the air gap length, two cases are concerned in the loss calculation. One is that the air gap is small enough to ignore the fringing effect, the other is that the air gap length is too large to ignore the fringing effect of the loss. Generally speaking, when lg/lc&lt;0.5%, where lg is the air gap length and lc is the equivalent magnetic circuit length, the influence of the fringing magnetic flux caused by the air gap on the inductance of the core can be ignored. But when lg/lc&gt;1.0%, due to the fringing diffusion of the air gap magnetic flux, the magnetic area of the air gap increases and the effective length of the air gap becomes shorter. Therefore, the influence of the fringing magnetic flux for core loss must be considered. Therefore, a modified Steinmetz empirical formula considering fringing flux is proposed, in which, the air gap length is used as a variable in the calculation and the precision is improved. Fig. 2. shows the variation in core loss density between the experimental and calculated results at given frequency with the different air gap lengths and magnetic flux densities. From the ratio of the air gap length to the magnetic circuit length, it can be seen that for amorphous core, the fringing effect does not need to be considered when the air gap length is less than 1 mm. Similarly, the air gap length boundary point of the nanocrystalline core is 1.6 mm. It can be seen that most of the calculated results well agree with the experimental results. The average percentage errors of the modified Steinmetz formular with fringing effect are all within 10% for amorphous and nanocrystalline core. It is proved that the influence of the fringing magnetic flux can be minimized under an optimized air gap length, and the loss will be reduced accordingly. Moreover, the modified Steinmetz formula can predict the core loss of the C-type core under different air gap lengths well. The modified core loss calculation model can provide theoretical guidance for the high frequency inductor and transformer cores design and optimization.

**References:**

[1] Ayachit, Agasthya, and M. K. Kazimierczuk, IET Circuits Devices & Systems, Vol. 11.3, p. 209-215(2017). [2] G. Calderon-Lopez, Y. Wang and A. J. Forsyth, IEEE Transactions on Power Electronics, vol. 34, p. 4656-4664, (2019). [3] Y. Wang, G. Calderon-Lopez, and A. J. Forsyth, IEEE Transactions on Power Electronics, vol. 32.6, p. 4683-4690(2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5e253abb3cdfd1c7e01071e5e2cc67f1.jpg)
Fig. 1. The hysteresis loops of core under different air gap lengths (B = 0.1T, f = 10kHz).

![](https://assets.underline.io/uploads/markdown_image/1/image/b96a64a85226ae002049ed8fcad7189c.jpg)
Fig. 2. Core loss under different magnetic density and air gap lengths at fixed frequency.

Temperature Dependence of Powder Cores Magnetic Properties for High Frequency Applications

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