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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 (B&lt;sub&gt;s&lt;/sub&gt;&amp;gt;1.25 T), low coercivity (H&lt;sub&gt;c&lt;/sub&gt; &amp;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].&lt;br/&gt;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.&lt;br/&gt;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.&lt;br/&gt;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].&lt;br/&gt;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 H&lt;sub&gt;c&lt;/sub&gt;, maximal permeability µ&lt;sub&gt;max&lt;/sub&gt;, saturation flux density B&lt;sub&gt;s&lt;/sub&gt;, hysteresis losses P&lt;sub&gt;hys &lt;/sub&gt;and E&lt;sub&gt;k &lt;/sub&gt;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).&lt;br/&gt;[2] G. Herzer, “Grain structure and magnetism of nanocrystalline ferromagnets,” IEEE Trans. Magn., vol. 25, no. 5, pp. 3327–3329 (1989).&lt;br/&gt;[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).&lt;br/&gt;[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).&lt;br/&gt;[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).&lt;br/&gt;[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).&lt;br/&gt;[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:**





INTERMAG 2021

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

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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:**

poster

Permanent Magnet Synchronous Machines (PMSM) have gradually become the mainstream solution for drive motors. One main trend for advanced PMSM optimization is focused on new material application. Conventional PMSM iron core is fabricated by Non Grain-Oriented (NGO) silicon steel sheet lamination, based on traditional technic, the high-strength NGO silicon steel uses solid solution strengthening and precipitation strengthening methods to enhance mechanical strength [1]. As mentioned in [2-3], due to the increase in mechanical strength of high-strength NGO steel, a narrower magnetic bridge design can be applied in the rotor design. Thereby reducing the leakage flux to increase the output torque and the overall efficiency. Even though the high-strength NGO had higher iron loss, counting the reduction in the rotor bridge width, the overall performance can be significantly enhanced. The maximum speed of advanced PMSM is mostly greater than 12000rpm, thus the rotor sustains significant tensile stress due to centrifugal force. It’s easier to form the striped 180° domain with higher permeability under tensile stress [4]. While the frequency influence and thermal condition has not been discussed in [4]. In this paper, we designed an equivalent sample to simulate the condition of an iron core, similarly in [5], with different excitation and manufacture parameter such as laminated number and thermal condition. Three types of high-strength NGO (SW35YS600\SW35YS900\B35AHS500) and a controlled group (conventional NGO B35A270) has been tested. Magnetic performance of equivalent sample is measured by ring sample method. Two narrow sides of the sample are subjected to large tensile stress concentration, the lamination number is 5, 10, and 20. At high excitation frequencies, the level of iron loss improvement caused by tensile stress is significant. Four materials have also been annealed respectively at 720°C for 10 hours under argon atmosphere. After annealing, the tensile stress has lower effect on the magnetic properties for B35AHS500 and B35A270, but is significant for SW35YS600 and SW35YS900. Therefore, it is speculated that a large proportion of heat treatment process has been adopted during SW35YS600 and SW35YS900. In addition, we also conduct metallographic experimental observations on the material of the sample and the tensile fracture, and analyze the reasons for this result at the grain level. And in the subsequent experiment process, we further explored the influence of different environmental temperatures and different tensile stresses on the magnetic properties of these four NGO materials.

**References:**

[1] GONG, Jian, and Hai-wen LUO. "Progress on the research of high-strength non-oriented silicon steel sheets in traction motors of hybrid/electrical vehicles." Journal of Materials Engineering 43.6 (2015): 102-112. [2] Tietz, Marco, et al. "Effects and advantages of high-strength non grain oriented (NGO) electrical steel for traction drives." 2013 3rd International Electric Drives Production Conference (EDPC). IEEE, 2013. [3] Tanaka, Ichiro, et al. "Application of high-strength nonoriented electrical steel to interior permanent magnet synchronous motor." IEEE transactions on magnetics 49.6 (2012): 2997-3001. [4] Senda, Kunihiro, et al. "Magnetic properties and domain structure of non-oriented electrical steel under stress." IJTFM 131.10 (2011): 884-890. [5] Gao, Lingyu, et al. "Application of grain-oriented electrical steel used in super-high speed electric machines." AIP Advances 10.1 (2020): 015127.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ccde1a3a9953b57d9bd60bd246980599.jpg)
metallographic experimental observations

![](https://assets.underline.io/uploads/markdown_image/1/image/793eec53db2c5ec9c61420c606acc711.jpg)
sample of the tensile experiment and result of the magnetic test

 Magnetic Performance Improvement caused by Tensile Stress in Equivalent Iron Core fabricated by High-Strength Non-Oriented Electrical Steel

Grain-oriented (GO) electrical steel sheets, as a core material used in power transformers broadly, often holed at particular and suitable regions to make the stacking of the sheet easier. The magnetic properties around the hole will be deteriorated, and the local magnetic domain structure will be impacted [1]. These phenomena will significantly influence the performance of the transformer [2]. It is necessary to accurately measure and study the influence of hole on local vector magnetic properties to optimize the core structure. Some studies use the search coils wound by drilling through the sample to analyze the flux orientations [3]-[4]. Yet the distributions of local magnetic properties around the hole have not been clarified. To obtain a more comprehensive and accurate distribution of local vector magnetic properties, and avoid damaging the sample to wind the search coils, the needle probes and double H-coils, which were discussed in [5] and [6], are adopted and developed. In this paper, a novel local magnetic property testing system using an accurately-movable B-H sensor is designed and constructed to study the local vector magnetic properties around the hole in a transformer type core made of grain-oriented electric steel sheets. The influence of sizes and positions of the holes on the properties is compared and analyzed at 50-400 Hz. In addition, the changes of the magnetic domain are observed and analyzed. Fig. 1 shows the local testing system with an accurately-movable B-H sensor and sample with 300 mm × 300 mm studied in this paper. The distance between the needles of B sensor is 3.5 mm, and H-sensor coil is 2 mm × 2 mm assembled using wire with 0.01 mm diameter. The number of turns is 600. The sensor is mounted to a XYZ-precise-positioning device, hence, the magnetic flux density, B, magnetic field strength, H, and core loss, P, of each point in the local area can be measured. Eight holes with diameter of D and interval of 100 mm are punched in the transformer sheets. W is the distance of the center of hole to the inner edge. Different D and W are studied in the paper. Single layer grain-oriented steel sheet (namely, B30P120) is tested. To study the vector magnetic properties around the hole, the square area (47 × 47 mm2) centered at the hole is measured and studied. The H = H (x, y), B = B (x, y) and P = P (x, y) are measured when the sensor is moved 1 mm in interval along the x-, or y-directions and the total number of measured points are 2000. As a criterion of measurements, the peak flux density is measured and controlled with a search coil, which wound uniformly around the sample. Fig. 2 shows P distributions around the hole with D = 4 mm and W = 25 mm when B is controlled to be 50 Hz sinusoidal waveform with 1.5 T amplitude. The domain structures at particular areas A1 and A2 are also shown in Fig. 2. The results show that the core loss P around the hole is much larger than that around points far to the hole. It could be attributed to the non-uniform flux density distributions, in particular, increasing flux density close to the hole. It is consistent with the observation of domain structure around the hole. The domain structure is disordered close to the hole due to strain introduced by hole punching while it is uniform at the point far to the hole. In addition, the distribution of the flux density B, field strength H, and core loss P around the hole with different diameters (D = 4, 6, 8, 10 mm) and different positions (W = 20, 25, 30 mm) are measured and analyzed in the flux density ranges of 0.1 – 1.5 T at 50 – 400 Hz. The experiment results show that the local B and H distributions are altered by the hole. The domain pattern is also restructured due to strain introduced by hole punching. As a result, the local losses are increased. In addition, the losses around the hole increase to 150 – 300 % compared with the losses at the far point depending on D value of 4 – 10 mm. However, the location of hole has minor influence on the losses, in particular, when the hole is located at the symmetrical position (W = 25 mm). In conclusion, small size of the hole and symmetrical position of the hole during stacking of the core can minimize the deterioration of local magnetic properties and improve the performance of the stacked electrical steel sheets ultimately.

**References:**

[1] T.Gunes, R. Schäfer and N.Derebasi, IEEE Transactions on Magnetics., Vol. 54, p.1-8 (2018) [2] G. teNyenhuis, S. Girgis and F. Mechler, IEEE Transactions on Power Delivery., Vol. 16, p.648-653 (2001) [3] T.Gunes, N.Derebasi and C.Erdonmez, IEEE Transactions on Magnetics., Vol. 51, p.1-4 (2015) [4] N Derebasi. C Erdonmez, Journal of Superconductivity and Novel Magnetism., Vol. 30, p.3309-3313 (2017) [5] S. Imamori, S. Aihara and H. Shimoji, Journal of Magnetism and Magnetic Materials., Vol. 500 (2020) [6] S Aihara, H Shimoji and T TodakaM, IEEE Transactions on Magnetics., Vol. 48, p.4499-4502 (2012)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dd07283974bbc51d0a8991dc1207b2ad.jpg)
Fig. 1.Novel local measurement system and measurement sample.

![](https://assets.underline.io/uploads/markdown_image/1/image/cf2651f0e011db64b56bc65193d42edc.jpg)
Fig. 2. Distributions of the core loss around the hole and magnetic domain structure at area A1, A2.

 Influence of Size and Position of Stacking-Hole on Local Vector Magnetic Properties of Grain-Oriented Steel Sheet

Introduction: Non-oriented silicon steel is widely used in the manufacture of motors and other equipments due to its excellent magnetic properties. In the production process, non-oriented electrical steel often needs to be punched to form the required shape. During the punching process the magnetic properties of silicon steel sheets will be deteriorated due to the mechanical stress [1-4]. As a result, the plastic deformation and residual stress emerge around the area of cutting edge, which have a significant impact on the magnetic properties and magnetic domain structure of electrical steel sheets. In this paper the effects of punching on the magnetic properties and magnetic domain structure of non-oriented electrical steel are studied. And the deterioration degree of the magnetic properties caused by different punching load are analyzed quantitatively. Ι Test samples and methods The test samples of cold-rolled non-oriented electrical steel B35A270 are punched on the precision punching machine by the 25-ton and 80-ton punching load, respectively. Then, two kinds of samples with a size of 49.5*49.5*0.35mm are obtained. The sample processed by 25 tons of punching load is denoted as sample A, and the one processed by 80 tons of punching load is denoted as sample B. The 2D magnetic properties measurement apparatus consists of two single C-shaped yokes, excitation windings and silicon steel sheet samples. An AC magnetic field with a frequency of 50 ~ 200Hz is applied along the rolling direction of the sample The samples supported by the sample holder are placed in the gap between the two yokes, and the yoke air gap matches the size of the sample. The sensing system is specially designed to measure the local magnetic properties in different position of the sample. In the sensing system, the micro-size H coil is wound on a 0.05mm thick PCB substrate with a length of 3mm to measure the H signal in the rolling direction of the sample. Two retractable B probes are fixed on a 1.5mm thick PCB with a spacing of 3.5mm to measure the B signal in the rolling direction of the sample. Taking the midline of the sample along the tangential direction as the measurement characteristic sampling line, the micro-size composite B-H sensor can be moved smoothly along the characteristic sampling line with a 2 mm distance step. ΙΙ Experimental results and analysis The core loss curves of the two samples measured at 50Hz sinusoidal signals are depicted in Fig.1 (a) and (b). The loss of the sample A increases by 0.9% ~ 15.25% in the range of 8 mm from the edge, especially in the range of 6 mm. The loss of the sample B increases by 6.8 % ~ 29.55%, while the deteriorated area expands to 14 mm. According to the Bertotti loss separation, the hysteresis, eddy current and excess loss coffficient are identified by the experimental results. It is concluded that the punching process cause an increase of the hysteresis loss. It can be attributed to plastic deformation and residual stress around the punching edge. The moving of magnetic domains can be hindered with the increase of the width of plastic deformation area. During the magnetization process, the movement resistance of the edge domain increases, so the hysteresis loss increases, which increases the iron loss of the sample. At the edge of the sample A, the magnatic coercivity increases by 5.5%, the magnetic remanence and permeability decreases by 11.7% and 29.2%. The magnatic coercivity increases by 24.3%, the remanence and the permeability decreases by 35.9% and 47.9% at the edge of the sample B. ΙΙΙ Observation of magnetic domain structure In order to investigate the mesoscopic properties of punching effect, the 8*8mm sample need to be prepared for Kerr microscope, which is cut by wire electrical discharge machining from the above sample A and B in the edge and center area of the samples.After sanding, mechanical polishing and other steps, shiny mirror-like samples are obtained. Using a Kerr microscope to observe the magnetic domains of the sample, as shown in Fig. 2(a), the center of the sample A is dominated by sheet-like magnetic domains, while there are a large number of labyrinth domains near the punching edge as shown in Fig. 2 (b). The size and shape of the domains also change. In addition, the magnetic domain in the center is parallel to the rolling direction, while the direction of the magnetic domain at the edge changes, which makes it difficult to magnetize. This leads to the increase of iron loss and the deterioration of magnetic properties. IV Conclusion Based on the local 2D magnetic measurement and magnetic domain observation, the magnetic properties of non-oriented electrical steel deteriorate by the punching processing. Furthermore, the deterioration degree of the magnetic properties become more significant by larger punching load.

**References:**

[1] Campos M F D , Sablik M J, and Landgraf F J G . Journal of Magnetism & Magnetic Materials., Vol.320, p.e377-e380(2008) [2] René Siebert, Wetzig A, and Beyer E. IEEE Electric Drives Production Conference., (2013) [3] Nakata T. IEEE Translation Journal on Magnetics in Japan., (2008) [4] Senda K , Ishida M, and Nakasu Y. Journal of Magnetism and Magnetic Materials., Vol.304, p.e513-e515, (2006)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2e1b0ece638ad406cd008f90715dcef9.jpg)
Fig.1 Core loss curves of sample A and B

![](https://assets.underline.io/uploads/markdown_image/1/image/b2c57ff57baf50342830843dfc45b66b.jpg)
Fig.2 Magnetic domain structure of sample A

 Effect of Punching on Magnetic Properties of Non-Oriented Electrical Steel

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.

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