France



Fluxgate sensors are among the most sensitive devices for the detection of weak magnetic fields (in the range of 10&lt;sup&gt;-6&lt;/sup&gt; T) with resolutions of 100 pT at room temperature [1]. In conventional configuration, a fluxgate magnetometer consists of two ferromagnetic cores around which two coils for excitation and two coils for detection are wound and differentially connected. The residence times difference (RTD) fluxgate sensor first proposed by Bruno Andò, et al [1] consist of a single soft ferromagnetic core and two coils (one for excitation and one for detection). The sensor detects the external magnetic field strength through its corresponding relationship with the residence times difference of the induced peeks that appear when the excitation field cycles the magnetization of the core. One of the materials showing potential for the development of RTD sensors is represented by the glass-coated microwires exhibiting large Barkhausen effect, i.e., magnetization switching in a single step when the external excitation field is reversed. Recently, a new method to switch the axial magnetization in bistable glass-coated microwires has been reported [2, 3]. The method, detailed in [2], consists in applying a current directly through a magnetic sample subjected to controlled torsion.&lt;br/&gt;Using this method as a basis, we report here the development of a new RTD magnetic sensor that does not require an excitation coil. The sensor electronics was built using a dsPIC microcontroller which generates the signal for sensor excitation and measures the time difference between induced peaks (Fig.1). The time resolution of the electronics is about 1/(384x10&lt;sup&gt;6&lt;/sup&gt;) s. The sensor performance was studied comparatively using as sensitive elements glass-coated microwires with nominal compositions of the magnetic core Fe&lt;sub&gt;77.5&lt;/sub&gt;Si&lt;sub&gt;7.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt;, Co&lt;sub&gt;68.18&lt;/sub&gt;Fe&lt;sub&gt;4.32&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; and Fe&lt;sub&gt;73.5&lt;/sub&gt;Si&lt;sub&gt;13.5&lt;/sub&gt;B&lt;sub&gt;9&lt;/sub&gt;Cu&lt;sub&gt;1&lt;/sub&gt;Nb&lt;sub&gt;3&lt;/sub&gt; (FINEMET), having metallic core diameters (Φ&lt;sub&gt;metal&lt;/sub&gt;) of 10, 20 and 30 mm, respectively, and 7 mm glass coating thickness.&lt;br/&gt;The transfer functions (time difference versus applied field) were measured for different configuration of the sensor excitation current and torsion values.&lt;br/&gt;The value of the sensor sensitivity (S) decreases, and the dynamic range (DR) increases when the excitation current amplitude (I) increases. For annealed Co&lt;sub&gt;68.18&lt;/sub&gt;Fe&lt;sub&gt;4.32&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; microwires, having a metallic core diameter of 20 μm, we obtained a sensitivity value of 84 μs/(A/m), with a dynamic range of 17 A/m, for an excitation current amplitude of 10 mA. For an excitation current with an amplitude of 40 mA we obtained a sensitivity value of 11.7 μs /(A/m) and a dynamic range of 180 A/m. For current amplitudes of 50 mA and above, the dynamic range decreases due to the fact that the induced peaks become poorly defined, with low amplitudes, and cannot be easily distinguished by the electronic detection system.&lt;br/&gt;The annealed Co&lt;sub&gt;68.18&lt;/sub&gt;Fe&lt;sub&gt;4.32&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; microwires show wider measuring range and higher linearity of the transfer function as compared to all the other analyzed compositions (DR = ± 130 A/m for Φ&lt;sub&gt;metal&lt;/sub&gt; = 20 μm and I=30 mA). The Fe&lt;sub&gt;77.5&lt;/sub&gt;Si&lt;sub&gt;7.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; microwires show a fairly high noise on the measured transfer graph and lower dynamic range as compared to the Co&lt;sub&gt;68.18&lt;/sub&gt;Fe&lt;sub&gt;4.32&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; microwires (DR = ± 32 A/m for Φ&lt;sub&gt;metal&lt;/sub&gt; = 20 μm and I=30 mA). The annealed Fe&lt;sub&gt;73.5&lt;/sub&gt;Si&lt;sub&gt;13.5&lt;/sub&gt;B&lt;sub&gt;9&lt;/sub&gt;Cu&lt;sub&gt;1&lt;/sub&gt;Nb&lt;sub&gt;3&lt;/sub&gt; wires show an extremely low linear variation transfer function (± 9 A/m for Φ&lt;sub&gt;metal&lt;/sub&gt; = 20 μm and I=30 mA) as compared to the other compositions analyzed.&lt;br/&gt;For annealed Co&lt;sub&gt;68.18&lt;/sub&gt;Fe&lt;sub&gt;4.32&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; microwires with different core diameters, we observed that for the same excitation current of 30 mA and the same torsion of 483 Rad/m, the sensitivity of the sensor decreases from 27.7 μs/(A/m) for wires with a diameter of 10 μm, to 12.7 μs/(A/m) for wires having 30 μm in diameter, the dynamic range increasing at the same time from 41 A/m for wires with 10 μm in diameter, to 200 A/m for the samples with 30 μm in diameter (Fig 2). This behavior follows the evolution of the switching field of the same samples, which decreases from 45 A/m for wires with a diameter of 10 μm to 21 A/m for wires with a diameter of 30 μm.&lt;br/&gt;The influence of torsion on the transfer function of the sensor is relatively low. Thus, for Co&lt;sub&gt;68.18&lt;/sub&gt;Fe&lt;sub&gt;4.32&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; wires with a diameter of 30 μm we obtained a sensitivity of 12 μs/(A/m) for a torsion of 120 Rad/m (one end rotation of 45&lt;sup&gt;0&lt;/sup&gt; on a wire with a length of 6.5 mm) and 12.7 μs/(A/m) for 483 Rad/m (one end rotation 180&lt;sup&gt;0&lt;/sup&gt; on a wire with a length of 6.5 mm). For higher torsion values, a sharp decrease in field sensitivity is observed, most likely due to the strong increase of the mechanical stresses induced in the wire.&lt;br/&gt;&lt;br/&gt;Work supported by the Nucleu Programme (Project PN 19 28 01 01) and Contract No. 11PFE/16.10.2018 financed by the Romanian Ministry of Education and Research.

**References:**

1. B. Andò, S. Baglio, A.R. Bulsara et al., IEEE Instrum Meas Mag, Vol.8(4), 2005&lt;br/&gt;2. S. Corodeanu, H. Chiriac, A. Damian et al., Scientific Reports, Vol. 9, No. 5868, 2019.&lt;br/&gt;3. V. Zhukova, J. M. Blanco, A. Chizhik et al., AIP Adv. 7, 056026, 2017.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bfb14137e3ddfb99b934821adb3b5624.jpg)
Fig. 1. Schematic representation (a) and picture (b) of the RTD fluxgate sensor and the typical output voltage for a sinusoidal excitation signal (c).

![](https://assets.underline.io/uploads/markdown_image/1/image/232054e41dfbb608104ce6b41997f805.jpg)
&lt;!--[endif]----&gt;&lt;!--[endif]----&gt;&lt;!--![endif]----&gt;&lt;!--![endif]----&gt;Fig. 2. The transfer graph obtained for Co&lt;sub&gt;68.18&lt;/sub&gt;Fe&lt;sub&gt;4.32&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; microwires, annealed at 300&lt;sup&gt;0&lt;/sup&gt;C-1h, having different diameters of the metallic core.&lt;!--[endif]----&gt;&lt;!--[endif]----&gt;&lt;!--![endif]----&gt;&lt;!--![endif]----&gt;

INTERMAG 2021

 RTD fluxgate sensors based on current induced magnetization reversal in twisted glass-coated microwires

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Fluxgate sensors are among the most sensitive devices for the detection of weak magnetic fields (in the range of 10-6 T) with resolutions of 100 pT at room temperature [1]. In conventional configuration, a fluxgate magnetometer consists of two ferromagnetic cores around which two coils for excitation and two coils for detection are wound and differentially connected. The residence times difference (RTD) fluxgate sensor first proposed by Bruno Andò, et al [1] consist of a single soft ferromagnetic core and two coils (one for excitation and one for detection). The sensor detects the external magnetic field strength through its corresponding relationship with the residence times difference of the induced peeks that appear when the excitation field cycles the magnetization of the core. One of the materials showing potential for the development of RTD sensors is represented by the glass-coated microwires exhibiting large Barkhausen effect, i.e., magnetization switching in a single step when the external excitation field is reversed. Recently, a new method to switch the axial magnetization in bistable glass-coated microwires has been reported [2, 3]. The method, detailed in [2], consists in applying a current directly through a magnetic sample subjected to controlled torsion. Using this method as a basis, we report here the development of a new RTD magnetic sensor that does not require an excitation coil. The sensor electronics was built using a dsPIC microcontroller which generates the signal for sensor excitation and measures the time difference between induced peaks (Fig.1). The time resolution of the electronics is about 1/(384x106) s. The sensor performance was studied comparatively using as sensitive elements glass-coated microwires with nominal compositions of the magnetic core Fe77.5Si7.5B15, Co68.18Fe4.32Si12.5B15 and Fe73.5Si13.5B9Cu1Nb3 (FINEMET), having metallic core diameters (Φmetal) of 10, 20 and 30 mm, respectively, and 7 mm glass coating thickness. The transfer functions (time difference versus applied field) were measured for different configuration of the sensor excitation current and torsion values. The value of the sensor sensitivity (S) decreases, and the dynamic range (DR) increases when the excitation current amplitude (I) increases. For annealed Co68.18Fe4.32Si12.5B15 microwires, having a metallic core diameter of 20 μm, we obtained a sensitivity value of 84 μs/(A/m), with a dynamic range of 17 A/m, for an excitation current amplitude of 10 mA. For an excitation current with an amplitude of 40 mA we obtained a sensitivity value of 11.7 μs /(A/m) and a dynamic range of 180 A/m. For current amplitudes of 50 mA and above, the dynamic range decreases due to the fact that the induced peaks become poorly defined, with low amplitudes, and cannot be easily distinguished by the electronic detection system. The annealed Co68.18Fe4.32Si12.5B15 microwires show wider measuring range and higher linearity of the transfer function as compared to all the other analyzed compositions (DR = ± 130 A/m for Φmetal = 20 μm and I=30 mA). The Fe77.5Si7.5B15 microwires show a fairly high noise on the measured transfer graph and lower dynamic range as compared to the Co68.18Fe4.32Si12.5B15 microwires (DR = ± 32 A/m for Φmetal = 20 μm and I=30 mA). The annealed Fe73.5Si13.5B9Cu1Nb3 wires show an extremely low linear variation transfer function (± 9 A/m for Φmetal = 20 μm and I=30 mA) as compared to the other compositions analyzed. For annealed Co68.18Fe4.32Si12.5B15 microwires with different core diameters, we observed that for the same excitation current of 30 mA and the same torsion of 483 Rad/m, the sensitivity of the sensor decreases from 27.7 μs/(A/m) for wires with a diameter of 10 μm, to 12.7 μs/(A/m) for wires having 30 μm in diameter, the dynamic range increasing at the same time from 41 A/m for wires with 10 μm in diameter, to 200 A/m for the samples with 30 μm in diameter (Fig 2). This behavior follows the evolution of the switching field of the same samples, which decreases from 45 A/m for wires with a diameter of 10 μm to 21 A/m for wires with a diameter of 30 μm. The influence of torsion on the transfer function of the sensor is relatively low. Thus, for Co68.18Fe4.32Si12.5B15 wires with a diameter of 30 μm we obtained a sensitivity of 12 μs/(A/m) for a torsion of 120 Rad/m (one end rotation of 450 on a wire with a length of 6.5 mm) and 12.7 μs/(A/m) for 483 Rad/m (one end rotation 1800 on a wire with a length of 6.5 mm). For higher torsion values, a sharp decrease in field sensitivity is observed, most likely due to the strong increase of the mechanical stresses induced in the wire. Work supported by the Nucleu Programme (Project PN 19 28 01 01) and Contract No. 11PFE/16.10.2018 financed by the Romanian Ministry of Education and Research.

**References:**

1. B. Andò, S. Baglio, A.R. Bulsara et al., IEEE Instrum Meas Mag, Vol.8(4), 2005 2. S. Corodeanu, H. Chiriac, A. Damian et al., Scientific Reports, Vol. 9, No. 5868, 2019. 3. V. Zhukova, J. M. Blanco, A. Chizhik et al., AIP Adv. 7, 056026, 2017.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bfb14137e3ddfb99b934821adb3b5624.jpg)
Fig. 1. Schematic representation (a) and picture (b) of the RTD fluxgate sensor and the typical output voltage for a sinusoidal excitation signal (c).

![](https://assets.underline.io/uploads/markdown_image/1/image/232054e41dfbb608104ce6b41997f805.jpg)
Fig. 2. The transfer graph obtained for Co68.18Fe4.32Si12.5B15 microwires, annealed at 3000C-1h, having different diameters of the metallic core.

poster

Ferrimagnetic films of rare earth-transition metal (RE-TM) alloys are successfully used as an effective source of internal magnetic bias in exchange-coupled magnetically hard/soft bilayers, including those which demonstrate a hysteresis-free magnetization process. The last feature is in demand for many applications, for example, magnetic sensors [1]. It is known that the magnetic properties of RE-TM films are largely determined by their chemical composition. In particular, amorphous Tb-Co films with the Tb content in the range of 15-40 at. % can display a perpendicular magnetic anisotropy [2]. Within a certain temperature range, the shape anisotropy becomes dominant, and the magnetization orients in the film plane. Thus, the spontaneous spin reorientation transition takes place [3]. Therefore, in these exchange-spring systems, the magnetizations of adjacent soft magnetic and hard magnetic layers can lie in the plane of the film, be perpendicular to the plane, or be orthogonal to each other. Models of the magnetization reversal processes for both planar and perpendicular exchange-spring systems are successfully developed [1,4,5]. At the same time, the reason for the onset of exchange interaction between layers, the magnetizations of which are orthogonal to each other, is not entirely clear. Several models have been proposed to explain this phenomenon. Within one of them, the RE-TM layer is considered as a heterophase system, the magnetizations of different phases are oriented parallel or perpendicular to the film plane [6]. The second model assumes that there is a transition region in the RE-TM layer, within which a gradual reversal of spins occurs from an orientation parallel to the interface of the layers to a perpendicular one [7]. The third model assumes that the exchange bias effect originates from the chiral spin texture of the interfacial domain wall. The creation of the chiral interfacial domain wall is a consequence of the interplay between Dzyaloshinskii-Moriya-interaction in Dy-Co and ferromagnetic exchange coupling between the Ni-Fe and Dy-Co layers [8]. Investigation of changes in the magnetic properties of hard/soft bilayers near the spin reorientation transition of ferrimagnetic hard layer can provide additional information on the exchange bias mechanism in the systems with orthogonal orientation of layer magnetizations. This work presents the results of a study of the magnetic properties of exchange-coupled Tb-Co/FeNi films with different composition of Tb-Co layer in a wide temperature range. Ta(5 nm)/Tb-Co(20 nm)/FeNi(40 nm)/Ta(5 nm) multilayered films were prepared by magnetron sputtering. The films were deposited on Corning glass substrates in the presence of a constant magnetic field of 250 Oe oriented in the plane of the substrate. Magnetic measurements of the multilayered films were carried out in the temperature range of 5-350 K by means of MPMS-XL7 and PPMS DynaCool 9T devices. It was found that a relatively small change in the composition of the Tb-Co layer results in a sizeable change in the hysteresis loops of bilayers measured both along and perpendicular to the plane of the samples (Fig. 1). A change in the temperature of the sample is accompanied by a change in the sequence of magnetization reversal of the layers. In addition, at a certain temperature, the value of which depends on the composition of the Tb-Co layer, instead of layer-by-layer switching, magnetization reversal of the Tb-Co/FeNi film occurs as a whole structure magnetization reversal. An analysis of the obtained results suggests that in the course of deposition of the Tb-Co layer onto the FeNi layer, an interlayer magnetic boundary is formed, the parameters of which depend on the composition of the Tb-Co layer. The features of this boundary determine the value of the exchange bias and its temperature dependence. This work was financially supported by the Russian Science Foundation (RSF), project No. 18-72-10044.

**References:**

[1] C. Vogler, M. Heigl, A.-O. Mandru, et al. Phys. Rev. B 102 (2020) 014429. [2] K. Umadevi, A. Talapatra, J. Arout Chelvane, et al. J. Appl. Phys. 122 (2017) 065108. [3] V.O. Vas’kovskii, A.N. Gor’kovenko, et al. Phys. Met. Metallogr. 120 (2019) 1055. [4] E.E. Fullerton, J.S. Jiang, S.D. Bader. J. Magn. Magn. Mater. 200 (1999) 392. [5] D. Chumakov, R. Schäfer, D. Elefant, et al. Phys. Rev. B 66 (2002) 134409. [6] G.I. Frolov, V.Yu. Yakovchuk, et al. Tech. Phys. 50 (2005) 1605. [7] W.C. Cain, M.H. Kryder. J. Appl. Phys. 67 (1990) 5722. [8] K. Chen, A. Philippi-Kobs, V. Lauter, et al. Phys. Rev. Appl. 12 (2019) 024047.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7db57c54aa8f8588e53c294b6b60f8c0.jpg)
Figure 1. The hysteresis loops measured at T = 5 K in the field oriented along (a,b,c) and perpendicular (d,e,f) to film plane for Tb-Co/FeNi films with different Tb-Co layer composition.

 Spin reorientation transition and exchange bias in hard/soft Tb-Co/FeNi films

A model of exchange bias in polycrystalline bilayers based on a thermal fluctuations [1] was extended to account for an arbitrary magnetization angle of the FM layer. It allows a more accurate description of the behavior of the thermally activated reversal of the Néel vector of a grain since the extended model takes into account a variation of barrier height relative to the magnetization angle of the FM layer. Field annealing (setting of the exchange bias) and further relaxation of the FM/AFM bilayer was simulated using a sequence of iterations based on this model. At each iteration step we tracked the average value of exchange bias field amplitude and its angle, until a convergence was reached. We defined the array of grains in an AFM layer as having a lognormal distribution of grain volumes [2] and a uniform in-plane distribution of the uniaxial anisotropy axis. We have chosen the parameters of the lognormal distribution based on the fit to the experimentally-measured temperature dependence of exchange bias in our FM/AFM samples. We observed a small angle deviation from the initial field annealing direction due to the relaxation of exchange bias in a finite ensemble of AFM grains. Applying a relatively strong magnetic field at an angle to exchange bias (i.e. non-collinear depinning) for a certain time and then releasing it, gives rise to a shift of the final angle of exchange bias and a slight variation of its amplitude. Generally, the direction of the exchange bias is more affected by the FM layer non-collinear depinning than its amplitude, which recovers within a certain time interval upon release of the external field. Sweeping the angle of applied field from - to and back we observed the hysteretic behavior of exchange bias. Again, the exchange bias angle is mainly affected, rather than its amplitude. Angular variation of the exchange bias degradation and its time, field and temperature dependencies were also simulated and analyzed in the framework of this extended model.

**References:**

[1] H. Xi and R. M. White, J. Appl. Phys. 94, 5850 (2003). [2] K. O’Grady, L. E. Fernandez-Outon, and G. Vallejo-Fernandez, J. Magn. Magn. Mater. 322, 883 (2010).

**Images:**

 Angular deviation of the exchange bias in bilayer CoFe/IrMn under rotating magnetic field

High-pressure torsion (HPT) as a severe plastic deformation (SPD) technique is a well-known method of material processing [1,2]. A key feature of SPD techniques per se is the constancy of sample’s volume and shape during the deformation process and therefore allowing the production of nanocrystalline samples exhibiting bulk dimensions. One of its further advantages is the avoidance of many processing limits of binary and ternary systems that exhibit large miscibility gaps in their thermodynamic equilibrium. It allows the production of alloys with non-equilibrium compositions at low temperatures [3]. In this study, different compositions of Fe and Cr are processed with the principal goal of having a bulk material of alternating phases of ferromagnetic Fe and antiferromagnetic Cr on the nanoscale, enabling exchange bias. By HPT, the production of a supersaturated nanocrystalline FeCr alloy is possible. During a subsequent annealing treatment, decomposition might occur in closely spaced phases of separated Fe and Cr. Thus, it offers the possibility to induce exchange bias phenomena after field cooling below the Néel temperature. The nanocrystalline microstructure of the HPT-deformed samples increases the amount of interfaces; thus, increasing the effect. In a previous study of Weissitsch et al. [4] on Fe-Cr materials, it has been shown that homogeneous nanocrystalline microstructures can be produced by HPT at room temperature for compositions inside the miscibility gap. The nanocrystalline nature of the material and the identical crystal structure of Fe and Cr at room temperature (body centred cubic) with almost identical lattice parameters, make the microstructural investigation of the HPT-deformed material very challenging. Synchrotron results are ambiguous in peak deconvolution due to peak broadening and the above mentioned similarity in crystal structure. Scanning electron microscopy, including space-resolved chemical characterization, is difficult to perform due to the strongly refined microstructure. Still, the initial state has to be characterized before any further annealing treatments. An alternative characterization way is the measurement of magnetostrictive properties of the as-deformed alloys. Bormio-Nunes et al. [5] measured a large, positive magnetostriction for arc-melted supersaturated single phase FeCr alloys with up to 30 at% Cr. An increase in saturation magnetostriction with increasing Cr-content is further reported. Thus, it is of interest to study magnetostrictive properties of materials with even higher Cr-content. The saturation magnetostriction of Fe with 30% Cr (3/2λs ~ +30 to +70 ppm) found in [5], is slightly higher compared to our measurements (see Figure 1), bearing in mind the completely different involved microstructures. In the present study, the maximum saturation magnetostriction is found for 30 at% Cr as well. For an even higher Cr content of 50at%, a positive but decreasing saturation magnetostriction was measured. For a material only containing 30at%Fe, magnetostriction is about zero, which is in accordance with the very small values reported on pure Cr [6]. Due to this findings, the largest magnetostriction would have to be searched for compositions close to 30 at% Cr. Figure 1 depicts the pronounced difference magnetostrictive behaviour of FeCr compared with of pure Fe (3/2λs ~ -14 ppm). Thus, it can be stated that Fe and Cr are in a supersaturated state after HPT deformation at room temperature. To achieve an exchange bias coupled material, an improved understanding of the decomposition behaviour of the HPT-deformed FeCr alloys is crucial. Therefore, the influence of annealing treatments on the microstructural evolution and magnetostrictive properties is further investigated in this study. Annealed samples (1h at 500°C) do not show pronounced changes in magnetostrictive behaviour, i.e. the supersaturated state seems to prevail. To achieve the goal of exchange coupling, a proper concatenation of annealing treatments at even higher temperatures and subsequent HPT-deformation, producing a nanocrystalline microstructure again, is the next step. This study demonstrates that magnetostrictive measurements are an efficient tool to characterize the microstructure of nanocrystalline FeCr alloys deformed by HPT deformation, which are difficult to investigate by other techniques. Large magnetostriction is found in the as-deformed and annealed states of Fe-rich materials. HPT deformation combined with subsequent annealing treatments is a first step towards processing of Fe-Cr composites showing exchange bias phenomena. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 757333).

**References:**

[1] R. Valiev, R. Islamgaliev, I. Alexandrov, Progress in Materials Science. 45 (2000) 103–189. [2] R. Pippan, S. Scheriau, A. Taylor, M. Hafok, A. Hohenwarter, A. Bachmaier, Annual Review of Materials Research. 40 (2010) 319–343. [3] K.S. Kormout, R. Pippan, A. Bachmaier, Advanced Engineering Materials. 19 (2017). [4] L. Weissitsch, M. Stückler, S. Wurster, R. Pippan, A. Bachmaier, Materials Science Forum. 1016 (2021) 1603–1610. [5] C. Bormio-Nunes, J.P. Serra, F.S. Barbosa, M.B.S. Dias, R.S. Turtelli, M. Atif, R. Grossinger, IEEE Trans. Magn. 52 (2016) 1–4. [6] E.I. Kondorskii, T.I. Kostina, V. Yu. Galkin, Sov. Phys. JETP 42 (890) 890-891.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c218e9438d71e8e2fddeb74c82210c55.jpg)
Figure 1: Magnetostriction as a function of applied field, measured for HPT-deformed FeCr materials, spanning the composition range from 30at% to 70at% Fe. A comparison with the markedly different magnetostrictive behaviour of pure Fe is given.

 Severe plastically deformed, supersaturated FeCr alloys – a candidate material for exchange bias and enhanced magnetostriction

We study the extrinsic factors influence on FMR LW in polycrystalline systems F/AF with exchange bias, by varying AF layer thickness for different sequence of F and AF layers deposition. We observe that the exchange bias has a negligible effect on FMR LW. Instead, the contributions of uniaxial anisotropy, microstructure and F/AF interface roughness can be of major extrinsic factors. Using DC magnetron sputtering, Ta(30nm)/NiFe(10nm)/IrMn(tAF)/Ta(30nm) (TS) and Ta(30nm)/IrMn(tAF)/NiFe(10nm)/Ta(30nm) (BS) multilayers on silicon substrate were prepared with the AF thickness tAF = 10, 20, 30 and 40 nm. A permanent in-plane magnetic field of 420 Oe was applied during the deposition. Sample surface morphology was investigated by atomic force microscopy to obtain the mean square roughness σrms. The magnetic characteristics were investigated using FMR at a constant frequency ω/2π = 9, 65 GHz and with magnetic field H directed along the sample surface and scanned in the range up to 6 kOe. The main magnetic characteristics of the samples were obtained from the angular dependences (AD) of the resonant magnetic field, Hr(α),where α is the angle between the direction of the FMR field and the direction of the magnetic field applied during the deposition of the sample. Despite some quantitative differences, the qualitative form of the dependency of the exchange bias on the AF layer thickness is the same for both TS and BS structures. However, there is a significant discrepancy in the widths of the FMR lines for TS and BS structures: ΔHTS is smaller than ΔHBS. In addition, in the case of TS, the values of ΔH for α = 0o and α = 90o coincide within the experimental accuracy and synchronously repeat the variations with thickness. These observations indicate that the effect of the exchange bias on the FMR LW is negligible small compared to the influence of other factors. The roughness, σrms, for TS samples is greater than for BS, the dependence σrms,(tAF) is nonmonotonous and is in antiphase for TS and BS structures. The effect of the sample surface roughness on the FMR LW is quite noticeable. The experimental data can be approximated for TS samples by the dependence ΔHTS ~ (σrms S)1/3 , where S is the average area of defects and the FMR line width is propotional to the average linear size of defects on TS sample surface. This tendency is qualitatively consistent with the known results [1], where a linear relationship between ΔH and the pore radius on the sample surface was predicted. In BS samples, as compared with TS, the picture is quite different. The roughness is weaker while the LW is larger. That assumes that the roughness does not play a dominant role in LW of BS samples. Evidently, the features of the layers growth lead to different magnetic properties of AF/F and F/AF samples at the same chemical content of the F and AF layers. When the F layer grows on the AF layer, the microstructure of the AF layer can affect the properties of the F layer deposited on it. An increase in the AF layer thickness can lead, for example, to an increase in the size of AF grains in the bulk and at the AF/F interface. The F layer deposited on top takes on a typical AF grain size, i.e., the F grain size, possibly, increases with increasing AF layer thickness. In this case, the uniaxial magnetocrystalline anisotropy HK becomes the dominant factor affecting the broadening ΔH. Taking into account that the samples have a polycrystalline structure, we assume that the approximation of strongly bonded grains with HK &lt;&lt; 4πMs works. In this approximation, a polycrystal is regarded as a homogeneous medium with an inhomogeneous effective field, which is affected by the presence of grains with different crystallographic orientations. The magnetic fluctuations of the grains are coupled to each other through demagnetizing fields [2], which leads to uncompensated crystallographic anisotropy, which enhances uniaxial anisotropy and causes smooth spatial oscillations of magnetization. Spatially fluctuating magnetization, the so-called “micromagnetic ripple” observed in Lorentz transmission microscopy [3, 4], correlates with the grain size [3] and can be, if not the main, then an important additional source of broadening of the FMR line [5]. We show that FMR LWs in the BS samples decrease with increase of AF layer thickness, approximately, as 1/tAF β, with β = 2±1 and the difference in LW values measured along HA and EA in BS samples varies proportionally to the square of HK.

**References:**

1. M. Sparks, R. Loudon, and C. Kittel, Phys.Rev. vol. 122, p.791 (1961) 2. A.G. Gurevich, G.A. Melkov. Magnetization Oscillation and Waves, CRC Press, New York (1996). 3. N.G. Chechenin, C.B. Craus, A. Chezan, et al IEEE Trans. Magn. MAG 38, p. 3027 (2002). 4. N.G. Chechenin. J. Magn. Magn. Mater. Vol. 300, 198 (2006). 5. N.G. Chechenin, Phys. Solid State vol. 46, p. 479 (2004)

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 Influence of extrinsic factors on FMR linewidth in systems with exchange bias

Graphene (Gr) is one of the most outstanding materials for room temperature (RT) spintronics due to its unique and intrinsically tunable electronic properties [1,2]. Some important effects such as high spin injection efficiency, antiferromagnetic coupling, Rashba, spin filtering, TMR or enhanced PMA have been found when Gr is coupled with ferromagnetic materials. Its electronic properties can be tuned by proximity with heavier metallic atoms, which may allow for the technological development of more efficient devices based on spin-orbit effects. However, the development of Gr-based hybrid structures requires the capability of engineering high-quality interfaces, as it has a direct impact in the functional properties of the system [3]. On this regard, metal intercalation has been widely used for the fabrication of functional Gr/FM/HM heterostructures. Gr promotes a layer-by-layer growth of the metal at the interface with a heavy metal substrate, resulting in high quality epitaxial interfaces. Moreover, Gr protects the intercalated material from air exposition avoiding its oxidation and preserving its physical properties. It has been recently demonstrated by the authors that if the intercalated species is a FM, one can prepared highly perfect and flat hybrid Gr/FM/HM epitaxial heterostructures onto insulating oxides with enhanced perpendicular magnetic anisotropy (PMA), large DMI and stable Néel-type chiral magnetic nanometer sized objects [4]. In the present work we report on the fabrication of high quality epitaxial Gr/Fe/Pt asymmetric magnetic structures with extremely abrupt interfaces. Samples were fabricated entirely in UHV following a methodology previously stablished [5]. Thermal intercalation of Fe in Gr/Pt(111) interfaces is studied in detail by means of X-ray photoelectron spectroscopy, observing a shift of the C1s core level main contribution to higher binding energies due to the transition from n-doped to p-doped graphene due to graphene-iron interaction. High surface and interface quality is demonstrated by means of HR-TEEM, LEED and XRR. Atomic resolution images prove an epitaxial and conmensurate growth of Fe on Pt(111) with a characteristic ABC stacking of the fcc structure. EELS elemental mapping of the heterostructures confirms the good chemical differentiation of all the layers in the system. Magnetic characterization was performed by MOKE at ambient conditions varying Fe thickness in a range between 1 to 4 MLs. Our results show the presence of PMA in the system for 1 ML of Fe, with a complete transition to in plane magnetization for thicknesses above 3 MLs.

**References:**

[1] A. H. Castro Neto et al., Rev. Mod. Phys. 81, 109-162 (2009) [2] W. Han et al., Nature Nanotech 9, 794–807 (2014) [3] W. J. Wells et al., Phys. Rev. B 95, 054428 (2017) [4] F. Ajejas et al., Nano Lett. 18, 9, 5364-5372 (2018) [5] F. Ajejas et al., ACS Appl. Mater. Interfaces. 12, 4088-4096 (2020)

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 Tuning work function in Graphene by thermally assisted metal intercalation

It has been shown that a number of phases are formed in the interface between Ni and Ge layers. Main peculiarities of these properties: the low temperature hysteresis loop shift and the difference between FC and ZFC magnetization temperature dependences are explained satisfactory by the magnetic order appearance in the interface layers. According to the modern tendencies in industry, Ge is a proper candidate to replace Si in some spintronic devices. Ge demonstrates the higher carrier mobility [1] and has a larger exciton Bohr radius comparing to Si [2]. Nickel germanide Schottky contacts are ideal for p-channel Ge metal-oxide-semiconductor field-effect transistor (MOSFET): the highest Schottky barrier for electrons combined with the close to zero barrier for holes were obtained with rapid thermal annealing technique [3]. These features attract the growing interest to the thin film structures based on Ge and its compounds with some metals, especially, with Ni (e.g., [4-7]. Along with the special electrical properties, magnetic characteristics of the films can be of interest because of their contribution to the structures functionality. Recently, we revealed several peculiarities in the temperature and magnetic field dependences of the layered Ni/Ge films magnetization [8] that were ascribed to the effect of the interface between Ni and Ge layers. The present work is aimed to elucidate the interface structure and the mechanism of its interaction with Ni layers. Ni/Ge and Ge/Ni/Ge/Ni/Ge films with different thicknesses of the component layers were fabricated with the ion-plasma sputtering technique described in Ref [8]. Insert Table 1 – The interplanar distances, d, obtained from SAED data for the Ni/Ge (9nm/14nm) film in comparison with data for Ni (Fm3m) and several NiGe compounds. The X-ray fluorescent analysis (X-ray spectrometer S4 PIONEER, Bruker), EXAFS/XANES spectroscopy and X-ray reflectometry using synchrotron radiation station in the National Research Center «Kurchatov Institute», transmission electron-microscope (JEOL JEM-2100 (LaB6), energy dispersive X-ray spectrometer (Oxford Instruments INCA x-sight), and selected-area electron diffraction (SAED) were used to characterize films. Magnetic properties of the film samples were studied with a SQUID magnetometer, operating in the 4.2–300 K temperature range at a maximum applied magnetic field H = 1 kOe. Structural data have shown that Ni layers were polycrystalline of Fm3m face centered phase, Ge layers were amorphous, Ni and Ge oxides were detected in trace amounts. Intermediate layers of about 9 nm in thickness were shown to form between Ni and Ge layers. Micro-diffraction images of the layered samples cross-section images revealed not only all the reflections characteristic for Ni but also reflexes, which can be compared with some Ni oxides. According to the interplanar distances presented in Table 1, these could be Ni3Ge, Ni5Ge2, Ni5Ge3. At that, Ni3Ge and Ni5Ge3 are ferromagnetic with different temperature dependences of magnetization. In particular, the Ni3Ge magnetization increases almost five times in the range 290 - 77 K. Therefore, the data obtained do not allow determining the interface structure unambiguously. However is clear that Ni layers border with NixGey layers but not with Ge layers. This neighborhood can effect in the layered films magnetic behavior essentially. Insert Fig. 1. Hysteresis loop of Ni/Ge film at T = 5 K. One of the most pronounced features of the layered films investigated is the low temperature hysteresis loop broadening and shift along the magnetic field axis (Fig. 1). The magnetization loop shift is observed usually in the film structures consisting of a ferromagnetic (FM) and the antiferromagnetic (AFM) layers or including magnetic soft and hard layers and explained by the exchange interaction between these layers [9, 10]. One can assume that the hard FM layer (for example, Ni3Ge) in the boundary adjacent to a soft nickel layer, and the observed hysteresis loop shift is due to the exchange interaction between these layers. The processes of Ni layer magnetization in such situation depend on the direction of an external field with respect to the direction of the magnetic moment of the adjacent interface layer. When the magnetic moment of the hard FM layer and the external magnetic field are oriented in the same direction, the soft magnetic layer magnetized homogeneously in the same direction in relatively low magnetic field. The change of the external magnetic field direction leads to the formation of the helical structure in the soft FM layer similar to the Bloch wall [11]. The helix pitch depends on the thickness of the soft layer and on the magnitude of the exchange interaction between adjacent layers. The increase in thickness of the soft FM reduces a degree of an influence of the hard FM layer on the soft layer magnetic state. It has been shown that a number of phases are formed in the interface between Ni and Ge layers. These phases are close to Ni3Ge, Ni5Ge2, and Ni5Ge3, influencing on the magnetic properties of the films. Main peculiarities of these properties: the low temperature hysteresis loop shift and the difference between FC and ZFC magnetization temperature dependences are explained satisfactory by the magnetic order appearance in the interface layers.

**References:**

 1. S.M. Sze and K.K. Ng, Physics of Semiconductor Devices, Wiley, New York, (2007) 789. 2. Y. Maeda, N. Tsukamoto, Y. Yazawa, Y. Kanemitsu, and Y. Masumoto, Appl. Phys. Lett. 59 (1991) 3168. 3. D.R. Gajula, D.W. McNeill, B.E. Coss, H. Dong, S. Jandhyala, J. Kim, R.M. Wallace, and B.M. Armstrong, Appl. Phys. Lett. 100 (2012) 192101. 4. B. De Schutter, W. Devulder, A. Schrauwen, K. van Stiphoub, T. Perkisas, S. Bals, A. Vantomme, C. Detavernier, Microelectronic Engineering 120 (2014) 168. 5. S. Kazan, B.Kocaman, A.Parabas, F.Yildiz, B.Aktas, J. Magn. Magn. Mater. 73(2015)164. 6. Yunsheng Deng, Osamu Nakatsuka, Jun Yokoi, Noriyuki Taoka, Shigeaki Zaima, Thin Solid Films 557 (2014) 84. 7. Phyllis S. Y. Lim, Dong Zhi Chi, Poh Chong Lim, Xin Cai Wang, Taw Kuei Chan, Thomas Osipowicz, and Yee-Chia Yeo, Appl. Phys. Lett. 97 (2010) 182104. 8. I.S. Edelman, D.A. Velikanov, A.V. Chernichenko, D.A. Marushchenko, E.V. Eremin, I.A. Turpanov, G.V. Bondarenko, Yu.E. Grebenkova, and G.S. Patrin, Physica E 42 (2010) 2301. 9. W.H Meiklejohn, C.P. Bean, Phys. Rev.105 (1957) 904. 10. J. Nogues, J. Sort, V. Langlais, V. Skumryev, S. Surinach, J.S. Munoz, and M.D. Baro, Physics Reports 422 (2005) 65. 11. A. Hubert and R.Schäfer, Magnetic Domains: The Analysis of Magnetic Microstructures. Springer (2008) 216.

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 Layered Ni/Ge Thin Films: The Ni-Ge Interface Effect in The Films Magnetic Properties

We have successfully fabricated Fe3O4/GaAs Schottky barrier on n-type GaAs (100) substrates with high carrier concentrations (3Χ10-18cm-3) by photolithography and mesa etching. 10ML Fe was deposited on GaAs substructure and annealed in an oxygen environment. Current-Voltage measurements were carried on over the temperature range of 80- 290K in Nonlocal and Local device structure. We extracted ideality factor n and barrier height ΦB from I-V curves which are fitted with the equation based on Thermionic Emission Diffusion theory and Back to back Schottky diodes theory. In local structure, there are Fe3O4/GaAs/Fe3O4 back to back diode model. Barrier height with Symmetric distribution in local device and the ideality factor is closer to unity in low temperature. In the Nonlocal device structure, we annealed Indium in vacuum atmosphere base pressure with 10-8 torr. When temperatures over 200k, the experimental I-V curves obey the ideal thermionic emission model, and the ideality factors near a constant 1.88. However, the apparent barrier heights decrease with decreasing temperature. This abnormal behavior is interpreted by the assumption of a Gaussian distribution of barrier heights when we used Gaussian distribution to modified Richardson plot, the experimental data are fitted well by the modified Richardson equation and we got a constant barrier value 0.55ev. Finally, we find from the temperature dependence of Fe3O4/GaAs Schottky barrier in different device structures that and the barrier heights decrease with decreasing temperature (&gt;200K), which is attributed to a Gaussian distribution of barrier heights.

**References:**

1. Chiquito AJ, Amorim CA and Berengue OM. J Phys Condens Matter 24, 225303 (2012). 2. Karata, Altlndal . Materials Science and Engineering: B 122, 133-139 (2005).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4a2b4dcb8c41d426d0ef58c2a6390e0e.jpg)
Fig.1 Local device :(a) The forward bias current-voltage characteristics of Fe3O4 on GaAs substrates at various temperatures. All these curves are fitted with the equation based on back to back diode theory. 
(b) The left and right Fe3O4 /GaAs barrier heights as a function of temperature.

![](https://assets.underline.io/uploads/markdown_image/1/image/e9838e43fccf74f05107890c057ac4d5.jpg)
Fig.2 Nonlocal device :(a)Schottky barrier height and ideality factor derived from the fitting as function of temperature for Fe3O4 contacts on GaAs substrates. (b) The experimented data are fitted by the modified Richardson equation.

 Study of the Schottky contacts of ultrathin Fe3O4 films Schottky contacts on GaAs substrates

1. Introduction With the increasing penetration of power electronic devices, wide-bandwidth oscillation events are frequently reported in recent years [1]. To meet the demand of analyzing wide-bandwidth oscillation without prior knowledge of detailed parameters of the concerned system, the impedance-based stability method [2] is now a widely used technique. However, the accuracy of the impedance-based stability method heavily relies on the precise measurement of the impedance of the concerned system, which is determined by following three critical factors. 1) Response Signal Sensing: The limited bandwidth of sensor can jeopardize the accuracy of impedance measurement over a wide bandwidth. In [3], shunt resistor is used to measure the current response from 1 Hz to 1 kHz. The drawback of shunt resistor is that the resistance shifts with ambient temperature, frequencies and rated current. Besides, the Hall-effect current transducers can be used to obtain the current response. However, the narrow bandwidth of Hall-effect current transducers makes them not suitable for wide bandwidth impedance measurement [4]. 2) Perturbation Injection: Most existing work sets the current or voltage injection as 10% of rated value to obtain a good signal-to-noise ratio [5]. However, for certain concerned systems, especially under weak grid, even 10% disturbance can make the system deviates from the equilibrium point and interferes with the normal operation of the system. Besides, it is also costly and challenging to design an injection source with high injection capacity and broadband injection at the same time in high-power application. 3) Response Components Extraction: Another inevitable problem is the inaccurate response components extraction due to the spectral leakages of FFT-based algorithm. A Hanning window in [6] is applied to improve the accuracy of measured impedance by solve the spectral leakages in Fourier analysis. However, the impedance measurement results vary significantly with the selection and design of window function. To overcome these limitations, this paper proposes a wide bandwidth impedance measurement technique with a small perturbation injection based on magnetic sensing and Prony-FFT extraction algorithm. Firstly, a low-cost tunnel magnetoresistance (TMR) sensor is applied to measure the desired impedance result over a wide bandwidth. Besides, the high sensitivity of TMR sensor enables the impedance measurement with small perturbation injection. Finally, to extract the magnitude and phase of the response component precisely from the sensing response signal, an improved algorithm based on Prony-FFT is developed to avoid the spectral leakages and lighten the computation burden in high frequency band. Hence, the proposed measurement technique can potentially be an effective tool in modern power system because of its wide bandwidth, high sensitivity, light computation burden. 2. Experiments For a selected frequency band of interest, the impedance of a RL circuit was measured experimentally by proposed impedance measurement technique. The result was compared with the one measured with a commercial AC current clamp (i400s, FLUKE). Meanwhile, the reference impedance value of the RL was obtained by a vector network analyzer (VNA, E5061B, Keysight). A programmable AC power source (61704, Chroma) was used to inject a wide-bandwidth perturbation into the RL circuit as shown in Fig. 1. Thirty injection frequencies were spaced between 10 Hz to 2 kHz. Then, the voltage of the RL was measured by a differential voltage probe (A042, PICO). Meanwhile, a TMR sensor (TMR2305M, MultiDimension Technology) with high sensitivity of 25 mV/V/Oe was selected to measure the input current of the RL circuit. The output of TMR sensor was amplified by a differential amplifier (AD620). The frequency response of TMR sensor with amplifier was investigated as shown in Fig. 2(a). The gain deviation of the TMR sensor was within 0.2 dB over the bandwidth whereas the variation of phase was within 3 degree. Thus, the TMR sensor could enable wideband impedance measurement with constant gain and negligible phase shift. Then, the impedance measurement results with 10% injection magnitude based on the proposed technique and AC current clamp were compared in Fig. 2(b). Compared with the impedance measured by the VNA, the average magnitude deviation measured by the TMR sensor was 0.9 Ω whereas that measured by the AC current clamp was 1.6 Ω. Besides, the phase deviation of impedance based on TMR sensor was within 2 degree, while the maximum phase deviation of the result measured by the AC current clamp reached 8 degree over the wide frequency band of measured. Furthermore, the impedance measurement with 3% injection magnitude based on proposed technique was compared with the 10% injection magnitude based on AC current clamp in Fig. 2(c). The measured result with 3% injection magnitude based on TMR sensor had maximum phase deviation of 3 degree, which was still smaller than the result measured by the AC current clamp with 10% injection magnitude. 3. Results and Discussion Compared with the impedance measured by the AC current clamp, the proposed impedance measurement technique based on TMR sensor achieved higher accuracy in magnitude and less phase shift over a wide bandwidth. Meanwhile, the proposed technique can measure the impedance under smaller injection magnitude without sacrificing the measurement accuracy. In the full paper, the details of the impedance extraction algorithm based on Prony-FFT and more experimental results will be presented.

**References:**

[1] M. Amin, M. Molinas, and L. Jing, "Oscillatory phenomena between wind farms and HVDC systems: The impact of control," IEEE, 2015, pp. 1-8. [2] S. Jian, “Impedance-Based Stability Criterion for Grid-Connected Inverters,” TPEL, vol. 26, no. 11, pp. 3075-3078, 2011. [3] D. A. Howey, P. D. Mitcheson, V. Yufit, G. J. Offer, and N. P. Brandon, “Online Measurement of Battery Impedance Using Motor Controller Excitation,” TVT, vol. 63, no. 6, pp. 2557-2566, 2014. [4] A. Patel, and M. Ferdowsi, “Current Sensing for Automotive Electronics-A Survey,” TVT, vol. 58, no. 8, pp. 4108-4119, 2009. [5] T. Roinila, M. Vilkko, and S. Jian, “Online Grid Impedance Measurement Using Discrete-Interval Binary Sequence Injection,” JESTPE, vol. 2, no. 4, pp. 985-993, 2014. [6] C. Xin, Z. Yang, W. Shanshan, C. Jie, and G. Chunying, “Impedance-Phased Dynamic Control Method for Grid-Connected Inverters in a Weak Grid,” TPEL, vol. 32, no. 1, pp. 274-283, 2017.

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 A wide-bandwidth impedance measurement technique with small perturbation injection based on magnetic sensing

Pipelines have played an essential role in transporting basic energy sources such as oil, natural gas and hydrogen. In recent years, non-destructive testing (NDT) technology for the structural integrity of various pipes has increased their demands due to the increase and deterioration of the energy resource network. There are various types of NDT methods, and magnetic flux leakage (MFL) and eddy current testing (ECT) technologies are most widely used for evaluating the integrity of pipelines, steam generator tube and aircraft components [1], [2]. Both MFL and ECT have inherent several weaknesses from their operation principle. A defect signals by MFL inspection have an ambiguity in distinguishing between defects in the inner surface and outer surface. ECT inspection must consider the effect of skin effect, thus the driving frequency is strictly limited by material and thickness of specimen. Consequently, each limit greatly affects the inspection performance and speed, so that this makes the bottleneck for the precise and versatile evaluation. In order to overcome constraints of conventional MFL and ECT, many research and development have been conducted by combining MFL and ECT into a single sensor [3]. This method inspects the ferromagnetic steel by applying DC biased magnetic field to the steel and measuring the outer surface or subsurface of steel wall with an ECT sensor. If the DC magnetic flux is distorted due to the existence of the defect, the magnetic permeability changes based on the nonlinear and hysteretic characteristics of the ferromagnetic material. Then, the defect signal can be measured as the perturbation of the permeability. Consequently, the skin effect no longer limits to the measurement of specific defects at the given frequency. Compared to other NDT methods, DC-biasing ECT is relatively recently introduced so that detailed descriptions of methodologies for the design and analysis are still short including optimal operating conditions, and signal analysis. To estimate the operating performance of DC-biasing ECT, both static magnetic field by permanent magnet or electromagnet, and time-harmonic magnetic field must be considered simultaneously. The finite element method (FEM) can compute the problem accurately, but the fine discretization of near surface, which requires high computational resources and time. The driving conditions are different depending on the application environment of the sensor, and a design is required for this, which causes a large time and cost aspect for development. In this paper, a semi-analytical method using finite element method for static magnetic field computation and analytical method for eddy current problem is suggested. The time consumption for determining the operating condition of DC-biasing ECT sensor can be greatly reduced by using the suggested approach. Fig. 1 illustrates the traditional method and proposed method to evaluate the performance of DC- biasing ECT. Both methods requires the calculation of static magnetic field by permanent magnet (PM) or electromagnet (EM), and the subsequent calculation of time-harmonic magnetic field by sensor coil. The ferromagnetic specimen includes both nonlinear and hysteretic characteristics, but this study would not consider the effect of magnetic hysteresis, which will be dealt in a future research. The magnetic flux density in each element is calculated by inputting the magnetization curve of the specimen, and the permeability determined by the magnetic flux density is stored for time-harmonic field problem. Since the amplitude of time-varying magnetic field by sensor coil is very small compared to the magnitude of static magnetic field, the permeability can be considered as the derivatives of the magnetization curve at the operating point of static field. Computation of high frequency magnetic field by using FEM requires very large number of discretization due to severe skin effect near surface of sensor coil. The performance of DC-biasing ECT sensor depends on many parameters such as static field and, frequency and the material of specimen. Thus, the computational time and cost should be reduced for the efficient sensor design. In this study, analytical method is used as an alternative to the calculation of time-harmonic field problem. The transformer model is formulated in analogy with the interaction between the sensor coil and eddy currents. Then, the different permeability distribution on the specimen is transformed in to a homogenized plane to reduce computational complexity. The detailed formulation of the transformer model and homogenization will be included in the full manuscript. Fig. 2(a) shows the schematic diagram of DC-biasing ECT. The electromagnet was used to control DC magnetic field and reflection probe constructed with coaxial driving coil and sensing coil. The impedance response is calculated and results are shown in Fig. 2(b). The number of turns of electromagnet is 400 and exciting current is 3.5A. The calculated values of both normal and defective specimen are compared, and measurement setup and result will be dealt to complement the correspondence with the prototype. When the frequency increases, the normalized value of imaginary part of sensing voltage decreases while the real part of voltage increases. The proposed method can estimate the response of the sensor throughout the wide frequency range.

**References:**

[1] J. Wu et al, IEEE Transactions on Magnetics, vol. 54, pp. 1-8 (2018) [2] Y. Xu, Y. Yang and Y. Wu, IEEE Sensors Journal, vol. 20, pp. 10502-10510 (2020) [3] J. Wu, J. Zhu, H. Xia, C. Liu, IEEE Transactions on Industrial Informatics, vol. 15, pp. 6252-6259 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/45a7b2687e110c66e5844a4cacd37a36.jpg)
Fig. 1. Comparison of calculation scheme between traditional and proposed method

![](https://assets.underline.io/uploads/markdown_image/1/image/a85ded0cae883d868e1252099f9dc2a5.jpg)
Fig. 2. (a) Schematic diagram of DC-biasing ECT and (b) comparison of two calculated results

 Semi-Analytical Modeling of High Frequency Eddy Current Sensor in Ferromagnetic Steel with DC Bias

I. Introduction To achieve a higher power density of power electronic modules, the switching frequency of the power electronic devices is increasing significantly. Especially, the next-generation power electronic devices utilizing wide-bandgap semiconductor materials such as SiC and GaN which can realize the switching frequency in megahertz [1]. The current sensing is essential for the control purpose, condition monitoring, protection, and power management in power electronic modules. Although the shunt resistor can be used to measure the current, it is non-isolated and the parasitic impedance introduced may incur extra power losses and jeopardize the reliability of power electronic modules [2]. The Hall-effect current transducers are extensively exploited for current measurement in power electronic modules. Nevertheless, they are inapplicable in high-bandwidth current sensing due to the limited bandwidth of typically less than 200 kHz [3]. Since the magnetic sensor such as magnetoresistive (MR) sensor can measure current up to several megahertz non-invasively [4], there are researches on using the MR sensors for current measurement in power electronics [5-8]. Due to the skin effect, the high-bandwidth current tends to be distributed on the surface of a conductor and the skin depth decreases with the frequency. Thus, the main challenge is that the magnetic field of current varies with frequency causing the nonlinearity of MR sensors. It was studied that the frequency response can be improved by placing a copper sheet around the MR sensor [5]. Although the planar copper concentrator can concentrate the magnetic field [6], the magnetic flux density (B) still varies with the frequency. The copper foil is used to wrap the MR sensor to achieve a unity normalized gain until 83.3 kHz, but the gain increases for higher frequency [7]. Besides, the field summing and decoupling methods are adopted to reduce the phase shift and extend the bandwidth to 1 MHz with an error of 5 % by using two MR sensors [8]. Therefore, the technique for a single magnetic sensor to measure a high-bandwidth current is still lacking. In this paper, a technique using a specially designed wire loop and differential amplifier based calibration circuit is developed for the magnetic sensor to measure high-bandwidth current. The skin effect of rectangular wire on the printed circuit board (PCB) is analyzed mathematically. The effects of concentrators in various structures on B are investigated based on simulation results. The effectiveness of the proposed wire loop on concentrating magnetic field of current up to 10 MHz is evaluated. The experimental results verify that the proposed technique using the wire loop and differential amplifier based calibration circuit can sense the high-bandwidth current in high accuracy. II. Analysis of High-Bandwidth Current Sensing Technique Generally, the PCB trace of a power electronic module is rectangular as shown in Fig. 1 (a). Considering a 1 oz copper trace in a width of 2.54 mm, the height is 35 μm which is much less than the width. Thus, magnetic vector potential (A) of the position (x, y) can be calculated by [9] A=Iμo/8πw{(w+x)log[(w+x)2+y2]+(w-x)log[(w-x)2+y2]+2y[tan-1(w+x)/y+tan-1(w-x)/y]-4w} where 2w and 2h are the width and height of the PCB wire respectively, μo is the vacuum permeability. When the trace is carrying a high-bandwidth current, the skin effect should be considered. The skin depth can be calculated by δ=√(2ρ/ωμo) where δ is the skin depth, ρ is the electrical resistivity of copper, ω is the angular frequency. The skin depth decreases with the frequency. This affects the A and thus the B since B = ▽×A. As shown in Fig. 1 (b) and (c), the magnetic sensor is located on the top layer of the PCB and the trace with a current of 1 A is on the bottom layer, the average B of the magnetic sensor located region (Bavg) decreases from 0.0746 mT to 0.0725 mT when the frequency increases from 1 kHz to 1 MHz. A copper sheet of 25.4 μm can be used to concentrate the Bavg to 0.141 mT at 1 MHz as shown in Fig. 1 (d). However, in this case, the Bavg increases with the frequency. The problem that Bavg varies with frequency still exists. A wire loop is designed to reduce the variation of Bavg with frequency as shown in Fig. 2 (a). The bottom-layer current passes through a rectangular wire with a cross-section of 0.2 mm × 0.2 mm located 0.35 mm above the magnetic sensor and then passes to the top layer. In this way, the Bavg is 0.242 mT when the frequency is 1 kHz and 100 kHz as shown in Fig. 2 (b) and (c). It only decreases by 0.826 % to 0.240 mT at 10 MHz. Thus, a stable B can be achieved by this method, and thus current can be sensed accurately by the magnetic sensor despite the high frequency. In the full paper, the influence of skin effect on high-bandwidth current sensing will be analyzed. The effects of concentrators in various structures on B will be investigated and presented. The principle of the proposed wire loop and differential amplifier based calibration circuit will be elaborated. The effectiveness of the proposed technique for high-bandwidth current sensing will be verified and evaluated experimentally.

**References:**

[1] E. Santi, K. Peng, and H. A. Mantooth, IEEE Transactions on Electron Devices., Vol. 62, pp. 434-442 (2015). [2] S. Ziegler, R. C. Woodward, and H. H.-C. Iu, IEEE Sensors Journal., Vol. 9, pp. 354-376 (2009). [3] A. Patel and M. Ferdowsi, IEEE Transactions on Vehicular Technology., Vol. 58, pp. 4108-4119 (2009). [4] J. Lenz and S. Edelstein, IEEE Sensors Journal., Vol. 6, pp. 631-649 (2006). [5] P. E. Schneider, M. Horio, and R. D. Lorenz, IEEE Transactions on Industry Applications., Vol. 48, pp. 1432-1439 (2012). [6] S. J. Nibir and B. Parkhideh, IEEE Transactions on Industrial Electronics., Vol. 65, pp. 2766-2774 (2018). [7] S. Shao, N. Yu, and X. Xu, IEEE Transactions on Power Electronics., Vol. 35, pp. 10930-10944 (2020). [8] M. Sheng, M. H. Alvi, and R. D. Lorenz, IEEE Journal of Emerging and Selected Topics in Power Electronics., (2020). [9] K. J. Binns and P. J. Lawrenson, Analysis and Computation of Electric and Magnetic Field Problems. Elsevier (2013).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ed98288a51e289100f50bc2581a3c0e8.jpg)
Fig. 1. PCB trace. (a) Cross-section. Magnetic flux at (b) 1 kHz, (c) 1 MHz, and (d) 1MHz with a copper concentrator.

![](https://assets.underline.io/uploads/markdown_image/1/image/30af824e42f7b3345abdd284eed45dd0.jpg)
Fig. 2. Wire loop. (a) Layout. Magnetic flux at (b) 1 kHz, (c) 100 kHz, and (d) 10 MHz.

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