France



I. Introduction&lt;br/&gt;Wireless power transfer (WPT) system can effectively make up for the shortcomings of traditional electric energy transmission and has a wide range of application prospects in the fields of electric vehicles, biomedicine, and portable equipment [1-3]. There are several ways to realize WPT, among which the WPT based on magnetic coupling resonance has many advantages, such as long transmission distance, high efficiency, simple implementation, and so on, which can meet the requirements of most scenarios.&lt;br/&gt;The WPT system needs a stable and efficient high-frequency power supply. The Class E Amplifier, with only one switch component, can realize soft-switching by matching the appropriate bypass capacitor and then get a high efficiency (close to 100%) in MHz [4]. Hence, the Class E Amplifier is extremely suitable for a high-frequency WPT system. At present, the scholars’ research generally focuses on the short-range and high-efficiency WPT systems within 20cm, whose transmission distance is insufficient [5-6]. Silicon MOSFET can not meet the needs of the high-frequency power supplies, GaN components can work at a higher frequency and higher efficiency [7].&lt;br/&gt;Herein, a mid-range high-efficiency wireless power transfer system based on class E power amplifier and Gan components is proposed. This paper optimizes the coupling coil and load in theory and simulation and gives the system parameter design method of ZVS (Zero Voltage Switching) operation of the class E power amplifier. Finally, the Wide Band-gap Semiconductor GaN component is used to build the physical model to verify the accuracy of the design. More detailed results and discussion will be presented in the extended paper.&lt;br/&gt;&lt;br/&gt;II. Double coil wireless power transmission system based on the class E power amplifier&lt;br/&gt;The wireless power transmission system mainly includes three subsystems, class E power amplifier, coupling coil, and load. And the topology is shown in Figure 1.&lt;br/&gt;According to the circuit model, the factors that affect the transmission efficiency and power of the system are analyzed, and it is concluded that the mutual inductance of the coils, the load, and the AC resistance of the coils have a great influence on the transmission characteristics.&lt;br/&gt;&lt;br/&gt;III. Design and optimization of the flat spiral coils for the WPT system&lt;br/&gt;The parameters of the coupling coils are closely related to the performance of the WPT system. The design and optimization are carried out through theory and simulation, and the comparison is carried out through experimental measurement.&lt;br/&gt;a. Calculation of coil self-inductance and mutual-inductance&lt;br/&gt;According to Neumann’s formula [8], the mutual inductance calculation method of the flat spiral coil is derived. The self-inductance and mutual-inductance of the coil are calculated by theory and COMSOL electromagnetic field simulation tool.&lt;br/&gt;b. Calculation of the coil AC resistance and determination on the spacing between coil turns&lt;br/&gt;To reduce the coil AC resistance as much as possible, the relationship between coil AC resistance and turn spacing is analyzed by COMSOL Multiphysics. And then determines the spacing between coil turns is 2mm.&lt;br/&gt;The theoretical calculation, finite element simulation, and experimental measurement results are compared and analyzed, and the results are quite consistent.&lt;br/&gt;&lt;br/&gt;IV. System circuit simulation calculation and experimental verification&lt;br/&gt;Powered by a 24V DC power supply, the optimal load resistance is 10Ω and set the transmission distance to 40cm, then we determine the parameters of the system components.&lt;br/&gt;a. Circuit simulation using PSIM&lt;br/&gt;Build the system simulation model in PSIM, the circuit realizes soft switching, and the simulation results are shown in Figure 2. The output power of the load is 26.85W and the transmission efficiency is 87.89%.&lt;br/&gt;b. System experiment verification&lt;br/&gt;In particular, in view of the low on-resistance and small parasitic capacitance of GAN devices, which enable them to maintain high efficiency during high-frequency operation, GaN devices are introduced as switching devices in the experiment.&lt;br/&gt;According to the design parameters, we build the experimental model and carry out the relevant measurement. The experimental results are in good agreement with the simulation results. When the distance between coils is 40cm, the output power of the load is 25.99W and the transmission efficiency is 87.34%.&lt;br/&gt;&lt;br/&gt;V. Conclusions&lt;br/&gt;Aiming at the problem of low efficiency of medium and long-distance wireless power transmission, this paper conducts comprehensive efficiency optimization from coil parameter optimization, load, and class E power amplifier. Using new GaN devices, a wireless power transmission system that takes into account the characteristics of mid-range and high efficiency has been developed.

**References:**

[1] Y. Bu, S. Endo, T. Mizuno, IEEE Transactions on Magnetics, vol. 54, pp. 1(2018)&lt;br/&gt;[2] F. Benassi, D. Masotti, A. Costanzo, 2019 IEEE International Conference on RFID Technology and Applications (RFID-TA), pp. 306(2019)&lt;br/&gt;[3] N. Hasegawa, S. Yoshida, S. Furuta, et al., 2014 IEEE Wireless Power Transfer Conference, pp. 21(2014)&lt;br/&gt;[4] F. Tamjid, A. Ghahremani, M. Richardson, et al., 2017 IEEE Topical Conference on RF/Microwave Power Amplifiers for Radio and Wireless Applications (PAWR), pp. 25(2017)&lt;br/&gt;[5] L. Kou, J. Lu, P. Di Maso, 2019 IEEE 7th Workshop on Wide Bandgap Power Devices and Applications (WiPDA), pp. 205(2019)&lt;br/&gt;[6] H. Li, J. Li, K. Wang, W. Chen, et al., IEEE Transactions on Power Electronics, vol. 30, pp. 3998(2014)&lt;br/&gt;[7] J. Song, M. Liu, C. Ma, IEEE Transactions on Industrial Electronics, vol. 67, pp. 8281(2019)&lt;br/&gt;[8] H. A. Wheeler, Proceedings of the Institute of Radio Engineers, vol. 16, pp. 1398(1928)&lt;br/&gt;[9] H. L. Chan, K. W. E. Cheng, D. Sutanto, 2000 Eighth International Conference on Power Electronics and Variable Speed Drives, pp. 69(2000)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e87a9716c1b30438f50eeea535a90b25.jpg)
Fig. 1  Topology of the WPT system

![](https://assets.underline.io/uploads/markdown_image/1/image/ad2c8f9ba024d557ada47c36613f662c.jpg)
Fig. 2  System circuit simulation results using PSIM

INTERMAG 2021

 Research on Mid-distance High-efficiency Wireless Power Transmission System using Class E Amplifier

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I. Introduction Wireless power transfer (WPT) system can effectively make up for the shortcomings of traditional electric energy transmission and has a wide range of application prospects in the fields of electric vehicles, biomedicine, and portable equipment [1-3]. There are several ways to realize WPT, among which the WPT based on magnetic coupling resonance has many advantages, such as long transmission distance, high efficiency, simple implementation, and so on, which can meet the requirements of most scenarios. The WPT system needs a stable and efficient high-frequency power supply. The Class E Amplifier, with only one switch component, can realize soft-switching by matching the appropriate bypass capacitor and then get a high efficiency (close to 100%) in MHz [4]. Hence, the Class E Amplifier is extremely suitable for a high-frequency WPT system. At present, the scholars’ research generally focuses on the short-range and high-efficiency WPT systems within 20cm, whose transmission distance is insufficient [5-6]. Silicon MOSFET can not meet the needs of the high-frequency power supplies, GaN components can work at a higher frequency and higher efficiency [7]. Herein, a mid-range high-efficiency wireless power transfer system based on class E power amplifier and Gan components is proposed. This paper optimizes the coupling coil and load in theory and simulation and gives the system parameter design method of ZVS (Zero Voltage Switching) operation of the class E power amplifier. Finally, the Wide Band-gap Semiconductor GaN component is used to build the physical model to verify the accuracy of the design. More detailed results and discussion will be presented in the extended paper. II. Double coil wireless power transmission system based on the class E power amplifier The wireless power transmission system mainly includes three subsystems, class E power amplifier, coupling coil, and load. And the topology is shown in Figure 1. According to the circuit model, the factors that affect the transmission efficiency and power of the system are analyzed, and it is concluded that the mutual inductance of the coils, the load, and the AC resistance of the coils have a great influence on the transmission characteristics. III. Design and optimization of the flat spiral coils for the WPT system The parameters of the coupling coils are closely related to the performance of the WPT system. The design and optimization are carried out through theory and simulation, and the comparison is carried out through experimental measurement. a. Calculation of coil self-inductance and mutual-inductance According to Neumann’s formula [8], the mutual inductance calculation method of the flat spiral coil is derived. The self-inductance and mutual-inductance of the coil are calculated by theory and COMSOL electromagnetic field simulation tool. b. Calculation of the coil AC resistance and determination on the spacing between coil turns To reduce the coil AC resistance as much as possible, the relationship between coil AC resistance and turn spacing is analyzed by COMSOL Multiphysics. And then determines the spacing between coil turns is 2mm. The theoretical calculation, finite element simulation, and experimental measurement results are compared and analyzed, and the results are quite consistent. IV. System circuit simulation calculation and experimental verification Powered by a 24V DC power supply, the optimal load resistance is 10Ω and set the transmission distance to 40cm, then we determine the parameters of the system components. a. Circuit simulation using PSIM Build the system simulation model in PSIM, the circuit realizes soft switching, and the simulation results are shown in Figure 2. The output power of the load is 26.85W and the transmission efficiency is 87.89%. b. System experiment verification In particular, in view of the low on-resistance and small parasitic capacitance of GAN devices, which enable them to maintain high efficiency during high-frequency operation, GaN devices are introduced as switching devices in the experiment. According to the design parameters, we build the experimental model and carry out the relevant measurement. The experimental results are in good agreement with the simulation results. When the distance between coils is 40cm, the output power of the load is 25.99W and the transmission efficiency is 87.34%. V. Conclusions Aiming at the problem of low efficiency of medium and long-distance wireless power transmission, this paper conducts comprehensive efficiency optimization from coil parameter optimization, load, and class E power amplifier. Using new GaN devices, a wireless power transmission system that takes into account the characteristics of mid-range and high efficiency has been developed.

**References:**

[1] Y. Bu, S. Endo, T. Mizuno, IEEE Transactions on Magnetics, vol. 54, pp. 1(2018) [2] F. Benassi, D. Masotti, A. Costanzo, 2019 IEEE International Conference on RFID Technology and Applications (RFID-TA), pp. 306(2019) [3] N. Hasegawa, S. Yoshida, S. Furuta, et al., 2014 IEEE Wireless Power Transfer Conference, pp. 21(2014) [4] F. Tamjid, A. Ghahremani, M. Richardson, et al., 2017 IEEE Topical Conference on RF/Microwave Power Amplifiers for Radio and Wireless Applications (PAWR), pp. 25(2017) [5] L. Kou, J. Lu, P. Di Maso, 2019 IEEE 7th Workshop on Wide Bandgap Power Devices and Applications (WiPDA), pp. 205(2019) [6] H. Li, J. Li, K. Wang, W. Chen, et al., IEEE Transactions on Power Electronics, vol. 30, pp. 3998(2014) [7] J. Song, M. Liu, C. Ma, IEEE Transactions on Industrial Electronics, vol. 67, pp. 8281(2019) [8] H. A. Wheeler, Proceedings of the Institute of Radio Engineers, vol. 16, pp. 1398(1928) [9] H. L. Chan, K. W. E. Cheng, D. Sutanto, 2000 Eighth International Conference on Power Electronics and Variable Speed Drives, pp. 69(2000)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e87a9716c1b30438f50eeea535a90b25.jpg)
Fig. 1 Topology of the WPT system

![](https://assets.underline.io/uploads/markdown_image/1/image/ad2c8f9ba024d557ada47c36613f662c.jpg)
Fig. 2 System circuit simulation results using PSIM

poster

Spin pumping is a technique widely used to generate pure spin current and characterize the spin-charge conversion efficiency of heavy metals，which utilizes a microwave to excite the precession of the magnetic moments. However, the microwave irradiation may also bring possible thermoelectric artifacts. Both the eddy currents in conductors and magnon–phonon scattering in ferromagnet could heat the samples [1]. Typically, for devices with a thin film deposited on a thick substrate, the temperature increase might establish a perpendicular temperature gradient, which gives rise to thermoelectric signals such as the longitudinal spin Seebeck effect (LSSE) [2] and the anomalous Nernst effect (ANE) [3]. Therefore, the spin pumping signals are potentially contaminated with thermoelectric contributions [4]. The separation of the LSSE and ANE contributions from the spin pumping signal is not straightforward. Under an out-of-plane (perpendicular) temperature gradient, the LSSE and ANE produce thermoelectric signal with Eth∝▽ZT×M, where M represents the magnetization direction of ferromagnet. One can readily find that the spin pumping, LSSE, and ANE voltages all share the same symmetry with the same angular dependence, hence inseparable and additive. Furthermore, if the thermoelectric contributions are dominating, the measured signal in the ferromagnet/heavy metal structure may even fail to denote the spin Hall angle sign of the heavy metal [5]. Therefore, it is important to develop a quantitative method to separate thermoelectric contributions in the spin pumping experiments. In this work, we present a universal and quantitative method to obtain the thermoelectric contributions in spin pumping voltage via the assistance of the microwave-photoresistance measurements. We apply this method on two typical systems, i.e., Py(Ni80Fe20)/Pt and YIG(Y3Fe5O12)/Pt bilayers, and find that the microwave radiation indeed can raise the sample temperatures and create a perpendicular temperature gradient. This vertical temperature gradient induces a sizable thermal voltage due to the LSSE and the ANE near zero magnetic field, which acts as a background for spin pumping signals at higher fields. However, the additional heat dissipation due to magnon-phonon scattering at the ferromagnetic resonance condition is negligibly small, in consistent with previous findings [6]. This conclusion is further supported by the field-dependent microwave absorption measurement using a vector network analyzer. Therefore, we conclude that the thermoelectric contributions are little, if any, as compared with the spin pumping signal in our measurement geometry.

**References:**

[1] N. Yoshikawa and T. Kato, J. Phys. D: Appl. Phys. Vol. 43, p. 425403 (2010). [2] K. Uchida, H. Adachi and E. Saitoh, Appl. Phys. Lett. Vol. 97, p. 172505 (2010). [3] T. Miyasato, N. Abe and Y. Tokura, Phys. Rev. Lett. Vol. 99, p. 086602 (2007). [4] Y. Huo, F. L. Zeng and Y. Z. Wu, Phys. Rev. Appl. Vol. 8, p. 014022 (2017). [5] W. W. Lin and C. L. Chien, arXiv :1804.01392(2018). [6] P. Noel, M. Cosset-Cheneau and J. P. Attane, J. Appl. Phys. Vol. 127, p. 163907 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a7adaa058098cf7f0ce5f5806dbff6a6.jpg)
Fig. 1 (a) Schematic illustration of the experimental setup for spin pumping measurements of Py/Pt bilayer. (b) Field-dependent voltage for a Py(6 nm)/Pt(3 nm) bilayer stripe with 8.5 GHz microwave irradiation, where the magnetic field is applied along the y-direction. The black symbols represent the experimental data, and the red lines are the Lorentz line fittings. The inset presents the zoomed-in feature near zero magnetic field. 2△V0 denotes the difference of the voltage background for the positive and negative fields. (c) Microwave frequency f dependent resonance field Hr. Black circles are the experimental data, and the red line is the fitting with Kittel equation. (d) Microwave input power dependent Vr (black hexagon, left scale) and △V0 (red triangle, right scale). The lines are linear fittings.

![](https://assets.underline.io/uploads/markdown_image/1/image/ddf6716071faa41eb5e55e19f5e780c7.jpg)
Fig. 2 (a) R-T curve of a Py(6 nm)/Pt(3 nm) bilayer near room temperature, with a slope of 7.12(±0.02) Ω/K. R300K = 8.86 kΩ. (b) Magnetic field-dependent voltages with dc current +I0 (+0.9 mA, red curve) and −I0 (−0.9 mA, black curve) for the Py/Pt sample, respectively. (c) The resistance difference △R of the Py/Pt bilayer between microwave on and off states. (d) Linear relation between the thermoelectric ground △V0 and the resistance difference background △Rb. (e) Magnetic field dependent △R for different α. The curves are shifted for clarity. (f) Magnetic field-dependent S21 parameter data for a “7 mm×7 mm” Py(6 nm)/Pt(3 nm) film.

 Quantitative Estimation of Thermoelectric Contributions in Spin Pumping Signals through microwave photoresistance measurements

Spin-orbit coupling (SOC) is one of the most important parts of spintronics. The momentum and spin of electrons are coupled by spin-orbit interaction. Two of the representative phenomena that originated from SOC are Rashba-Edelstein effect (REE) [1] and spin Hall effect (SHE) [2, 3]. There are numerous studies on REE and SHE, but direct observation of those effects has been elusive. Concerning the spin Hall effect, a current-induced spin accumulation has been directly observed using the magneto-optic Kerr effect (MOKE). [4, 5] However, there has been no direct observation of spin accumulation induced by the Rashba-Edelstein effect. In this study, we investigated the current-induced spin accumulation in InAs two-dimensional electron gas (2DEG) channel directly by using the MOKE. As a result, the in-plane spin accumulation throughout the channel by REE and the out-of-plane spin accumulation at the edges of the 2DEG channel by SHE were directly observed. Our result is of importance because it exhibits both spin accumulation components originating from REE and SHE in the same structure and they are unambiguously separated. Moreover, we determined the current-induced magneto-optic constant of InAs 2DEG, which is essential for further optical studies on this structure.

**References:**

[1] V. M. Edelstein, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Communications 73, 233-235. (1990) [2] M. I. D’yakonov, and V. I. Perel, Current-induced spin orientation of electrons in semiconductors. Phys. Lett. 35A, 459 (1971) [3] M. I. D’yakonov, and V. I. Perel, Possibility of Orienting Electron Spins with Current. Sov. Phys. JETP Lett. 13, 467 (1971) [4] Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Observation of the spin Hall effect in semiconductors. Science 306, 1910-1913. (2004) [5] C. Stamm, C. Murer, M. Berritta, J. Feng, M. Gabureac, P. M. Oppeneer, and P. Gambardella, Magneto-Optical Detection of the Spin Hall Effect in Pt and W Thin Films. Phys. Rev. Lett 119, 087203. (2017)

**Images:**

 Direct magneto-optical observation of current-induced spin accumulation in InAs two-dimensional electron gas (2DEG) structure

The generation and detection of spin currents are key a role in investigating basic physics phenomena and for applications in the field of spintronics. One method of generating spin current is the spin Seebeck effect (SSE) via applying a heat current along with the magnetic materials. The spin current can be converted to an electrical voltage in large spin-orbit coupling materials due to the inverse spin Hall effect (ISHE). Recently, many reports have been shown that paramagnetic, ferrimagnetic, and antiferromagnetic materials reveal large spin-to-charge current conversion [1-4]. In this work, we investigate the SSE in thin-film the antiferromagnetic PtMn on top of sputtered YIG films. We prepared the following film stacks using rf and dc magnetron sputtering: substrate/buffer/Y3Fe5O12 (100 nm)/800 C/Pt0.35Mn0.65 (10 nm)/MgO (2 nm)/Ta (1 nm)/375 C, where the temperatures are the post-annealing temperatures, and the films are grown at the room temperature. We used four substrate/buffer combinations: Gd3Ga5O12 (GGG) sub., Si/SiO2 sub., Si/SiO2/Ta (5 nm), and Si/SiO2/Ta (5 nm)/Pt (5 nm). We optimized the YIG’s sputtering growth condition for stoichiometry, high saturation magnetization, low ferromagnetic resonance damping constant, and low surface roughness. The PtMn is made with rich Mn composition having an fcc phase. Subsequently, we measured the SSE. We applied a thermal gradient across the thickness direction of the substrate, and measured the conversion of generated spin current to electric voltage by means of ISHE in PtMn. Figure 1(a-b) shows our measurement result in the Si/SiO2/YIG /PtMn and GGG/YIG/PtMn samples as a function of applied magnetic field Hx at ΔT = 4 K. We observed that SSE voltage VSSE is revealed in both samples. Moreover, the magnitude of VSSE is proportional to ΔT as shown in Fig. 1(c-d). Even though our films are antiferromagnetic and have a Mn-rich composition, the magnitude of VSSE in our samples is comparable to what is found in YIG/Pt systems [4]. Further data and discussion will be presented. This work was supported by the Center for Science and Innovation in Spintronics (CSIS), Center for Spintronics Research Network (CSRN), Tohoku University, and by JSPS KAKENHI Grant Number JP19K15429. JP20H02185

**References:**

[1] Nakata et al., "Spin Seebeck voltage enhancement by Mn system metals insertion at the interface between YIG and nonmagnetic layer." Japanese Journal of Applied Physics 58, no. SB (2019): SBBI04. [2] Seki et al., "Observation of inverse spin Hall effect in ferromagnetic FePt alloys using spin Seebeck effect." Applied Physics Letters 107, no. 9 (2015): 092401. [3] Kikkawa et al. "Longitudinal spin Seebeck effect free from the proximity Nernst effect." Physical review letters 110, no. 6 (2013): 067207. [4] Mendes et al., "Large inverse spin Hall effect in the antiferromagnetic metal Ir 20 Mn 80." Physical Review B 89, no. 14 (2014): 140406

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ae6968b7c2263f52936059e4033429d1.jpg)
(a-b) Field dependence of SSE voltage in the PtMn at ΔT=4 K, (c-d) ΔV as a function of ΔT .

 Spin Seebeck Effect in Antiferromagnetic PtMn/YIG(Yttrium Iron Garnet) Thin Films

Thermoelectric conversion elements using the spin Seebeck effect (SSE) have attracted much attention owing to their unique physical properties as well as the industrial applications in a relatively simple structure [1-3]. Many studies using Y3Fe5O12 (YIG) have been reported as a magnetic insulator for SSE measurements. Since YIG is an insulator with high Curie temperature that allows magnons to propagate over a long distance, it is suitable for SSE observation. SSE measurements are often carried out using YIG prepared in a sintered bulk or a film grown by a physical vapor deposition method, SSE has also been studied using YIG films prepared by metal–organic decomposition (MOD) which is a simple process used for surface coating [3]. We have previously observed SSE in YIG films prepared on a Si substrate by co-precipitation, which consist of densely packed YIG nanoparticles [4]. In order to enhance the SSE voltage, the YIG films are required to have a flat film surface made by a different chemical process, which enables magnons to coherently propagate. In this paper, we report on the longitudinal SSE (LSSE) voltage in YIG films prepared on a Si or gadolinium gallium garnet (GGG) substrate by sol-gel spin-coating to investigate the annealing-temperature dependence of LSSE voltage in the samples. YIG film samples were synthesized by sol-gel and subsequent spin-coating processes, followed by annealing at Ta = 1073-1273 K for 0.5 hour in air. From the XRD spectra of the YIG films, diffraction peaks associated with the garnet phase are readily observed in the spectra of all the annealed samples, proving that they are polycrystalline YIG. Figure 1 shows a surface morphological SEM image from a YIG film made on a Si substrate annealed at 1173 K. The average surface roughness measured by SPM is ~10 nm or less, which is 30% smaller than that of YIG films prepared by co-precipitation. The areal fraction of voids estimated in the film surface by SEM imaging is ~10%, which is 75% smaller than those of YIG films prepared by co-precipitation. The obtained results indicate that the YIG films with a flatter surface can be made by the sol-gel method. To conduct SSE voltage measurements, a 5 nm Pt metal was sputtered on the YIG films. A temperature gradient △T was applied between the top of each sample (Pt side) and the bottom of the substrate to measure the voltage induced by LSSE. Figure 2 shows the variation of the SSE constant S with the annealing temperature Ta. The values of S in each sample are calculated from the △T dependence of the saturation SSE voltage VSSESat. The value of S for YIG/Pt films made on a Si substrate decreases with increasing Ta, showing the same trend as those observed for co-precipitated YIG films, which is attributable to the microstructural evolution of the nanocrystalline YIG films upon annealing. Besides, the magnitude of S is at least 30% smaller than that of co-precipitated YIG films. It is speculated that the observed decrease in the magnitude of S is owing to the increase in the interfacial area between densely packed nanoparticles as the increase in the coercive force of YIG films prepared by sol-gel is observed according to their magnetic measurements by VSM. The values of S in the YIG/Pt films synthesized on a GGG substrate annealed at 1173 K are larger than those made on a Si substrate presumably because a single crystal YIG film is formed on the GGG substrate which yields a high efficiency of magnon excitation.

**References:**

[1] K. Uchida et al, Nature, Vol. 455, p. 778 (2008) [2] K. Uchida et al, Nat. Mater. Vol. 9, p. 894 (2010) [3] A. Kirihara et al, Nat. Mater. Vol. 11, p. 686 (2012) [4] K. Yamada et al, IEEE Trans. Magn. Vol. 55, p. 4500104 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/140878e2be751346f3eeaa41cb7e47b2.jpg)
SEM surface image of a YIG film annealed at 1173 K.

![](https://assets.underline.io/uploads/markdown_image/1/image/fba6a1da143f2ae7c0b37407d6894e1b.jpg)
SSE constants S of Pt(5 nm)/YIG films on a Si or GGG substrate plotted as a function of Ta.

 Annealing temperature dependence of longitudinal spin Seebeck voltage in YIG films prepared by sol-gel spin coating method

Introduction: Biomagnetic measurement systems, such as a magnetoencephalography (MEG), are commonly composed of multi-channel magnetic sensor array more than 100. It is very important to know the positions, orientations, and sensitivities of the magnetic sensors precisely to accurately estimate the neuronal activity. So far, a calibration technique is employed to measure the sensor geometry and sensitivity after assembling or cooling the sensor arrays [1]. This calibration technique is performed by estimating the geometry and sensitivity of the sensors from the measured magnetic field distribution generated by a multi-coil array. However, there is no discussion about the accuracy of the estimation because the coil array itself has not been calibrated and its accuracy has not been evaluated. Therefore, we propose the calibration technique for the coil array based on the three-dimensional (3D) measurement using an X-ray computed tomography (CT). In this paper, we present a calibration result of the coil array and a comparison of the accuracy of the MEG source localization between using the designed and calibrated coil array geometries to measure positions, orientations, and sensitivities of MEG sensors. We fabricated a 18-channel coil array. This coil array was composed of 6 coil modules that have concentric 3 coils orthogonal to each other. The diameter and the distance between each coil were designed 30 mm and about 70 mm, respectively. (1) 3D measurement using X-ray CT The 3D measurement was performed using an X-ray CT machine (inspeXio SMX-225CT FPR HR, Shimazu Corporation). The center position, the orientation of the normal vector, and the radius of each coil were obtained by fitting a circle equation to the 3D data. We call this process “calibration of the coil array”. (2) Measurement of the MEG sensor geometries In this study, we used a whole-head MEG system, which was installed at the Kanazawa Institute of Technology [2]. This MEG system consisted of 160 arrayed SQUID (superconducting quantum interference device) sensors, which had the first-order axial gradiometers. The coil array was placed at the center of the helmet of the MEG cryostat, and the magnetic signals were generated by applying sinusoidal current waveform (80 Hz) to each coil. After measuring the magnetic signals, we estimated the sensor array layout (position, orientation, and sensitivity of each sensor). The sensor array layouts were obtained by solving the inverse problem using (A) designed and (B) 3D measured coil array geometry. (3) MEG source localization In order to confirm that the performance of the MEG system can be improved by employing the 3D-measured coil array geometry, we compared the source localization accuracy using the sensor layouts between (A) and (B). An MEG phantom, which emulates the neuronal activity in human brain as equivalent current dipoles (ECDs) [3], was used to provide the signal sources. The magnetic signals from the ECDs were measured by the MEG sensors, then the sources were localized using the sensor layouts (A) and (B). Results and Discussions: (1) 3D measurement using X-ray CT Figure 1 shows the results of the 3D measurement of the coil array using the X-ray CT. Figure 1 (a) is the entire polygon data converted from the X-ray CT image, and Fig.1 (b) shows the designed geometries of the coils in the module 1 (blue) and the obtained circles based on the X-ray CT measurement (red). The differences between designed and the 3D-measured coil geometries were 0.6±0.3 mm, 0.7±0.4 degrees, and 0.3±0.1 mm (mean±standard deviation of 18 coils) in the center position, the orientation of the normal vector, and the radius, respectively. (2) Measurement of the MEG sensor geometries The sensor array layouts were estimated using the designed and the 3D-measured coil array geometries. The differences of the estimated layouts were 1.2±0.9 mm, 1.0±0.6 degrees, and 0.7±1.9 % (mean±standard deviation of 160 sensors) in position, orientation, and sensitivity, respectively. (3) MEG source localization Figure 2 shows the differences between true value and localized values of the sources in position and orientation, respectively. Both displacements in position and orientation decreased by using the 3D-measured coil array geometry. It was demonstrated that the source localization accuracy was improved by defining the sensor layout using the calibrated coil array geometry. Conclusion: We demonstrated the calibration method of the coil array based on the 3D measurement using the X-ray CT machine. Although the coil array was fabricated preciously, the calibration of the coil array is necessary to bring the best out of the MEG system.

**References:**

[1] T. Yoshida, et al., “Calibration system for multichannel SQUID magnetometer,” in Proc. 16th Annu. Int. Conf. IEEE Eng. Adv. New Opportunities Biomed. Eng., pp.171-172 (1994). [2] H. Kado, et al., “Magnetoencephalogram systems developed at KIT,” IEEE Trans. Appl. Supercond., vol. 9 (2), pp. 4057-4062 (1999). [3] D. Oyama, et al., “Dry phantom for magnetoencephalography － Configuration, calibration, and contribution,” J. Neurosci. Methods, vol. 251, pp. 24-36 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2321ed5ac6ba860c99e1487530a02181.jpg)
Fig. 1 Results of X-ray CT measurements of the coil array. (a) entire polygon data, (b) designed and 3D-measued geometries of the coils on the module 1.

![](https://assets.underline.io/uploads/markdown_image/1/image/bf4370f47df771b814ee17abdf75c1a6.jpg)
Fig. 2 Results of the source localization experiment. This graph shows the differences between the true value and the localized values of the signal sources in position and orientation. The lengths of the squares and the error bars indicate the mean and the standard deviation of 49 signal sources).

 Calibration of a Coil Array Geometry Using an X-ray Computed Tomography

Inrush current is the reason why large power transformers cannot close without load[1]. Controlling the closing phase of circuit breaker can effectively reduce the inrush current when the circuit breaker is closed. However, it is necessary to know the value and direction of residual flux in the transformer core to control the closing phase angle. Therefore, the accurate detection of residual flux has important reference significance for the protection of power transformer. This paper proposes a method of measuring residual flux density in single-phase transformers based on the phase difference between the test voltage and the transient current, and establishes the relationship between the phase difference and residual flux based on the magnetic properties of the iron core. The finite element method is used to model and analyze the measured square transformer core, and the fitting relationship between residual flux and phase difference is obtained according to the calculation result. The experimental results show that the relative error between the finite element calculation results and the experimental results is within 5.93%, which verifies the feasibility of the proposed method and the accuracy of the relation obtained by the finite element calculation. The relationship between different residual flux and phase difference is obtained, which provides effective information for controlling the closing phase of circuit breaker.

**References:**

[1] Y. Wang, Z. Liu and H. Chen, "Research on Residual Flux Prediction of the Transformer," IEEE Transactions on Magnetics, Vol. 53, no. 6, pp. 1-4, June 2017.

**Images:**

 Residual Flux Density Measurement Method of the Single-Phase Transformer Based on Phase Difference

I. Introduction Observation and analysis of magnetic domain structure of magnetic materials with high spatial resolution are essential for understanding and improving the magnetic properties of the materials. In this regards, magnetic force microscopy (MFM) is widely used to observe the magnetic domain structure with high spatial resolution. MFM detects the gradient of magnetic field of which direction is the same as that of MFM tip magnetization. The control of the measuring direction is important to analyze the magnetic domain structure precisely. However, the measuring direction control is not easy especially for hard magnetic materials because the tip magnetization often varies by the strong sample magnetic field at the measuring position. In recent years, we have developed new novel MFM, which enables to fix the measuring field direction on DC magnetic field imaging, based on our developed alternating magnetic force microscopy (A-MFM) [1] and highly sensitive Co-GdOx superparamagnetic tip (SP tip) [2] of which magnetization direction is parallel to the applied magnetic field. A-MFM detects magnetic force gradient near the sample surface with high spatial resolution by using the frequency modulation of cantilever oscillation caused by off-resonant alternating magnetic force [1]. For the imaging of hard magnetic materials, the SP tip, which is magnetized normal to the sample surface by homogeneous AC magnetic field, is used and the SP tip detects the alternating magnetic force between AC tip magnetization and DC magnetic field from the sample and measure the gradient of magnetic field normal to the sample surface [3]. We successfully observed the magnetic domain structure of a very rough fractured Sr ferrite magnet without topographic crosstalk by fixing the measuring direction of DC magnetic field normal to the sample surface [3]. In this study, by using an observed A-MFM image of NdFeB sintered magnet of which measuring direction of magnetic field is normal to the sample surface, we demonstrate three-dimensional magnetic field gradient imaging by measuring field direction transformation, which is based on MFM tip transfer function [4]. A-MFM images, which were measured by SP tip, satisfy the necessary condition of the proposed three-dimensional imaging that the measuring detection of magnetic field for the observed image is fixed. II. Principle of three-dimensional magnetic field gradient imaging Generally, MFM signal of ∂Fz/∂z can be expressed by mx(∂2Hx/∂z2)+my(∂2Hy/∂z2)+mz(∂2Hz/∂z2), where the z direction is normal to the sample surface and m=(mx, my, mz) and H=(Hx, Hy, Hz) are the tip magnetization and the magnetic field from the sample, respectively. Here our used Co-GdOx SP tip is composed of magnetically separated magnetic nanoparticles of which diameter is less than 7 nm and each nanoparticle is thought to behave as a magnetic dipole m. The magnetic field gradient component can be expressed by the transfer function G for sample’s magnetic charge ρm , which is the source of magnetic fields [4]. For examples, gradient of perpendicular magnetic field (∂2Hz/∂z2) is expressed by the following in wave number k space. (∂2Hz/∂z2)(kx, ky, z) =G[∂2Hz/∂z2](kx, ky, z-z0)ρm(kx, ky, z0) ,where the z-z0 is the tip-sample distance. In the case of obtaining the (∂2Hx/∂z2) image from (∂2Hz/∂z2) image, the measuring direction transformation filter G[∂2Hx/∂z2]/G[∂2Hz/∂z2] is used in the following. (∂2Hx/∂z2)(kx, ky, z) =G[∂2Hx/∂z2](kx, ky, z-z0)ρm(kx, ky, z0)=G[∂2Hx/∂z2]/G[∂2Hz/∂z2] (∂2Hz/∂z2)(kx, ky, z) The ∂2Hy/∂z2 image can be obtained in the similar way. The proposed method enables to obtain three magnetic field gradient components from only one component. Various images, such as the amplitude and direction of magnetic field gradient also can be obtained by using these three components. III. Experimental procedure Our A-MFM system was based on a magnetic force microscope with an electromagnet to apply AC magnetic field to the tip for generating off-resonant alternating magnetic force between the AC tip magnetization and DC magnetic field from the sample. A-MFM image was observed at room temperature in air atmosphere using home-made high susceptibility superparamagnetic Co-GdOx granular alloy film [2] coated Si tip. The film thickness was 100 nm. The amplitude and the frequency of the AC magnetic field were 200 Oe and 89 Hz, respectively. A sample of demagnetized NdFeB anisotropic sintered magnet with c-plane was placed over the electromagnet. IV. Results Fig.1(a) shows the∂2Hz/∂z2 image of NdFeB demagnetized sintered magnet. Fig(b) and (c) show the transformed ∂2Hy/∂z2 and ∂2Hy/∂z2 image from the∂2Hz/∂z2 image, respectively. Fig(d), (e) and (f) show the images of the intensity of magnetic field gradient |∂2H/∂z2|, polar angle θ and azimuthal angle Φ of the magnetic field gradient, respectively. As seen in these figures, magnetic field distribution is clearly observed. This method needs only one MFM image of which the measuring detection of magnetic field is fixed, while most methods of three-dimensional magnetic field imaging needs three magnetic field sensors for each three-dimensional direction. The proposed imaging is thought to be useful to obtain the precise information of magnetic field distribution and analyze the magnetic domain structure.

**References:**

[1] H. Saito, H. Ikeya, G. Egawa, S. Ishio, S. Yoshimura, J. Appl. Phys., Vol. 105, p.07D524(2009), [2] Y. Cao, P. Kumar, Y. Zhao, Y. Suzuki, S. Yoshimura, H. Saito, J. Magn. Magn. Mater., Vol. 462, p.119 (2018), [3] Y. Cao, Y. Zhao, P. Kumar, S. Yoshimura, H. Saito, J. Appl. Phys., Vol. 123, p.224503 (2018), [4] H. Saito, J. Chen, S. Ishio, J. Magn. Magn. Mater., Vol. 191, p.153 (1999)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/05cbc7fd1bd1fde3f98a8ae521210af6.jpg)
Fig.1 (a) Measured perpendicular magnetic field gradient image ∂2Hz/∂z2 and its signal transformed images [(b) ∂2Hx/∂z2, (c) ∂2Hy/∂z2, (d) |∂2H/∂z2|, (e) polar angle θ and (f) azimuthal angle Φ ] for a NdFeB sintered magnet.

 Three-dimensional magnetic field gradient imaging of permanent magnet by alternating magnetic force microscopy: Transformation of measuring magnetic field direction based on MFM tip transfer function

INTRODUCTION In recent years, imaging of magnetic nanoparticles (MNPs) has attracted attention as a new diagnostic imaging technique for the imaging of certain targets, such as cancer cells [1]. We previously proposed an MNP imaging method, “magnetic nanoparticle tomography” (MNT), that uses multiple magnetic sensors [2], [3]. In the previous study, an inverse problem analysis was performed to estimate the position of MNPs using the non-negative least squares method (NNLS), which is often used for magnetic particle imaging (MPI). The NNLS method achieves high sensitivity and spatial resolution. However, due to the existence of measurement noise and high sensitivity of NNLS, some MNPs are incorrectly estimated, that is, some artefacts appear. In this study, we apply the minimum variance spatial filter (MV-SF), which is often used in magnetoencephalography (MEG) inverse problem analysis [4], to reduce the artefacts. METHODS The experimental setup is presented in Fig. 1. The Resovist MNP sample was arranged in a sinusoidal magnetic field, which was generated using an excitation coil. The third harmonic magnetic field from MNPs was detected using 16 detection coils. To improve the sensitivity, a cancelation circuit for the fundamental magnetic field was employed. The two-dimensional concentration map of the MNP sample was subsequently obtained by the application of the MV-SF. The distance between the MNP sample and the imaging system (excitation coil and detection coils) was set from 25 mm to 40 mm at intervals of 5 mm. We used two samples with different concentrations of 100 µg-Fe and 500 µg-Fe and estimated the positions for each of them. RESULTS The result of the reconstructed map when the MNP sample was set at are shown in Fig. 2. The white circle in the figure represents the actual sample position. Fig. 2 (a) depicts the result for a sample containing 500 µg-Fe. This result reveals that a sharp signal peak position is observed in the vicinity of the sample position. Fig. 2 (b) exhibits the result for a sample containing 100 µg-Fe. This result indicates that the error between a sharp signal peak position and the actual sample position is within 10 mm. No artefacts appear in both results, contrary to the results using NNLS [3]. From these results, we can conclude that MV-SF is useful for reducing the artefact and estimating the positions of MNPs in magnetic nanoparticle tomography. ACKNOWLEDGMENTS This work was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Young Scientists [grant number JP19K14996], and by a research grant from the Mazda Foundation.

**References:**

[1] T. Knopp and T. M. Buzug, “Magnetic Particle Imaging—An Introduction to Imaging Principles and Scanner Instrumentation,” Springer, 2012. [2] T. Sasayama, T. Yoshida, K. Enpuku, “Two-Dimensional Magnetic Nanoparticle Imaging Using Multiple Magnetic Sensors Based on Amplitude Modulation,” Journal of Magnetism and Magnetic Materials, Vol. 505, 2020, Art. no. 166765. [3]T. Sasayama, N. Okamura, and T. Yoshida, “Sensitivity Improvement of Magnetic Nanoparticle Imaging by Compensation with Digital-to-Analog Converter,” IEEE Trans. Magn. In press. DOI: 10.1109/TMAG.2020.3014375. [4] K. Sekihara and S. S. Nagarajan, “Adaptive Spatial Filters for Electromagnetic Brain Imaging,” New York, USA: Springer-Verlag, 2008.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d77d396ce684c3b306bcd9bb12e3471f.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/c12c936808039c93bb5834187a35adca.jpg)

 Inverse Problem Analysis in Magnetic Nanoparticle Tomography with Minimum Variance Spatial Filter

Introduction Magnetocardiography (MCG) is a noninvasive technique that detects the magnetic field generated by the electrical activity of the heart [1]. The estimation of MCG current sources is useful technics for clinical application [2]. Exact low resolution brain electromagnetic tomography (eLORETA) [3] spatial filter is used for visualizing brain activity, as it is a genuine inverse solution with exact, zero error localization in the presence of measurement and structured biological noise. However, it tends to reconstruct a large spatial extension for deep sources due to the decreasing sensitivity of the sensors. In this study, we aim to reduce the influence of the source depth in the reconstructed current sources using multiple spatial filters. Method In order to solve the problem of the large spatial extension for deep sources, in addition to the conventional measurement at the front (chest) of the body, the back is also measured. It is possible to improve the estimation accuracy for a deep signal source. Estimation of MCG current sources was used eLORETA spatial filter. We examined two types of spatial filters for two-side measurement. The first method (128ch method), a spatial filter (128ch) was produced by a read-field matrix using two 64ch sensors as one 128ch sensor. In this method, the regularization parameter λ which determines noise immunity has the same value on the front side and the back side. The second method (2 × 64ch method), two spatial filters (64ch) were separately calculated then one spatial filter (2 × 64ch) was produced from the two spatial filters (64ch). In this method, different λ can be determined on the front side and the back side, and the optimum noise immunity can be given to each. In this study, a spatial filter was created by setting λ as 1% of the maximum eigenvalue in 128ch method, 1% of the maximum eigenvalue on the front side and 5% on the back side in 2 × 64ch method. We estimate MCG current sources within a 175 mm × 175 mm × 995 mm volume. Three thousand two hundred and forty voxels were divided with the size of each voxel being 10 mm × 10 mm × 10 mm. For the forward problem, we calculate the lead-field matrix K using the Biot-Savart Law. For each current source location, K includes two columns that represent X component and Y component, respectively. Results and Discussions We estimated MCG sources at R peak, which indicates the activities of ventricle. Fig.1 (a), (b), and (c) show the estimation results by the conventional 64ch spatial filter, the proposed 128ch spatial filter, and the 2 × 64ch spatial filter, respectively. The upper side is a front view of the heart, and the lower side is a below view of the heart. Each frame represents an analytic space. The estimation result shows voxels with a threshold of 90% or more of the strongest point of the estimated source. Compared to Fig. (a), the estimated sources of Fig. (b) and Fig. (c) are able to suppress the spatial extension of the estimated sources due to the effect of providing the measurement surface on the back side. Moreover, the estimated source of Fig. (b) is not estimated correctly because it appears not only in the ventricle but also in the vicinity of the atrium. It is considered that the estimation is incorrect due to the influence of noise because λ is constant. On the other hand, in Fig. (c), the estimated source appears at the ventricular position, and it is thought that the active position of the heart can be estimated more accurately. Conclusion We proposed two types of spatial filter produced method of eLORETA by two-side measuments of the front and back of the body. By using the back side in addition to the front side, the spatial extension of the estimated source could be suppressed. Among them, the signal source could be estimated at the correct position by produced using a 2 × 64ch spatial filter that can determine the regularization parameter λ on the front side and the back side respectively.

**References:**

 [1] D. Cohen, E.A. Edelsack, J.E. Zimmerman,” Magnetocardiograms taken inside a shielded room with a superconducting point-contact magnetometer”, Applied Physics Letter, Vol. 16, pp. 278-280, 1970. [2] J. S. W. Kwong, B. Leithäuser, J.-W. Park, C.-M. Yu, “Diagnostic value of magnetocardiography in coronary artery disease and cardiac arrhythmias: A review of clinical data,” Int. J. Cardiol., vol. 167, pp. 1835-1842, Sep. 2013. [3] R.D. Pascual-Marqui, “Discrete, 3D distributed, linear imaging methods of electric neuronal activity. Part 1: exact, zero error localization”, Mathmatical Physics, arXiv: 0710. 3341, 2007.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1c828343ab32aef6e8439143ad174be6.jpg)
Fig. 1. The estimation results by (a) the conventional 64ch spatial filter, (b) the proposed 128ch spatial filter, (c) the 2 × 64ch spatial filter. The upper side is a front view of the heart, the lower side is a below view of the heart. Each frame represents an analytic space. The voxel is the estimated source with a threshold of 90% or more of the strongest source.

 Estimation of Magnetocardiography Current Sources using Multiple Spatial Filters

In rotational ac machines, interlocking is a commonly used manufacturing method to fix the silicon steel laminations. To analyze the range of degradated magnetic properties caused by the interlocking process more accurately, the distribution of magnetic properties around the interlock was investigated and the areas damaged to varying degrees was quantified. This work is meaningful for the accurate modeling and simulation of machines. I. Introduction Electrical steel sheets are usually assembled into core laminations through interlocking, welding or gluing. In comparison, interlocking is suitable for batch production and become the main method of fixing among electrical steel sheets currently. However, the deterioration of the magnetic properties caused by interlocking cannot be ignored. The formation of interlocks is always accompanied by plastic deformation and generation of residual stress, which will change the movement of magnetic domain under magnetization, and the hysteresis characteristics will be significantly influenced. Furthermore, the interlocking process destroys the insulation, resulting in inter-lamination short circuits. At high frequencies, the interlaminar eddy current loss even contributes more to the deterioration of magnetic properties. There have been several magnetic measurements of interlocks on lamination ring cores with primary winding and secondary winding before, and they have investigate the effect of the interlocks number, sizes, and shapes on the overall magnetic properties of lamination ring cores[1-3]. However, the overall magnetic properties of ring cores cannot be served for accurate simulation of the interlocking process. Some preliminary attempts for interlocking localized magnetic measurements are also in progress, but they mainly focus on interlocks with a single size and a single magnetization direction[4]. Therefore, a more comprehensive localized magnetic properties measurement is necessary. II. Experimental and Results A localized magnetic measurement sensor with two B-needle probes and a H-coil have been manufactured. The distance between the B-needle probes is 3.5 mm and the size of the H-coil is 3 mm×3 mm. As is shown in Fig. 1(a), the sensor was connected to a three-axis precision positioning table, and the displacement accuracy of the sensor is 0.1 mm. Then four hollow square shaped samples with interlocks were wound by the exciting coils. The detailed information of samples and interlocks was shown in Fig 1(b). More than three hundred measurement points are taken on the concave and convex surfaces around each interlock to achieve higher resolution measurements of the local vector magnetic properties. Due to the length limitation of the abstract, Fig. 2 shows part of measured results at 50 Hz with 0.5 T sinusoidal excitation. The white rectangle represents the the upper part of the interlocking position. For the single sheet, it can be seen that the loss increases and the magnetic permeability decreases near the interlock. This is attributed to the generation of residual stress during the formation of the interlocks. For the ten-layer laminate, in addition to the residual stress, the insulation between laminations is destroyed near the interlocks and interlaminar short circuits is formed, which will produce extra eddy current loss. The ratio of loss increment and the ratio of permeability decrement of the three interlocks at 50Hz and 0.5T magnetic density will be provided in the whole paper. The damaged areas of varying degrees was quantified. Besides, the size of the interlocks can also cause different influence on the magnetic properties near the interlocks. The measurement were performed with Sample 2 and Sample 4, and the results show that the magnetic properties deterioration area around larger interlocks is bigger. The deterioration area hardly change with different magnetic flux. III. Conclusions In this paper, we concluded the influence of interlocks on the magnetic properties as follows: 1) The size of the interlock and the degree of localized magnetic degradation are positively but not linearly correlated. The requirements for fastened strength should be taken into consideration when selecting a appropriate size. 2) The local magnetic degradation caused by interlocking in the rolling direction is much lower than that in the transverse direction. 3) On the basis of planar distribution of magnetic degradation, different levels of magnetic degradation caused by interlocking can be quatified. Applying these results to the electrical machines can contribute to the improvement in simulations of them.

**References:**

[1] J. Shen, G. Zhou, S. Jin and H. Hao, 2015 International Conference on Sustainable Mobility Applications, Renewables and Technology (SMART) IEEE., p.1-4(2015). [2] K. Senda, H. Toda, and M. Kawano, Ieej Journal of Industry Applications., Vol. 4, p.496-502(2015). [3] S. Imamori, S. Steentjes and K. Hameyer. IEEE Transactions on Magnetics., Vol. 53,(2017). [4] S. Imamori, S. Aihara and H. Shimoji, et al. Journal of Magnetism and Magnetic Materials., Vol. 500, (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8931710e06488033fcd3d967d8528c76.jpg)
Fig 1. (a)The measuring device.(b) The detailed information of samples and interlocks.

![](https://assets.underline.io/uploads/markdown_image/1/image/18b10ed4fde7b21f1354a164e8b2d0a2.jpg)
Fig2. Part of the experimentally measured planar distribution of magnetic properties at 50Hz and 0.5T magnetic density. (a) Upper part of the permeability around the interlock on the convex surfaces of Sample 1. (b) Upper part of the loss around the interlock on the concave suface on the Sample 2.

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