France



Composite multiferroic materials represent a novel class of functional materials where multiple types of ferroic ordering coexist. Further, coupling between different types of ferroic materials can result in additional ordering, which can be leveraged to fabricate new multifunctional devices.&lt;sup&gt;1, 2&lt;/sup&gt; One-dimensional composite magnetoelectric nanofibers, free of substrate-based constraints provide an ideal platform for achieving magnetoelectric coefficients that are orders of magnitude greater than those in ideal thin films.&lt;sup&gt;3&lt;/sup&gt; Here, we will present the synthesis of one-dimensional magnetoelectric nanofibers via electrospinning followed by device assembly. Electrospinning can be used to fabricate composite nanowires in a range of configurations by varying the orientation of the piezoelectric and magnetoelectric phases, including random, core-shell, or Janus. Here, we will focus on the synthesis and assembly of bi-phasic magnetoelectric Janus nanofibers, this structure retains external access to each phase as well as to the interface, making them well suited to form modular structures (Figure 1).&lt;br/&gt;&lt;br/&gt;As-electrospun fibers are amorphous and form a continuous fiber network, requiring subsequent processing steps to both crystallize the nanofibers while also taking advantage of thermal stresses to break the nanofibers into shorter nanowires for device applications. The final nanowire length can be controlled by the electrospinning parameters (e.g., applied voltage) as well as the calcination ramp rate. Shorter nanowires (&amp;lt;10 mm) result from as-spun nanofibers with a smaller initial diameter, and/or faster calcination ramp rates. Aligned arrays of the nanowires can then be assembled into device architectures via dielectrophoresis (Figure 1b-d). The efficiency of nanowire assembly via dielectrophoresis can be enhanced solvent choice as well as the frequency of the applied voltage. We found optimum assembly using butanol and an applied voltage of 42 volts peak to peak at a frequency of 5kHz. Additionally, prior to assembly it may be necessary to perform an acid rinse of the nanofibers to remove any undesired carbonate phases that may hinder assembly. This method results in a linear density of assembled nanowires of ~20 nanowires/mm.&lt;br/&gt;&lt;br/&gt;The assembled arrays of magnetoelectric nanowires can then be used for a variety of devices, including zero-power magnetic field and current sensors.&lt;sup&gt;4&lt;/sup&gt; Figure 2 shows the magnetoeletric coefficients of BaTiO&lt;sub&gt;3&lt;/sub&gt;/CoFe&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;4&lt;/sub&gt; nanowire arrays. These nanowire arrays have a magnetoelectric coefficient of 514+/- 27 mV cm&lt;sup&gt;-1&lt;/sup&gt; Oe&lt;sup&gt;-1&lt;/sup&gt; at 1 kHz, considerably larger than bulk values 104 mV cm&lt;sup&gt;-1 &lt;/sup&gt;Oe&lt;sup&gt;-1&lt;/sup&gt;. Figure 2 also shows corresponding device sensitivities.&lt;br/&gt;&lt;br/&gt;Magnetoelectric nanowires can be assembled into arrays for low power sensors, including magnetic field and current sensors and they can also be developed for biomedical applications where the remote delivery of electric fields is desired, such as for neural modulation.&lt;sup&gt;5&lt;/sup&gt; Here, we will demonstrate the versatility of magnetoelectric nanowires, their synthesis, and applications. This work opens new opportunities and applications for magnetoelectric materials. This work was support by the NSF I/UCRC on Multi-functional Integrated System Technology (MIST Center) IIP-1439644. The authors acknowledge the use of the Major Analytical Instrumentation Center (MAIC) and Nanoscale Research Facility (NRF) at the University of Florida.

**References:**

1. Spaldin, N. A., &lt;i&gt;Proc. R. Soc. A &lt;/i&gt;2020, &lt;i&gt;476&lt;/i&gt; (2233), 20190542.&lt;br/&gt;2. Nan, C.-W.; Dong, S.; Viehland, D.; Srinivasan, G., &lt;i&gt;Journal of Applied Physics &lt;/i&gt;2008, &lt;i&gt;103&lt;/i&gt; (3), 031101.&lt;br/&gt;3. Xie, S.-H.; Liu, Y.-Y.; Li, J.-Y., &lt;i&gt;Front. Phys. &lt;/i&gt;2012, &lt;i&gt;7&lt;/i&gt; (4), 399-407.&lt;br/&gt;4. Bauer, M. J.; Wen, X.; Tiwari, P.; Arnold, D. P.; Andrew, J. S., &lt;i&gt;Microsystems &amp; Nanoengineering &lt;/i&gt;2018, &lt;i&gt;4&lt;/i&gt; (1), 37.&lt;br/&gt;5. Ferson, N. D.; Uhl, A. M.; Andrew, J. S., P. &lt;i&gt;IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control &lt;/i&gt;2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5dbf229eb0b210860d8fcd24301da24c.jpg)
Figure 1. (a) scanning electron microscope image of a biphasic magnetoelectric nanowire suspended across an electrode gap (b) optical microscope image of an electrical assembly (c) a schematic magnetoelectric voltage source consisting of composite magnetoelectric nanowires and (d) a schematic of a possible architecture suitable if the density of the assembled nanowires is found to be generally uniform.

![](https://assets.underline.io/uploads/markdown_image/1/image/3c329a99c16139ffe78fbd2b64a3eabc.jpg)
Figure 2. Magnetoelectric coefficients and corresponding device sensitivities of BaTiO&lt;sub&gt;3&lt;/sub&gt;/CoFe&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;4&lt;/sub&gt; nanowire arrays as a function of frequency measured at angles of approximately no inductive effects, the angle of maximum constructive induction, and maximum destructive induction.

INTERMAG 2021

 Magnetoelectric Nanowires and Their Applications INVITED

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Composite multiferroic materials represent a novel class of functional materials where multiple types of ferroic ordering coexist. Further, coupling between different types of ferroic materials can result in additional ordering, which can be leveraged to fabricate new multifunctional devices.1, 2 One-dimensional composite magnetoelectric nanofibers, free of substrate-based constraints provide an ideal platform for achieving magnetoelectric coefficients that are orders of magnitude greater than those in ideal thin films.3 Here, we will present the synthesis of one-dimensional magnetoelectric nanofibers via electrospinning followed by device assembly. Electrospinning can be used to fabricate composite nanowires in a range of configurations by varying the orientation of the piezoelectric and magnetoelectric phases, including random, core-shell, or Janus. Here, we will focus on the synthesis and assembly of bi-phasic magnetoelectric Janus nanofibers, this structure retains external access to each phase as well as to the interface, making them well suited to form modular structures (Figure 1). As-electrospun fibers are amorphous and form a continuous fiber network, requiring subsequent processing steps to both crystallize the nanofibers while also taking advantage of thermal stresses to break the nanofibers into shorter nanowires for device applications. The final nanowire length can be controlled by the electrospinning parameters (e.g., applied voltage) as well as the calcination ramp rate. Shorter nanowires (&lt;10 mm) result from as-spun nanofibers with a smaller initial diameter, and/or faster calcination ramp rates. Aligned arrays of the nanowires can then be assembled into device architectures via dielectrophoresis (Figure 1b-d). The efficiency of nanowire assembly via dielectrophoresis can be enhanced solvent choice as well as the frequency of the applied voltage. We found optimum assembly using butanol and an applied voltage of 42 volts peak to peak at a frequency of 5kHz. Additionally, prior to assembly it may be necessary to perform an acid rinse of the nanofibers to remove any undesired carbonate phases that may hinder assembly. This method results in a linear density of assembled nanowires of ~20 nanowires/mm. The assembled arrays of magnetoelectric nanowires can then be used for a variety of devices, including zero-power magnetic field and current sensors.4 Figure 2 shows the magnetoeletric coefficients of BaTiO3/CoFe2O4 nanowire arrays. These nanowire arrays have a magnetoelectric coefficient of 514+/- 27 mV cm-1 Oe-1 at 1 kHz, considerably larger than bulk values 104 mV cm-1 Oe-1. Figure 2 also shows corresponding device sensitivities. Magnetoelectric nanowires can be assembled into arrays for low power sensors, including magnetic field and current sensors and they can also be developed for biomedical applications where the remote delivery of electric fields is desired, such as for neural modulation.5 Here, we will demonstrate the versatility of magnetoelectric nanowires, their synthesis, and applications. This work opens new opportunities and applications for magnetoelectric materials. This work was support by the NSF I/UCRC on Multi-functional Integrated System Technology (MIST Center) IIP-1439644. The authors acknowledge the use of the Major Analytical Instrumentation Center (MAIC) and Nanoscale Research Facility (NRF) at the University of Florida.

**References:**

1. Spaldin, N. A., Proc. R. Soc. A 2020, 476 (2233), 20190542. 2. Nan, C.-W.; Dong, S.; Viehland, D.; Srinivasan, G., Journal of Applied Physics 2008, 103 (3), 031101. 3. Xie, S.-H.; Liu, Y.-Y.; Li, J.-Y., Front. Phys. 2012, 7 (4), 399-407. 4. Bauer, M. J.; Wen, X.; Tiwari, P.; Arnold, D. P.; Andrew, J. S., Microsystems & Nanoengineering 2018, 4 (1), 37. 5. Ferson, N. D.; Uhl, A. M.; Andrew, J. S., P. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5dbf229eb0b210860d8fcd24301da24c.jpg)
Figure 1. (a) scanning electron microscope image of a biphasic magnetoelectric nanowire suspended across an electrode gap (b) optical microscope image of an electrical assembly (c) a schematic magnetoelectric voltage source consisting of composite magnetoelectric nanowires and (d) a schematic of a possible architecture suitable if the density of the assembled nanowires is found to be generally uniform.

![](https://assets.underline.io/uploads/markdown_image/1/image/3c329a99c16139ffe78fbd2b64a3eabc.jpg)
Figure 2. Magnetoelectric coefficients and corresponding device sensitivities of BaTiO3/CoFe2O4 nanowire arrays as a function of frequency measured at angles of approximately no inductive effects, the angle of maximum constructive induction, and maximum destructive induction.

technical paper

The GSR sensor is a highly sensitive magnetic sensor that utilizes GHz pulses and amorphous wire1) . The detection principle is that a GHz pulse is applied to an amorphous wire, and makes the rotation of the spins near the surface and the resulting magnetization rotation are detected by the detection coil. In order to achieve higher performance, it is necessary to solve the problem of the induced EMFs in Zero Magnetic field and non-linearity due to the residual twisting stress in the wire. In this study, we report the results that those problems have been solved by using an opposing-current type element. The opposing-current type element has the feature that the current is passed from the center of the element to both ends, and the electromotive force detected by the two identical coils placed on the left and right sides is added and output. Fig.1 shows that when the direction of the current is reversed in the single coil type element, the electromotive force generated by the pulse current energization becomes positive and negative, and is canceled when added. Based on the result, we experimented with the counter-current type element and confirmed that in the case of falling detection, the induced electromotive force in the case of magnetic field H=０A/m almost disappears and only the electromotive force dependent on the magnetic field is generated. This result means that the coil voltage signal can be amplified significantly to give the improved detection power. Furthermore, as shown in Fig. 2, the output was found to be subject to the positive and negative magnetic fields, resulting in a clean sinusoidal function. This means that the linearity of the output can be greatly improved. The development of the counter-current device is expected to improve the sensitivity and linearity of GSR sensors.

**References:**

１）Y.Honkura, S.Honkura;JMMM,513(2020)167240

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3dbcb965a6f87a2818b4b1005476f55b.jpg)
Fig. 1 Effect of current direction on induced electromotive force in zero magnetic field

![](https://assets.underline.io/uploads/markdown_image/1/image/9d5c027899da6ddc74563eda6b74c3b0.jpg)
Fig. 2 Sinusoidal output characteristics of the opposing current type GSR element

 Development of Opposing Current Type GSR Sensor Element to Reduce Induced EMFs in Zero Magnetic Field

Introduction Magnetoresistive (MR) sensors increase explosively and are used widely in many fields due to its small weight, low power consumption, and high sensitivity, whereas the 1/f noise is larger in the low-frequency region and degrades the low-frequency magnetic field detection limit [1]. To reduce the impact of 1/f noise, MEMS-based magnetic flux concentrators (MFCs) are utilized to modulate the low-frequency field to a high-frequency region where the 1/f noise vanishes and improve the detection limit. MEMS-based MFCs consist of MEMS resonators vibrating with a high frequency and the high relative permeability magnetic film deposited on the surface of MEMS resonators, the combinations of them have been already tested and reported for high-frequency magnetic field modulation, resonance frequency detection, and 1/f noise of MR sensor cancellation [2-5]. When the MR sensor is integrated with MEMS-based MFCs and modulating the low-frequency magnetic field to the high-frequency region, the larger the modulation efficiency, the lower the detection limit. However, the modulation efficiency of existing modulation ways is not high, and the low-frequency magnetic field detection limit is low. To improve the low-frequency detection limit of the MR sensor, a new modulation way called synchronous motion modulation (SMM) is proposed. Theory of SMM SMM is evolved from gap-change modulation (GCM) [2]and vertical motion modulation (VMM) [3] with the highest modulation efficiency in the existing literature, as shown in Fig. 1. For GCM, the magnetic film deposited on the bottom of the piezoelectric cantilever resonator is static, and the MFCs deposited on the comb-driven resonator vibrate horizontally. But for VMM, the MFCs are static, and the magnetic film deposited on the bottom of the piezoelectric cantilever vibrates vertically. When the MFCs vibrate horizontally and the piezoelectric cantilever vibrates vertically, this is SMM, which modulates the magnetic flux in the position of the MR sensor to the high-frequency region. In this case, the direct current (DC) magnetic field will be modulated to an alternating current (AC) field and be measured by the MR sensor and bridge circuit. To compare the modulation efficiency of these three modulation ways, the vibration amplitude of comb-driven resonator is the same in SMM and GCM, the vibration amplitude of piezoelectric cantilever resonator is the same in SMM and VMM. The theoretical analyses show that the modulation efficiency of VMM increases with increasing amplitude and decreasing the initial height of magnetic film, but the modulation efficiency of GCM increases with increasing amplitude and decreasing the initial gap of MFCs. Additionally, the modulation efficiency of SMM is the sum of the modulation efficiency of VMM and GCM when two resonators have the same frequency and their phase difference is 180 degree. Validation and results To demonstrate the theoretical analysis above, the finite element method (FEM) simulation is done. Assuming that the magnetic film and MFC with the same frequency of 10 kHz, the same amplitude of 10 um , and the phase difference of 180 degree, the results are shown in Fig. 2 (a). It is found that the DC magnetic field, 1 uT , is modulated into a high-frequency magnetic field, and the modulated magnetic field waveform is a slightly distorted high-frequency sine wave. The reason is that the modulated magnetic field has many harmonic components, but the amplitude of the first-order component and DC component is much larger than other components. The peak-peak amplitude of the modulated magnetic field of SMM is larger than that of GCM and VMM, the modulation efficiency of VMM, GCM, and SMM is 38.55%, 66.82%, and 100.31%, respectively, and the modulation efficiency of SMM is nearly equal to the sum of modulation efficiency of VMM and GCM. Additionally, the situations when the MEMS resonators vibrate from 1 um to 10 um with the step of 1 um are investigated, as shown in Fig. 2 (b). The results show that the modulation efficiency increases linearly with increasing the amplitude, and the SMM has the maximum modulation efficiency among three modulation ways. What's more, the theoretical values are coincident well with the simulated results, which demonstrates the utility of the theory. Conclusion Therefore, we can conclude that SMM can significantly improve the modulation efficiency of the MEMS-based MR sensor and improve the low-frequency magnetic field detection limit, and the amplitude of MEMS resonator as large as possible is desired. Of course, fabricating two MEMS resonators as like in this paper and synchronizing them are not easy, the current feasible method is to use MEMS bonding technology and an interface circuit based on a phase-locked loop.

**References:**

 [1] Z. Q. Lei, G. J. Li, W. F. Egelhoff, P. T. Lai, and P. W. T. Pong, "Review of Noise Sources in Magnetic Tunnel Junction Sensors," IEEE Transactions on Magnetics, vol. 47, no. 3, pp. 602-612, 2011. [2] A. S. Edelstein, G. A. Fischer, M. Pedersen, E. R. Nowak, S. F. Cheng, and C. A. Nordman, "Progress toward a thousandfold reduction in 1f noise in magnetic sensors using an ac microelectromechanical system flux concentrator (invited)," Journal of Applied Physics, vol. 99, no. 8, p. 08B317, 2006. [3] J. Hu, M. Pan, W. Tian, D. Chen, and J. Zhao, "Magnetostatic detection using magnetoresistive sensors with vertical motion flux modulation," Rev Sci Instrum, vol. 83, no. 5, p. 055009, May 2012. [4] A. Guedes, R. Macedo, G. Jaramillo, S. Cardoso, P. P. Freitas, and D. A. Horsley, "Hybrid GMR Sensor Detecting 950 pT/sqrt(Hz) at 1 Hz and Room Temperature," Sensors (Basel), vol. 18, no. 3, Mar 6 2018. [5] Q. Du et al., "High Efficiency Magnetic Flux Modulation Structure for Magnetoresistance Sensor," IEEE Electron Device Letters, vol. 40, no. 11, pp. 1824-1827, 2019.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b307e2cbf9f889d1c9d804229f7a036c.jpg)
Fig.1 synchronous motion modulation (SMM). (a) The simplified schematic of SMM. The brown part is Tower-shaped MFC deposited on the surface of comb-driven resonator. The blue part is the magnetic film deposited on the bottom of the end of the piezoelectric cantilever resonator. The yellow part is the MR sensor that is used to sense the AC magnetic field; (b) fabricated comb-driven resonator; (c) fabricated piezoelectric cantilever resonator.

![](https://assets.underline.io/uploads/markdown_image/1/image/9ca4ba3cdc07e2b98c96e6fef86ac2a4.jpg)
Fig. 2 The comparison of three modulation ways. (a) The time-domain curves of the modulated magnetic field in two periods; (b) the theoretical and simulated modulation efficiency of three modulation ways versus vibration amplitude of two resonators. 'T' and 'S' represent the theoretical results and simulated results.

 Magnetic Flux Synchronous Motion Modulation for Improving the Low-frequency Magnetic Field Detection Limit of Magnetoresistive Sensor using MEMS Resonators

It has been demonstrated that perovskite oxides with the general formula ABO3 (A - lanthanides, alkaline-earth metals, B - transition metal cations) exhibit the colossal magnetoresistance (CMR) phenomenon and can be used for various spintronics applications [1]. Many efforts were made in structural and chemical engineering of such materials in order to tune their functional properties along a wide range of temperatures and magnetic fields. It was found that epitaxial films exhibit high magnetoresistance (MR) values only in the vicinity of phase transition temperature, while polycrystalline films exhibit significant MR in a wide range of temperatures. Engineering of lanthanum manganites with special nanocrystalline (polycrystalline with nanosize grains) structure enabled to develop so-called CMR-B-scalar sensors, which are capable to measure the magnitude of pulsed magnetic fields in very small volumes independently on field direction [2]. Such sensors have been used in advanced scientific equipment to measure magnetic field dynamics [3-4]. It is worth to note, that in the past decades the most extensive research was performed on A-site doped manganites. This doping results in a mixed valance state of the manganese ions (Mn3+ and Mn4+) giving rise to the ferromagnetic (FM) double exchange (DE) interaction, which determines transport and magnetic properties of these materials. On the other hand, it was proposed that the B-site doping with 3d ions (Co, etc.) would destroy the long-range FM ordering of the Mn3+-O2--Mn4+ network resulting in a complex glassy state which arises from the competition of FM and antiferromagnetic (AFM) interactions. Therefore, significant change of the magnetic and electrical properties of manganites is expected. It was demonstrated, that substitution of Co for Mn in La1-xSrxMnO3 results in increased room temperature MR [5]. A variety of competing magnetic interactions in Co-doped manganites [6] still remains unclear, especially in nanostructured films, therefore, their investigations are of great interest. In addition, the long-term stability [7] of magnetoresistive properties of such films is very important for magnetic field sensors applications. In this study, the resistivity ρ and MR of nanostructured Co-doped manganite films deposited at different growth rate was investigated in magnetic fields up to 20 T at room and cryogenic temperatures. The change of these parameters were studied during the long-term storage of the films and accelerated ageing by annealing the films at O2 and Ar atmosphere. The La0.81Sr0.19Mn1.09Co0.06O3 films (LSMCO) with a thickness of 360 nm were deposited by using a Pulsed-Injection Metal-Organic Chemical Vapor Deposition (PI MOCVD ) technique onto a polycrystalline Al2O3 substrate at 600 °C temperature keeping different growth rates (9 nm/min, 13 nm/min, and 27 nm/min). The Ag electrodes of the samples were thermally deposited on a Cr sublayer and post annealed at 450°C for 1 h. The ρ dependence on temperature was measured in the temperature range of (5–310) K. The MR measurements were performed in permanent (0-0.8) T magnetic field at (25–290) K and pulsed fields up to 20 T at (80–290) K temperatures. The ρ and MR of films deposited at different growth rates was investigated after such preparation steps: 1) formation of electrodes and post annealing at 450°C for 1 h in Ar or O2 atmosphere; 2) long-term storage at room temperature for 6 months; 3) accelerated ageing procedure: additional annealing at 100 °C for 8 h in Ar or O2. It was found that electrode formation conditions and the long-term storage significantly changes the properties of the films (see Fig.1). After 6 months the resistivity maximum ρm of all films significantly increased and the metal-insulator transition temperature Tm shifted to lower temperatures. The annealing at 100 °C for 8 h in O2 decreased the ρ due to oxygen saturation of the films. The resistivity of nanostructured films mostly depends on the quality of grain boundary material, therefore, the largest changes were obtained for LSMCO film grown at the highest rate (27 nm/min). The annealing in Ar only slightly affected the ρ values. The low-field (0.7 T) MR (Fig.2) changed insignificantly in all temperature range (25-290) K. This is probably related with the change of a number of charge carriers’ hopping centers Mn3+-O2--Mn4+, which depends on the oxygen saturation level. Therefore, despite the resistivity changes, the MR=100%×[ρ(B)/ρ(0)-1] was only slightly affected. At 20 T the MR also insignificantly depended on preparation conditions and was ~(65-70)% at 80 K and (55-60)% at 290 K. It was concluded, that for magnetic field sensors application the LSMCO films grown at lower rate (9 nm/min) and annealed at Ar atmosphere are preferable due more stable parameters.

**References:**

[1] D. Pla, C. Jimenez, M. Burriel, Advanced Materials Interfaces, Vol. 4, p. 1600974 (2017) [2] T. Stankevic, L. Medisauskas, V. Stankevic et al., Rev. Sci. Instrum., Vol. 85, p. 044704 (2014) [3] T. L. Haran, R. B. Hoffman, S. E. Lane, IEEE Trans. Plasma Sci., Vol. 41, p. 1526 (2013) [4] V. Stankevic, J. Lueg-Althoff, M. Hahn et al., Sensors, Vol. 20, p. 5925 (2020) [5] J. Hu, H. Qin, J. Chen et al., J. Appl. Phys., Vol. 91, p. 8912 (2002) [6] H. Zhao, X. G. Chen, J. Z. Wei et al., IEEE Trans. Magn., Vol. 51, p. 1200205 (2015) [7] M. Egilmez, M.M. Sabera, M. Abdelhadi et al., Phys. Lett. A, Vol. 375, p. 4049 (2011)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1aa2b57e13215f46e6ebeb58279e63d0.jpg)
Fig.1. Resistivity vs. temperature dependences of LSMCO films grown at different growth rates and annealed in O2 or Ar (inset) atmosphere. Solid curves – after formation of electrodes; dashed curves – after long-term storage at room temperature during 6 months; dotted curves – after annealing for 8 h at 100 °C.

![](https://assets.underline.io/uploads/markdown_image/1/image/98645855a0054417199d5c2cd57618ff.jpg)
Fig.2. Magnetoresistance vs. temperature dependences of LSMCO films grown at different growth rates and annealed in O2 or Ar atmosphere. Symbols show MR values measured at B=0.7 T. The insets present MR(B) dependences: solid curves – after formation of electrodes; dashed curves – after annealing for 8 h at 100 °C.

 Influence of Preparation Conditions on Long-Term Stability of Magnetoresistive Properties of Nanostructured La-Sr-Mn-Co-O Films Grown by PI MOCVD

Monitoring the occurrence of defects in steel structures of crucial applications such as pipelines, aircraft, bridges, etc. is necessary to prevent any fatal accidents from happening in the future. Particularly for cracks, their early detection can be difficult to be achieved as their progression may start at micrometer in size [1]–[3]. To enable detection of these micrometer-sized defects occurred in high permeability materials such as mild steel components, it is important to increase the eddy current signal against the magnetization signal of the material so that the eddy current variation due to the defects will not completely be buried within the strong magnetization signal [2], [4]. Here, the detection area plays an important role where a small detection area will result in a higher ratio of the eddy current signal to the magnetization signal. Compared to the conventional sensing technique using detection coils, in this work, we utilized miniature fluxgates to sense the variation of the eddy current at a high degree of locality while benefiting from their high sensitivity at a low-frequency region for sub-surface defect detection. It also can be expected that the sensitivity of the fluxgates will enable the evaluation of sub-surface defects in a high magnetic permeability material such as mild steels, owing to the increase of the eddy current’s penetration depth at the low-frequency region. By using miniature fluxgates (DRV 425, Texas Instruments), we configured the fluxgates and their circuits on a custom-made printed circuit board as shown in Fig. 1 (a). Furthermore, to increase the eddy current intensity within a small area, the generated excitation field was concentrated by using small unshielded ferrite inductors. The inductors were arranged uniformly in two layers so that the eddy current induced between the two layers will flow in the same direction as the layers. Each of the inductors had an inductance of 10 mH and a DC resistance of 30.5 Ohm. Moreover, the fluxgates were also arrayed in 2 layers and fixed equidistantly between the layers of the inductors. This arrangement was expected to enable the construction of the eddy current components in x- and y- directions by taking the differential of the z-component field Bz in y- and x- directions, respectively [1]. This probe is also intended for a mobile application, i.e., low current consumption, where a 20-mA AC current source was used to drive the inductors. We first evaluate the magnetic noise characteristic of the fluxgate where it was measured in a tri-layer magnetic shield. The sensor showed a magnetic noise lower than 10 nT/sqrt(Hz) from 3 Hz until 1 kHz. The fluxgate exhibited a sensitivity of 5V/mT when it was shunted with a 200-Ohm resistor and operated within a region from -0.5 mT to 0.5 mT. Using the developed probe, we measured the magnetic responses Bz induced from 5 artificial slits, whose depth ranges from 2 to 10 mm. The artificial slits were engraved on a mild-steel plate with a thickness of 12 mm, as shown by the schematic drawing of the steel plates in Fig. 2 (a). All of the slits had the same width and length, which were 1 mm and 30 mm, and they were arranged in a parallel direction, separated by a 30-mm distance. The magnetic response Bz of the slits was evaluated by mapping the Bz distribution over the slit area, and it was measured on the top surface with a 1-mm lift-off. A set of frequencies was selected for the excitation field, which is from 10 Hz to 310 Hz, in order to investigate the effect of skin depth penetration. The signal from the sensor was sampled by a data acquisition card (NI-USB 6210) at a 20-kHz sampling frequency and processed using a digital lock-in technique, implemented in Labview. In order to determine a suitable reference signal of the lock-in technique, we implemented a dynamic referencing technique where one of the sensor outputs of the fluxgates was used as the reference signal [4]. Using this referencing technique, we were able to separate the strong magnetization signal from the detected signal, in which the separated signal is mostly dominated by the phase information of the induced signal, i.e., the eddy current signal. The result for the eddy current distribution at the 30-Hz excitation frequency is shown in Fig. 2 (b). The positions of the slits were located at y = 29 mm (10-mm slit), 59 mm (8-mm slit), 89 mm (6-mm slit), 119 mm (4-mm slit), and 149 mm (2-mm slit), respectively. The signal change due to the existence of the slits could be clearly observed from the constructed eddy current distribution. It could be observed that the eddy current was reduced at the location of the slits where the reduction intensity was proportional to the slit depth. The developed probe shows a promising characteristic in assessing steel defects at a high detection sensitivity. Acknowledgments This work was supported by the Ministry of Higher Education of Malaysia under the grant number of FRGS/1/2019/TK04/UMP/02/4 (RDU1901154) and the Research Management Center of Universiti Malaysia Pahang under the grant number of RDU1903100.

**References:**

[1] M. M. Saari et al., “Design of Eddy Current Testing Probe for Surface Defect Evaluation,” Int. J. Automot. Mech. Eng., vol. 16, no. 1, pp. 6357–6367, 2019, doi: https://doi.org/10.15282/ijame.16.1.2019.19.0481. [2] K. Tsukada, M. Hayashi, Y. Nakamura, K. Sakai, and T. Kiwa, “Small Eddy Current Testing Sensor Probe Using a Tunneling Magnetoresistance Sensor to Detect Cracks in Steel Structures,” IEEE Trans. Magn., vol. 54, no. 11, pp. 1–5, 2018, doi: 10.1109/TMAG.2018.2845864. [3] P. A. Petcher and S. Dixon, “Weld defect detection using PPM EMAT generated shear horizontal ultrasound,” NDT E Int., vol. 74, pp. 58–65, 2015, doi: 10.1016/j.ndteint.2015.05.005. [4] M. A. Hadi Putera Zaini, M. Mawardi Saari, N. A. Nadzri, A. Mohd Halil, and K. Tsukada, “An MFL Probe using Shiftable Magnetization Angle for Front and Back Side Crack Evaluation,” Proc. - 2019 IEEE 15th Int. Colloq. Signal Process. its Appl. CSPA 2019, no. March, pp. 157–161, 2019, doi: 10.1109/CSPA.2019.8696064.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7bc98d523964dffa884faceb271567a5.jpg)
Fig. 1. a) Arrangement of inductors and miniature fluxgate DRV425. b) Magnetic noise characteristic of the miniature fluxgate.

![](https://assets.underline.io/uploads/markdown_image/1/image/23a65720a32602330616987a883eeff5.jpg)
Fig. 2. a) 5 artificial slits with different depths from 2 mm to 10 mm on a 12-mm mild steel plate. b) Distribution of the eddy current component in the x-direction detected by the proposed probe using a 30-Hz and 20-mA excitation current.

 A Low-frequency Eddy Current Probe Based on Miniature Fluxgate Array for Defect Evaluation in Steel Components

Introduction When an electromagnetic sensor composed of a static excitation coil and a detection coil is moved in a steel tube at high speed, an eddy current is generated in the steel tube. If a defect is present in the steel tube, the defect may be detected by the change in the eddy current. Generally, the heat transfer tubes with ferromagnetism in power plants or oil plants are inspected for defects by moving an internally inserted electromagnetic sensor at a high speed of about 1 m/s [1]. In this research, an inner-type electromagnetic sensor using the static magnetic field that moves inside these steel tubes at high speed and detects on the outer side defect in the steel tubes is proposed. The generated eddy current inside the steel tube by constant velocity movement of the static magnetic field is analyzed by the 3-D nonlinear eddy current FEM analysis using step-by-step method. In addition, verification experiment is also conducted. Inspection Model and Electromagnetic Conditions Fig.1 shows the proposed electromagnetic sensor using only the static magnetic field and an inspection steel tube (STB340SC). This sensor is composed of two static excitation coils in series, a pair of differential detection coils, and a magnetic yoke of permendur material. The direct current of 1 A is passed through two excitation coils in series so that the plus z-direction of the sensor is the S-pole and the minus z-direction is the N-pole. The permendur material is an alloy of iron and cobalt. The two excitation coils and the differential detection coil are 220 turns × 2 and 100 turns × 2, respectively. The outer diameter, length, and thickness of this inspection steel tube are f 19 mm, 460 mm, and 2 mm, respectively. The proposed sensor is inserted in the steel tube at a speed of 1 m/s for minus z-direction. The distance (lift-off: Lo) between the sensor and the steel tube is equal to 0.5 mm. Analysis and Experimental Results Fig.2 shows the distribution of only one layer in the y-direction of eddy current density inside the steel tube when the sensor is moved in the minus z-direction of the steel tube without defect at 1m/s. This figure denotes that the directions of the eddy currents generated on the upper side and the lower side of the steel tube are opposite. Since the lower part of the sensor in the moving direction is the N-pole, the eddy current is generated inside the steel tube near the lower part of the sensor in the direction of canceling the N-pole magnetic field. On the other hand, since the upper part of this sensor is the S pole, an eddy current is generated inside the steel tube near it in the direction of canceling the S-pole magnetic field. In addition, Fig.2 denotes that both the upper and lower eddy currents in the thickness of the steel tube are concentrated on the inner surface of the steel tube by skin effect. Fig.3 shows the distribution of the flux density inside the steel tube when the sensor is moved in the minus z-direction of the steel tube without defect at 1m/s. This figure denotes the flux density inside the steel tube near the lower side of the sensor is distributed in the plus z-direction, since the eddy current is generated inside the steel tube in the direction of canceling the N-pole magnetic field. On the other hand, the flux density on the inner surface of the steel tube near the upper side of the sensor is offset because the eddy current is generated in the opposite direction to when the N-pole of lower side of the sensor passed. However, the distribution of flux density in the steel tube near the central region of the sensor is almost uniform. Fig.4 shows comparison results of analysis and experiment of the steel tube with an outer slit defect in the circumferential direction. The width for the z-direction and the depth for the x-direction of the defect are 10 mm and 0.5 mm, respectively. The horizontal axis of the figure indicates the moving position of the sensor, and the vertical axis indicates the differential voltage output by the pair of detection coils in the sensor. This figure shows that an electromagnetic sensor using only a static magnetic field is detected the outer side defect on the steel tube. Moreover, this figure denotes that the calculated result is in agreement with measurement.

**References:**

[1] M. Zec, R. P. Uhlig, M. Ziolkowski, and H. Brauer, “Finite Element Analysis of Nondestructive Testing Eddy Current Problems with Moving Parts”, IEEE Transactions on Magnetics vol.44, no.8, pp.4785-4794 (2013).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/98aefef80aa754ec6f73137b1cfdd52b.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/c8a51b13b5da909ba1b6aa71e5ae87a4.jpg)

 Examination of insertion type electromagnetic inspection for outer side defect on ferromagnetic steel tube by speed effect using only static magnetic field

Linear variable differential transformer (LVDT) sensors offers many advantages in low power consumption, high sensitivity, low hysteresis, etc. These features allow them to be used in wide range of possible applications in critical environments [1]. However, they suffer from some disadvantages like temperature dependence of output, sensitivity to stray magnetic fields and others. Most of the disadvantages arises from the fact that LVDT sensors sense variation of permeability of magnetic core to external stimuli like magnetic field or temperature. Some of the problems can be solved using glass-coated magnetically bistable microwire as a variable core for linear position sensor. Glass-coated amorphous microwires are composite materials having metallic nucleus covered by glass-coating [2]. They are produced by Taylor-Ulitovski method applying drawing and quenching of molten metal that fills glassy capillary. Having positive magnetostriction, they show magnetic bistability (only two oppose saturation magnetic states are allowed in static state) and switching between the two states appears through the single Barkhaussen jump. This gives us possibility to separate contribution of external magnetic field, temperature, stress or position [3]. Apart from the above mentioned feature, they offer advantages in small size, glass-coating that provides insulation from chemically aggressive environment, or simple, fast and cheap production of large amount of microwire (up to kilometre of wire can be produced from few grams of master alloy). In the given contribution, we show the linear position sensors similar to LVDT based on magnetically bistable microwire. It consists of two coils (excitation and sensing) having single microwire coaxially placed on linearly moving piston. In contrary to classical LVDT sensors, where position defines the amplitude of the signal measured on the sensing coil, we detect the switching field that is proportional to the position. Application of triangular shape of excitation field allows us to measure switching time that is proportional to the switching field. Using fluxgate like sensing system and measuring the positive and negative switching time, we are able to avoid stray fields dependence of linear position piston sensing. We show, how temperature independence of sensing can be solved by proper chemical composition. Such a sensors show no hysteresis and requires quite small power consumption. Proper design allows to obtain sensitivity down to 20 µm within the range 0-6 cm (see fig. 2). However, sensitivity and range can be adjusted by properly selecting the shape of excitation coil. This work was partially supported by Slovak Grant Agencies VEGA 1/0053/19 and APVV-16-0079.

**References:**

[1] D. S. Nyce, Linear Position Sensors: Theory and Application, John Wiley & Sons, Inc. (2004) [2] M. Vázquez: Advanced magnetic microwires. In: Kronmüller, H., Parkin, S. S. P. (eds.) Handbook of Magnetism and Advanced Magnetic Materials, Wiley, Chichester, West Sussex, England (2007) [3] R. Jurc, L. Frolova, D. Kozejova et al. Sensoric application of glass-coated magnetic microwires in Magnetic Nano- and Microwires, Second edition, ed. by M. Vázquez, Woodhead Publishing, (2020), ISBN: 9780081028322.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/805a4234dba066457bf55254449c52f5.jpg)
SEM figure of glass-coated microwire (left), Schematic view of linear position sensor with bistable microwire (right)

![](https://assets.underline.io/uploads/markdown_image/1/image/7112c598e9108dbb47fe8ef47ee2420f.jpg)
Dependence of magnetic response of linear position sensor on piston position

 Linear position sensor using magnetically bistable microwire

A Wiegand sensor is composed of a strip of Wiegand wire and a pickup coil. From literature. the Wiegand wire was initially made of NiFe alloy [1-2]. However, it was reported that the wire made of FeCoV alloy offered the optimum performance in generating the Wiegand effect [3]. Diameter of the Wiegand wire is about 0.25 mm. Heat treatment such as quenching and annealing are applied to the wire in order to change grain size of the alloy. After heat-treatment, cold-treatment such as stretching and twisting are then introduced to the wire to make exhibition of different coercivity in its surface region and center region, respectively [1-6]. When external magnetic field passing through axial direction of the wire with different coercivity reaches a certain threshold, the “soft layer” with relatively low coercivity of the wire can fast reverse its direction of magnetization. The fast magnetization reversal of the soft layer leads to generation of large Barkhausen jump, resulting in changes of magnetic flux in the pick-up coil such that the pulse voltage is induced with 10 µs pulse width and up to 8 V peak voltage [5]. This pulse voltage is also called Wiegand pulse. The peak voltage and pulse width of the pulse is reported to be independent of driving frequency, so it can be used as a zero-speed sensor. Reported in [3], the Wiegand sensor was able to generate electrical power of 600 nJ, which could be used for energy harvesting driving small power components. The material of the Wiegand sensor is stable and cheap, and the pulse energy did not reduce after million times of switching. Advantaged by the above features, the Wiegand sensors have been used in rotary speed measurement [7], Batteryless hall sensors [3], and multi-turn absolute encoders [8]. In this study, we apply Wiegand sensor to linear positioning system so that Wiegand impulse can be used as battery-less limiting switch or reference mark. The focus of this work is placed on the design of the system’s magnetic circuits so that the Wiegand pulse can be triggered effectively. In our experiments, data acquisition NI USB-6216 with up to 400 Ks/s sampling rate and 16-bit resolution to measure Wiegand pulse in different magnetic circuits are employed. The relationship between different magnetic circuits and pulse peak were investigated and obtained in this study. To design the magnetic circuits for the Wiegand sensor, generation of Wiegand pulse if of primary importance. In previous work [1][6], it was reported that to be able to repeatedly generate Weigand pulse, external magnetic field should pass through the wire’s axial axis. To be able to reach this objective, appropriate strength of external magnetic field should be first applied through the axial axis of Wiegand wire so as to magnetize the wire, followed by decreasing external magnetic field to let Wiegand wire have remanence (Br). Lastly, opposite direction of external magnetic field should be applied to the Wiegand wire so that the wire’s soft layer can suddenly reverse its polarity to yield Wiegand pulse. Based on the Wiegand effect mentioned above, we use single magnet to produce external magnetic field. The direction of magnetic field around both sides of the magnet is opposite to that around center of the magnet. The placements of the Wiegand sensor and the magnet are shown and depicted in Fig. 1(a) and Fig. 1(b), respectively. The linear motor carrying the magnet is set to move back and forth at a speed of 30 mm/s along Y-axis, from which the mean value of the pulse peak is computed every 50 runs. The relationship between the mean value of peak voltage and the Flying height (H) is shown in Fig. 2(a), whereas the relationship between pulse signal and time is shown in Fig. 2(b). From measurement results, it was observed that when H is lower than 3.5 mm, the triggering of the pulse signal was limited. As the linear motor moved from left to right, it was observed that the Weigand sensor first generated small pulse signal under 0.1 V first, followed by generation of relatively large pulse signal with magnitude over 0.3 V. This phenomenon was investigated through finite-element simulation. When the magnet moving from left to right, the simulated magnetic flux density in the soft layer of the wire is depicted in Fig. 2(c) showing unsymmetrical hysteresis loop according to the change of magnetic flux density. Based on this unsymmetrical hysteresis loop, one can see that the Br values at state 2 and state 4 are significant different, leading to generation of relatively small pulse signal first at state 2 then relatively large pulse signal at state 4. From Fig. 2(b), it was found that when H is below 3.5 mm, the Wiegand pulse could not be triggered. As illustrated in the comparison in Fig. 2(d), when H=1 mm, the whole soft layer can’t perform fast magnetization reversal at the same time as the case when H=5 mm. Through this study, we conclude that should one need to effectively trigger Wiegand pulse, appropriate strength of external magnetic field should be applied and whole soft layer of Wiegand wire not fast reversing at the same time should be avoided.

**References:**

[1] J. R. Wiegand, “Switchable magnetic device,” U.S. Patent No 4,247,601, 1981. [2] J. R. Wiegand, “Method of manufacturing bistable magnetic device,” U.S. Patent No 3,892,118, 1975. [3] Y. Takemura et al., “Batteryless hall sensor operated by energy harvesting from a single Wiegand pulse,” IEEE Transactions on Magnetics, 53.11: 1-6, 2017. [4] S. Abe, A. Matsushita, and M. Naoe, “Annealing and torsion stress effect on magnetic anisotropy and magnetostriction of Vicalloy fine wire,” IEEE Transactions on Magnetics,33.5: 3916-3918, 1997. [5] S. Abe, A. Matsushita, and M. Naoe, “Dependence of large Barkhausen jump on length of a vicalloy fine wire with torsion stress.” IEEE Transactions on Magnetics, 34.4: 1318-1320, 1998. [6] X. Sun, T. Yamada, and Y. Takemura, “Output characteristics and circuit modeling of Wiegand sensor,” Sensors, 19.13: 2991, 2019. [7] E. Zabler and P. Hauler, “Level amplitude output rotary speed transducer,” U.S. Patent No 4,150,314, 1979. [8] W. Mehnert and T. Theil, “Absolute high resolution segment or revolution counter,” U.S. Patent No 8,655,615, 2014.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c5adaac1a38b3f932e9ecb59aa21c950.jpg)
Fig. 1 (a) isometric and (b) top views of placement of Wiegand sensor and magnet.

![](https://assets.underline.io/uploads/markdown_image/1/image/e1c623ee2fbd72fa918ebee60a5a8c04.jpg)
Fig. 2 Measured and simulated results of (a) pulse voltage obtained from the Wiegand sensor, (b) mean value of peak voltage in different H. Magnetic flux density in different location and hysteresis loop of Wiegand wire is shown in (c) exampled by magnetization direction of soft layer when H=1 mm and 5 mm, respectively in (d).

 Effect of Magnetic Circuit on Pulse Voltage Generated by Wiegand Sensor in a Linear Positioning System

Linear and rotary types of positioning systems have been research and development focus in particular to facilitate precision manufacturing with machine tools. Encoders inside the positioning systems are commonly classified into two types, namely optical and magnetic types. The optical type uses light source reflection to target for position in between, whereas the magnetic type uses a magnetic field to measure position of the target. Although optical encoders may have a greater resolution, magnetic encoders have better performance in harsh environments and dust resistance. Moreover, comparing with the same level of product specifications, magnetic encoders have lower cost and fewer components. These advantages make magnetic encoders more commonly used in machine tools [1]. A magnetic encoder usually consists of a sensor head and a magnetic medium, where the medium is composed of a substrate, and a ferromagnetic material covering on its surface, to generate different alternating polarity pattern by magnetizing the ferrite-magnetic medium under an external magnetic field. Even when the external magnetic field is removed, the magnetization polarity could be still maintained [2]. These patterns are not only used in linear positioning systems, but are also used to obtained spindle shaft angular position by assembling a rotary magnetic encoder in robotics joints or rotating machines. Because of its accuracy performance directly affects the workpiece appearance, factors affecting accuracy of the rotating machines play a significant role in the machining process. In the process, an inevitable thermal expansion cannot be ignored under high-speed machining, particularly for the axial elongation of the machine’s spindle shaft. This axial elongation can lead to catastrophic failure in the rotating machine if it is not adequately monitored. Therefore, the magnetizer in this paper aims to present a different pattern arrangement, which was conceived by Shih and Hsiao [3] to verify elongation of the spindle shaft in axial direction. In the present study, the aforementioned alternating polarity pattern is magnetized on CoMnP ferromagnetic material on the magnetic ring in the way as illustrate in Fig.1(a). A NdFeB35 permanent magnet serves as an external magnetization source, and special magnetization head shape are utilized to concentrate the magnetic flux to create the designed magnetic pattern. The magnetic ring is concentrically attached to the spindle shaft accompanied with a magnetoresistive (MR) sensor to establish a measurement system along the shaft’s axial direction as shown in Fig.1(a). This MR sensor is composed of two Wheatstone bridges, each bridge consisting solely of 4 equally arranged MR elements placed above the magnetic ring. The MR elements can read out a sinusoidal or cosinusoidal voltage signal caused by changes in magnetic field when relative displacement occurs between the medium ring and the sensor. However, the angle between the magnetization vector and the element’s current can be altered as the magnetic field signals are affected subsequently due to assembly errors between the sensor and the ring. These problems result in a high position error. In this paper, finite element studies and experiments are adopted to investigate the effect of assembly errors, including flying height, pitch, yaw, and roll errors between the MR sensor head and the magnetic patterns on the ring as illustrated in Fig.1(b) [4]. We aim to reduce position error by optimizing the sensor’s installation. From the studies, the optimized flying height is found to be 0.6 to 0.7 mm from the MR element or equivalently 0.1 to 0.2 mm when package dimensions of the senor head are considered. It is observed that with this optimal flying height, an optimal signal performance can be achieved in which frequency multiplication can be reduced in the measured magnetic signals. As depicted in Fig.2(a), when the sensor head rotates in pitch and yaw directions from 0° to 1.16° with 0.29° and 0.2° steps, respectively, the error percentage is strictly increased by 81.4% and 29.6%, respectively. Moreover, in error percentage of the sensor increases only 3.8% when it rolls from 0° to 1°, implying that sensor assembly in the roll direction possesses more mounting tolerance than other directions. On the other hand, in order to make the measurement system reach to application level for the spindle shaft axial thermal elongation measurement in a high-speed motor (24,000 rpm), a system with a built-in field-programmable gate array to improve firmware sampling rate to 2 kHz is instrumented so that the measured magnetic signals can accurately reflect spindle shaft’s actual elongation from unreal or distorted signal waveform due to insufficient sampling rates. As shown in Fig.2(b), along with temperature measurement, the spindle shaft’s axial displacements measured by the aforementioned system are compared with commercially available eddy current sensor when the spindle rotates from 1,000 to 24,000 rpm. It can be seen that not only the trends are the same, the difference between the two are neglectable. This suggests that the proposed method and system can instantly measure the spindle’s axial thermal elongation in response to the change of temperature in the machine tools.

**References:**

[1] K. Miyashita, T. Takahashi and M. Yamanaka, “Features of a magnetic rotary encoder.” IEEE Transactions on Magnetics, vol. 23, no. 5 pp. 2182-2184, Sep.1987. [2] Y.-J. Luo, E.-T. Hwang, and S.-M. Huang, “Multi-pole magnetization of high resolution magnetic encoder.” Proceedings of Electrical/Electronics Insulation Conference. IEEE, Oct.1993. [3] S.-W. Shih, H.-S. Hsiao, J.-Y. Chang, “The magnetic encoder apparatus and measuring the displacement of the rotation axis.” Taiwan Patent I662255, July. 2018. [4] K.-Y. Peng and J.-Y. Chang, “Effects of assembly errors on axial positioning accuracy for rotating machinery with magnetoresistance-based magnetic encoders” Microsystem Technologies, January, 2021.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/98c95c7d3c2e06a55caa9dbf7f85bfd7.jpg)
Fig. 1 Schematics of (a) magnetic ring with alternative polarities pattern attached to spindle shaft with (b) sensor assembly errors.

![](https://assets.underline.io/uploads/markdown_image/1/image/be5e7d23f770fbe381f60df660b97f80.jpg)
Fig. 2 (a) error percentage at different angles and (b) comparison of the shaft’s measured axial thermal elongation.

 A Magnetization System for Spindle Axial Thermal Elongation Measurements

The calculation of demagnetization factor and apparent permeability of magnetic core is essential in induction and fluxgate sensors design [1].The calculations and analyses of demagnetization factors for ellipsoidal and non-ellipsoidal shapes of single element were studied in detail in various publications [1]-[8]. For instance, demagnetization factor for sphere can be analytically calculated and it is 1/3 [2]. Demagnetization factor for single ellipsoidal has closed-form equation [1], but the apparent permeability depends on material permeability (only for very high permeability it depends only on geometry). Demagnetization factor for non-ellipsoidal shape of single element, for example solid cylindrical wire and hollow cylinder, cannot be described in single closed-form formula, however approximations using curve fitting were used [1], [4] and [6]. Magnetic permeability of wire has high impact on the demagnetization [7]-[8]. Using finite element method (FEM) or complex analytical modeling are common methods to take into account magnetic permeability effects on the demagnetization. However, effects of finite relative magnetic permeability can be taken into account using curve fitting [4] and [6] in the closed form equation of the demagnetization factor. The demagnetization factors are categorized to two cases: Fluxmetric (ballistic or central) and magnetometric; magnetometric demagnetization factor is of main interest for sensors applications. we have calculated demagnetization factor and corresponding apparent permeability for multiwire arrays using magnetostatic 3D FEM in [1]. The effect of distance between magnetic wires on the demagnetization factor and apparent magnetic permeability was studied at different relative magnetic permeability. We also compared the simulations with experimental results up to 91 wires. Unfortunatelly the complexity of the 3D model is increasing fast with the number of wires and 3D FEM simulations of large wire arrays are impossible. This is why we propose novel simplified equivalent 2D model for wire arrays in this paper. The simplified model consists of hollow cylinders and it is axisymmetrical. The basic geometry of the 2D equivalent model is shown in Fig. 1. The model was derived for hexagonal arrays, but similar models can be made for other lattices. The mean diameter of each hollow cylinder is calculated by the average of the circumdiameter (maximal diameter) and the innerdiameter (minimal diameter) of the hexagon.The thickness of each hollow cylinder is obtained assuming the same volume as the volume of wires on the circumference of the corresponding hexagon. The validity and the accuracy of our model is tested by the calculations shown in Fig. 2, with relative material permeability of mr-max= 500. The first calculation shows the magnetometric (using volume integral of the flux density B) and fluxmetric (using surface integral of B in the midplane) apparent permeability of the central wire in the array of n wires as a function of n. The results of our simplified 2D model fit very well the full 3D FEM simulations. We have studied apparent permeability and magnetometric demagnetization factors of arrays up to 2000 wires as a function of wire aspect ratio, wire distances and material properties. Two different hexagonal and square arrangements for wires will be considered in the full paper. Increasing wire distance increases apparent permeability and decreases demagnetization factor, which is similar to comparison between solid cylinder and hollow cylinder for demagnetization factor [3]. We will also show the results of the verification measurements on array of Permalloy wires. The simulation results are also valid for the arrays of microwires and even large arrays of nanowires, as for the practically achievable distances the wire interaction is mainly magnetostatic. This study was supported by the Grant Agency of the Czech Republic within the Nanofluxgate project (GACR GA20-27150S).

**References:**

[1] P. Ripka, V. Grim, M. Mirzaei, acc. for publ. in JMMM, 2021 [2] M. Stafl, Electrodynamics of Electrical Machines, Publisher: Iliffe , 1st March 1968 [3] S. G. Sandomirskii, Russian Electrical Engineering, vol. 80, pp. 109–112, 2009 [4] S. G. Sandomirskii, Russian Electr. Eng. 84, pp. 376-381, 2013 [5] V. F. Matyuk, A. A. Osipov, and A. V. Strelyukhin, Russian Journal of Nondestructive Testing, vol. 43, no. 3, pp. 154–162, 2007 [6] M. Nirei, S. Suzuki, K. Tashiro, and H. Wakiwaka, Journal of the Japan Society of Applied Electromagnetics and Mechanics, vol. 17, no. 3, pp. 449-452, 2009 [7] D.-X. Chen, J. A. Brug, and R. B. Goldfarb,”, IEEE Trans. on Magn.. 27, , pp. 3601-3619, 1991 [8] D.-X. Chen, E. Pardo, A. Sanchez, “Fluxmetric and magnetometric demagnetizing factors for cylinders,”JMMM 306, pp. 135–146, 2006

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/83e685bd809a1efe045b10918b3686dc.jpg)
Fig. 1 The wire array and its equivalent 2D model based on the hollow cylinders

![](https://assets.underline.io/uploads/markdown_image/1/image/94cfaa14032d2e088b2f7c7b1141e354.jpg)
Fig. 2 Apparent permeability (magnetometric using volume integral and fluxmetric using surface integral) of the wire array as a function of the number of wires, n. Calculated by 3D FEM and by the 2D equivalent model

 A simplified 2D equivalent model for magnetic wire array

The sensitivity and automation capabilities of modern superconducting quantum interference device magnetometers are currently unmatched [1]. The measured moment values are, however, prone to deviations from their actual value due to geometric effects, namely sample size, shape, and radial offset [2,3]. A knowledgeable operator will correct measured moment values taking these effects into account. The current procedure for the MPMS3 magnetometer is based on an available simulation tool, valid for both SQUID-VSM and DC-scan methods [4]. Still, determining the correction factor requires samples with well-defined geometric shapes together with accurate sample dimensions and the usually difficult to determine radial offset [5]. There is no current solution to correct geometry effects of irregular shaped samples. Via an extensive use of the available Sample Geometry Simulator tool [4], in all available geometries, with sample dimensions and radial offset values limited only by the sample chamber volume, we find a systematic relation between the difference of SQUID-VSM and DC-scan measurements and the corresponding geometric correction factors of the MPMS3 SQUID-VSM device. This relation follows a clear trend, independent of sample size, shape, or radial offset, for a given pair of DC-scan length and SQUID-VSM amplitude values. Exploiting this trend, a geometry-independent correction method is presented and validated by measurements of two different geometries of the same Al piece, two different radial offsets of a Ni square, and metallic Fe powder using a far from optimal sample mounting. In this last case, we improved the initial maximum observed deviations from about 35% to better than 3%, by following the proposed correction method, as shown in Table 1. While the presented methodology requires both DC-scan and SQUID-VSM data, its ease of use on correcting magnetization measurements of irregular shaped samples and unknown radial offset values, can be of wide application by the magnetism/ magnetometry community.

**References:**

[1] M. Buchner, K. Höfler, B. Henne, V. Ney, A. Ney, J. Appl. Phys. Vol. 124, p. 161101 (2018) [2] P. Stamenov, and J. M. D. Coey, Rev. Sci. Instrum. Vol. 77, p. 015106 (2006) [3] Quantum Design MPMS Application Note 1500-015 (2010) [4] Quantum Design MPMS Application Note 1500-020 (2014) [5] G. Morrison, and H-C zur Loye, J. Solid State Chem. Vol. 221, p. 334 (2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ddcfcf8354cffc5511d7f0e84ac2a256.jpg)
Simulated correction factors as a function of the relative difference x = (MVSM −MDC) /MVSM for three different pairs of DC-scan lengths and SQUID-VSM amplitudes.

![](https://assets.underline.io/uploads/markdown_image/1/image/b22be110a92d165fa1ffc58f3f5f794f.jpg)
Measured saturation magnetization and respective corrected values of several Fe powder samples. The measurements were performed using a 1mm SQUID-VSM amplitude and a 30mm DC-scan length.

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