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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.&lt;br/&gt;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.&lt;br/&gt;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.&lt;br/&gt;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.&lt;br/&gt;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

INTERMAG 2021

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

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This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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

technical paper

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Magnetic field sensors in a rigid format have been typically associated with recording heads, hard disk drives and the automotive industry. Unlocking new application scenarios requires changing the intrinsic properties of these sensors to make them adaptable to new challenges. One way to accomplish this goal, is to allow these sensors to change shape and be flexible, stretchable or solution-processable, what we call shapeable magnetoelectronics [1]. This technology relies on the smart combination of inorganic thin films prepared directly on flexible or elastomeric substrates. Shapeable magnetoelectronics resulted from the cooperative effort of fundamental and application-oriented communities in the field of curvilinear magnetism [2], and the involvement of fabrication methods for flexible electronics [3], [4]. The combination of these research fields has resulted in a variety of flexible [5], [6], printable [7]–[9], stretchable [10]–[12] and imperceptible17,35–37 magnetic field sensing elements. Stemming from these developments, various applications like automotive [19], consumer electronics and point of care [6], [13], [14], and virtual reality [15]–[17], have emerged. For automotive purposes, shapeable magnetic sensors can be useful to monitor the magnetic field profile the nonplanar and narrow gaps inside electrical motors, to minimize losses and improve the overall efficiency [5]. In point-of-care applications, they can enable fast biosensing methods for wearable health monitoring based on magnetofluidics [6], [13]. For virtual reality they allow a whole new set of touchless interaction possibilities using the ambient magnetic fields as input stimuli [15]–[17]. One example of this application is an on-skin sensor, which can dim the intensity of a virtual lightbulb based on the relative angle between the sensor and the magnetic field of a permanent magnet [16]. This idea was further improved to remove the need for permanent magnets and instead use the earth’s magnetic field as input stimulus. Reaching this level of sensitivity required the use of barber pole [18] modified anisotropic magnetoresistive (AMR) sensors, which allowed detecting magnetic fields of µT with a flexible on-skin patch. Aside from enable artificial magnetoception, the patch can be used as an interactive device for virtual reality which only uses the geomagnetic field [15] (Fig. 1). Further works have improved the sensitivity to about 200 nT, which could have applications for highly sensitive point-of-care devices [14]. In recent works, we have demonstrated shapeable magnetoelectronics which are multimodal, so that they transduce and discriminate both tactile (via mechanical pressure) and touchless (via magnetic field) stimuli in real time [17]. Such a feat is attained by fabricating a magnetic microelectromechanical platform (m-MEMS), which combines flexible magnets based on polymer composites and mechanically compliant magnetic sensors. These m-MEMS e-skins enable complex interactions with magnetically functionalized objects in the real world, which supplement the content data appearing in virtual reality. For example, an augmented reality menu with multiple layers of interaction can be operated with one single sensor using its embedded multidimensional touch (Fig. 2, top). A challenging aspect for shapeable magnetoelectronics is the fact that output signals are usually amplified by rigid components outside the flexible supports. This readout scheme can introduce substantial noise through the cabling which is then amplified together with the signals. Eliminating this noise requires including amplifying elements directly on the flexible support, which implies using intrinsically flexible, thin-film transistor technologies. We have demonstrated such an approach, by combining highly sensitive magnetic field sensorics with high performance InGaZnO based readout electronics, on the same flexible support [19] (Fig. 2, bottom). Although entirely flexible, this platform outperforms commercial rigid magnetic sensor systems in responsivity by at least one order of magnitude. This noteworthy performance is achieved by designing a giant magnetoresistive sensor bridge connected to a cascade of differential and power amplifiers acting as readout circuity. Combining all these features in robust on-skin devices will propel this field beyond exploratory research and towards full-fledged applications, where shapeable magnetic sensors can be crucial for maximizing device performance.

**References:**

[1] D. Makarov, M. Melzer, D. Karnaushenko, and O. G. Schmidt, “Shapeable magnetoelectronics,” Applied Physics Reviews, vol. 3, no. 1, p. 011101, Mar. 2016, doi: 10.1063/1.4938497. [2] R. Streubel et al., “Magnetism in curved geometries,” J. Phys. D: Appl. Phys., vol. 49, no. 36, p. 363001, Aug. 2016, doi: 10.1088/1751-8113/48/12/125202. [3] S. Huang, Y. Liu, Y. Zhao, Z. Ren, and C. F. Guo, “Flexible Electronics: Stretchable Electrodes and Their Future,” Advanced Functional Materials, vol. 29, no. 6, p. 1805924, 2019, doi: https://doi.org/10.1002/adfm.201805924. [4] Y. Liu, M. Pharr, and G. A. Salvatore, “Lab-on-Skin: A Review of Flexible and Stretchable Electronics for Wearable Health Monitoring,” ACS Nano, vol. 11, no. 10, pp. 9614–9635, Oct. 2017, doi: 10.1021/acsnano.7b04898. [5] M. Melzer et al., “Wearable Magnetic Field Sensors for Flexible Electronics,” Advanced Materials, vol. 27, no. 7, pp. 1274–1280, Feb. 2015, doi: 10.1002/adma.201405027. [6] G. Lin, D. Makarov, M. Melzer, W. Si, C. Yan, and O. G. Schmidt, “A highly flexible and compact magnetoresistive analytic device,” Lab Chip, vol. 14, no. 20, pp. 4050–4058, 2014, doi: 10.1039/C4LC00751D. [7] D. Karnaushenko, D. Makarov, C. Yan, R. Streubel, and O. G. Schmidt, “Printable Giant Magnetoresistive Devices,” Advanced Materials, vol. 24, no. 33, pp. 4518–4522, Aug. 2012, doi: 10.1002/adma.201201190. [8] D. Karnaushenko, D. Makarov, M. Stöber, D. D. Karnaushenko, S. Baunack, and O. G. Schmidt, “High-Performance Magnetic Sensorics for Printable and Flexible Electronics,” Adv. Mater., vol. 27, no. 5, pp. 880–885, Feb. 2015, doi: 10.1002/adma.201403907. [9] D. Makarov, D. Karnaushenko, and O. G. Schmidt, “Printable Magnetoelectronics,” ChemPhysChem, vol. 14, no. 9, pp. 1771–1776, 2013, doi: 10.1002/cphc.201300162. [10] M. Melzer et al., “Stretchable Magnetoelectronics,” Nano Letters, vol. 11, no. 6, pp. 2522–2526, Jun. 2011, doi: 10.1021/nl201108b. [11] M. Melzer, D. Karnaushenko, G. Lin, S. Baunack, D. Makarov, and O. G. Schmidt, “Direct Transfer of Magnetic Sensor Devices to Elastomeric Supports for Stretchable Electronics,” Advanced Materials, vol. 27, no. 8, pp. 1333–1338, Feb. 2015, doi: 10.1002/adma.201403998. [12] M. Melzer, D. Makarov, and O. G. Schmidt, “A review on stretchable magnetic field sensorics,” J. Phys. D: Appl. Phys., vol. 53, no. 8, p. 083002, Feb. 2020, doi: 10.1088/1361-6463/ab52cf. [13] G. Lin, D. Makarov, and O. G. Schmidt, “Magnetic sensing platform technologies for biomedical applications,” Lab Chip, vol. 17, no. 11, pp. 1884–1912, May 2017, doi: 10.1039/C7LC00026J. [14] P. N. Granell et al., “Highly compliant planar Hall effect sensor with sub 200 nT sensitivity,” npj Flexible Electronics, vol. 3, no. 1, p. 3, Feb. 2019, doi: 10.1038/s41528-018-0046-9. [15] G. S. Cañón Bermúdez, H. Fuchs, L. Bischoff, J. Fassbender, and D. Makarov, “Electronic-skin compasses for geomagnetic field-driven artificial magnetoreception and interactive electronics,” Nature Electronics, vol. 1, no. 11, p. 589, Nov. 2018, doi: 10.1038/s41928-018-0161-6. [16] G. S. Cañón Bermúdez et al., “Magnetosensitive e-skins with directional perception for augmented reality,” Science Advances, vol. 4, no. 1, p. eaao2623, Jan. 2018, doi: 10.1126/sciadv.aao2623. [17] J. Ge et al., “A bimodal soft electronic skin for tactile and touchless interaction in real time,” Nat Commun, vol. 10, no. 1, p. 4405, Dec. 2019, doi: 10.1038/s41467-019-12303-5. [18] K. Kuijk, W. van Gestel, and F. Gorter, “The barber pole, a linear magnetoresistive head,” IEEE Transactions on Magnetics, vol. 11, no. 5, pp. 1215–1217, Sep. 1975, doi: 10.1109/TMAG.1975.1058886. [19] N. Münzenrieder et al., “Entirely Flexible On-Site Conditioned Magnetic Sensorics,” Advanced Electronic Materials, vol. 2, no. 8, p. 1600188, Aug. 2016, doi: 10.1002/aelm.201600188.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3ba71cee33031382721e1689312e1f2a.jpg)
Fig. 1 Shapeable magnetic sensors as touchless interactive devices for virtual reality. (left) Human hand wearing the on-skin magnetic sensor and approaching a permanent magnet. (center) As the user turns it hands over the magnet, the intensity of virtual lightbulb is dimmed. This two panels are adapted from reference [18]. (right) Applying the same concept but changing the sensing principle allows controlling a virtual character on screen using only the earth's magnetic field. This panel is adapted from reference [17]

![](https://assets.underline.io/uploads/markdown_image/1/image/c1fa368c68af4887c7567f763724f9c8.jpg)
Fig. 2 Multimodal shapeable magnetoelectronics and fully flexible conditioning electronics. (top left) Schematic of a m-MEMS. (top center) Approaching an object using the touchless mode of the m-MEMS activates the first layer of interaction. (top right) Touching the object activates a second layer of interaction and opening a new menu. (center) Entirely flexible and on-site conditioned magnetic field sensing platform containing a power amplifying cascade (bottom left) and a giant magnetoresistive sensor Wheatstone bridge (bottom right).

 Mechanically shapeable magnetic field sensor technologies INVITED

In recent years, magnetoelectric ΔE-effect sensors have been investigated for the detection of small amplitude and low-frequency magnetic fields that typically occur in many biomedical and diagnostic applications. Such sensors are based on magnetoelectric composite resonators, which consist of mechanically coupled magnetostrictive and piezoelectric materials. They can be processed on a large scale by microelectromechanical system (MEMS) technology with dimensions of a few millimeters down to a few micrometers and are compatible with complementary metal-oxide-semiconductor (CMOS) electronics. Furthermore, they can be operated at room temperature with a broad-bandwidth and a large dynamic range and are robust against microphony and mechanical noise. Such sensors utilize the ΔE-effect of the magnetostrictive material, i.e. the change of the mechanical stiffness tensor with magnetization and hence, with an applied magnetic field. Since our first publication of this sensor concept in 2011 [1], much progress has been made in understanding the complex interplay of magnetic, mechanical, and electrical properties and their influence on signal and noise of the sensor system. This holds for different designs of magnetoelectric MEMS cantilevers, but also for surface acoustic wave devices [2]. Here, we present recent experimental and theoretical results on the ΔE-effect, the sensitivity, and the noise of magnetoelectric ΔE-effect sensors. The sensors consist of magnetoelectric MEMS resonators with sputter-deposited AlN or Al73Sc27N as a piezoelectric material and soft-magnetic (Fe90Co10)78Si12B10-based single or multilayers. A magnetoelastic macrospin model of the ΔE-effect in all stiffness tensor components is presented and combined with a finite element electro-mechanical model of the resonator. First and higher order torsion (Fig. 1) and bending modes are compared and analyzed regarding the sensitivity and the ΔE-effect [3]. Measurements and simulations reveal the dependency of the sensitivity on the mode number, caused by the geometry, mode shape, and the ΔE-effect in different stiffness tensor components. Specific rules for the resonator design are derived as a result. Besides the geometric and magnetic material properties, we find that the resonator loss and the piezoelectric material have a decisive impact on signal and noise. The influence of the quality factor Q [4] and the piezoelectric material [5] on signal and noise are investigated experimentally and explained by combining the previous model with a signal-and-noise equivalent circuit model (Fig. 2). Both quantities, Q and the piezoelectric material show the promising potential of significantly increasing the sensitivity and improving the limit of detection (LOD). Yet, an improvement in the LOD is currently limited by magnetic noise that becomes dominant at large operating voltage amplitudes [6]. Hence, understanding the specific origins of magnetic noise in such magnetostrictive resonant structures is crucial for sensor improvement in the future. A physical magnetic noise model is presented to identify the origin of stress-amplified, thermal-magnetic noise. It combines large scale finite differences micromagnetism with the mechanical equations of motion to capture magnetostrictive self-energy and frequency effects. Including the piezoelectric constitutive relation and the operating electronics the sensor’s output voltage noise density can be estimated. With the model, we evaluate and discuss experimental results and explain the dependency of magnetic noise on the excitation amplitude and the magnetic bias field. The model provides detailed insights into general noise limits, which arise from using the ΔE-effect as the sensing principle. Finally, we briefly present first applications in cell imaging [7] and show that small signal measurements with simultaneous localization are enabled by a dual-mode operation scheme with compact self-biased ΔE-effect sensors [8]. This is of particular interest for typical biomedical inverse solution problems where the precise knowledge of the sensor’s position and orientation is essential. Such applications could benefit from sensor arrays that provide many measurements with a high spatial resolution. The noise equivalent model is extended to arrays of parallel sensor elements and compared with measurements. Implications and prospects for sensor developments in the future are discussed in a conclusion.

**References:**

[1] B. Gojdka, R. Jahns, K. Meurisch, et al., APL Vol. 99, p.1-4 (2011); Nature Vol. 480, p.150 (2011) [2] J. Schmalz, A. Kittmann, P. Durdaut, et al., Sensors, Vol. 20, p.1–17 (2020) [3] B. Spetzler, C. Kirchhof, E. Quandt, et al., Phys. Rev. Appl., Vol. 12, p.1-13 (2019) [4] B. Spetzler, C. Kirchhof, J. Reermann, et al, APL., Vol. 114, p.183504 (2019) [5] B. Spetzler, J. Su, R.-M. Friedrich, et al., APL Materials., invited, submitted (2021) [6] P. Durdaut, E. Rubiola, J. Friedt, et al., J. Microelectromech. Syst., Vol. 29, p.1347 - 1361 (2020) [7] N. Lukat, R. M. Friedrich, B. Spetzler, et al., Sensors Actuators A Phys., Vol. 309, 1–8 (2020) [8] B. Spetzler, C. Bald, P. Durdaut, et al., Sci. Rep., accepted, (2021)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1ddee42922239ae2a14790371e63be23.jpg)
Normalized resonance frequencies fr/fr,max of the first three torsion modes (TM1-3) as functions of the magnetic flux density µ0H applied along the long axis of the cantilever; inset: top photograph of the MEMS cantilever with visible electrodes. A soft magnetic FeCoSiB-Cr multilayer is sputter deposited on the other side.

![](https://assets.underline.io/uploads/markdown_image/1/image/9c28120fbc2c2f322ee01c1b390d8acb.jpg)
Measured and simulated limit of detection (LOD) of two sensors of identical design that differs only in the piezoelectric material, which is AlN and AlScN, respectively. At large excitation voltage amplitudes ûex magnetic noise imparis the LOD.

 ΔE-Effect Magnetic Field Sensors

Compact, ultra-low power magnetic field sensors are desirable for applications in multiple fields from biomedical engineering to military sensors [1,2,3]. Through direct coupling of magnetostrictive and piezoelectric strain, an on-chip sensor can be designed by exploiting the interface between thin films which can generate a charge when under an external magnetic field bias that depends not only on the magnitude of the measured field, but also the magnetic field direction enabling vector sensing capabilities. Magnetoelectric MEMS-scale heterostructures deposited in layers on silicon wafers and etched to create beams and cantilevers operating at the eletromechanical resonance were shown to work in a stress reconfigurable mode [4,5]. In this work we demonstrate magnetic field and directional response of FeC/AlN MEMS double-clamped heterostructure resonators. Through coupled strain engineering we are able to exploit the magnetic anisotropy and create a preferred axial response along the easy axis length of the suspended heterostructure beam. Resonant frequency response to the external magnetic field produces a sensitive measure of the angular dependence depending on the field vector components along the long and short axes. Figure 1a illustrates the heterostructure design of the double clamped ME MEMS structure and Figure 1b depicts a set of beams fabricated in a rosette pattern between Helmholtz coils used to apply a magnetic field to study the resonance response. The resonant peak shift with applied external magnetic field can be seen in Figure 2a where the butterfly loop has a linear slope df/dH near coercive field at 100G of 35 Hz/mT or 47 Hz/mT depending on the loop leg denoting the best bias response working point for this sensor. Polar plot of the resonance peak vs field at 15° increments can be seen in Figure 2b showing the directional response of the double clamped ME MEMS structures. Limit of detection measurements and further resonant peak angular dependence will be presented and deposition conditions will be discussed to illustrate the necessary conditions required to optimize creation of a high-quality MEMS sensor.

**References:**

[1] M. Hämäläinen, R. Hari, R.J. Ilmoniemi, and O. V. Lounasmaa, Reviews of Modern Physics 65, 413–497 (1993), DOI: 10.1103/RevModPhys.65.413 [2] J. W. Mooney, S. Ghasemi-Roudsari, E. Reade Banham, and B. T. H. Varcoe; Biomed. Phys. Eng. Express 3 (2017) 015008, DOI: 10.1088/2057-1976/3/1/015008 [3] T. R. Clem, Naval Engineers Journal 110, 139–149 (1998), DOI: 10.1111/j.1559-3584.1998.tb02393.x [4] S. P. Bennett, J. W. Baldwin, M. Staruch, and P. Finkel; Applied Physics Letters 111, 252903 (2017), DOI: 10.1063/1.5011728 [5] M. Staruch, et al.; Physical Review Applied 11, 034028 (2019); DOI:10.1103/PhysRevApplied.11.034028

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/50e45a3a8b51d1152352d15c4537b1ae.jpg)
Figure 1: (a) A top view and side view of magnetoelectric arched beam resonator, consisting of a layered film stack on a silicon wafer consisting of Si3N4 support, Pt back electrode with Ta adhesion layer, AlN piezoelectric layer, and Fe0.7Co0.3 top electrode and magnetostrictive layer. (b) Rosette pattern of beams fabricated on a silicon chip between Helmholtz coils, with rotation for angular dependence measurements.

![](https://assets.underline.io/uploads/markdown_image/1/image/d02c2d26681eeb936087c33b918db727.jpg)
Figure 2: (a) Frequency shift of resonance peak vs bias magnetic field applied parallel to long axis of the beam. (b) Polar plot of the magnetic field response at 15° intervals for 0, 200, 300, 500, and 1000 Gauss.

 Directional Magnetic Field Response of FeCo/AlN Heterostructure Magnetoelectric Resonators

Magnetoresistive field sensors have a wide range of uses, such as in biomedical applications, in the automotive industry, robotics, or smart city technologies. Figures of merit like sensitivity, detectivity and spatial resolution are used to evaluate the performance of such sensors [1]. At low frequencies, the 1/f noise component is dominant and is in fact responsible for hindering the device's detectivity, and, consequently, its performance. There is an active research effort to reduce this noise component and tackle this limitation [2]. Vortex-based devices, in which the free layer exhibits a vortex magnetization distribution in its equilibrium state, are promising magnetic field sensors due to their large linear detection range [3] and the fact that they show practically no hysteresis in this range. Besides, these devices are often considered as model systems for the study of magnetization dynamics. In this study, we focus on the analysis of the 1/f noise in a particular type of magnetic sensor based on a vortex magnetic configuration integrated in a magnetic tunnel junction (MTJ) spin torque nano-oscillator. These devices present excellent rf characteristics for future radio-frequency devices and applications, such as rf generation [4], detection [5] or neuromorphic computing [6]. While the use of vortex-based spin-torque nano-oscillators for applications such as these mentioned here has been largely studied, they are newcomers in the magnetic field sensing landscape. In this work, we analyse the 1/f low-frequency noise in vortex-based spin-torque nano-oscillators by determining the Hooge parameter in different conditions. The Hooge parameter is typically used to characterize and compare sensor’s noise properties. Firstly, we find that in the uniform states the Hooge parameter of the studied device is comparable to that measured in state-of-the-art TMR sensors with similar RA product, α = 10-11 - 10-10 µm2. In the vortex state, the measured noise level is around one order of magnitude greater than in the parallel (and antiparallel) state, see Fig. 1a. This is due to the increased probability of pinning of the vortex core into defects or inhomogeneities of the free layer. Secondly, we determine that the dynamics of the vortex core strongly influence the noise level of the device. For a current above a certain threshold, the spin transfer torque surpasses the intrinsic damping of the free layer resulting in self-sustained oscillations of the vortex core [7]. In the self-sustained oscillations' regime, the noise decreases to a level close to that of the antiparallel state, see Fig. 1b. Furthermore, we present a novel strategy for reducing the 1/f low-frequency magnetic noise, through the application of an in-plane rf field or injection of an rf current [8]. By using this approach while the device is operating in the self-sustained regime, we are capable of further decreasing the measured noise level to values close to the minimum attainable, see Fig. 2. We find that this noise reduction is non-resonant, see Fig. 2a. As such, we can have a vortex-based STNO with relevant noise properties, comparable to those of state-of-the-art TMR field sensors. At the same time, we profit from the specific advantages of vortex-based spin-torque nano-oscillators for sensing applications: large linear detection range, virtually no hysterisis and high spatial resolution. This noise reduction technique based on the spin-torque dynamics of the vortex can have an impact on the sensors' industry, which may profit from the advantages of the vortex configuration. The work is supported by the French ANR project “SPINNET” ANR-18-CE24-0012.

**References:**

[1] D. C. Leitão et al., Nanotechnology 27, 045501 (2015) [2] L. Huang et al., Journal of Applied Physics 122, 113903 (2017); J. Moulin et al., Appl. Phys. Lett. 115, 122406 (2019) [3] D. Suess et al., Nat. Electronics 1, pages 362–370 (2018) [4] S. Wittrock et al., Phys. Rev. B 99, 235135 (2019) [5] A. S. Jenkins et al., Nat. Nanotech. 11, 360 (2016); D. Marković et al., Phys. Rev. Applied 13, 044050 (2020) [6] M. Romera et al., Nature 563, 230–234 (2018); J. Torrejon et al., Nature 547, 428-431 (2017) [7] A. Dussaux et al., Nat. Comm. 1, 8 (2010) [8] M. Jotta Garcia et al., arXiv:2012.09616 [cond-mat.mes-hall] (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f1e2a4020c2f2daf24d07405919ec60f.jpg)
Fig.1 a) Hooge parameter as a function of an in-plane magnetic field that is swept from the parallel to the anti-parallel state and back. b) Evolution of the Hooge parameter with the applied bias current. The inset shows the oscillation power of the rf emission due to the emerging vortex dynamics. The red dotted line represents the Hooge parameter measured in the AP state.

![](https://assets.underline.io/uploads/markdown_image/1/image/8659329698821b38c65d8cb8989eb4a3.jpg)
Fig. 2 a) Hooge parameter as a function of the frequency of the applied oscillating field, with Prf = 1 mW. The red line indicates the value measured in the absence of this field. b) Hooge parameter as a function of the power amplitude of the rf field at a fixed frequency, f = fres = 243.1 MHz. The green dotted lines represent the Hooge parameter measured in the P state.

 Spin-torque Dynamics for Noise Reduction in Vortex-based Sensors

The final goal of our project is to develop a device that acts as a bypass for restoring neuronal signals in regions with spinal cord injuries1. To detect such signals, a magnetic field sensor can be employed, placed near the spinal cord. This in turn sets several constraints for the sensor itself. It must be of reduced size, operate at zero or very small external biasing field and achieve low detectivity at low frequency, while operating at body temperature (310K). The detectivity of a magnetic sensor is determined both by its sensitivity and its intrinsic noise. If the target signal is in the low frequency region, which is the case for biomedical applications, Anisotropic Magnetoresistance (AMR) sensors become competitive when compared to Tunnelling Magnetoresistance (TMR) and Giant Magnetoresistance (GMR) technologies, due to its low 1/f noise, even if they do not reach same sensitivity values. Additionally, AMR sensors can be of much simpler fabrication, not requiring the stacking of several thin films. We will present results obtained with AMR sensors made of 30 to 60 nm thick epitaxial La2/3Sr1/3MnO3 thin films, which present low intrinsic noise2, deposited on 4° , 6° or 8° vicinal SrTiO3 (STO) substrates and etched in a Wheatstone Bridge design. This design is also referenced in literature as Planar Hall Effect Bridge3 (PHEB). Pulsed Laser Deposition (PLD), photolithography and Ion Beam Etching (IBE) were used for in-lab samples fabrication. The use of a vicinal substrate, which presents a surface miscut angle regarding the crystallographic plane, was selected so as to induce uniaxial anisotropy and an easy magnetic axis along the step edges4. The measured AMR curves can be compared to the expected behaviour when considering the Stoner-Wohlfarth model for coherent magnetization reversal. This coherent magnetization reversal process was checked by Magneto-optical Kerr imaging (see figure 1). In order to achieve a higher sensitivity, thus lower detectivity, PLD deposition was performed at different temperatures, which leads to a change in thin film Curie temperature Tc and therefore affects the anisotropy field Ha. A clear reduction in Ha can be seen when changing the deposition temperature from 730° C to 680°C. The anisotropy field depends also on the angle of vicinality, the smaller the angle the smaller the anisotropy field. For vicinal angles ranging from 4° to 8°, the uniaxial anisotropy of the film is preserved. Changing the temperature deposition or the vicinality does not degrade the 1/f noise of the films. The so far achieved detectivity @ 310K is as low as 1nT/Hz1/2 at 1 Hz and 300 pT/Hz1/2 at 1 kHz in a single-layer sensor (see figure 2) without using performance enhancing techniques such as focusers.

**References:**

1 http://www.byaxon-project.eu/ FET Open 2017-2020 2 L Méchin et al, J. Phys. D: Appl. Phys.46, 202001 (2013), https://doi.org/10.1088/0022-3727/46/20/202001 3 A.D. Henriksen et al, Appl. Phys. Lett. 97, 013507 (2010), https://doi.org/10.1063/1.3460290 4 P Perna et al Adv. Funct. Mater., 27, 1700664 (2017), https://doi.org/10.1002/adfm.201700664

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ea6a5b53513212ecfb41390187c4856c.jpg)
Figure 1: MOKE Imaging of the magnetization reversal process in the AMR Wheatstone bridge sensor and local magnetization loop

![](https://assets.underline.io/uploads/markdown_image/1/image/c7f186f0d7d8cfc247aaaec8b6576132.jpg)
Figure2: Detectivity spectrum at 310K as a function of the polarization of the AMR Wheatstone bridge

 Sub-nT resolution of single layer sensors based on the AMR effect in single layer La2/3Sr1/3MnO3 thin films

Some of the early parallel fluxgate sensors had cores made of magnetic wires and this design is still used in many devices, including gradiometers and low-cost sensor arrays in magnetoelastic torque meters [1]. Wire and also multiwire cores are also being used in transverse fluxgates [2]. Despite their larger noise and lower temperature stability compared to ring-core fluxgates, wire-core parallel fluxgates have several advantages [3]: 1. their sensing direction is precisely defined by the direction of the sensor core 2. they have excellent spatial selectivity which is important for the detection of magnetic particles [4] 3. High sensitivity allows decreasing the core length 4. The large shape anisotropy gives them low crossfield error [5]. The sensitivity of ring-core and race-track fluxgate sensors is well understood and described in the literature [6,7], while such study on wire-cored sensors is missing. We offer it in this paper for the case of voltage output. We calculate the sensitivity as a function of core and pickup coil geometry and configuration of wire core by Finite-element modeling and compare these results with the measurements. We analyze both existing configurations (single-core, Foerster and Vacquier) and propose multiwire fluxgates of two types: with collective excitation and pickup coils and with individual pickup coils. This paper is based on model cores made of 36 mm long, 0.2 mm diameter Permalloy wires with chemical composition Ni78Fe15Cu4Mo3. The wires were annealed for 3 hours in a dry hydrogen atmosphere at 1080 °C to obtain near-zero magnetostriction. Our simulation models were based on constant permeability and also on the magnetization curve estimated from the measurement on the wire. Sensitivity and noise properties were measured for sensors containing 2 to 12 wires with different distances between the wires. The model can be upscaled for magnetic rods and downscaled for bundles of microwires and arrays of nanowires. However, the results strongly depend on the aspect ratio of the used wires. Fig. 1 shows examples of the measured fluxgates. The multiwire type has a 3D printed honeycomb bobbin which allows insertion of different configurations of wires in glass or ceramic capillaries. For each configuration, we found the optimum working point (excitation frequency and amplitude) to maximize the sensitivity and minimize the noise. In order to simplify the problem, we did not use the parametric amplification of the output voltage. We studied the effect of pickup coil geometry by FEM modeling and verified the results experimentally: the optimum coil length is 80 % of the core length and the coil diameter should be minimized as the sensitivity is inversely proportional to the pickup coil diameter as shown in Fig.2. In this regard’s fluxgate behaves differently from induction sensors without excitation, which shows the increase of sensitivity with the pickup coil diameter. This dependence does not change with the wire permeability. This decrease of the sensitivity is the reason, why multiwire fluxgate with large common pickup coil has larger noise (0.7 to 14 nT/√Hz at 1 Hz, depending on configuration) than single-core (180 pT/√Hz@1Hz) and Vacquier type (51 pT/√Hz@1Hz) sensors. The effective solution to this problem is to use an individual pickup coil for each wire instead of a collective coil common for all wires. The sensitivity of the multiwire fluxgate is increasing with the wire pitch and the noise is inversely proportional to the wire pitch. This is caused by two factors: 1. With increasing wire distance their magnetostatic interaction is decreasing, which results in lower demagnetization 2. With increasing distance the noise correlation between wires is decreasing and the total noise is reduced by the averaging effect, which is stronger for independent noise sources This study was limited to the initial selection of optimum geometry of the wire core and pickup coil of the voltage-output parallel fluxgate. Further increase of sensitivity and noise reduction can be achieved by tuning the pickup coil by the parallel capacitor to the mode of parametric amplification at second harmonics. This study was supported by the Grant Agency of the Czech Republic within the Nanofluxgate project (GACR GA20-27150S).

**References:**

[1] P. Ripka, Magnetic sensors and magnetometers, Artech House, 2001 [2] M. Butta, M. Vazquez, R. P. del Real et al., AIP Advances Vol. 10, (2020) [3] M. Janosek, "Parallel fluxgate magnetometers," in High Sensitivity magnetometers, Springer, 2017 [4] J. Lei, T. Wang, C. Lei et al. Applied Phys. Lett. Vol. 102, 022413 (2013) [5] P.Ripka, W. Billingsley, Sens. Act. A Vol. 81, p. 176-179 (2000) [6] C. Hinnrichs, J. Stahl, K. Kuchenbrandt et al., IEEE Trans. Magn. Vol. 37, p. 1983 (2001) [7] L. Perez, I. Lucas, C. Aroca et al., Sens. Act. A Vol. 130, p. 142 (2006)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/197886eeec5ca839cbd0ec0c6da03e29.jpg)
Figure 1 Experimental fluxgate sensors: a) single core, b) Vacquier, c) multiwire

![](https://assets.underline.io/uploads/markdown_image/1/image/b8f674df538b8b10c95c207e3fa16986.jpg)
Figure 2 Relative flux of the 36 mm long pickup coil with diameter D as a function of its relative diameter D/d – values calculated by 2D FEM for 36 mm long, d = 0.2 mm diameter magnetic wire core

 Sensitivity and Noise of Multiwire Parallel Fluxgate Sensors

In the context of miniaturization, energy conservation, smart devices and IOT, magnetic field sensors based on magnetic tunnel junctions (MTJ) constitute an attractive choice, with small size, very high intrinsic sensitivity and low power consumption. The specific sensor response curve is determined by the magnetization configuration and hysteresis loop behavior of the soft (sensing) layer of the MTJ. A possible implementation is the vortex-based sensor, in which the junction sensing layer magnetization is in a vortex configuration at zero field, consisting of a small central core with out-of-plane magnetization and an in-plane magnetization rotating around the core with a specific chirality (clockwise or counterclockwise). Depending on the geometry, the vortex can be the natural stable micromagnetic configuration of the sensor, with the lowest energy at remanent state. This is the case for circular dots of soft ferromagnetic materials with sufficient thickness [1]. Circular vortex-state sensors typically exhibit much lower sensitivity compared to uniform-magnetization sensors, but are naturally linear and exhibit low hysteresis in a limited field range [2]. Here we use micro-magnetic simulations to study the effect of geometrical asymmetry [3] on the vortex properties, in particular on the vortex nucleation, chirality and magnetization cycle. We explore different modifications of the magnetic dot shape that ensure the control of the vortex chirality. We specifically study magnetic disk or ellipse with a cut on one side of different size and shape. Then we determine the geometrical parameters (in particular the position and size of the cut) that also allow a large nucleation field, thus leading to a quasi-linear response on a large field range. However, due to the asymmetric shape, the control of the vortex chirality is obtained at the cost of a small hysteresis: in general, the magnetization is not exactly zero at remanence. In order to reduce this hysteresis, we study magnetization at remanence for different dots with cut by varying the geometrical parameters and show that certain combination of parameters give zero magnetization at remanence. An analytical model also describes this result, obtained by micromagnetic simulations. Finally, another route to reduce hysteresis is to take advantage of magnetostatic interaction between magnetic dots within a 2D array [4]. The stray field of neighboring dots influences the vortex core position and may thus reduce the magnetization at remanence. This effect is explored for pairs of asymmetric dots at different distance and position. Our results show various means to reduce and even cancel the hysteresis.

**References:**

[1] R. Cowburn, D. Koltsov and D. Tricker, Physical Review Letters, Vol. 83, p.1042 (1999) [2] D. Suess, A. Bachleitner-Hofmann and H. Brückl, Nature Electronics, Vol. 1, p. 362 (2018) [3] S. Agramunt-Puig, N. Del-Valle, and A. Sanchez, Applied Physics Letters, Vol. 104, p. 012407 (2014) [4] O. Sukhostavets, J. Gonzalez and K. Guslienko, Physical Review B, Vol. 87, p. 094402 (2013)

**Images:**

 Control of Chirality and Hysteresis in Asymmetric Vortex-based TMR sensors

Magnetic viscosity, the long time-scale magnetization drift in response to changes in applied field, can directly impact the accuracy of high sensitivity tunneling magnetoresistance (TMR) based field sensors operating with large dynamic field ranges or utilizing long time scales. Recent studies have demonstrated benefits arising from an understanding of magnetic viscosity in the context of field sensing; for instance, as a source of spurious signals from buried ferrite during landmine detection by induction sensors [1], as a tool providing insight into magnetization dynamics [2-5], and even as a novel immunoassay characterization technique for biochemical detection through so-called magnetorelaxometry [6,7]. Although the mechanism of magnetic viscosity has been well described [8,9], quantifying the impacts of the effect in sensor applications and establishing relationships between those impacts and tunable material properties has remained under explored. Therefore, in this work we characterize the magnetic viscosity in a variety of commercial and custom magnetic tunnel junction (MTJ) based sensors, as well as explore the potential impacts of integration with flux concentrator shielding. Utilizing accessible electrical measurements of the TMR or sensor output, a wide range of viscosity behavior is revealed. The results in commercial sensors demonstrate order-of-magnitude differences ranging from 0.2 – 2 μT in the effective sensor output field viscosities, with accuracy implications due to the hysteric nature of the viscous drift in the sensor output. To elucidate underlying differences in the selected commercial sensors, we fabricate and compare custom MTJs with variable free layer thicknesses tFL as well as patterned devices utilizing a variety of flux concentration shielding (with up to 30x flux concentration factors). Fig. 1(a) presents an illustrative case of the magnetoresistance vs applied field for one of the custom MTJs where tFL = 4 nm for a biased sensing layer. For each measurement, the device is first initialized in a saturating field μ0H0 of approximately 30 mT. The field is then abruptly reduced to the measurement field μ0Ha, ranging from -25 to 25 mT. The time-dependent rate of change of the MTJ’s resistance for such a measurement with the specified value of Ha is shown in Fig. 1(b), illustrating that the observed drift of the device resistance is logarithmic in time and strongly field dependent as expected. These measurements are then used to extract the magnetoresistance’s viscosity parameter. The patterned MTJs studied show a 3x increase in sensitivity between tFL = 4 to 20 nm but a corresponding 43% decrease in the magnetic viscosity parameter [Fig. 2(a-b)]. Relationships between the viscosity, magnetic active volumes, and anisotropy will be discussed. These results highlight simple design pathways useful to consider when attempting to enhance or mitigate viscous output effects in high sensitivity MTJs. In addition, the viscosity parameter in certain fabricated MTJs is found to exhibit a strong asymmetric field dependence that is not observed in the sensitivity [Fig. 2(a-b)], highlighting complexities of the reversal mechanism, as well as the deeper insight into magnetization dynamics gained from viscosity characterization.

**References:**

[1] Y. Das, IEEE Trans. Geosci. Remote Sens. 44, 1444 (2006). [2] B. Dolgin et al., J. Phys. Condens. Matter 25, 076004 (2013). [3] A. Lisfi et al., AIP Adv. 8, 056438 (2018). [4] S.J. Collocott and V. Neu, J. Phys. D. Appl. Phys. 45, 035002 (2012). [5] C. Leighton and I.K. Schuller, Phys. Rev. B 63, 174419 (2001). [6] F. Wiekhorst, U. Steinhoff, D. Eberbeck, and L. Trahms, Pharm. Res. 29, 1189 (2012). [7] C.C. Huang, X. Zhou, and D.A. Hall, Sci. Rep. 7, 1 (2017). [8] R. Street and J.C. Woolley, Proc. Phys. Soc. Sect. A 62, 562 (1949). [9] E.P. Wohlfarth, J. Phys. F Met. Phys. 14, L155 (1984).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1ea0569f5040dd3d929ea0dce090e75e.jpg)
Fig. 1. (a) Resistance vs applied field for patterned MTJ bit strings with free layer thickness tFL= 4 nm. (b) Viscosity measurement of the change in resistance ΔR (relative to measured resistance at time t = 90 sec) for specified μ0Ha between 25 and 0 mT. Saturating initial field μ0H0 = 27 mT.

![](https://assets.underline.io/uploads/markdown_image/1/image/67998c22b032e35251be5070029002e6.jpg)
Fig. 2. Sensitivity (black) and magnetoresistance viscosity parameter SMR (red) as a function of applied field for MTJs with free layer thickness of either (a) 4 nm, or (b) 20 nm. The initial saturating field μ0H0 = 27 or 15 mT as specified. SMR is shown in parts per million, normalized to the resistance at zero-field.

 Magnetic Viscosity in High Precision Magnetoresistive Field Sensors

Tunnel magnetoresistance (TMR) magnetic sensors using CoFeB/MgO/CoFeB magnetic tunnel junction (MTJ) are promising for detection of magnetic field with various magnitude and frequency. The soft-magnetic property of the free layer (sensing layer) influences the sensing performance, which is particularly important for detection of small magnetic field such as biomagnetic field. NiFe (permalloy) is frequently used as a soft-magnetic sensing layer of TMR sensors. However, the large film roughness and the fcc 111-texture of the NiFe polycrystalline film tend to lower the TMR ratio. Amorphous ferromagnets such as CoFeSiB [1] have been developed as alternative materials for the sensing layer of TMR sensors. However, the soft-magnetic nature of CoFeSiB is prone to be degraded due to crystallization by annealing at &gt; 300 °C [2], which is the typical annealing temperature for TMR sensors. In this work, we demonstrate an amorphous CoFeBTa material, whose crystallization temperature is ~500 °C [3], to the TMR sensing layer and investigated the magnetic, magnetoresistive and low-frequency noise properties. A top-pinned spin-valve structure of bottom lead / Ta(5) / CoFeBTa(20) / Ta(0.3) / CoFeB(3) / MgO(1.8) / CoFeB(2.5) / CoFeBTa(0.6) / CoFe(0.5) / Ru(0.8) / CoFe(3) / IrMn(8) / Ru(8) capping layer (nm in unit) was sputter-deposited [4]. The spin-valve film was annealed twice (two-step annealing) under magnetic fields in two directions that were orthogonal each other. The first annealing at 350 °C induces a uniaxial magnetic anisotropy in the CoFeBTa/Ta/CoFeB free layer in e.g. y-direction and the second annealing at 200 °C defines the pinning direction in the orthogonal direction (x-direction). The pattered TMR devices by photolithography were characterized by dc 4-probe method. Figure 1(a) shows the resistance (R)-magnetic field in x-direction (Hx) curve of a single TMR device (MTJ diameter: 50 μm). The TMR ratio was 160% and the resistance-area product was 40 kΩ μm2. A linear R-H transfer curve with a small hysteresis was realized in the intermediate magnetization state after the two-step annealing process. The maximum sensitivity (1/Rmin dR/dH) of ~70 %/mT was obtained at Hx = 1 mT. Figure 1(b) shows the noise voltage density (√SV) spectra of the TMR device at various magnetization states. For the noise measurements, bias voltage (Vb) was supplied using a 1.5 V dry cell battery and a ballast resistor. The magnitude of the noise at the intermediate magnetization state (Hx = 1 mT) was larger than those of the parallel and anti-parallel magnetization states, indicating that the 1/f noise is dominated by some distinct magnetic origins. The noise voltage density increased with increasing Vb, and the Hooge’s noise parameter αH was determined to be ~ 4×10-8 μm2 at Hx = 1 mT. The minimum detectivity (field-equivalent noise) defined by √SV/(1/Rmin dR/dH Vb) was 2.2 nT/√Hz at 10 Hz at Hx = 1 mT. For comparison, we fabricated a similar TMR sensor device with a NiFe(20 nm) soft-magnetic layer instead of CoFeBTa. The NiFe sensor showed larger detectivity of 4.5 nT/√Hz at 10 Hz than that of the CoFeBTa sensor mainly due to its larger 1/f noise. Thus, the CoFeBTa amorphous soft-magnetic layer has a clear advantage over the NiFe one for magnetic sensor applications. We also fabricated a full-bridge magnetic sensor using the CoFeBTa-based TMR devices. Each leg of the full-bridge is composed of 50 TMR devices connected in series as shown in Fig. 2(a). Figure 2(b) shows the output voltage (Vout) vs. H curve under various Vb. The non-linearity and hysteresis in the Vout-H curve can be attributed to variation of the R-H curve shape of the individual TMR devices of the array, which should be improved in the future. The bridge sensor showed an improved detectivity of 0.5 nT/√Hz at 10 Hz independent of Vb.

**References:**

[1] Kato, Oogane, Fujiwara et al., Appl. Phys. Express Vol. 6, p. 103004 (2014). [2] Jimbo, Fujiwara and Shimizu, J. Appl. Phys. Vol. 117 p. 17A313 (2015). [3] Choi, Nakatani, Read et al., Appl. Phys. Express Vol. 10 p. 013006 (2017). [4] Rasly, Nakatani, Li et al. J. Phys. D: Appl. Phys. Vol. 54, p. 095002 (2021).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/534585ecb598bac58972238c575642c6.jpg)
Fig. 1(a) R-H curve and (b) noise spectra of the TMR sensor.

![](https://assets.underline.io/uploads/markdown_image/1/image/c7e8832260ba352e8b04a54949d46447.jpg)
Fig. 2(a) Schematic of full-bridge sensor and (b) output voltage vs. magnetic field.

 Tunnel magnetoresistance sensors with CoFeBTa amorphous soft-magnetic sensing layer

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

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