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The aerospace industry has become increasingly reliant on carbon fibre composite (CFC) as a structural component in aircraft, due to its strength to weight ratio. One of the disadvantages of CFC are their vulnerability to impact damage and external environment changes during flight, which causes barely visible damage to the structure. One solution to this is structural health monitoring (SHM), which monitors the composite structure to provide early detection for damage. Previous work has found that magnetostrictive ribbons [1] and inkjet printed copper coils used as actuator-sensor pairs have good resolution to detect damage to CFC [2]. This research has focused on inkjet printing magnetic sensors, which can be directly attached to the surface of the composite.&lt;br/&gt;&lt;br/&gt;JetLab IV (by MicroFab) with piezoelectric print head (60um diameter orifice) was used. The sensor designs were printed using Magnetite (20% in DMF, IPA and water) and nickel (2% in NMP and water) nanoparticle dispersion inks, manufactured by Nanoshel LLC on photo paper (25x25mm) (fig 1). A MPMS3-SQUID magnetometer was used to characterise the ink’s magnetisation (fig 2). Magnetite and nickel has saturation magnetisation values of 78 and 27 emu/g respectively. Different designs and printer parameters were explored and their magnetic performance evaluated the magnetic performance of the printed designs using simple mechanical testing such as 3-point bending test and impact testing.

![](https://assets.underline.io/uploads/markdown_image/1/image/93225e2ded45120b9d7b64a6504b9660.jpg)

Fig 1. Magnetite printed design on photo paper

![](https://assets.underline.io/uploads/markdown_image/1/image/b678abbf59eac3de5f65db1d82d9bf3b.jpg)

Fig.2 Hysteresis loop of magnetite and nickel ink

2022 Joint MMM-INTERMAG

Printing magnetostrictive materials for structural health monitoring of carbon fibre composite

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INTERMAG 2021

The aerospace industry has become increasingly reliant on carbon fibre composite (CFC) as a structural component in aircraft, due to its strength to weight ratio. One of the disadvantages of CFC are their vulnerability to impact damage and external environment changes during flight, which causes barely visible damage to the structure. One solution to this is structural health monitoring (SHM), which monitors the composite structure to provide early detection for damage. Previous work has found that magnetostrictive ribbons [1] and inkjet printed copper coils used as actuator-sensor pairs have good resolution to detect damage to CFC [2]. This research has focused on inkjet printing magnetic sensors, which can be directly attached to the surface of the composite. JetLab IV (by MicroFab) with piezoelectric print head (60um diameter orifice) was used. The sensor designs were printed using Magnetite (20% in DMF, IPA and water) and nickel (2% in NMP and water) nanoparticle dispersion inks, manufactured by Nanoshel LLC on photo paper (25x25mm) (fig 1). A MPMS3-SQUID magnetometer was used to characterise the ink’s magnetisation (fig 2). Magnetite and nickel has saturation magnetisation values of 78 and 27 emu/g respectively. Different designs and printer parameters were explored and their magnetic performance evaluated the magnetic performance of the printed designs using simple mechanical testing such as 3-point bending test and impact testing.

![](https://assets.underline.io/uploads/markdown_image/1/image/93225e2ded45120b9d7b64a6504b9660.jpg)

Fig 1. Magnetite printed design on photo paper

![](https://assets.underline.io/uploads/markdown_image/1/image/b678abbf59eac3de5f65db1d82d9bf3b.jpg)

Fig.2 Hysteresis loop of magnetite and nickel ink

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. 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 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

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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.

Since the advent of spin-torque nano-oscillators (STNOs) {1}, mutual synchronization of two or more STNOs has been of intense interest as it not only improves both the microwave signal power and the signal quality factor (Q-factor) appealing to communication technology but can also be used directly for neuromorphic computing due to the tunable magnetic nature of the interaction between STNOs. Thanks to the spin Hall effect, a new class of spintronic oscillators known as spin Hall nano-oscillators (SHNOs) has emerged. Compared to STNOs, they rely on the current flowing in-plane, which makes their fabrication easier and allow for a large number of SHNOs to synchronize in both chains and arrays. {5,6} In this work, we explore mutual synchronization in nano-constriction (NC) based SHNO chains and demonstrate robust synchronization of SHNOs for longer chains with up to 21 Oscillators [Fig. 1(a&b)]. We investigate both NiFe(4 nm)/Pt(5 nm) {6,7} and W(5 mm)/CoFeB(1.4 nm)/MgO(2 nm) {8,9} SHNOs. We report that the robust mutual synchronization can deliver an enhanced output power and significantly lower linewidth (Fig. 2(a&b)). A sub-MHz linewidth [Fig. 2(b), as low as 300 kHz for NiFe/Pt] can be achieved for 21 synchronized oscillators. The high-frequency operation results in a very high quality factor (Q=f/△f) of &gt;30,000 for NiFe/Pt and &gt;25000 for W/CoFeB/MgO, which is the highest reported in chains. A linear decrease in linewidth and increase in output power (up to in-phase synchronization) is observed with the number of oscillators [Fig. 2(c)]. The low current and low field operation of these oscillators along with wide frequency tunability (2-28 GHz) with both current and magnetic fields, make these oscillators ideal candidates for various spintronic applications.

![](https://assets.underline.io/uploads/markdown_image/1/image/f0e099e3c61e0350cd61b894af51a975.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/c1278063a10ddeee4cc0d0ca490c6969.jpg)

Robust mutual synchronization of spin Hall nano-oscillator chains

Robust mutual synchronization of spin Hall nano-oscillator chains

A noise-suppression sheet (NSS), which is composed of very thin soft magnetic flake particles with organic binder, is indispensable to suppress the electromagnetic compatibility problem for recent mobile communication devices. NSS is mounted on the circuit board and absorbs extra-electromagnetic waves inside the mobile device. This absorption property is characterized as a peak of imaginary complex permeability μ’’ owing to the ferromagnetic resonance [1]. Although a commercial NSS with flake particles of Sendust (Fe-Si-Al alloy) generally exhibits a bimodal μ’’ spectrum, the physical origin of this behavior has not been understood so far. This situation would be a bottleneck for the next generation mobile communication. In this study, we investigated the μ’’ spectra of NSSs with various magnetic materials (Fe74.8Al25.2, Fe50.2Co47.6V2.2, and Fe) and compared with those of constituent single flake particles. μ’’ spectrum measurements of single flake particles are realized by means of TC-PERM which is the newly developed complex permeability measurement method with very high sensitivity [2]. Figure 1 shows the complex permeability of NSS of Fe and the constituent single flake grain of 180 μm in diameter and 1 μm in thickness. As well as the commercial NSS of Sendust, the bimodal μ’’ spectrum is clearly observed for NSS of Fe. Moreover, quite similar μ’’ spectrum is also observed for the single flake grain. This fact strongly indicates that the bimodal μ’’ spectrum of NSS is attributed to the nature of a constituent single flake. We found that the magnetic vortex model can reasonably explain this bimodal μ’’ spectrum, that is, the low- and high-frequency peaks are owing to the resonances of vortex core gyration motion and flux closure magnetization state, respectively. The calculated low- and high-frequency peaks quantitatively agree with the experimental results as marked in Fig. 1(b). This good agreement can be also confirmed for other materials. This work is supported by MIC SCOPE JP195003002.

![](https://assets.underline.io/uploads/markdown_image/1/image/f99cbc0953a7d799ac41a9fe1edbc7b8.jpg)

Fig. 1 Complex permeability spectra of (a) NSS and (b) a single constituent flake grain of Fe.

Physical origin of bimodal complex permeability spectrum of a noise-suppression sheet

The patch antenna is advantageous in many applications because of its simple and inexpensive structure. However, one disadvantage is its large size. One of the methods to reduce the size of an antenna is to utilize ferrite material [1]. While this does effectively miniaturize the antenna, the peak realized gain (PRG) is decreased by 8.3 dBic due to the magnetic loss of the ferrite core. In this paper, we take the multi-layer ferrite and dielectric approach to reduce the patch antenna size. All antennas were simulated using ANSYS HFSS for their performance. Fig. 1 shows the specifications and designs of the patch antennas. The baseline patch antenna has the dimensions given in [2] and uses a 1.4 mm thick FR-4 substrate (permeability (μr) = 1, permittivity (εr) = 4.4). The dielectric and magnetic loss tangents (tanδe and tanδu) are 0.02 and 0.00, respectively, at UHF band frequency, and its volume (V) is 9800 mm3. To realize the multi-layer concept in the antenna size reduction, 0.8 mm thick layers of ferrite (μr = 6, εr =13, tanδu = 0.05, tanδe = 0.02, and V = 2720 mm3) are inserted into the FR-4 substrate. Three topologies are investigated: one ferrite layer, two ferrite layers, and three ferrite layers. For each topology, the volume of the ferrite remains the same. For the cases with more than one ferrite layer, the inner-most layer has a constant V = 600 mm3, and the remaining volume is divided equally among the outer layers. Antenna performance results are summarized in Table 1. For one ferrite layer, 16.7% miniaturization is achieved, but the PRG decreases by 14.1 dBi. However, as the number of layers increases to two, 49.8% miniaturization is achieved with a decrease in PRG of 5.6 dBi. For three layers, 49.3% miniaturization is observed with a 5.6 dBi decrease in PRG. Compared to the case with the all-ferrite substrate (V = 9800 mm3), the patch antenna with two ferrite layers has a 4.4 dBi higher PRG. Ferrite and dielectric substrate contributes remarkably to antenna size reduction.

![](https://assets.underline.io/uploads/markdown_image/1/image/e68b9a4e3e72ffd5c9f56c3ee81cfc08.jpg)

Fig. 1. Design and specifications of (a) baseline patch antenna, (b) ferrite-dielectric layering, and (c) multi-layer patches

![](https://assets.underline.io/uploads/markdown_image/1/image/74ed72c7f2f5ae5991e9a4a0fc105818.jpg)

Table 1. Comparison of antenna performance results

Miniaturizing Patch Antenna with Multi-layer Soft Ferrite and Dielectric Substrate Structure

Recently, 45 μm thick Ti3C2Tx (MXene) showed high total shielding effectiveness (SE) of 92 dB between 8 and 12 GHz [1]. However, MXene mitigates the unwanted EM signal via reflection, and the reflect signal generates another spurious signal, harming neighboring electronic components or systems. This is because the high conductivity and paramagnetic properties of MXene cause impedance mismatch. To improve the impedance matching and absorption intensity, many researchers investigated the MXenes with magnetic material and reported a high SE via absorption but mostly in X-band (8-12 GHz) [2-3]. In this paper, we investigated MXene and M-type hexaferrite (BaFe12O19) composite to absorb EM wave occurring in Ka Band (26.5-40 GHz) for mmWave 5G application. We chose BaFe12O19 because it possesses a ferrimagnetic resonance (FMR) frequency of 42.5 GHz [4]. MXene was synthesized by the LiF-HCl etching method reported in [2], and BaFe12O19 nanopowder, purchased from Sigma Aldrich, was used. The composite was obtained by dispersing 0.25 g of MXene into 50 mL of deionized water and then ultrasonicated with 2.5 g polyvinylpyrrolidone (PVP) for 30 minutes. The sample was mixed with 0.25 g of BaFe12O19 powders and stirred for 12 hours. Finally, the composite was centrifuged and dried in an oven for 12 h. First, the phase of the synthesized composite was characterized by X-ray diffraction (XRD: Bruker D8 Discover) using Cu kα radiation, as shown in Fig. 1. Both MXene and BaFe12O19 was confirmed in the composite. Fig. 2 shows the static magnetic property of the composite, which is measured by a vibrating sample magnetometer (VSM: MicroSense EV9). Compositing MXene with BaFe12O19 increased saturation magnetization (Ms) from 0 for MXene to 10.5 emu/g and intrinsic coercivity (Hci) from 4.8 to 889 Oe. We will discuss the dynamic properties (complex permittivity, complex permeability, and reflection loss) of the MXene/BaFe12O19 composite in the paper. This work was supported in part by NSF-IUCRC under Grant No. 1650564.

![](https://assets.underline.io/uploads/markdown_image/1/image/70aed31acce356eea2293fb5d5eec926.jpg)

Fig. 1. XRD pattern of MXene, BaFe12O19, and MXene/BaFe12O19 composite.

![](https://assets.underline.io/uploads/markdown_image/1/image/d728a89e771a010b4d9419ef20265a20.jpg)

Fig. 2. Magnetic hysteresis loop of MXene, BaFe12O19, and MXene/BaFe12O19 composite.

Microwave Absorption Performance of M-type Hexagonal Ferrite and MXene Composite

This paper discusses magnetic material technology to improve receiver sensitivity in an IC chip. The idea is to use FMR losses to supress conduction noise in receiver circuit. We studied conventional NiZn ferrite particle composite and thin plate. While their materials’ FMR frequency is below 1 GHz, strong demagnetization given by the narrowness of current-carrying wires on interposer may shift up the FMR frequency to GHz range and hence useful to suppress electromagnetic noise in the GHz range. While Y and Z-type hexagonal ferrite [1] composite materials are good candidates for this application [2], this idea may widen the range of material selection NiCuZn spinel ferrite particles (commercially available) were embedded in epoxy resin to form composite sheet. Sintered plate was also prepared. Y and Z type hexagonal ferrites [2] are tested for comparison. Average diameter of the particle is 0.1~3.6 μm. The particles are mixed with a polymer binder to form a powder composite. Volume ratio of magnetic particle is nominally 50 %. Thickness of each power composite is about 50 μm to fit the space between interposer and IC chip die, as shown in Fig. 1. Noise suppression performance is proportional to the parameter 2*pai*f* ur”, It was 73@ 1 GHz for NiCuZn plate. This peak intensity was doubly higher than hexagonal ferrite composites. The composites and plate was mounted to an IC chip interposer asshown in Fig. 1 A magnetic near field probe (Langer XF-R 3-1) was placed on the IC chip package and measured radiated emission noise from the test IC chip driven by 100-200 MHz clock. The 4.8 GHz component of magnetic near filed was successfully suppressed by the proposed sintered magnetic plate. Degree of suppression counts 4-17 dB, comparing IC only and NiCuZn(17 dBmax), BaZn-Y hexagonal ferrite composite(10 dBmax) at 4.8 GHz, which is higher than material’s FMR frequency of NiCuZn ferrite. 3D RF EM simulation (HFSS Ver.14.0) predicts that current crowding at narrow current-carrying wires on chip or interposer could shifted the FMR toward higher frequency and it effected to yield high noise suppression beyond material’s FMR frequency.

![](https://assets.underline.io/uploads/markdown_image/1/image/a3cea1678471facb6553aa572b174f36.jpg)

Fig. 1. Cross section of an IC chip interposer.

NiZn ferrite noise suppressor embedded in IC interposer

To cope with the increasingly serious microwave radiation pollution, an extensive search for efficient microwave absorption materials (MAMs) has attracted great attention recently [1-3]. We have already reported the lightweight ferrite nano-hollow spheres (NHS) to exhibit enhanced electromagnetic (EM) wave absorption [4]. Herein, the deposition of the dielectric SiO2 layer on MnFe2O4 (MnFO) NHSs is found to be an effective strategy to enhance EM wave attenuation for a larger bandwidth. EM wave absorption properties of as-synthesized bare and SiO2 coated MnFe2O4 NHSs with different coating thicknesses are investigated within a widely-used frequency range. Larger interfacial area, higher magnetic anisotropy, internal reflections and scattering from NHSs along with higher magnetic permeability of MnFO are responsible for superior absorption properties of MnFO NHS. The higher dielectric permittivity of SiO2 coated on the surfaces of MnFO NHSs further improves microwave absorption for a large frequency bandwidth. The MnFO (~ 450 nm)/SiO2 (~ 68 nm) bi-layered NHSs (TEM micrograph shown in Fig.1) result in a sufficiently high RL ~ - 30.0 dB with a composite absorber of thickness only 3mm and filler concentration of 20% as shown in Fig.2. The above study on the variation of SiO2 thickness over MnFO NHSs helps us to optimize for maximum bandwidth and absorption with minimum composite absorber thickness. Analysis from the λ/4 model for best matching thickness (tm) displays a good agreement between experimental and simulated tm values. This study demonstrates the optimized MnFO/SiO2 NHS as a highly promising low-cost and lightweight EM wave absorber suitable for high-frequency filter applications.

![](https://assets.underline.io/uploads/markdown_image/1/image/8eeeb9d1dedd928bf661d78bf5d3079c.jpg)

Fig. 1 : Transmission Electron Micrograph of a MnFO/SiO2 NHS

![](https://assets.underline.io/uploads/markdown_image/1/image/7e2a9f7c39566099f818789ae491f7c2.jpg)

Fig. 2 : Three dimensional plot of reflection loss versus frequency and composite absorber thickness for MnFO (~ 450 nm)/SiO2 (~ 68 nm) bi-layered NHSs

Enhanced Electromagnetic Wave Absorption by Bi-layered Nano-hollow Spheres

We present an implementation of sequential Bayesian experiment design[1] for efficient Ramsey sequence magnetometry using NV centers in diamond. In the Ramsey sequence, the magnetic field is encoded as a phase difference between two spin states, where the phase accumulates over a selected precession time τ, and the experimental signal oscillates as a function of τ with precession frequency ω = γ B. The challenge is to choose values of τ that make efficient use of measurement time tm to reduce the field uncertainty σB. We use the equivalent noise sensitivity η = σB tm1/2 as a figure of merit. Sequential Bayesian experiment design chooses measurement settings (τ) by forecasting measurement outcomes and the effects they would have on the parameter distributions. The measurement benefit is quantified as the change in the information entropy of the parameter distribution and the measurement cost is the time required. With each measurement, more precise parameter distributions are inferred from new measurement data, improving forecasts and τ choices for later iterations. Results plotted in Fig. 1 compare the performance of sequential Bayesian experiment design with three other protocols: a non-adaptive variant of the quantum phase estimation algorithm (QPEA) [2], nonadaptive random selection of τ (Random), and an adaptive heuristic that chooses τ inversely proportional to the frequency uncertainty (Tau) [3]. For consistency, all measurement data is interpreted using Bayesian inference. The main figure plots the evolution of η against combined computation time and simulated measurement time. The vertical axis allows comparison of average uncertainty at a fixed measurement time. The inset plots η2, allowing comparison of time required to achieve a given uncertainty. The SBED protocol is faster than the Tau, Random, and QPEA protocols by factors of 2, 4 and 5, respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/5112480a93aec4b2523b3d94617abfa6.jpg)

Fig. 1. Comparison of equivalent noise sensitivity η = σB tm1/2 achieved by different measurement protocols. Initial measurements have small effects on the field uncertainty σB as tm increases. After 1 s of measurment, all protocols have converged to aymptotic σB∝ tm-1/2 behavior. The sequential Bayesian experiment design olffers the best performance.

Adaptive Measurements in Quantum Magnetometry

Magnetic nanoparticles (MNPs) have become a relevant technological topic as a result of their broad use in different fields, biomedicine, environmental applications, 3D printing, etc [1], [2], [3]. This wide use, together with the low MNPs concentrations used in most applications, requires the development of low-cost and high sensitivity detectors. So, this work explores the design of a Giant Magnetoimpedance effect (GMI) based detection platform for contactless MNPs detection, enabling its reuse in multiple applications. The GMI effect, based on huge changes in the high-frequency electrical impedance under external magnetic field, has revealed as a useful tool in the design of high sensitivity magnetic sensors [4]. The proposed device is formed by two soft magnetic amorphous wires (Co66Fe12Si13B15Cr4, length 2 cm) placed in parallel and connected electrically in series to increase the effective detection area [5]. Its working principle relies on the GMI response under the effect of the remnant magnetic field generated by Fe3O4 MNPs (diameter 140 nm). The detection target (sample) was prepared by depositing different MNPs masses, m, from 1 to 15 mg, on different glass substrates. The sample to detect was placed over the sensor surface at different distances, d, (0.31 - 13 mm) avoiding physical contact with the sensing wires. Using a voltage divider and a lock-in amplifier (current frequency f = 100 kHz and peak to peak current I = 15 mA.), the changes of the first V1f(H), and second harmonic V2f(H), components of the GMI voltage were studied as a function of m and d. The larger detection capacity (|(Vif(x)-Vif(xmax))/( Vif(xmax))|; i=1,2; x=m,d) under a similar amount of MNPs found for V2f (70%) respecting V1f (10 %), led to the selection of V2f in the final sensor prototype. A homemade electronics for sensor interfacing and signal conditioning was developed to improve both the sensitivity and spatial resolution where MNPs were detectable. The results show how the designed detection platform permits the quantification of low amounts of MNPs at larger distances (order of mm) than other detectors reported in the bibliography under the principles of low-cost, simple design, single-step measurement and reusability.

Non-Linear GMI Based Detection Platform for an Enhanced Contactless and Reusable Detection of Magnetic Nanoparticles

Superconducting quantum interference devices (SQUIDs), which are the most ultrasensitive magnetic sensors, are generally made by microfabrication of superconducting thin films. The bicrystal junction, which is often used in high-temperature superconducting (HTS) Josephson junctions (JJs), has problems expensive bicrystal substrates, and the fact that JJs can only be arranged in a fixed straight line [1-2]. Because the HTS thin film is a type-II superconductor, magnetic fluxes penetrates the HTS thin film and moves for the Lorentz force, which increases the flux noise at low frequencies. In this study, we investigated a method to fabricate low-noise SQUID magnetic sensors by Ga focused ion beam (FIB) irradiation of high-temperature superconducting thin films. When HTS thin film is irradiated with FIB, point defects are introduced into the HTS crystal structure, which leads to changing into normal conduction. The dependence of the critical current change ratio IC/IC0 on the dose was shown in Fig.1. The dependence of the normal resistance RN are also depicted. The thickness of the YBa2Cu3O7-δ (YBCO) film was 50 nm and it was protected by a thin Au layer. IC/IC0 decreased with irradiation fluence and changed into normal conduction at 2.0×1017 ions/cm2; after this point RN increased steeply. HTS nanobridge JJ, were fabricated by FIB irradiation. Figure 2 shows the V-I characteristics of a nanobridge with an HTS film thickness of 50 nm and a bridge width of 120 nm. The critical current was reduced to 264.5 μA and shows a clear Shapiro-steps under microwave irradiation with frequency of 10 GHz. As a method to reduce the magnetic flux noise, we also investigated the introducing of normal conducting pinning sites (anti-dots) into HTS thin films by FIB irradiation. We have confirmed that anti-dots with diameters of several hundred nm can be formed by point irradiation of HTS thin films with FIB. In the future, we will confirm SQUID operation at a nanobridge JJ with an YBCO film thickness of 50 nm and investigate the improvement of SQUID noise characteristics by introducing anti-dots.

![](https://assets.underline.io/uploads/markdown_image/1/image/809e70edfbb475e4d016f9bb15625221.jpg)

Fig. 1. Dependence of IC/IC0 and RN on FIB irradiation fluence.

![](https://assets.underline.io/uploads/markdown_image/1/image/081fb54ef9f65aa79ff804d2d9bcbfa1.jpg)

Fig. 2. V-I characteristics of the HTS nanobridge with a width of 120 nm.

Flux Noise Reduction of HTS SQUID Using Josephson Junctions Made by FIB

The cilium inspired tactile sensor is based on a magnetic sensor located below thin, elongated permanently magnetized elastic pillars. Deformations of the pillar caused by small flows, forces and surface textures change the magnetic field detected by the sensor, thus transducing deformation into an electric signal [1]. In this work, we present a tactile/force sensor based on AlOx tunnel barrier magnetoresistive (TMR) sensors integrated as a monolithic 2D sensitive device [2]. Each sensing direction includes TMR sensors in Wheatstone bridge to minimize noise contamination of the signal [3] and simplifying the signal processing chain. A polydimethylsiloxane matrix with embedded NdFeB particles (at a mass ratio of 65% particles to 35% PDMS) was used to form the cilium on top of the sensor (Fig. 1). The sensor voltage output is connected to a compact electronic interface, allowing it to be easily integrated within another application where sensitive tactile sensing is desired. The fabricated device presents a sensitivity of 3.1 mV/Oe and 3.0 mV/Oe and a bridge offset voltage of 107 mV/V and -13 mV/V in the X and Y sensitive directions, respectively. The characteristic of the cilia sensor, using cilia with and 400 μm diameter by 3 mm height and a magnetic moment of 58 emu cm-3 was compared to its simulated response. A good agreement between results and simulation was achieved, with an root mean square error (RMSE) error of 66 µV for each respective cilium dimension (Fig. 2a). Finally, the cilium was manually actuated in both X and Y directions, with a clear distinction between the actuations of each sensitive direction being observed (Fig. 2b).

![](https://assets.underline.io/uploads/markdown_image/1/image/56b174226d0e921e32fbf18edd4e97e3.jpg)

Fig. 1: Photograph of the assembled cilia sensor.

![](https://assets.underline.io/uploads/markdown_image/1/image/e29e154c204690332435e250463e92a9.jpg)

Fig. 2: a) Measured signal vs tip deformation characteristic and simulated results for a sensor with 3 mm height and 400 μm diameter cilium. b) Measured response for manual actuation of the cilium in both X and Y directions.

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Robust mutual synchronization of spin Hall nano-oscillator chains

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