France



&lt;br/&gt;Periodic array sensor structures on metamaterials operating at THz ranges are developed and presented. In the proposed formulation, the mutual inductance effects between unit cells and the periodic structures are taken into account with the network synthesis method. The resonant characteristics of THz periodic arrays have been investigated and presented. The analytical results are verified with simulation results for several different cases. Prototypes have then been built and tested. It is confirmed that the proposed method can be used to design and develop THz sensors on metamaterials and implemented for several applications including biomedical.&lt;br/&gt;&lt;br/&gt;&lt;i&gt;Main Body&lt;/i&gt;&lt;br/&gt;&lt;br/&gt;Metamaterial properties can be obtained by implementation of split-ring resonators (SRRs) [1]. SRRs are reported to be used in the design of biosensors at terahertz (THz) ranges in recent years. Terahertz thin-film sensors, plasmonic thin-film sensors, wireless strain sensors are designed with SRRs [2] to be used in biomedical applications. There are several advantages of using periodic structures due to their higher symmetry property than the unit cells [3]. Two of the other essential features of the periodic structures are their passband-stopband characteristics and the ability to support phase velocities which are much less than the light speed [4].&lt;br/&gt;In this paper, closed-form relations for periodic arrays taking into account of complete effects of mutual inductances in the structure are developed with the network synthesis method from microwave frequencies to THz ranges. The step-by step design procedure from development of unit cell to formation of periodic arrays is detailed. The electromagnetic mutual inductance effects that take place between unit cells in the array and substrate are taken into account in the closed form relations for the first time according to the authors’ knowledge for periodic arrays. The accuracy of the formulations and models for THz operation are verified with 3D EM simulator and ADS circuit simulator. The proposed method have been implemented for 2x3 until cell as shown in Fig. 1 and the agreement between the simulation and analytical results are illustrated in Fig. 2. Several prototypes have been built and measured. All the analytical, simulation and measurement results are compared, and close agreement is confirmed for all cases.

**References:**

References:&lt;br/&gt;D. R. Smith, W. J. Padilla, D. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” &lt;i&gt;Physical review letters&lt;/i&gt;, vol. 84, no. 18, p. 4184, 2000.&lt;br/&gt;H. K. Kim, D. Lee, and S. Lim, “A fluidically tunable metasurface absorber for flexible large-scale wireless ethanol sensor applications,” &lt;i&gt;Sensors&lt;/i&gt;, vol. 16, no. 8, p. 1246, 2016.&lt;br/&gt;F. Bayatur, “Metamaterial-Inspired Frequncy Selective Surfaces”, PhD Dissertation, 2009.&lt;br/&gt;R. Collin, “Foundation of Microwave Engineering”, &lt;i&gt;McGraw-Hill Book Co&lt;/i&gt;, New York, 1966.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/cb6792f9c684cac1a73b1de24d24215b.jpg)
Fig. 1 – 2x3 THz metamaterial periodic array sensor (a) EM Simulation (b) ADS Circuit Simulation

![](https://assets.underline.io/uploads/markdown_image/1/image/a789ffdaf6896a062e07d77a6d20fe18.jpg)
Fig. 2- Comparison of analytical and simulation results

INTERMAG 2021

 THz Periodic Array Sensor Design

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Periodic array sensor structures on metamaterials operating at THz ranges are developed and presented. In the proposed formulation, the mutual inductance effects between unit cells and the periodic structures are taken into account with the network synthesis method. The resonant characteristics of THz periodic arrays have been investigated and presented. The analytical results are verified with simulation results for several different cases. Prototypes have then been built and tested. It is confirmed that the proposed method can be used to design and develop THz sensors on metamaterials and implemented for several applications including biomedical. Main Body Metamaterial properties can be obtained by implementation of split-ring resonators (SRRs) [1]. SRRs are reported to be used in the design of biosensors at terahertz (THz) ranges in recent years. Terahertz thin-film sensors, plasmonic thin-film sensors, wireless strain sensors are designed with SRRs [2] to be used in biomedical applications. There are several advantages of using periodic structures due to their higher symmetry property than the unit cells [3]. Two of the other essential features of the periodic structures are their passband-stopband characteristics and the ability to support phase velocities which are much less than the light speed [4]. In this paper, closed-form relations for periodic arrays taking into account of complete effects of mutual inductances in the structure are developed with the network synthesis method from microwave frequencies to THz ranges. The step-by step design procedure from development of unit cell to formation of periodic arrays is detailed. The electromagnetic mutual inductance effects that take place between unit cells in the array and substrate are taken into account in the closed form relations for the first time according to the authors’ knowledge for periodic arrays. The accuracy of the formulations and models for THz operation are verified with 3D EM simulator and ADS circuit simulator. The proposed method have been implemented for 2x3 until cell as shown in Fig. 1 and the agreement between the simulation and analytical results are illustrated in Fig. 2. Several prototypes have been built and measured. All the analytical, simulation and measurement results are compared, and close agreement is confirmed for all cases.

**References:**

References: D. R. Smith, W. J. Padilla, D. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Physical review letters, vol. 84, no. 18, p. 4184, 2000. H. K. Kim, D. Lee, and S. Lim, “A fluidically tunable metasurface absorber for flexible large-scale wireless ethanol sensor applications,” Sensors, vol. 16, no. 8, p. 1246, 2016. F. Bayatur, “Metamaterial-Inspired Frequncy Selective Surfaces”, PhD Dissertation, 2009. R. Collin, “Foundation of Microwave Engineering”, McGraw-Hill Book Co, New York, 1966.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/cb6792f9c684cac1a73b1de24d24215b.jpg)
Fig. 1 – 2x3 THz metamaterial periodic array sensor (a) EM Simulation (b) ADS Circuit Simulation

![](https://assets.underline.io/uploads/markdown_image/1/image/a789ffdaf6896a062e07d77a6d20fe18.jpg)
Fig. 2- Comparison of analytical and simulation results

technical paper

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

MAGNETIQUE is an itinerant scientific exhibition for the general public with three different levels of reading, presented at the Palais de la Découverte in Paris in 2019-20. Through experiments, manipulations and observations, MAGNETIQUE invites the public to discover principles and effects of this omnipresent but unknown phenomenon. Its goal is to share "science in the making" (cf. Jean Perrin) and the scientific process with public: it brings visitors into the researcher's creativity and imagination. MAGNETIQUE includes some sixty interactive experiments specially designed for this exhibition and completed by many videos on touchscreens. Pedagogical experiments are shown to explain the origin of magnetic properties and everyday-life applications. They are essential to explain some of the recent research results. Do-it-yourself experiments invite visitors to be curious and answer many questions about the use of magnetism in computers and data storage. The exhibition is thus organized in a logical and progressive way around 5 thematic blocks: Block 1: Magnetism, where can it be observed? Visitors can test attraction - repulsion between two magnets. They also discover different kind of magnets, some of their fundamental properties, and the principles of the compass. Some experiments with iron powder or ferrofluids are exhibited to visualize the magnetic field produced by a permanent magnet. Visitors can then observe the various behavior of matters under magnetic field, or discover the magnetic field produced by an electric current and test its applications to waste-sorting. This block ends with the exploration of Earth magnetism. Block 2: Magnetism, how can it be explained? This block is devoted to the explanation of the origin of magnetism. Different experiments show characteristics of various magnetic states (diamagnetism, paramagnetism, hard or soft ferromagnetism). Block 3: Magnetism, how can it be useful? This block shows interactions between current and magnetic field. Visitors discover Laplace’s force, and its use in loudspeakers or electric motors. Later, they observe induction’s phenomenon and its applications to produce electricity in bicycle lighting systems or wind turbines. Two experiments demonstrate the existence of eddy currents and their use in truck breaks. The other experiments concern alternative currents: one illustrates the principle of electromagnetic levitation and its application for ultra-fast trains, other ones shed light on the application for induction heating, electrical transformer, Witricity used in wireless chargers, as well as RFID system used in anti-theft devices. Block 4: Magnetism, where to find it in computer? This block only deals with computers: its goal is to show how omnipresent magnetism is in data storage. After having learnt about binary coding, visitors discover how to write and read a byte on a magnetic media thanks to a giant experiment illustrating the principle of data storage. Then, visitors discover magnetic codes hidden in a credit card or a metro ticket, as well as Halbach networks hidden in a magnet. The end of this block is devoted to the explanation of the giant magnetoresistance phenomenon, and its applications in hard disk read heads. Recent research carried out to develop denser, faster and less energy-intensive information storage are discussed through two examples: writing by ultrashort laser pulses and coding in four states. Block 5: Magnetism, what research is being done? This block shows the experimental universe of a research laboratory, the Jean Lamour Institute (IJL), whose facilities allow the development of new nanomaterials with new magnetic properties. Visitors can therefore observe a 3D model of the Depositing and Analyzing nanomaterials under Ultra-high Vacuum (DAUM) platform. An old spectroscopic analysis chamber used in research is also exhibited. Models show crystal growth under ultra-high vacuum, structural and magnetic characterizations of samples and lithography to make three-dimensional nanometric objects. This bloc ends with experiments illustrating applied research topics: innovative sensors with giant magnetoresistance used in ABS, and magnetography as a secure printing technique useful for legal and banking services. The 5th bock is completed by a virtual and interactive immersive approach of the IJL’s DAUM platform developed with the collaboration of the compagny Com par l'image. The objective of this application is to invite public inside a virtual laboratory to share a growth layers deposition experience in order to produce materials with new properties. The scenario takes the sequence of real experiments in the laboratory: atomic deposition under ultra-high vacuum, characterization of in-situ surfaces, lithography … Visitors are then invited to realize by themselves a magnetoresistive virtual sensor used as position sensor in drones. MAGNETIQUE and the VIRTUAL DAUM are two achievements resulting from the commitment of a research laboratory to support out-reach activities in order to establish the difficult link between fundamental research and the general public. Why get involved in this type of mission? Is it a mission for a research laboratory? What about the mission of researchers in the public life? These are some of the questions that will be addressed in this presentation. MAGNETIQUE is available for rental. Contact: helene.fischer@univ-lorraine.fr

**References:**

- Hélène Fischer, Reflets de la Physique, Vol. 57, p. 32 (2018). - Hélène Fischer, Gazette du vide, Vol. 36, p. 04 (2020). - Hélène Fischer, Stéphane Mangin, Découverte, Vol. 430, p. 44 (2020). - Hélène Fischer, Stéphane Mangin, Découvrte, Vol 431, p. 24 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b68fe7a88b7d45bf13cfa0839e512268.png)
Fig.1 : MAGNETIQUE at the Palais de la découverte, copyright Ph. Levy-EPPDCSI

![](https://assets.underline.io/uploads/markdown_image/1/image/17370546461698490bddcdccd19a770a.jpg)
The Virtual DAUM

 MAGNETIQUE and the Virtual Daum, two out-reach activities carried out in a research laboratory: what about researchers’ engagement in knowledge sharing? INVITED

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.

 Magnetoelectric Nanowires and Their Applications INVITED

Giant MagnetoImpedance (GMI) is a magnetic phenomenon present in materials or structures with high magnetic permeability - like soft ferromagnetic conductors - that provides a large change of their impedance Z=R+jX when submitted to an external magnetic field H [1]. This effect is under investigation from many years moving promptly from fundamental studies to applicative domains. Indeed, more and more sensors based on this effect, such as magnetic or current sensors are largely deployed. The number and plurality of applications never stop growing up like target detection, high-density information storage, automotive and so on [2]. Up to now, it seems that GMI has never been used for cyber security purposes even though it is a major challenge to be taken up in the coming years, as the number of connected objects is constantly sprouting up [3]. Security and privacy are threatened by the increasing use of insufficiently protected electronic devices that manage, store and share personal or confidential data [4]. Indeed, software protections can be bypassed by attacks aimed at recovering a secret key by physical means (fig. 1) such as fault injection or side channel [5]. Countermeasures [6-7] must be necessarily implemented to prevent hackers from accessing or modifying these components; they must also provide an intrusion alert so that the integrated circuit (IC) can take appropriate action to protect sensitive information. The use of GMI as a hardware-based security offers several advantages in terms of technology (low additional cost, simple process flow, etc.) and cyber security (high sensitivity to the electromagnetic environment, significant Z impedance variation, etc). While the GMI sensor appears to have some very interesting cyber security properties, it also presents some challenges such as the negative impact of film’s width reduction [8]. For all these reasons, GMI structure as an active countermeasure (antiprobing layer embedded inside the packaging) will be evaluated in this article. A set of magnetic striplines with different widths from 2µm to 20µm were fabricated on 200 mm silicon wafers. The soft ferromagnetic/conductor Ni80Fe20/Al/Ni80Fe20 tri-layer with thicknesses of 100nm/200nm/100nm was deposited by dynamic sputtering under a linear magnetic field and patterned. Each device was characterized directly on wafer for both transversal (T) and longitudinal (L) deposition anisotropy between 1 MHz and 10 GHz by using a vector network analyzer. An internal DC current that generates a transversal magnetic field on the studied tri-layer was used as a polarization bias. The experimental procedure reveals that the 6 µm wide film with transversal (T) deposition anisotropy corresponds to the best tradeoff between GMI response and cybersecurity requisites. The film exhibits magneto-inductive effect higher than 100% on a wide frequency range (5MHz-700MHz). At 60MHz, a significant change of inductance of more than 300 % was observed providing a strong DC current variation sensitivity of 2nH/mA between 4mA and 9mA (fig 2). The resistive variation appears with increasing frequency of the AC current in the film with respect to the skin effect and ferromagnetic resonance. Moreover, the experiment highlights a strong influence of shape anisotropy on GMI’s answer for the films with transversal deposition anisotropy. This effect has to be taken into account in further studies. Nevertheless, the addition of the internal DC current polarization method and the outstanding magneto impedance effect of the 6µm wide GMI film makes it a suitable candidate as an antiprobing layer material. In case of an intrusion, the hacker will inevitably modify the design of at least one GMI mesh but also the general magnetic field distribution in the secured packaging due to the unusual polarization method. These first observations are encouraging for the development of a GMI countermeasure against physical attacks.

**References:**

 [1] M. Knobel and K. Pirota, Journal of magnetism and magnetic materials, Vol. 242-245, p.33 (2002) [2] M. H. Phan and H. X. Peng, Progress in Materials Science, Vol.53, p.323 (2008) [3] M. Semeria, IEEE 62nd International Electron Devices Meeting, p.9 (2016) [4] S. Bhunia, S. Ray and S. Sur-Kolay, “Fundamentals of IP and SoC Security” (2016) [5] M Tanjidur Rahman, Q.Shi and S.Tajik, IEEE 3rd International Verification and Security Workshop, p.93 (2018) [6] A. Lecavelier, M. Brizoux and A. Grivon, IMAPS MiNaPAD (2017) [7] S. Borel, L. Duperrex and E. Deschaseaux, Proceedings of IEEE 68th Electronic Components and Technology Conference, p.515 (2018) [8] L.V. Panina, D.P. Makhnovskiy, and D.J.Mapps, Journal of Applied Physics, Vol.89, p.7221 (2001)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b4675bafa48138c42aeb33f9aa4e4f18.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/79e3835a210cbdcb45305aa80fe4e35f.jpg)

 Evaluation of Magnetoimpedance in Narrow NiFe/Al/NiFe Thin Films for Secured Packaging

Magnetic sensors play an important role in modern life. They are actively used in many areas of science and technology from navigation systems and high-density data recording to security systems and biomedicine. The magnetoimpedance effect - the dependence of the material’s impedance on the applied magnetic field – became the working principle basis of somesensors. For advanced efficiency, large values of permeability were required. The discovery of the giant magnetoimpedance effect in amorphous materials [1] allowed the design of the new type of highly sensitive field detectors. Their pronounced soft magnetic properties make it possible to build magnetic field sensors for geomagnetic applications [2-3], as well as mechanical stress and temperature [4-5]. The GMI effect also allows the detection of bioelectrical activity [6]. The modified construction of the GMI sensor may help to avoid the appearance of parasitic effects caused by the intrinsic magnetic field of the detector. In this work, we consider the planar structure with a radial current distribution with GMI effect for sensor applications. The considered structure consists of two identical ferromagnetic disks separated by a dielectric layer and connected at the periphery by a continuous contact (Fig. 1), the contribution to the inductance of which can be neglected. This system is excited with alternating current I = I0exp (-iωt) from the outer plane of the disks. The contact area between the disc and the driving current lead can also be neglected, since it is small compared to the disc area. To determine theoretically the impedance of the disk, it is necessary to consider the distribution of fields in it. The cylindrical coordinate system (ρ, φ, z) was used for the impedance calculation. The expression for the impedance of the disk with radius a was obtained from the surface impedance which depends on the current frequency. Both real and imaginary part of the impedance were taken into account with the expression Z=Z'+iZ''. The impedance of the system was considered as the impedance of the oscillatory circuit, in which the inductance L = 2Ld with resistance R = 2Rd (factor 2 takes into account two disks) and the capacitor formed by the interlayer between the disks are connected in parallel. The component of impedance of such system Z'(f) and Z''(f) were calculated for the different permeability (Figure 2, theory). The experimental investigations were carried out using the samples, which prepared fromFe70Co24,5 Si2,9B3,1, and Co72Ni12,2Fe5,7Si6,5B3,6 amorphous ribbonswith thicknesses 0.025 and 0.02 mm, respectively. Two disks were cut from every ribbon. Copper leading wires were soldered to the center of the disk. The polyethylene film was used as a dielectric interlayer. Periphery parts of the disks were glued with a silver-based conductive glue. Impedance measurements were carried out using vector network analyzer Agilent FieldFox 9923A in the frequency range 2 MHz-1 GHz. The frequency dependences of real and imaginary impedance part obtained via calculations and in the experiment show similar resonant behavior. The described structure demonstrates resonant frequency dependences of the impedance and thus provides high sensitivity of the sensor. Using sputtering techniques the small-scaled structures can be manufactured for implementation into complex devices.

**References:**

[1] L.V. Panina et al. Appl. Phys. – 1994. - v. 76, N 10. - pp. 6198-6203. [2] A. Zhukov et al. Journal of Alloys and Compounds. – 2014. – Vol.586. - S279–S286. [3] J. Olivera et al. Sensors Actuators A. Phys. – 2011. - Vol.168. - pp.90–94. [4] M. Nowicki et al. Materials. – 2019. – Vol.12. – 2110. [5] J. Nabias et al. Sensors and Actuators, A: Physical. - 2019. – Vol. 289. – pp.50-56. [6] Z. Wang et al. IEEE ICMA 2016, 7558909, pp.2209-2214.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/841e8485db02592d4a245be290445b82.jpg)
Planar structure with radial current distribution – section by plane perpendicular to the sensor surface (left), radial current distribution (right).

![](https://assets.underline.io/uploads/markdown_image/1/image/c096006b08da509dec337ba120d3edce.jpg)
Theoretical and experimental frequency dependences of the real and imaginary impedance parts.

 Impedance of Planar Structures with Radial Current Distribution

Hydrogen sensing is one of the most important technology for nowadays and future industries since H2 is a candidate for the replacement of fossil fuels. It is worth noting that this gas is highly explosive–it is become dangerous if its concentration in air reaches a limit of 4 %. Hence, the development of highly sensitive and selective hydrogen sensors with a quick response is necessary for ensuring safety [1]. Optical methods of hydrogen detection have been actively developed in recent years [2-3]. They are based on changes in the optical absorption and refractive indices of gasochromic materials caused by the presence of a test gas. Palladium and platinum are known catalysts for the decomposition of molecular hydrogen into atomic. Thus, to increase the rate of dissolution of H atoms in, for example, tungsten trioxide Pd or Pt are usually used as a top layer covering it [4]. Magnetic materials can change their magnetic properties under hydrogen exposure too. For example, Pd-rich alloys [5] and Pd-included bi-layers [6] demonstrate transformation of the Kerr rotation angle upon H2 absorption. Magneto-optical methods of gas detection are of interest for gas sensors development due to possibility for monitoring the phase change (polarization rotation) instead of amplitude. In perspective, this feature can provide much more high sensitivity and selectivity to a target gas in a complex gas mixture. In our work, we studied oxidized permalloy nanofilms. Initial 20 nm-thick permalloy nanofilms were deposited on glass substrates by magnetron sputtering and then annealed in air in a temperature range of 300-475 °C for one hour at the heating rate 750 °C/h. Microscopy methods were used to investigate structural properties of as-deposited and annealed nanofilms, and a double-beam spectrophotometer Shimadzu UV-3600 Plus–to measure the transmission spectra of the samples. Magneto-optical spectra were obtained by a home-made setup based on J.A. Woollam V-VASE ellipsometer and electromagnet generating magnetic fields up to H=±5 kOe. Ellipsometer provides the ellipsometric parameters Ψ and Δ that represent the complex ratio of the reflection coefficients of the p- and s-polarized waves and illustrate a change in polarization; Ψ stands for rotation of the polarization plane (or the main axis of the polarization ellipsis) and Δ–for evolution of the polarization state. This is why the angle of Faraday rotation (θF) can be determined as (Ψ(+H)-Ψ(-H))/2. We found that during annealing a disordered array of nanopillars was grown on initially smooth surface (RMS = 1 nm) of as-deposited film (Fig.1a) [7]. The study of optical and magneto-optical spectra revealed the rise of transmission of fabricated permalloy nanofilms with the annealing temperature, and, in addition, the increase of their Faraday rotation in the near-infrared range of spectrum. The observed rise of transmittance and Faraday rotation is responsible for the increase of known characteristic of MO materials FOM=θF/K=θF√T, where θF is an angle of the Faraday rotation, K–absorbance coefficient, T–transmittance of the film. The sample annealed at 425 °C showed the highest value of FOM (Fig.1b). The magneto-optical response of 475 °C-annealed sample was about zero. We suppose that this effect is due to formation of Fe3O4 (to Fe2+ ions in octahedral site) at 425 °C followed by oxidation up to Fe2O3 at higher temperatures [8]. Fig. 1. (a) AFM image of a 20-nm thick annealed at 425 °C permalloy nanofilm. (b) Collected at H=3.8 kOe spectra of as-deposited and annealed at different temperatures permalloy samples. To study nanofilms sensitivity to hydrogen as-deposited and annealed at 425 °C samples were covered by a Pt layer with a thickness of about 5 nm by an e-beam deposition technique. To demonstrate the caused by H2 change of their magneto-optical properties nanofilms were placed in a non-magnetic cell and fed with a gas mixture of N2, O2 and H2 prepared by mass flow controllers (Bronkhorst). Measurements were carried out at room temperature at a constant gas flow. Faraday rotation spectra of studied samples in flow of artificial air (20% O2 + 80% N2) and in flow of 0.5% hydrogen in N2 are presented in Fig.2. It can be seen well that magneto-optical response of 425 °C-annealed nanofilm significantly changed under 0.5% H2 exposure—the maximum change was about 0.05 deg at a wavelength of 1 µm. Note that the Faraday rotation of as-deposited permalloy nanofilm was not altered at the same conditions. Fig. 2. Faraday rotation angle for Pt-covered oxidized at 425 °C permalloy nanofilm in artificial air and under 0.5% H2 exposure. This result indicates that hydrogenation of formed during annealing different metal oxides (NiO, Fe3O4, Fe2O3)–the hydrogen and oxygen diffusion around metal ion–define the observed change of the magneto-optical response. The detection of low hydrogen concentrations by measuring the Faraday rotation make it very perspective for further magneto-optical gas sensor development due accumulation of polarization rotation in the multipass regime.

**References:**

[1] T. Hübert, L. Boon-Brett, G. Black, et al, Sens.&Actuators B: Chem., Vol. 157(2), pp. 329-352 (2011) [2] A. Mirzaei, J.-H. Kim, H.W. Kim, et al, Appl. Sci. Vol. 9, p. 1775 (2019) [3] D.P. Kulikova, A.A. Dobronosova, V.V. Kornienko, et al, Opt. Express., Vol. 28, pp. 32049-32060 (2020) [4] A. Georg, W. Graf, V. Wittwer, Electrochim. Acta, Vol. 46(13-14), pp. 2001-2005 (2001) [5] P.-C. Chang, Y.-Y. Chang, W.-H. Wang, et al, Commun. Chem., Vol. 2:89 (2019) [6] D. Lederman, Y. Wang, E. H. Morales, et al, Appl. Phys. Lett., Vol. 85, p. 615 (2004) [7] D.P. Kulikova, K.N. Afanasyev, I.V. Bykov, et al, Opt. Mat., Vol. 107, p. 110067 (2020) [8] T. Tepper, F. Ilievski, C.A. Ross, et al, J. Appl. Phys., Vol. 93, p. 6948 (2003)

**Images:**

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Figure 1

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Figure 2

 Oxidized Permalloy Films As a Sensitive Element For Magneto-optical Hydrogen Gas Detection

Strain gauges are sensors that measure a strain generated by a stress applied to an object, metal and semiconductor gauges are widely used. The sensitivity of strain gauges is expressed using the gauge factor, which is about 2 for metal gauges and about 200 for semiconductor gauges. Recently, the SI (stress-impedance) sensor using an amorphous alloy with a gauge factor reaching 1260 has been developed, but it has not been put to practical use due to problems of handling and the influence of external magnetic fields [Shen et al., 1997]. In this paper, we report on the development of a flexible SI sensor element with a magnetic shield to suppress the influence of external magnetic fields. We use the SI element, which is a negative magnetostrictive amorphous wire (FeCoSiB) with a wire length of 2 mm and a diameter of 13 μm, and a flexible film substrate. The amorphous wire is placed on the film and is connected to the electrodes via lead wires from both ends of the wire using gold deposition technique. We manufacture the SI device with a magnetic shield. The shielded SI element uses permalloy plating around the amorphous wire. Figure 1 shows the results of measuring the impedance change by applying a stress to the element. The 18% impedance change was obtained when a tensile stress of 45 MPa was applied, which corresponds to a gage factor of 354. As shown in Figure 2, the effect of the magnetic shield was affected by an external magnetic field of 20 μT without the shield, but with the shield, the rate of change of the impedance of the SI element was reduced to less than 2% even at 100 μT. In this study, the SI element was miniaturized and mass-produced by placing a 2 mm long amorphous wire on a flexible film for use as a contact sensor. In addition, we have developed a SI device that can reduce the influence of the Earth's magnetic field by applying a magnetic shield. In the future, we plan to investigate the response to stress.

**References:**

K. Mohri, T. Kohsawa, K. Kawashima, H. Yoshida and L.V. Panina, Magneto-inductive effect (MI effect) in amorphous wires. IEEE Transactions on Magnetics, 28(5), pp.3150-3152, (1992). L.P. Shen, T. Uchiyama, K. Mohri, E. Kita and K. Bushida, Sensitive stress-impedance micro sensor using amorphous magnetostrictive wire, IEEE Transactions on Magnetics, 33(5), pp. 3355-3357, doi: 10.1109 / 20.617942 (1997).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a413c180d4ced40ef4e3085c07b5727d.jpg)
Fig. 1: Effect of stress on impedance change.

![](https://assets.underline.io/uploads/markdown_image/1/image/5e541388252910e1f469dafdde8036c6.jpg)
Fig. 2: Shielding effect.

 Development of High-Sensitivity SI Sensors Using Flexible SI Devices

Perpendicular magnetic tunnel junctions (pMTJs) constitute the basic element for magnetic random access memories [1], thanks to their non-volatility, high density, and low power consumption. Their multifunctional properties make it possible to operate also as magnetic field sensors, spin torque nano-oscillators (STNO) or microwave signal detectors [2]. However, quite generally their interfacial perpendicular anisotropy (iPMA) is very sensitive to temperature, and thus to Joule heating when an electric current is passed through them [3]. The induced heating decreases the perpendicular anisotropy and thereby reduces the thermal stability and the potential for memory applications of pMTJs. Nevertheless, here we demonstrate that Joule heating induced modifications of iPMA can be of advantage for radiofrequency (RF) signal generation and detection, that will find applications within wireless communication systems used for the Internet of things (IoT). Quite generally, one can distinguish two different RF dynamical regimes and excitations. The first one is the RF signal generation, where upon injection of a DC current, the spin transfer torque (STT) induces steady state oscillations. The second is the RF signal detection, where an injected RF voltage, (in absence or presence of an additional DC current), excites resonantly via STT the magnetization, which results in a rectified DC voltage in the output. Both regimes have been demonstrated in numerous experiments and are promising for RF applications such as wireless communications [4] or ultra-fast spectrum analysis [5], as well as for neuromorphic computation [6]. A major advantage of MTJ structures is their GHz operational frequency, their high frequency tunability, the possibility to sweep-tune the frequency on short time scales as well as their high sensitivity to low RF power signals [7]. Here we report on the Joule heating effects in pMTJs for both: STT induced RF signal generation and active (RF + DC) RF signal detection. Results are presented for two types of pMTJs, one for which the free layer (FL) thickness is t = 1.4 nm and one with t = 1.8 nm. This FL thickness determines the orientation of the FL magnetization (in-plane for t=1.8nm, out-of-plane for t=1.4nm) due to the competition between the iPMA and the demagnetizing energy. For pMTJs with FL thickness of t = 1.8 nm (in-plane FL), under in plane and/or out of plane bias fields, only damped oscillations have been detected when injecting a DC current. The most interesting result here is a very large frequency shift with DC current characterized by a slope of -4 GHz/mA that occurs for both current signs. We attribute this current-sign-independent frequency shift to the changes in the iPMA due to Joule heating. However, the STT effect is noticeable in the power of the excitations, see Fig. 1a. This will be important for the RF signal detection, where for one current sign it enhances the output voltage by a factor of 4, and strongly reduces it for the opposite sign. The frequency tuning via current will be of interest for the RF signal detection because it allows one to easily tune the detection frequency band in a relatively large range, as illustrated in Fig. 1b, without the need of an external applied field. We emphasize that this tuning is attributed to the Joule heating and not to the STT that does not lead to strong frequency shifts in the damped regime. However, a similarly high frequency tuning has also been observed in the steady state oscillation regime for devices with FL thickness t = 1.4 nm (out-of-plane FL) under DC current and out-of-plane field . The corresponding frequency tuning is close to - 3 GHz/mA (frequency redshift) with a minimum linewidth of 30 MHz. In view of applications, we tested the frequency modulation using sinusoidal rf signals. Modulation was observed for modulation frequencies larger than 1 GHz, which greatly exceeds the amplitude relaxation frequency given by ΓP ( ~ 200 MHz) of the uniform STNO. Analysis of the phase noise indicates that there are two cut-off frequencies one due to the amplitude relaxation and one due to the heating. To conclude, this work demonstrates how Joule heating in pMTJs can be exploited to add functionalities to RF signal generation and detection. The authors acknowledge partial funding from ERC MAGICAL No 669204, the Nanoscience Foundation (Grenoble, France) and the EU Horizon 2020 project GREAT No 687973.

**References:**

[1] IKEDA, S., MIURA, K., YAMAMOTO, H., et al. Nature materials, 2010, vol. 9, no 9, p. 721-724. [2] CHAVENT, A., IURCHUK, V., TILLIE, L., et al. Journal of Magnetism and Magnetic Materials, 2020,vol. 505, p. 166647. [3] STRELKOV, N., CHAVENT, A., TIMOPHEEV, A., et al. Physical Review B, 2018, vol. 98, no 21, p. 214410. [4] JENKINS, Alex S., ALVAREZ, Lara San Emeterio, FREITAS, Paulo P., et al. Scientific reports, 2020, vol. 10, no 1, p. 1-7. [5] LITVINENKO, Artem, IURCHUK, Vadym, SETHI, Pankaj, et al. Nano letters, 2020, vol. 20, no 8, p. 6104-6111. [6] GROLLIER, Julie, QUERLIOZ, Damien, CAMSARI, K. Y., et al. Nature electronics, 2020, vol. 3, no 7, p. 360-370. [7] FANG, Bin, CARPENTIERI, Mario, HAO, Xiaojie, et al. Nature communications, 2016, vol. 7, no 1, p. 1-7.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/52188146d083bb35c2153b447c2a32a4.jpg)
Fig.1 : Frequency tuning of damped oscillations observed for both current signs, measurement carried out under an 800 Oe in-plane bias field.

![](https://assets.underline.io/uploads/markdown_image/1/image/ab8dbe5ee73ac660f44ede16b088140f.jpg)
Fig.2 : RF rectification voltage vs DC current, for input signals of different frequencies: 10.4 GHz to 9 GHz.

 Broadband RF detection and GHz modulation rates enabled by Joule heating in perpendicular anisotropy magnetic tunnel junctions

Wireless sensor networks (WSN) are part of our daily lives and their applications are growing years after years, especially with the advent of the Internet of Things. The price to pay is an increase in energy demand. Hence, the development of autonomous, adaptive, and energy-efficient communicating sensor solutions is a topic of intense research. One way to drastically reduce energy consumption is to wake up the main radio receiver of a WSN for communication only when needed. For that purpose, a wake-up receiver (WuRx) is used, which itself should operate with ultra-low power consumption and provide immunity to parasitic radio signals. Spintronic Resonators (SR) based on Magnetic Tunnel Junctions (MTJ) offer a promising solution to be incorporated in integrated wake-up radio circuits since they are extremely compact and can serve as passive RF-DC converters [1]. Another significant advantage of these spintronic devices is that they provide RF filtering capability, responding in a narrow frequency band around their resonance frequency making it possible to demodulate amplitude or frequency modulated signals with high sensitivity [1, 2]. To achieve this, there is a need for an electrical model of MTJs used as RF-to-DC converters, to offer the possibility to investigate their potentialities once integrated in an actual radio receiver (sensitivity, energy consumption) and facilitate the choice for a modulation scheme in order to optimize the communication power efficiency. The model must be compact, include the physical equations, be generic (can be extended to other types of spintronic junctions), and easy to implement. As a preamble to this model extraction, we have explored the characteristics of one type of SR device, based on the vortex configuration (V-SR), for the case of passive detection and zero DC current biasing. Under zero external magnetic field, V-SRs are working in the 150-400 MHz range [2]. The observed characteristics concern i) RF-DC conversion efficiency ii) V-SRs input impedance matching, iii) demodulation capabilities. All these criteria will contribute to the final sensitivity of the V-SR based WuRx. The equivalent model is then proposed by considering the MTJ-based SR as an RF power controlled DC voltage source with internal resistance. To investigate input impedance matching, the RF equivalent circuit is derived, as illustrated in Fig. 1. This model has been developed on the basis of RF reflection coefficient measurements (S-parameters obtained through a vector network analysis), I(V) measurements, and the physical equations of the ferromagnetic resonance frequency and the rectification DC voltage. In order to evaluate the parasitic parameters external to the junction, an additional measurement is performed on an Open circuit, consisting of the same feeding accesses as in Fig. 1 but without including the V-SRs. Hence, S-Parameters measurements enable to extract the internal parasitic elements of the junction itself (junction capacitance and inductive effect of the magnetic layers due to their high permeability). Also, I(V) DC measurements reveal the non-linear behavior of the V-SRs, enabling to determine the coefficients of the polynomial characteristic, outside resonance [3]. Indeed, the model must consider the effect of the ferromagnetic resonance, the center of interest for the RF-DC conversion. Physical equations from [2] enable to determine the value of the ferromagnetic resonance pulsation and the DC rectification voltage from the geometry of the junction, the RF power, and the DC current injected into the junction. Finally, the behavioral model gathers all equations considering parasitic effects (junction and feeding lines), the non-linear junction resistance through the I(V) characteristics, and the ferromagnetic resonance response in order to predict the rectifying effect of the V-SR in the whole frequency band of interest. Thirdly, the V-SR model derived from RF and DC measurements is implemented using an electronic design automation software system (ADS) by implementing symbolically defined devices (SDD) [4]. The necessary variables for DC rectification are embedded in the SDD component and rectification is observed through harmonic balance (HB) simulations. Simulation results of the DC rectification voltage are presented in Fig. 2 and compared with the measurement results. Finally, in order to test the demodulation capabilities, the input RF carrier frequency is fixed at the ferromagnetic resonance in order to benefit from the maximum rectified DC voltage and then modulated with an On-Off Keying (OOK) modulation scheme. We obtain for V-SRs data rates up to 20 Mbit/s for an input RF power of -15 dBm leading to a signal to noise ratio of more than 14 dB, which guarantees a bit error rate as low as 10-6 . It has to be noticed that 20 Mbit/s is within a comfortable margin regarding the typical data rates reported for existing WuRx in the literature [5]. Based on this performance, a complete RF wake-up system will be designed and tested. Future studies will extend the developed model to other MTJ devices such as described in Ref. [6] that allow for operation at higher frequencies (1-10GHz). Authors acknowledge financial support from ANR-SPINNET ANR-18-CE24-0012.

**References:**

[1] B. Fang et al., Phys. Rev. Applied, vol. 11, p. 014022 (2019) [2] A.S. Jenkins, et al. Nature Nanotech, vol. 11, p. 360 (2016) [3] H. Simon, K. Wu. IEEE, vol. 102, p. 11 (2014) [4] J. Wood, D. E. Root, et N. B. Tufillaro, IEEE, vol. 52, p. 2274 (2004) [5] H. Bello, al., Sensors 2019, vol. 19, p. 3078 (2019) [6] A. Chavent, al., doi.org/10.1016/j.jmmm.2020.166647

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/eaa806106a8ae13b6e25aa6660a1e1dc.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/2d47b79ba214cd19f3e4ce528801ea51.jpg)

 Compact Model of a Spintronic Resonator for Rectifying Purposes in Wireless Sensor Network Applications

We theoretically consider a possibility of generation of electromagnetic radiation due to transitions of electrons between spin subbands in a ferromagnet. It is known that such electro-dipole transitions are forbidden if a uniform ferromagnet is considered in a Vonsovsky s-d exchange model. One possible way to remove this limitation is to suggest that the exchange constant depends on the conduction electron momentum. This mechanism was suggested in [1]. At first, it seems to be fully exchange. However the dependence of the exchange constant on the electron momentum may appear only due to spin-orbit interaction in the subsystem of localized d- or f- electrons which are responsible for magnetization of the medium in this model, and no t in the conduction electron subsystem. In the present work, we consider several different mechanisms of electron transitions between spin subbands with photon emission. The most simple mechanism is the magneto-dipole electron transitions which exist due to the magnetic field of the wave. The effects governed by this mechanism are usually very small. Another mechanism appears due to the spin-orbit interaction which exists in the conduction electron subsystem. In our model calculations, we take the Rashba spin-orbit coupling that exists at the medium surfaces. Finally, a fully exchange mechanism of intersubband electron transitions that exists in magnetic medium with non-collinear magnetization distribution is investigated. An example of non-collinear ferromagnet that allows intersubband electrodipole electron transitions is a magnetic helicoid which may be realized either in natural (holmium, MnSi, FeGe at low temperature) or artificial (magnetic spring structures) materials. For all suggested mechanisms, probabilities of electron transitions between spin subbands are found and estimations are made for realistic parameters. We show that both spin-orbit coupling and exchange coupling in a non-collinear magnetic medium may give reasonable values of electron transition probabilities. Finally, a possibility to create devices based on the investigated mechanisms is discussed. This work was supported by the Russian Science Foundation (Grant #19-72-00130).

**References:**

[1] A. Kadigrobov, Z. Ivanov, T. Claeson, et al., Europhys. Lett. 67, 948 (2004)

**Images:**

THz Periodic Array Sensor Design

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