France



In spintronics, one of the long standing questions is why the MgO barrier is almost the only option to achieve a large tunnelling magnetoresistance (TMR) ratio at room temperature (RT) but not as large as the theoretical prediction [1]. This can be due to the spin fluctuation at the ferromagnet/MgO tunnel barrier interfaces and/or spin-independent hopping within the barrier in a magnetic tunnel junction (MTJ) [2]. One of the approaches to overcome these issues is to employ the lattice softening of the ferromagnetic layers in MTJ. Recently a metastable body-centred cubic (bcc) Co&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Mn&lt;sub&gt;100-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt; (CoMn) ferromagnetic films have been reported to exhibit the enhancement of their magnetic moments with an ideal lattice matching with MhO [3], which can be an ideal candidate for the TMR enhancement in MTJ.&lt;br/&gt;MTJ stacks were grown using conventional magnetron sputtering on MgO(001) substrates with the structure of Cr (40)/Co&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Mn&lt;sub&gt;100-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt; (10)/MgO (2.4)/Co&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Mn&lt;sub&gt;100-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt; (4)/Co&lt;sub&gt;3&lt;/sub&gt;Fe(1.5)/IrMn (10)/Ru (5) (thickness in nm) [4]. For CoMn, four different compositions of &lt;i&gt;x&lt;/i&gt; = 66, 75, 83 and 86 were used, allowing to control the CoMn lattice constants. To promote the crystallisation of the seed and CoMn layers, &lt;i&gt;in-situ&lt;/i&gt; annealing was performed after the deposition of the Cr seed layer and Co&lt;sub&gt;x&lt;/sub&gt;Mn&lt;sub&gt;100-x&lt;/sub&gt; layers at 700&lt;sup&gt;o&lt;/sup&gt;C and 200&lt;sup&gt;o&lt;/sup&gt;C, respectively. MTJs were then post-annealed at 325&lt;sup&gt;o&lt;/sup&gt;C for their crystallisation after patterned into pillars with Ti/Au electrodes by photolithography. TMR measurements were carried out using the conventional four-terminal setup with elevating temperature, showing two distinctive TMR ratios of 229% and 142% at room temperature for &lt;i&gt;x&lt;/i&gt; = 75 and 86, respectively. The corresponding atomic structures were imaged by cross-sectional transmission electron microscopy (TEM, JEOL JEM-2100 Plus) at 600k magnification.&lt;br/&gt;Figures 1(a) shows a cross-sectional high-resolution (HR) TEM image of the MTJ with &lt;i&gt;x&lt;/i&gt; = 75 showing the larger TMR ratio. Fully epitaxial growth of the entire MTJ is confirmed with some dislocations, of which period is calculated to be (11.4 ± 0.3) nm. This indicates that the Co&lt;sub&gt;75&lt;/sub&gt;Mn&lt;sub&gt;25&lt;/sub&gt; layer may induce plastic deformation rather than elastic deformation with inducing dislocations at the boundaries between crystals. The &lt;i&gt;x&lt;/i&gt; = 86 sample, on the other hand, shows dark black regions at the CoMn/MgO interfaces indicating CoMn/MgO is not fully crystallised within the CoMn layer [see Fig. 1(b)]. These features are found to be induced by dislocations formed at the CoMn/MgO/CoMn interface with the period of (8.9 ± 0.3) nm. These dislocations may be the origin of the interfacial spin fluctuation.&lt;br/&gt;In the MgO layer for &lt;i&gt;x&lt;/i&gt; = 75, two distinctive crystallographic phases are observed as shown as the regions (i) and (ii), which are crystallised along MgO[001] and [100] directions, respectively, as similarly reported in previous reports [5]. For &lt;i&gt;x&lt;/i&gt; = 86, an additional partially crystallised MgO grains are found, which induces spin-independent hopping to reduce the corresponding TMR ratio.&lt;br/&gt;By measuring the lattice constants of CoMn and MgO in the HRTEM images, the top CoMn lattice constants are almost constant across MTJs apart from &lt;i&gt;x&lt;/i&gt; = 86, confirming the lattice softening of these layers with forming almost strain-free MTJ. These results were compared with &lt;i&gt;ab initio&lt;/i&gt; calculations on the lattice stability of the CoMn alloys. Calculations confirm the crystalline deformation stability across a broad compositional range in CoMn, proving a strain-free interface for larger TMR ratios. Further optimisation of the CoMn-based MTJs can achieve &amp;gt; 1,000% TMR ratio at RT.

**References:**

[1] A. Hirohata &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;J. Magn. Magn. Mater.&lt;/i&gt;, vol. 509, p. 166711 (2020).&lt;br/&gt;[2] C. H. Shang &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Phys. Rev. B&lt;/i&gt;, vol. 58, p. R2917 (1998).&lt;br/&gt;[3] R.J. Snow &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;J. Magn. Magn. Mater.&lt;/i&gt;, vol. 419, p. 490 (2016).&lt;br/&gt;[4] K. Kunimatsu &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Appl. Phys. Exp.&lt;/i&gt;, vol. 13, p. 083007 (2020).&lt;br/&gt;[5] G. X. Miao &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Appl. Phys. Lett.&lt;/i&gt;, vol. 93, p. 142511 (2008).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/cd295ebb917f5d44588a534b3c4a60c8.jpg)
Fig. 1 HRTEM images taken on the &lt;i&gt;x&lt;/i&gt; = (a) 75 and (b) 86 sample.



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 Strain-Free Magnetic Tunnel Junction with Metastable bcc CoxMn100-x(001) Ferromagnetic Layers

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In spintronics, one of the long standing questions is why the MgO barrier is almost the only option to achieve a large tunnelling magnetoresistance (TMR) ratio at room temperature (RT) but not as large as the theoretical prediction [1]. This can be due to the spin fluctuation at the ferromagnet/MgO tunnel barrier interfaces and/or spin-independent hopping within the barrier in a magnetic tunnel junction (MTJ) [2]. One of the approaches to overcome these issues is to employ the lattice softening of the ferromagnetic layers in MTJ. Recently a metastable body-centred cubic (bcc) CoxMn100-x (CoMn) ferromagnetic films have been reported to exhibit the enhancement of their magnetic moments with an ideal lattice matching with MhO [3], which can be an ideal candidate for the TMR enhancement in MTJ. MTJ stacks were grown using conventional magnetron sputtering on MgO(001) substrates with the structure of Cr (40)/CoxMn100-x (10)/MgO (2.4)/CoxMn100-x (4)/Co3Fe(1.5)/IrMn (10)/Ru (5) (thickness in nm) [4]. For CoMn, four different compositions of x = 66, 75, 83 and 86 were used, allowing to control the CoMn lattice constants. To promote the crystallisation of the seed and CoMn layers, in-situ annealing was performed after the deposition of the Cr seed layer and CoxMn100-x layers at 700oC and 200oC, respectively. MTJs were then post-annealed at 325oC for their crystallisation after patterned into pillars with Ti/Au electrodes by photolithography. TMR measurements were carried out using the conventional four-terminal setup with elevating temperature, showing two distinctive TMR ratios of 229% and 142% at room temperature for x = 75 and 86, respectively. The corresponding atomic structures were imaged by cross-sectional transmission electron microscopy (TEM, JEOL JEM-2100 Plus) at 600k magnification. Figures 1(a) shows a cross-sectional high-resolution (HR) TEM image of the MTJ with x = 75 showing the larger TMR ratio. Fully epitaxial growth of the entire MTJ is confirmed with some dislocations, of which period is calculated to be (11.4 ± 0.3) nm. This indicates that the Co75Mn25 layer may induce plastic deformation rather than elastic deformation with inducing dislocations at the boundaries between crystals. The x = 86 sample, on the other hand, shows dark black regions at the CoMn/MgO interfaces indicating CoMn/MgO is not fully crystallised within the CoMn layer [see Fig. 1(b)]. These features are found to be induced by dislocations formed at the CoMn/MgO/CoMn interface with the period of (8.9 ± 0.3) nm. These dislocations may be the origin of the interfacial spin fluctuation. In the MgO layer for x = 75, two distinctive crystallographic phases are observed as shown as the regions (i) and (ii), which are crystallised along MgO[001] and [100] directions, respectively, as similarly reported in previous reports [5]. For x = 86, an additional partially crystallised MgO grains are found, which induces spin-independent hopping to reduce the corresponding TMR ratio. By measuring the lattice constants of CoMn and MgO in the HRTEM images, the top CoMn lattice constants are almost constant across MTJs apart from x = 86, confirming the lattice softening of these layers with forming almost strain-free MTJ. These results were compared with ab initio calculations on the lattice stability of the CoMn alloys. Calculations confirm the crystalline deformation stability across a broad compositional range in CoMn, proving a strain-free interface for larger TMR ratios. Further optimisation of the CoMn-based MTJs can achieve &gt; 1,000% TMR ratio at RT.

**References:**

[1] A. Hirohata et al., J. Magn. Magn. Mater., vol. 509, p. 166711 (2020). [2] C. H. Shang et al., Phys. Rev. B, vol. 58, p. R2917 (1998). [3] R.J. Snow et al., J. Magn. Magn. Mater., vol. 419, p. 490 (2016). [4] K. Kunimatsu et al., Appl. Phys. Exp., vol. 13, p. 083007 (2020). [5] G. X. Miao et al., Appl. Phys. Lett., vol. 93, p. 142511 (2008).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/cd295ebb917f5d44588a534b3c4a60c8.jpg)
Fig. 1 HRTEM images taken on the x = (a) 75 and (b) 86 sample.

technical paper

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:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c9861268fdc85f10bca7347b0d6cb800.jpg)
Figure 1

![](https://assets.underline.io/uploads/markdown_image/1/image/df4d00987b69a2b403e5c1d53067d934.jpg)
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

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

 THz Periodic Array Sensor Design

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:**

 Electromagnetic wave generation in a ferromeagnet due to transitions between spin subbands

Anisotropic magnetoresistance (AMR) refers to an electrical phenomenon that the resistivity in a metallic ferromagnet depends on the mutual angle of the magnetization and electric current, which was first discovered by William Thomson in 1857 and is nowadays widely applied in magnetic sensors. Despite of a long history of study, AMR is usually explained vaguely as a complicated relativistic interaction of local magnetic moments and itinerant electrons. Nevertheless, the quantitative description of AMR for a particular magnetic material usually requires some tunable parameters that are determined by experimental measurement. Using first-principles transport calculations, we predict that the AMR of single-crystal CoFe alloys is strongly dependent on the current orientation and alloy concentration. An intrinsic mechanism for AMR is found to arise from the band crossing due to magnetization-dependent symmetry protection [1]. These special k points can be shifted towards or away from the Fermi energy by varying the alloy composition and hence the exchange splitting, thus allowing AMR tunability. The prediction is confirmed by delicate transport measurements, which further reveal a reciprocal relationship of the longitudinal and transverse resistivities along different crystal axes.

**References:**

[1] F. L. Zeng, Z. Y. Ren, Y. Li, J. Y. Zeng, M. W. Jia, J. Miao, A. Hoffmann, W. Zhang, Y. Z. Wu, and Z. Yuan, Physical Review Letters Vol. 125, p.097201 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/721d99ee7d03c6c285826d7d876f32b8.jpg)
Upper panel: Calculated band structure using the effective potentials of Fe in Co0.5Fe0.5 with the magnetization along [100]. The band gap at 0.25 eV above the Fermi level gradually shrinks when the magnetization is rotated towards [010], as shown in the inset. Lower panel: the nodal line formed by two energy bands in the (010) plane at M||[010] (left) and a gap opening up at M||[100] (right).

![](https://assets.underline.io/uploads/markdown_image/1/image/d17485d5cd6a1e42a3fa03d642fe1e36.jpg)
Calculated and experimental resistivity of CoFe alloy for different magnetization and current orientations, as well as the dependence on the alloy concentration.

 Intrinsic mechanism for anisotropic magnetoresistance and experimental confirmation in CoFe alloys INVITED

Magnetic tunnel junctions (MTJs) show great promise for implementation in high-performance spin transfer torque magnetic random-access memory (STT-MRAM) [1] and novel computing regimes such as magnetic domain wall logic [2] and neuromorphic computing [3]. MTJs consist of an insulating thin film tunneling barrier sandwiched between two ferromagnet electrodes. By altering the magnetization of the electrodes, the rate of tunneling across the barrier can be varied. This provides a mechanism to convert nonvolatile magnetic information to electrical information via modifying the resistivity of the device, achieving on/off tunnel magnetoresistance ratios (TMR) of over 600% at room temperature in state-of-the-art CoFeB/MgO/CoFeB MTJs [4]. Unfortunately, a handful of material setbacks stand in the way of the widespread adoption of even leading MgO MTJs over other emerging technologies, such as Resistive-RAM junctions, in next-generation architectures. MgO’s wide bandgap (7.8 eV) is associated with a high junction resistance-area (RA) product, greatly increasing power-draw and necessitating high operating voltages, which leads to device variability challenges and dielectric breakdown [5]. Additionally, MgO creates magnetic dead layers through the oxidation of interfacial Fe atoms and requires ultra-thin barrier layers that are difficult to fabricate and may contain pinholes [6]. These setbacks result in a reduction of the effective TMR and an increase in the RA-product, which motivates the search for new barrier materials. Here, we explore the properties of rock-salt structured Scandium Nitride (ScN) magnetoresistive junctions and find it a promising barrier material given its novel electron symmetry filtering properties, high TMR, and low RA-product. Fe/ScN/Fe MTJ supercells were constructed for 3,5,6,7 and 8 atomic layers of ScN, with the ScN lattice rotated by 45 degrees such that the N anions rest over the interfacial Fe, analogous to the Fe/MgO interface. Using the plane-wave basis density functional theory (DFT) package VASP [9], the MTJ supercells were converged and exported to Quantum Espresso [10] to calculate the complex bands, symmetry properties, and to perform spin-polarized electron transport calculations under the Landauer-Büttiker formalism as implemented in PWCOND [9]. A Hubbard +U correction of 4.5 eV was applied to Sc’s 3d orbital to correct the electronic band gaps using the PBE-GGA pseudopotentials. In this manner, the indirect Γ-X gap of the ScN was matched near to experimental values [7] at 1.31 eV. The conductance calculations find TMR ratios exceeding 1900% for sufficiently thick systems (&gt; 6 atomic layers of ScN), with spin-dependent transport dominated by unique Δ2’ band filtering through Sc’s 3d orbital in the 6-layer system analysed [12]. This mechanism is different from the spin filtering in Fe/MgO/Fe MTJs, where MgO selects for the half-metallic Δ1 band present in bcc Fe or CoFe electrodes [8]. Instead, ScN selects for Fe’s Δ2’ electrons with large crystal momentum, which is only provided in the majority spin of the Fe band structure at the fermi energy. Even with the high TMR and symmetry filtering in ScN, the layer-dependent calculations predict that the devices remain highly conductive with respect to barrier thickness, unlike in MgO systems where the dominant Δ1 electron wavefunctions decay rapidly across the barrier [8]. Fabricated in a system with minimal symmetry mixing and atomic dislocations, magnetoresistive ScN junctions could operate with a fraction of the power of MgO MTJs, while allowing for thicker barriers with more lenient manufacturing tolerances and maintaining high TMRs characteristic of MgO MTJs. Partial funding from Sandia National Lab (SNL). SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525

**References:**

[1] H. Noguchi, K. Ikegami, S. Takaya, ISSCC 132, (2016) [2] J. A. Currivan-Incorvia, S. Siddiqui, S. Dutta, Nat. Comms. 7, 3 (2016). [3] N. Hassan, X. Hu, L. Jiang-Wei, J. Appl. Phys. 124, (2018). [4] S. Ikeda, J. Hayakawa, Appl. Phys. Lett. 93, 1 (2008) [5] L. Xue, A. Kontos, IEEE Trans. Magn. 51, 1 (2015). [6] W. S. Zhao, Y. Zhang, T. Devolder, Microelectron. Reliab. 52, 1848 (2012). [7] D. Gall, M. Städele, Phys. Rev. B - Condens. Matter Mater. Phys. 63, 1251191 (2001). [8] W. H. Butler, STAM, 9(1), 014106. (2008) [9] G. Kresse and J. Furthmüller, Phys. Rev. B, 54:11169, (1996) [10] Giannozzi, P., Baroni, S., Bonini, N. Journal of Physics: Condensed Matter, 21(39), 395502 (2009) [11] A. Smogunov, A. Dal Corso, E. Tosatti, Phys. Rev. B 70, 045417 (2004) [12] S. Karki, V. Rogers, (under review) arXiv 2008.12770 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2eacbc5c29f6d3c4ffb033cdca39b0e2.jpg)
Fig. 1 Scattering states of parallel-magnetized Fe/6ScN/Fe majority spin (a) and minority spin (b) sampled at a high-transmission spike at kx = 0.02 (2π/a) and ky = 0.05 (2π/a).

![](https://assets.underline.io/uploads/markdown_image/1/image/9627d3f44227554116317204d460b021.jpg)
Fig. 2 Complex bands of Scandium Nitride sampled at the Γ and X point, with the symmetry-resolved real bands set in between. A small Hubbard +U bandgap correction is applied.

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