United States

Millimeter-wave electronics are crucial for next-generation (5G) electronic communication systems. However, the development of desirable millimeter (mm) wave absorbers remains an ongoing challenge due to the difficulties of fabricating suitable magnetic absorbers in mm regimes. For ideal mm wave magnetic absorbers, materials should have 1) large anisotropy field (HA) and 2) saturation magnetization (Ms). The resonance frequency is proportional to HA and thus materials must have a large HA are essential for their resonance frequency to be located in mm wave range (20-100 GHz)1. However, the permeability decreases with increasing resonance frequency according to Snoek’s limit2. Thus, materials with larger Ms, are also required to mitigate this challenge. Combing both properties will enable us to achieve enhanced absorption intensity and broaden the bandwidth at mm waves. Rather than focusing on optimization of a single material, here we employ exchange coupled core/shell strategies to generate composite structures with both large Ms and HA. Here, we have fabricated novel magnetic core/shell nanostructures with the goal to realize a highly efficient mm wave absorber. Specifically, we have successfully synthesized ε-Fe2O3 core particles and ε-Fe2O3/Co core/shell nanoparticles using wet-chemistry methods specifically via sol-gel and thermal decomposition of metal precursors. The structural analysis of core and core/shell structures was performed by TEM, HRTEM and EDX, revealing well-defined interfaces and good crystal structure. Furthermore, the coercivity of resulting ε-Fe2O3 core particles is in the range of 2 – 18 kOe, which is significantly affected by the synthetic conditions. Details of the magnetic and the frequency response from the mm wave range of ε-Fe2O3 core and ε-Fe2O3/Co core/shell nanostructures performed by DC-magnetometry, X-ray magnetic circular dichroism and custom built vector network analyzer system will be discussed in the presentation. Prepared by LLNL under Contract DE-AC52-07NA27344.References: 1. S. Ohkoshi, S. Kuroki, S. Sakurai, K. Masumoto, K. Sato, S. Sasaki, Angew. Chem. 119, 8544-8547 (2007). 2. J. V. I. Timonen, R. H. A. Ras, O. Ikkala, M. Oksanen, E. Seppälä, K. Chalapat, J. Li, G.S. Poraoanu, Magnetic Nanocomposites at Microwave Frequencies. In Trends in Nanophysics: Theory, Experiment and Technology; Bârsan, V., Aldea, A., Eds.; Springer Berlin Heidelberg: Berlin, Heidelberg, pp 257-285 (2010).

MMM 2020

Development of magnetic core/shell nanostructures for 5G mm wave absorbers.

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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technical paper

The miniaturization and integration is important market requirements for emerging electronic devices. Magnetic passive components are one of the most bulky components on the electronic boards. Therefore, a significant challenge for magnetic devices is miniaturization and integration towards system in package (SiP) and system on chip (SoC) [1]. Increasing the switching frequency in the applications is a way for miniaturization of magnetic components. On-chip inductors and transformers with magnetic materials fabricated on silicon are potential candidates for high switching frequency applications [2-4]. Developments of thin-film magnetic components in the last years show significant improvement in integration technology. In many works, newely developed microinductors and microtransformers were implemented in different electrical applications [5-10]. This paper will show the improved microtransformer on silicon with a bar magnetic core for data transmission applications [11]. The microtransformer can be used for higher frequencies data transmission application up to 25 MHz. The size of microtransformer device is 1.6 mm x 0.8 mm. The microtransformer consists of a bar magnetic core and interleaved primary and secondary windings Both windings feature 12 turns each. One turn has a length of 640 µm, width of 40 µm and thickness of 1 µm. A copper was applied for the windings. For magnetic core, a Co60Fe20B20 alloy is used. The magnetic core consists of two magnetic layers with dimensions 1400 µm x 500 µm x 0.4 µm. As insulating material SiO2 and Si3N4.are implemented. The inductance of the device is about 40 nH. The breakdown voltage is in the range of 1.5 kV. Using sputtering deposition a copper layer with only 1 µm is deposited, therefore the microtransformer device shows high electrical resistance of about 7 Ω. The coupling factor of the transformer has a value of over 0.6. For this reason, the microtransformer is suitable for data transmission applications. Fig. 1 shows a completed device.References: [1] C. O’Mathuna et al., IEEE Trans. Power Electron., 27(11), 4799–4816 (2012). [2] D. S. Gardner et al., IEEE Trans. on Magnetics, vol. 45, no. 10, pp. 4760-4766, 2009. [3] D. S. Gardner et al., IEEE Trans. on Magnetics, vol. 43, no. 6, pp. 2615-2617, 2007. [4] P. R. Morrow et al., IEEE Trans. on Magnetics, vol. 47, no. 6, pp. 1678-1686, 2011. [5] H. Wu et al., IEEE Trans. on Magnetics, vol. 52, no. 7, pp. 1-4, June 2016, Art. No. 8401204. [6] D. Dinulovic et al., IEEE Trans. on Magnetics, vol. 53, no. 11, pp. 1-7, Nov. 2017, Art no. 4700107. [7] H. T. Le et al., IEEE Trans. on Power Electronics, vol. 34, no. 1, pp. 74-85, 2019. [8] D. V. Harburg et al., IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 6, no. 3, pp. 1280-1294, 2018. [9] J. Michel et al., IEEE Trans. on Magnetics, vol. 55, no. 7, pp. 1-7, 2019, Art no. 8401207. [10] Z. Yue et al., 2019 IEEE Int. Solid- State Circuits Conference - (ISSCC), San Francisco, CA, USA, 2019, pp. 244-246. [11] D. Dinulovic et al., AIP Advance, vol. 10, no. 1, 2020, p. 015206.

On-Chip Thin-Film Microtransformer with Improved Coupling Factor for High Frequency Data Transmission

The performance of protection current transformers (CTs), which are one of the key components of the measurement chain for any protection device, have a significant impact on the performance of power system protection. The demagnetization of protection CTs is vital to ensuring the proper performance of power system protection [1]. However, the most difficulty of demagnetization is how to detect the remanent flux. This paper proposes a fluxgate theory based remanent flux detection method for protection CTs. The proposed circuit for remanent flux detection is shown in Fig. 1. The high-frequency square-wave voltage source, composed by a DC voltage source (VDC) and a full-bridge DC/AC converter, is connected to a resistor (R1) at the secondary side of the CT, and causes the core of the CT saturated slightly in the positive or negative direction. The polarity of the remanent flux is determined by the sign of integration of the voltage across R1. The level of the remanent flux is calculated with the linear relationship between the remanent flux and the second harmonic of the high-frequency component of the voltage across R1, as seen in Fig. 2. The linear relationship can be obtained in advance considering the fluxgate theory. The proposed method is tested for different hysteresis characteristics, different levels of remanent flux, with and without primary current, and errors in the assumed element parameters using EMTP-RV simulations. The results indicate that the proposed method can quickly and effectively detect the remanent flux of a protection CT in situ. The CT is not required to be disconnected from the substation, which means that the remanent flux can be detected in situ. The maximum detection time in all cases is smaller than 20ms. In addition, it is also confirmed that the slight distortion of the secondary current can be clearly filtered by a low pass filter, which consequently insure any protection device against maloperation.References: [1] T. Zheng, E. Hu, H. Yang, R. Zhao, Y. C. Kang, P. Wall and V. Terzija, “Fast, in Situ Demagnetization Method for Protection Current Transformers,” IEEE Trans. on Magnetics, Vol. 52, No. 7, July 2016, pp. 1-4.

Fast and in Situ Remanent Flux Detection Method for a Protection Current Transformer based on the Fluxgate Theory

Parallel control of milli-scale robots (milli-robots) is important for biomedical applications because it can improve fluidic delivery systems, which interface with cells and tissues. Systems based on diamagnetic levitation are advantageous because of frictionless transport around the workspace. The most common technique for contactless actuation in these systems is achieved through current traces in printed circuit boards or electromagnets to drive a milli-scale permanent magnet array levitated on graphite [1, 2]. Such systems have segmented work surfaces, limited motion in close proximity, and require extensive changes to expand the workspace. Automated optical actuation of diamagnetic pyrolytic graphite (PyG) levitating over permanent magnet arrays has been previously demonstrated using single laser sources for individual control [3, 4] and commercial projectors for parallel control [5]. Optical actuation allows accurate control of multiple PyG milli-robots that are able to move within close proximity to each other throughout an unsegmented work surface. Parallel control is demonstrated using three 17mmΦ levitating PyG milli-robots, which were simultaneously controlled using spotlights moving along pre-programmed paths forming the letters ‘U’, ‘S’, and ‘N’ as shown in Fig. 1. In this work, we demonstrate the potential use of multiple diamagnetically levitated milli-robots for delivering biological samples. As a proof of concept, we demonstrate loading, transporting, and releasing water into agar gel with microscale precision. End effectors, in the form of micropipettes, are placed on top of the PyG milli-robots. The fluid sample loads into the micropipette, which behaves as a horizontal capillary, through the aid of capillary action. The dimesions of the micropipettes and the properties of the fluid use dictate the time to fully load the capillary. A micropipette resting on top of a PyG milli-robot is shown in Fig. 2.References: [1] E. E. Hunter, et al., IEEE Robotics and Automation Letters 4.2 (2019): 997-1004. [2] A. Hsu, et al., IEEE Robotics and Automation Letters 5.2 (2020): 2913-2920. [3] M. Ewall-Wice, et al., IEEE Transactions on Magnetics 55.7 (2019): 1-6. [4] J. Young, et al. AIP Advances 9.12 (2019): 125038. [5] J. Young, et al. MOEMS and Miniaturized Systems XIX, 2020.

Optically Powered Diamagnetically Levitated Robots for Biomedical Applications

Permanent magnet dipole can generate magnetic field higher than the Br of the material with structures such as the Halbach array [1] and Stelter array [2]. These arrays usually generate magnetic field inside a cavity. And the magnetic field is perpendicular to the axis of the cavity. For applications such as Faraday Effect and erasing hard disks perpendicular media, a strong in-plane magnetic field is required. In the case of erasing hard disks, the disk needs to rotate in the air gap with magnetic field perpendicular to the surface of the disks. This requires that the dipole must open along the field direction. And it is often difficult to generate strong magnetic field when magnets can only be placed around the path of the magnetic flux. This paper presents a permanent magnet dipole design for strong in-plane magnetic field. The design starts with a Halbach structure that generates strong magnetic field in the cavity. To create access to the cavity from the in-plane field direction, a pair of magnets with orientation opposite to the magnetic field of the Halbach dipole are substituted along the field direction. The magnetic field from the substitute magnets is analyzed using current sheet equivalent method. This field is then subtracted from the Halbach magnet to generate the magnetic field from the new structure. We then used Bound Analysis software to simulate the structure. For the prototype, we choose an 8-segment Halbach magnet as the basic structure and used triangular magnets so that the magnets fit inside a rectangular steel housing. The magnetic material is NdFeB 48 MGOe with Br of 13600 G. Fig 1 shows the prototype dipole and the magnetic field in the air gap. In conclusion, this paper proposes a permanent magnet dipole with strong in-plane magnetic field. The prototype dipole generates strong in-plane magnetic field that is in line with the predictions from the analytical equation as well as our BEA analysis. This strong dipole can be used in many applications such as Faraday Effect and hard disk erase. The design is granted with US patent 10529362 [3]References: [1] K.Halbach, “Design of permanent multipole magnets with oriented rare earth cobalt materials”, Nucl. Instru. and Methods, Vol.169, pp 1-10 (1980) [2] Richard E. Stelter, US patent 5635889, 1997 [3] Chun Li, US patent 10,529,362, 2020

Permanent Magnet Dipole Design with Strong In-plane Magnetic Field

I Introduction Accurate modeling of the hysteresis characteristics of magnetic materials is of great significance to analysis the electromagnetic performance of electrical equipment[1]. The Preisach model is widely used in the simulation of the magnetic characteristic of transformers through the FEM calculation, while its parameter identification problem is still a complicated task[2]. This paper proposed a new parameter identification method based on an intelligent optimization algorithm with the explicit-form Everett function, which can speed the identification process. II Method and Discussion Firstly, the hysteresis loops of the B30P105 steel under quasi-static conditions are measured according to the IEC60404-2; Secondly, the Preisach model is built through the explicit-form Everett function. The explicit-form Everett function transformed the integral on the Preisach plane into the sum of a series of exponential functions which gives an explicit expression of the Everett function. To simulate the hysteresis loops of the material by the proposed method, the parameters identification problems of the explicit function need to be fully investigated. The optimization process of calculating the Everett function is shown in Figure 1 (where a, b, c, γ, Hs, Ms are the parameters of the proposed model); Finally, a Velocity-Controlled Particle Swarm (VCPSO) algorithm, which only needs the limiting hysteresis loop of the experimental data is developed and implemented to find the optimal parameters of the model. The simulation results are in good agreement with the experimental data as shown in Figure 2. III Conclusion A new parameter identification method of the Preisach model with explicit Everett function is proposed. By using the VCPSO algorithm, a fast parameter identification process, which only needs the limiting loop of the experimental data is developed. The proposed method are proved to be very efficient and accurate to construct the Preisach model, which has great significance on fast simulating magnetic performance of the transformer when considering hysteresis properties.References: [1] X. Zhao, X. Liu, Z. Zhao, X. Zou, Y. Xiao, and G. Li, "Measurement and modeling of hysteresis characteristics in ferromagnetic materials under DC magnetizations," Aip Advances, vol. 9, no. 2, Feb 2019, Art no. 025111, doi: 10.1063/1.5054948. [2] S. Hussain and D. A. Lowther, "An Efficient Implementation of the Classical Preisach Model," IEEE Trans. Magn., vol. 54, no. 3, Mar 2018, Art no. 7300204, doi: 10.1109/tmag.2017.2748100.

Parameter Identification of Preisach Model Based on Velocity-Controlled Particle Swarm Optimization Method

Thermomagnetic materials are a new type of magnetic energy materials, which enable the conversion of low temperature waste heat to electricity by three routes: Thermomagnetic motors, oscillators, and generators. Taking our recent work on thermomagnetic generators with different magnetic field topologies (TMG, Fig. 1 and 2) [1] as a starting point, in this talk we also analyse the material requirements for a more energy and economic efficient conversion. We present experiments of our TMG using different thermomagnetic materials (La-Fe-Si-Co with different transition temperatures and Gd). We compare the suitability of these materials and from this derive a generalized approach to evaluate the suitability of different thermomagnetic materials, which is different compared to magnetocaloric materials. We show that the thermodynamic efficiency of the best thermomagnetic materials outperforms thermoelectric materials when harvesting low temperature waste heat. Furthermore, the low raw materials cost results in a price per watt more than one order of magnitude lower than today’s power plants and thermoelectrics, which makes them also economically competitive. As summary, we present a materials library, which allows selecting the best available thermomagnetic materials in two Ashby plots as figures of merit and gives guidelines for future development of this material class [2]. At the end of this talk, approaches towards micro systems for harvesting low temperature waste heat are described.References: [1] A. Waske et al. Nature Energy 4, 68 (2019) [2] D. Dzekan et al, arXiv: 2001.03375 (2020)

Thermomagnetic harvesting of low temperature waste heat INVITED

INTRODUCTION - This paper proposes a new application of skin effect suppression technology [1]-[5] for long wiring on high-speed & low-delay I/O board.In previous research [6], a lower loss structure of electroplated conductor/magnetic multilayer was clarified by changing thickness of each layer with an electromagnetic field calculation theory for rectangular multilayer transmission line. A challenge in this paper is to clarify the structure with the lowest loss by the method of changing each layer’s thickness. Also an electroplated conductor/magnetic multilayer transmission line will be able to used as a band pass filter, utilizing characteristics of the magnetic material. VERIFICATION - Cu and NiFe were selected as metal conductor material and negative permeability magnetic material, respectively. Permeability and Q factor of NiFe were estimated by the L.L.G. equation. The Cu and NiFe films are alternately stacked to form the multilayer, as shown in Fig. 1. An electromagnetic field distribution, which considers the skin effect in a rectangular multilayer transmission line, is derived based on Maxwell's equation. The current density of each layer and the total loss can be obtained by the equations (1) and (2) in Fig. 1. The loss of transmission line whose total thickness is 12.67 µm was compared under the following conditions. 1) A 33 layered structure by a constant ratio, Cu tN = 0.51 µm and NiFe tF = 0.25 µm. 2) A 33 layered optimal design we proposed at 16 GHz. 3) A 17 layered optimal design we proposed at 16 GHz. RESULTS AND DISCUSSION - Fig. 2 shows the frequency characteristics of loss in each model. At 16 GHz, where NiFe has the best Q value, compared to conventional thickness by a constant ratio, it was estimated that the loss is 80% in optimal thickness of 33 layers. In the structure we proposed, the loss increases compared to the conventional one in the outside band of optimal frequency. It can be expected to obtain a steeper filter function utilizing the frequency characteristics of the magnetic material by designing a transmission line we proposed.References: [1] B. Rejaei and M. Vroubel, J. Appl. Phys., Vol. 96, p.6863 (2004) [2] Y. Zhuang, B. Rejaei and H. Schellevis, IEEE Electron Device Lett., Vol. 29, pp.319–321 (2008) [3] M. Yamaguchi, N. Sato and Y. Endo, Proc. 40th Eur. Microw. Conf., pp.1182-1185 (2010) [4] N. Sato, Y. Endo and M. Yamaguchi, J. Appl. Phys., Vol. 111, pp.07A501-1-07501-3 (2012) [5] M. Yamaguchi, T. Yanai and H. Nakayama, IEEE Trans. Magn., Vol. 54, pp.1-5 (2018) [6] Y. Aizawa, H. Nakayama, K. Kubomura, R. Nakamura, and H. Tanaka, AIP Advance, Vol. 10, p.015124 (2020)

Consideration on Lowering Loss design of Skin Effect Suppressed Multi-layer Transmission Line with Positive/Negative (Cu/NiFe) Permeability Materials for High Data-Rate and Low Delay-Time I/O Interface Board

Half-metallic ferromagnets (HMFs) and spin gapless semiconductors (SGSs) are promising materials for spintronics with almost 100% spin polarization of charge carriers. They possess a gap near the Fermi energy for the current carriers with spin down. However, for the opposite spin projection, these materials have a difference: the energy gap is absent in HFMs [1], while it is zero in SGSs. Parameters of the energy gap and, consequently, physical properties can vary quite strongly in different X2YZ Heusler alloys [2, 3, 4], where Y-elements are 3d-transition metals and Z-components are s- and p-elements. Thus, the aim of the work is to follow the changes in the electrical, magnetic and galvanomagnetic properties and to establish their interconnection and basic behavior patterns of the Co2YSi (Y = Ti, V, Cr, Mn, Fe, Co, Ni) and Co2MnZ Heusler alloys (Z = Si, Al, Ge, Sb) in the HMF and/or SGS states. The electrical resistivity was measured in a wide temperature range from 4.2 to 300 K, the field and temperature dependences of magnetic and galvanomagnetic properties being studied too. Significant changes in the values of the coefficients of the normal and anomalous Hall Effect, magnetization, residual resistivity, type, and concentration of current carriers and their mobility were found. At the same time, the correlation between the changes in these electronic and magnetic characteristics depending on the number of valence electrons are observed. The work was performed within the framework of the state assignment of the Ministry of Science and High Education of Russia (the themes “Spin”, No. AAAA-A18-118020290104-2-2 and “Quantum” No. AAAA-A18-118020190095-4) with partial support from the RFBR (project No. 18-02-00739 and 20-32-90065) and the Government of the Russian Federation (Decree No. 211, Contract No. 02.A03.21.0006).References: [1] M.I. Katsnelson, V.Yu. Irkhin, L. Chioncel et al., Rev. Mod. Phys., Vol. 80, p. 315 (2008). [2] V.V. Marchenkov, Yu.A. Perevozchikova, N.I. Kourov et al., J. Magn. Magn. Mat., Vol. 459, p. 211 (2018). [3] Yu.A. Perevozchikova, A.A. Semiannikova, A.N. Domozhirova, P.B. Terentyev, E.B. Marchenkova, E.I. Patrakov, M. Eisterer, P.S. Korenistov and V.V. Marchenkov, Low Temp. Phys., Vol. 45, p. 789 (2019). [4] Yu.A. Perevozchikova, A.A. Semiannikova, P.B. Terentyev, M. Eisterer, P.S. Korenistov and V.V. Marchenkov, Journal of Physics: Conf. Series, Vol. 1389, p. 012110 (2019).

Electroresistivity, magnetic and galvanomagnetic properties of Co-based Heusler alloys in the states of half-metallic ferromagnet and spin gapless semiconductor

Spin transfer electronics or spintronics offers the possibility of enhancement of regular electronic devices [1]. Because of that, the demand for materials that acquire high values of spin polarization is growing. From several groups of materials, half-metallic Co2-based Heusler alloys are well appropriate materials for spintronic devices due to their high Curie temperature, high magnetic moment, and low Gilbert dumping [2]. The majority of Heusler alloys are usually prepared in the form of ribbons, bulk, or thin films. However, due to technological progress, Heusler alloys face a new production challenge in the nano-scale regime. Several publications deal with the preparation of Heusler nanowires, but with the lack of the spin polarization measurements [3]. Magnetic nanowires prepared in the form of dense array offer the possibility for the development of next-level 3D magnetic “racetrack” memory. Here, the information is stored in the domain wall pattern and shift with spin-polarized current [4]. Therefore, it is essential to determine the spin polarization of the material, which is considered for possible spintronic applications. In the present work, Co2FeSn nanowires have been prepared using template-assisted electrochemical deposition. The nanowires have been grown in the pores of Anodic Alumna Oxide membranes. The spin polarization values have been determined using Point-Contact Andreev Reflection spectroscopy. We show that the spin polarization is preserved in the nanoscale, and by creating a contact with the fresh surface, it is possible to achieve high spin polarization values up to 100 %. This research was supported by Slovak Grant Agency VEGA 1/0053/19, Slovak Grant Agency grant number APVV-16-0079 and VVGS-2019-1231.References: [1] J. P. DeGrave, A. L. Schmitt, R.S. Selinsky, Nano Lett., 11, 4431-4437(2011). [2] M. Jourdan, J. Minár, J. Braun, Nat. Commun., 5, 3974 (2014). [3] L. Galdun, V. Vega, Z. Vargova, ACS Appl. Nano Mater., 1, 7066-7074 (2018). [4] S. S. P. Parkin, M. Hayashi, L.Thomas, Magnetic Domain-Wall Racetrack Memory. Science, 320, 190-194 (2008).

Co2FeSn Heusler Nanowires with High Spin Polarization

Interest in ferrimagnetic metals as active elements in spintronic devices is growing due to their intriguing magnetization effects close to compensation [1]. Mostly studied in alloys, the SOTs that arise from the negative exchange interaction attribute to interesting Hall measurements and can be manipulated through control of temperature [1, 2]. Here we demonstrate another unique feature of these systems: temperature-driven switching. We measured the anomalous Hall effect (AHE) in a van der Pauw geometry on a Ta(3nm)/Pt(3nm)/Co(.5nm)/Gd(1.8nm)/Pt(3nm) synthetic ferrimagnet stack, where the antiferromagnetic exchange coupling between the Co and Gd layers forms the ferrimagnet [3]. The observed compensation temperature is between 150 and 155 K as seen in the diverging coercivity of the sample when measuring AHE vs. perpendicular external field (Figure 1). At 115 K, the AHE displays an external field dependent hysteresis with a coercivity around 300, and 1200 Oe at 150 K (Figure 1). Because this is beneath the compensation temperature, the saturation voltage at 1500 Oe is more negative than at -1500 Oe, creating two anomalous Hall voltage states influenced by the net Gd moment. At 155 and 165 K the coercivities are 850 and 250 Oe respectively, yet the saturation voltages are reversed (Figure 1). This indicates the influence of the net Co moment above the compensation temperature, and the divergence of the coercivity between 150 and 155 K. By then applying a static external field, the AHE state can be switched as the temperature of the sample is lowered or raised above the compensation temperature. In Figure 2, a constant external magnetic field of 450 Oe is applied, and the AHE shows temperature dependent coercivity and hysteresis. This confirms that temperature can be used to write a magnetization state of a ferrimagnet, with a memory window between 145 and 156 K in the case of this sample.References: [1] X. Jiang, L. Gao, J. Z. Sun, and S. S. P. Parkin, Phys. Rev. Lett. 97, 217202 (2006). [2] R. Mishra, J. Yu, X. Qiu, Phys. Rev. Lett. 118, 167201 (2017). [3] P. Hansen, C. Clausen, G. Much, J. Appl. Phys. 66, 756 (1989). Funding acknowledgements: B. L. Zink Group: NSF DMR 1709646

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On-Chip Thin-Film Microtransformer with Improved Coupling Factor for High Frequency Data Transmission

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