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The patch antenna is advantageous in many applications because of its simple and inexpensive structure. However, one disadvantage is its large size. One of the methods to reduce the size of an antenna is to utilize ferrite material [1]. While this does effectively miniaturize the antenna, the peak realized gain (PRG) is decreased by 8.3 dBic due to the magnetic loss of the ferrite core.&lt;br/&gt;In this paper, we take the multi-layer ferrite and dielectric approach to reduce the patch antenna size. All antennas were simulated using ANSYS HFSS for their performance. Fig. 1 shows the specifications and designs of the patch antennas. The baseline patch antenna has the dimensions given in [2] and uses a 1.4 mm thick FR-4 substrate (permeability (μ&lt;sub&gt;r&lt;/sub&gt;) = 1, permittivity (ε&lt;sub&gt;r&lt;/sub&gt;) = 4.4). The dielectric and magnetic loss tangents (tanδ&lt;sub&gt;e&lt;/sub&gt; and tanδ&lt;sub&gt;u&lt;/sub&gt;) are 0.02 and 0.00, respectively, at UHF band frequency, and its volume (&lt;i&gt;V&lt;/i&gt;) is 9800 mm&lt;sup&gt;3&lt;/sup&gt;. To realize the multi-layer concept in the antenna size reduction, 0.8 mm thick layers of ferrite (μ&lt;sub&gt;r &lt;/sub&gt;= 6, ε&lt;sub&gt;r &lt;/sub&gt;=13, tanδ&lt;sub&gt;u &lt;/sub&gt;= 0.05, tanδ&lt;sub&gt;e&lt;/sub&gt; = 0.02, and &lt;i&gt;V &lt;/i&gt;= 2720 mm&lt;sup&gt;3&lt;/sup&gt;) are inserted into the FR-4 substrate. Three topologies are investigated: one ferrite layer, two ferrite layers, and three ferrite layers. For each topology, the volume of the ferrite remains the same. For the cases with more than one ferrite layer, the inner-most layer has a constant &lt;i&gt;V &lt;/i&gt;= 600 mm&lt;sup&gt;3&lt;/sup&gt;, and the remaining volume is divided equally among the outer layers. Antenna performance results are summarized in Table 1. For one ferrite layer, 16.7% miniaturization is achieved, but the PRG decreases by 14.1 dBi. However, as the number of layers increases to two, 49.8% miniaturization is achieved with a decrease in PRG of 5.6 dBi. For three layers, 49.3% miniaturization is observed with a 5.6 dBi decrease in PRG. Compared to the case with the all-ferrite substrate (&lt;i&gt;V &lt;/i&gt;= 9800 mm&lt;sup&gt;3&lt;/sup&gt;), the patch antenna with two ferrite layers has a 4.4 dBi higher PRG. Ferrite and dielectric substrate contributes remarkably to antenna size reduction.

![](https://assets.underline.io/uploads/markdown_image/1/image/e68b9a4e3e72ffd5c9f56c3ee81cfc08.jpg)

Fig. 1. Design and specifications of (a) baseline patch antenna, (b) ferrite-dielectric layering, and (c) multi-layer patches

![](https://assets.underline.io/uploads/markdown_image/1/image/74ed72c7f2f5ae5991e9a4a0fc105818.jpg)

Table 1. Comparison of antenna performance results

2022 Joint MMM-INTERMAG

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

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ACL-IJCNLP 2021

The great event is jointly organized by the Association for Computational Linguistics (ACL) and Asian Federation of Natural Language Processing (AFNLP).

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

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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To increase an areal density (AD) of an ultra-high density bit-patterned magnetic recording (BPMR) system [1], we have proposed track mis-regristration (TMR) correction method combined with the soft information adjustor (SIA) to cope with the effects of TMR and two-dimensional (2D) interference [2]. However, we found that soft information or log-likelihood ratio (LLR) can be improved to earn better bit-error rate (BER) performances. Therefore, we propose to use two deep neural networks (DNNs), e.g., multi-layer perceptron (MLP) [3] and long short-term memory (LSTM) network [4] that are operated together with an early SIA on a two-head/two-track (2H2T) BPMR system as shown in Fig. 1. The user sequences, xl,k ∈ {±1} of the l-th track and k-th bit, are recorded onto the medium. All readback signals are produced using two readers, which are then sent to TMR predictor [2]; meanwhile, they are equalized by the consistent 2D equalizers. Then, the equalized sequences, zl,k, are fed into the 2D detectors to output LLRs. The SIA is used to first improve the reliability of each LLR sequence before passing them to our proposed schemes based on DNNs to decide the estimated recorded bits, x'l,k.. The LLR that is obtained from SIA under various TMR effects is given as an input dataset, while the recorded sequence is fixed as an output dataset of DNNs. All of readback signals that relate to considered datasets are interrupted with several electronic noise levels. Here, we set all input and output datasets as 5,200 files, each file consists of 2×32,768 bits, which are directly mapped to be as a pair of input and output datasets. Fig. 2 shows BER performances between the proposed and conventional SIA systems [2]. It is clear that the proposed systems yield better BER performances over the conventional system at all TMR levels with and without position jitter. At BER = 10-5, the proposed LSTM gains for about 4.0 and 4.4 dBs over the conventional SIA system for both cases at TMR 0%. We found that LSTM network slightly provides better performance.

![](https://assets.underline.io/uploads/markdown_image/1/image/afd71bdcfbf70e159df7e3a4f923b601.jpg)

A 2H2T BPMR channel with the DNNs based soft-information improvement.


![](https://assets.underline.io/uploads/markdown_image/1/image/2e01171687412c0b995a541bf1789349.jpg)

BER performances of the conventional SIA [2] and proposed systems.

Deep Neural Networks based Soft-Information Improvement for Two-Head/Two-Track Bit-Patterned Magnetic Recording

Bit patterned media (BPM) technology is intended to provide ultimate areal recording density for hard disk drives. However, for data read back, if a reader has to only read a single track, the read width might become the limiting factor, rather than that of the technology itself. In this study, a machine learning data detection channel is employed to a relatively wide reader with a read width covering two data tracks, as shown in Fig. 1(a). Adjacent data tracks are staggered by half of the bit separation B, which is also the pitch of patterned bits, in the down-track direction. Perpendicular magnetization is assumed for each patterned bit. The read-back signal consists of equal contributions from both the targeted track and interference tracks and is sampled at equal time intervals as input to the neural network. A convolution neural network (CNN) is applied here. This network has four hidden layers with 40 channels per hidden layer and all the filters in each hidden layer have a kernel size of three. The number of input neurons is determined to cover the entire spread of inter symbol interference. The number of input neurons is 9 in the case shown here, corresponding to the PW50/B=1.4 used. The weights of the filters are determined through the training process. Specifically, the rectified linear unit (ReLU) is used for the taps. Only the corresponding binary data of the target track are used in the training process for the “learning” purpose. The entire network consists of 15,000 learnable parameters or weights. Figure 1(b) shows the detection error rates, as a function of the number of bits used in training. For the case in which the signal is sampled at an interval of B (blue curve), the detection error becomes zero over one million different bit sequences after the network is trained over 50,000 bits. If the sampling frequency doubles (red curve), i.e. sampled at an interval of B/2, the zero error detection can be achieved with just 1,000 training bits. Note that the two cases shown here are noise-free. With noise added, more training bits will be needed. In the talk, results on the detection bit error rates for practical signal-to-noise ratios will be presented.

![](https://assets.underline.io/uploads/markdown_image/1/image/5e641bb8ed57ba10ad8b1314d15f0209.jpg)

Machine Learning Detection Channel Enabling Wide Reader for Bit Patterned Media

A new mechanism of recording for a MRAM cell, which is based on a parametric resonance, has been proposed [1] and experimentally studied. The parametric mechanism requires a substantially smaller spin torque for the magnetization reversal due to the resonance nature of this recording mechanism and, therefore, it can be a solution for further reduction of the recording energy for the MRAM operation. Two parametric mechanisms for the magnetization reversal are proposed, studied and experimentally evaluated. The first mechanism is due to a modulation of the magnetic field of the Spin- Orbit Torque. The second mechanism is due to modulation of the anisotropy field. For both mechanisms, a parametric torque is created by a RF modulated current, which resonantly enhances the magnetization precession until a magnetization reversal. Additionally, a parametric mechanism for magnetization reversal by a DC current is proposed and studied. This parametric mechanism may occur in a magneto-resistive structure, in which a magnetization precession modulates an electrical current. It results in a positive feedback loop, in which a magnetization precession creates a torque, which more enhances the precession.

![](https://assets.underline.io/uploads/markdown_image/1/image/542c9b5a32048ecc7a06babee370e4ca.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/256f37dab48ea38e1c2550f583dbc4f5.jpg)

Experimental evolution of two parametric mechanisms of magnetization reversal in FeCoB nanomagnet.

Experimental evolution of two parametric mechanisms of magnetization reversal in FeCoB nanomagnet.

Properties of higher-order magnetic anisotropy constants in soft-hard nanocomposite materials still attract much debate [1]. We investigated the magnetic anisotropy in a L10/A1 FePt system using the VAMPIRE software package [2]. An elongated, faceted cylindrical core-shell was constructed with a L10-FePt core of varied size surrounded by an A1-FePt shell. The system exchange interaction was 3-dimensional and accounted up to the third-nearest neighbours. A 2-ion Fe-Pt anisotropy component was incorporated to the system Hamiltonian following Mryasov et al. [3]. The angular dependence of the restoring torque was calculated from 0K to 1000K in 5K steps using a constrained Monte-Carlo integrator. Temperature-dependent anisotropy constants were then determined from fitting to the system torque as a function of the constrained angle. We find that the core-shell structure exhibits an unexpected 4th-order anisotropy term of which magnitude depends on the core-size ratio R. The K2/K1 ratio, with K1 and K2 being the 2nd and 4th-order anisotropy constant respectively, displays a non-monotonic pattern with a peak occurring at R ~ 0.55 [Fig.1]. We find that K2 scales with (M/Ms)~2 at temperatures below Tc [Fig.2] - a remarkable deviation from the established Callen-Callen theory [4] which instead predicts a scaling with (M/Ms)10. A simple analytical model shows the 4th-order term to arise from canting of the core and shell magnetisation. Further, the model demonstrates that the magnitude of the 4th-order term is proportional to K12/J, with J the exchange coupling. Given that the 2-ion K1 term scales approximately with M2 and J with M2, the predicted scaling exponent is 2 in agreement with the simulations. Generally, the 4th-order anisotropy constant is shown to exhibit a strong dependence on the system geometry, thus suggesting that the Callen-Callen power law is not universal and valid only for single-ion anisotropies.

![](https://assets.underline.io/uploads/markdown_image/1/image/22a9ca96de68d358f16ce046a83fffba.jpg)

Fig.1: A low temperature scan displays a non-monotonic dependence of K2/K1 on core size ratio R with a peak at R ~ 0.55.

![](https://assets.underline.io/uploads/markdown_image/1/image/bb578e32eb2732e857794fddce38fa58.jpg)

Fig.2: K2 scaling with M/Ms for R=0.50 results in a scaling exponent β ~ 1.81 not 10 as predicted by Callen-Callen.

Higher-order magnetic anisotropy in soft-hard nanocomposite materials

Embedded Mask Patterning (EMP) has been demonstrated as a potential HAMR media solution with formation of ultra-fine and highly-ordered L10-phase FePt grains[1]. We used a hybrid model including both reactive and pair-wise interatomic potentials in the classic Molecular Dynamic (MD) simulation to study the methanol-based reactive plasma etching mechanism of the FePt lattice. The major reactive redical etchants in the methanol plasma are identified as Carbon monoxide and Hydrogen spieces[2]. Adsorbed Carbon monoxide molecules reacts with the Fe and Pt atoms and forms caronyl bonds. With assisted ion beams such as Ar+ or He+, we show the chemical etch yield is increased. The ordering change of FePt crystal surface during the etch are also simulated.

![](https://assets.underline.io/uploads/markdown_image/1/image/83abf9422e8c50f158b238db1a099582.jpg)

MD Simulation of Plasma Etch of FePt Media

Reactive Molecular Dynamic Simulation of Plasma Etching Process of L10-FePt HAMR Media in Embedded Mask Patterning

In granular FePt-L10 HAMR media. sufficient grain volume is critical for achieving expected areal density capability (ADC) [1][2]. Grain height needs to be increased as the grain size decreases. We present an experimental study on the fabrication of HAMR media with tall/high aspect ratio FePt-L10 grains. The underlayer stack consists of Ta(5nm)/Cr(40nm)/MgO(8nm) prior to the magnetic layer deposition. A 0.5 nm FePt layer is deposited on the MgO underlayer for initial grain nucleation, followed by the deposition of 2 nm FePt-BN (35% boron nitride) both at 700 oC. Over the FePt/FePt-BN stack, FePt-SiOx of 10nm thickness is deposited in the following manner: The first 3.5nm are deposited at 600 oC followed by immediately turning-off of the substrate heating and the rest of the layer is then deposited while the substrate undergoes naturally cooling. The ending temperature is 430 oC . The volumetric SiOx concentration of the FePt-SiOx layer is also graded from 40% at the bottom to 18% at the top. The L10 order parameter is S=0.72, calculated based the XRD measurement. Figure 1 shows the plan view HAADF TEM image (left) and cross-section view TEM image (right). The plan view image clearly shows well separated grains with average grain size around 6nm. The cross-section image shows columnar grains with well-defined grain boundaries and a grain aspect ratio ranging from 1.7 to 2. In this film stack, the SiOx grain boundaries are vertically matched with boron-nitride grain boundaries at the interface of the two layers. If the deposition temperature exceeds 650 oC, the majority of the adjacent FePt grains could become laterally connected over the entire thickness of the FePt-SiOx layer whereas the BN grain boundaries remains intact. While we vary the deposition conditions of the FePt-SiOx layer, the FePt/FePt-BN stack acts as a fixed template layer for the grain growth on top. For the FePt-SiOx layer, the graded SiOx composition combined with the graded deposition temperature serves the key to (1) ensure columnar grains that are well separated by SiOx grain boundaries and (2) avoid the formation of 2nd layer FePt grains.

![](https://assets.underline.io/uploads/markdown_image/1/image/89ab165f3824e2641ad4a23daad4429d.jpg)

Fig. 1. Planview HAADF (Left) and Cross-section (Right) TEM image of the entire medium stack.

Fabrication of Granular FePt-L10 HAMR Media with High Grain Aspect Ratio

Transition curvature limits the performance of Heat-assisted Magnetic Recording (HAMR), especially when bit length is reduced below 10nm. The dependence of this transition curvature on bit length was obtained micromagnetically in our previous work [1]. In the current study, the dependence of signal-to-noise ratios (SNRs) and bit error rates (BERs) on HAMR transition curvatures is further investigated. More than 20,000 bits are written ideally (with an infinite thermal gradient) with various bit lengths and realistic transition curvatures. A pseudorandom binary sequence is used. The width of the read head is 20nm, shield to shield distance is 22nm, and element thickness is 4nm. Magnetic fly height is 6nm. A Viterbi algorithm is applied to decode the readback signals and calculate BERs. Fig. 1 and 2 show how SNRs and BERs change with transition curvatures (characterized by the coefficient to the quadratic term of the defining parabola) for a minimum bit length of 7.5nm. Clearly, larger transition curvatures result in lower SNRs and higher BERs, thus negatively affecting HAMR performance. Although the results in the figures represent very small bits compared to the readback resolution, our calculations for longer bits and/or narrower shield-shield spacing show similar results, albeit with improved SNR and BER, as will be shown in the presentation.

![](https://assets.underline.io/uploads/markdown_image/1/image/16d047464ce2c11df0f3338173afaea4.jpg)

Fig. 1 Dependence of SNRs on HAMR transition curvatures with a bit length of 7.5nm.

![](https://assets.underline.io/uploads/markdown_image/1/image/53a95ed559b573a5cfb00cb65785b952.jpg)

Fig. 2 Dependence of BERs on HAMR transition curvatures with a bit length of 7.5nm.

Dependence of Bit Error Rates on HAMR Transition Curvatures

Acoustically-driven ferromagnetic resonance (ADFMR) (1,2) is a powerful technique used to transmit RF surface acoustic waves (SAWs) and tune their transmission using a thin magnetic film and a static magnetic field HDC. We explore tunability of ADFMR devices for their potential in agile RF communications applications. Two examples are nonreciprocal ADFMR devices, and devices with curved interdigital transducers (IDTs), which focus SAWs with enhanced intensity in the magnetic film. Nonreciprocity of RF transmission has an important role in critical components like isolators and circulators. We demonstrate that a thin synthetic antiferromagnet using FeGaB (3) can selectively absorb waves travelling in one direction with 48.4 dB isolation- performance that can compete with state-of-the-art commercial devices despite much smaller package size and power draw. Another tuning knob which can have device impacts is nonlinearity. With curved interdigitated transducers (IDTs), we focus SAW energy to a small, intense region near the center of the magnet. We then study the dependence of the magnetoacoustic interaction on input power. Reaching moderate input powers of 10 dBm or less allows access to a nonlinear regime previously unavailable in these devices. Using a scanning acoustic-wave interferometer, we can observe the change in amplitude of the acoustic waves as they travel across the device surface. The power dependence is studied in depth, and an applied magnetic field modifies the amplitude wherever the magnet is present. Using these tools we gain new insight into how the magnetoelastic coupling works in ADFMR, which guides our understanding in the pursuit of new tunable RF communications device types.

![](https://assets.underline.io/uploads/markdown_image/1/image/2590b73047f4f871dd45b187b9cd8f14.jpg)

Operation of a magnetoacoustic isolator. With external magnetic field applied in one direction, the device transmits RF unidirectionally with 48.4 dB isolation. Reversing the external field switches the direction of RF transmission.

![](https://assets.underline.io/uploads/markdown_image/1/image/bd4fddee8bbe14c38d434b0fda5a4473.jpg)

A) Image of a focused IDT ADFMR device. Curved IDTs transmit and receive SAWs, which travel across a 20-nm-thick Ni film on a y-cut LiNbO3 substrate. B) ADFMR pattern showing output with 860-MHz 27-dBm input as a function of HDC angle and magnitude. C) SAW amplitude measured by interferometry.

Tuning RF Acoustic Waves via Magnetism

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

Robust mutual synchronization of spin Hall nano-oscillator chains

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

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