France



Magnetoresistive field sensors have a wide range of uses, such as in biomedical applications, in the automotive industry, robotics, or smart city technologies. Figures of merit like sensitivity, detectivity and spatial resolution are used to evaluate the performance of such sensors [1]. At low frequencies, the 1/f noise component is dominant and is in fact responsible for hindering the device&#39;s detectivity, and, consequently, its performance. There is an active research effort to reduce this noise component and tackle this limitation [2].&lt;br/&gt;Vortex-based devices, in which the free layer exhibits a vortex magnetization distribution in its equilibrium state, are promising magnetic field sensors due to their large linear detection range [3] and the fact that they show practically no hysteresis in this range. Besides, these devices are often considered as model systems for the study of magnetization dynamics. In this study, we focus on the analysis of the 1/f noise in a particular type of magnetic sensor based on a vortex magnetic configuration integrated in a magnetic tunnel junction (MTJ) spin torque nano-oscillator. These devices present excellent rf characteristics for future radio-frequency devices and applications, such as rf generation [4], detection [5] or neuromorphic computing [6]. While the use of vortex-based spin-torque nano-oscillators for applications such as these mentioned here has been largely studied, they are newcomers in the magnetic field sensing landscape.&lt;br/&gt;In this work, we analyse the 1/f low-frequency noise in vortex-based spin-torque nano-oscillators by determining the Hooge parameter in different conditions. The Hooge parameter is typically used to characterize and compare sensor’s noise properties. Firstly, we find that in the uniform states the Hooge parameter of the studied device is comparable to that measured in state-of-the-art TMR sensors with similar RA product, α = 10&lt;sup&gt;-11 &lt;/sup&gt;- 10&lt;sup&gt;-10&lt;/sup&gt; µm&lt;sup&gt;2&lt;/sup&gt;. In the vortex state, the measured noise level is around one order of magnitude greater than in the parallel (and antiparallel) state, see Fig. 1a. This is due to the increased probability of pinning of the vortex core into defects or inhomogeneities of the free layer. Secondly, we determine that the dynamics of the vortex core strongly influence the noise level of the device. For a current above a certain threshold, the spin transfer torque surpasses the intrinsic damping of the free layer resulting in self-sustained oscillations of the vortex core [7]. In the self-sustained oscillations&#39; regime, the noise decreases to a level close to that of the antiparallel state, see Fig. 1b.&lt;br/&gt;Furthermore, we present a novel strategy for reducing the 1/f low-frequency magnetic noise, through the application of an in-plane rf field or injection of an rf current [8]. By using this approach while the device is operating in the self-sustained regime, we are capable of further decreasing the measured noise level to values close to the minimum attainable, see Fig. 2. We find that this noise reduction is non-resonant, see Fig. 2a. As such, we can have a vortex-based STNO with relevant noise properties, comparable to those of state-of-the-art TMR field sensors. At the same time, we profit from the specific advantages of vortex-based spin-torque nano-oscillators for sensing applications: large linear detection range, virtually no hysterisis and high spatial resolution. This noise reduction technique based on the spin-torque dynamics of the vortex can have an impact on the sensors&#39; industry, which may profit from the advantages of the vortex configuration.&lt;br/&gt;&lt;br/&gt;The work is supported by the French ANR project “SPINNET” ANR-18-CE24-0012.

**References:**

[1] D. C. Leitão et al., Nanotechnology 27, 045501 (2015)&lt;br/&gt;[2] L. Huang et al., Journal of Applied Physics 122, 113903 (2017); J. Moulin et al., Appl. Phys. Lett. 115, 122406 (2019)&lt;br/&gt;[3] D. Suess et al., Nat. Electronics 1, pages 362–370 (2018)&lt;br/&gt;[4] S. Wittrock et al., Phys. Rev. B 99, 235135 (2019)&lt;br/&gt;[5] A. S. Jenkins et al., Nat. Nanotech. 11, 360 (2016); D. Marković et al., Phys. Rev. Applied 13, 044050 (2020)&lt;br/&gt;[6] M. Romera et al., Nature 563, 230–234 (2018); J. Torrejon et al., Nature 547, 428-431 (2017)&lt;br/&gt;[7] A. Dussaux et al., Nat. Comm. 1, 8 (2010)&lt;br/&gt;[8] M. Jotta Garcia et al., arXiv:2012.09616 [cond-mat.mes-hall] (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f1e2a4020c2f2daf24d07405919ec60f.jpg)
Fig.1 a) Hooge parameter as a function of an in-plane magnetic field that is swept from the parallel to the anti-parallel state and back. b) Evolution of the Hooge parameter with the applied bias current. The inset shows the oscillation power of the rf emission due to the emerging vortex dynamics. The red dotted line represents the Hooge parameter measured in the AP state.

![](https://assets.underline.io/uploads/markdown_image/1/image/8659329698821b38c65d8cb8989eb4a3.jpg)
Fig. 2 a) Hooge parameter as a function of the frequency of the applied oscillating field, with P&lt;sub&gt;rf&lt;/sub&gt; = 1 mW. The red line indicates the value measured in the absence of this field. b) Hooge parameter as a function of the power amplitude of the rf field at a fixed frequency, f = f&lt;sub&gt;res &lt;/sub&gt;= 243.1 MHz. The green dotted lines represent the Hooge parameter measured in the P state.

INTERMAG 2021

 Spin-torque Dynamics for Noise Reduction in Vortex-based Sensors

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Magnetoresistive field sensors have a wide range of uses, such as in biomedical applications, in the automotive industry, robotics, or smart city technologies. Figures of merit like sensitivity, detectivity and spatial resolution are used to evaluate the performance of such sensors [1]. At low frequencies, the 1/f noise component is dominant and is in fact responsible for hindering the device's detectivity, and, consequently, its performance. There is an active research effort to reduce this noise component and tackle this limitation [2]. Vortex-based devices, in which the free layer exhibits a vortex magnetization distribution in its equilibrium state, are promising magnetic field sensors due to their large linear detection range [3] and the fact that they show practically no hysteresis in this range. Besides, these devices are often considered as model systems for the study of magnetization dynamics. In this study, we focus on the analysis of the 1/f noise in a particular type of magnetic sensor based on a vortex magnetic configuration integrated in a magnetic tunnel junction (MTJ) spin torque nano-oscillator. These devices present excellent rf characteristics for future radio-frequency devices and applications, such as rf generation [4], detection [5] or neuromorphic computing [6]. While the use of vortex-based spin-torque nano-oscillators for applications such as these mentioned here has been largely studied, they are newcomers in the magnetic field sensing landscape. In this work, we analyse the 1/f low-frequency noise in vortex-based spin-torque nano-oscillators by determining the Hooge parameter in different conditions. The Hooge parameter is typically used to characterize and compare sensor’s noise properties. Firstly, we find that in the uniform states the Hooge parameter of the studied device is comparable to that measured in state-of-the-art TMR sensors with similar RA product, α = 10-11 - 10-10 µm2. In the vortex state, the measured noise level is around one order of magnitude greater than in the parallel (and antiparallel) state, see Fig. 1a. This is due to the increased probability of pinning of the vortex core into defects or inhomogeneities of the free layer. Secondly, we determine that the dynamics of the vortex core strongly influence the noise level of the device. For a current above a certain threshold, the spin transfer torque surpasses the intrinsic damping of the free layer resulting in self-sustained oscillations of the vortex core [7]. In the self-sustained oscillations' regime, the noise decreases to a level close to that of the antiparallel state, see Fig. 1b. Furthermore, we present a novel strategy for reducing the 1/f low-frequency magnetic noise, through the application of an in-plane rf field or injection of an rf current [8]. By using this approach while the device is operating in the self-sustained regime, we are capable of further decreasing the measured noise level to values close to the minimum attainable, see Fig. 2. We find that this noise reduction is non-resonant, see Fig. 2a. As such, we can have a vortex-based STNO with relevant noise properties, comparable to those of state-of-the-art TMR field sensors. At the same time, we profit from the specific advantages of vortex-based spin-torque nano-oscillators for sensing applications: large linear detection range, virtually no hysterisis and high spatial resolution. This noise reduction technique based on the spin-torque dynamics of the vortex can have an impact on the sensors' industry, which may profit from the advantages of the vortex configuration. The work is supported by the French ANR project “SPINNET” ANR-18-CE24-0012.

**References:**

[1] D. C. Leitão et al., Nanotechnology 27, 045501 (2015) [2] L. Huang et al., Journal of Applied Physics 122, 113903 (2017); J. Moulin et al., Appl. Phys. Lett. 115, 122406 (2019) [3] D. Suess et al., Nat. Electronics 1, pages 362–370 (2018) [4] S. Wittrock et al., Phys. Rev. B 99, 235135 (2019) [5] A. S. Jenkins et al., Nat. Nanotech. 11, 360 (2016); D. Marković et al., Phys. Rev. Applied 13, 044050 (2020) [6] M. Romera et al., Nature 563, 230–234 (2018); J. Torrejon et al., Nature 547, 428-431 (2017) [7] A. Dussaux et al., Nat. Comm. 1, 8 (2010) [8] M. Jotta Garcia et al., arXiv:2012.09616 [cond-mat.mes-hall] (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f1e2a4020c2f2daf24d07405919ec60f.jpg)
Fig.1 a) Hooge parameter as a function of an in-plane magnetic field that is swept from the parallel to the anti-parallel state and back. b) Evolution of the Hooge parameter with the applied bias current. The inset shows the oscillation power of the rf emission due to the emerging vortex dynamics. The red dotted line represents the Hooge parameter measured in the AP state.

![](https://assets.underline.io/uploads/markdown_image/1/image/8659329698821b38c65d8cb8989eb4a3.jpg)
Fig. 2 a) Hooge parameter as a function of the frequency of the applied oscillating field, with Prf = 1 mW. The red line indicates the value measured in the absence of this field. b) Hooge parameter as a function of the power amplitude of the rf field at a fixed frequency, f = fres = 243.1 MHz. The green dotted lines represent the Hooge parameter measured in the P state.

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As the current recording media for the heat assisted magnetic recording (HAMR), the granular L10-FePt thin film needs to have uniform grain size with small pitch distance and well-defined grain boundaries. To achieve the targeted microstructure with proper L10 ordering using sputtering techniques, FePt along with grain boundary materials (segregants) are co-deposited on MgO underlayers at elevated temperature. The columnar growth of FePt is desired to have sufficient grain volume without grain size expansion. The fabrication of grains at small grain pitch with well-defined grain boundaries has been proven to be challenging.[1] Over the past decade, segregant materials, such as carbon, have attracted extensive attention for producing isolated FePt grains with well-defined grain boundaries but has experienced difficulty at reducing grain pitch distance and making grains with large aspect ratio. Though the columnar growth of FePt can be achieved by using some oxide segregant materials, such as TaOx[2] and TiOx[3], the resulting films always show poor L10 ordering and poor magnetic properties. Proper ordering of FePt can be achieved with SiOx[4], but the resulting microstructure tends to be maze-like. Therefore, exploiting multilayer deposition is a promising strategy to achieve the desired microstructure with proper ordering and magnetic properties. In this study, we utilize a dual-layer strategy of FePt-BN/FePt-SiOx on polycrystalline MgO underlayer in order to obtain the desired media microstructure with good L10 ordering and magnetic properties. The film stack of Ta(5)|Cr(40)|MgO(6)|Media(6.5) was deposited on Lotus NXT glass substrate with the numbers in parentheses in nm. Lotus NXT glass is one of the promising glass substrates for high-temperature deposition of HAMR media. The Ta and Cr layers were DC sputtered at room temperature and 280°C, respectively. The samples were subsequently annealed at 650°C for 1 hour in order to promote the texture and grain size of Cr buffer layer. The MgO underlayer was RF deposited on Cr buffer layer after the sample cooled down to room temperature. There are two magnetic layers in the media layer, where FePt was co-sputtered with BN and SiOx, respectively, for the first (M1) and the second (M2) magnetic layer. The deposition temperatures of the M1 layer and the M2 layer were fixed at 700°C and 550°C, respectively. From the microstructural point of view, the main objective of the M1 layer is to obtain well-isolated FePt grains to set the grain center-to-center pitch distance, whereas the M2 layer aims to suppress the lateral growth and to promote the columnar growth of the FePt grains. Fig. 1 (a) shows the in-plane HAADF image of the film stack Lotus NXT glass |Ta(5)|Cr(40)|MgO(6)|Media(6.5) with its (b) grain size distribution profile and (c) grain center-to-center pitch distance distribution profile. The figure demonstrates well-isolated FePt grains with mean grain size of 6.3 nm and mean pitch distance of 8.3 nm. As shown in the XRD pattern of this media in Fig. 1 (d), there are only (001) and (002) peaks from FePt, indicating the c-axis of FePt grains are predominantly perpendicular to the film plane. The broad peak at around 23.5° corresponds to the amorphous peak from Lotus NXT glass substrate. The order parameter (S) considering the relative integrated intensity ratio between (001) and (002), I001/I002, with the absorption factor and Lorentz factor is 0.7, suggesting good chemical ordering in FePt grains. Fig. 1 (e) shows the perpendicular and in-plane hysteresis loops of this media. The perpendicular coercivity (Hc⊥) is 26 kOe. The in-plane loop shows a small opening with the coercivity (Hc//) of 2.9 kOe and the normalized remanence magnetization (Mr//) of 0.08. The remanent ratio, which is Mr// /Mr⊥, is 0.09, suggesting a minor in-plane component of FePt grains in the sample. By exploiting the dual-layer structure of FePt-BN/FePt-SiOx, we have demonstrated well-isolated columnar FePt grains with small mean pitch distance of 8.3 nm. The XRD pattern shows that the grains are well-textured and highly ordered. As a result, the perpendicular coercivity reaches 26 kOe. The utilization of multilayer deposition strategy with segregants BN and SiOx provides a promising technique to achieve desired HAMR media microstructure without sacrificing FePt chemical ordering and magnetic properties.

**References:**

[1] Y. Kubota et al., IEEE Trans. Magn., vol. 54, no. 11, p. 3201206, 2018 [2] B. Lim et al., J. Appl. Phys., vol. 105, no. 7, p. 07A730, 2009 [3] B. S. D. C. S. Varaprasad et al., IEEE Trans. Magn., vol. 49, no. 2, p. 718–722, 2013 [4] H. Ho et al., Appl. Phys. Lett., vol. 102, no. 11, p. 112411, 2013

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/44d762af9dd6d7af7c27e30c471fccc1.jpg)
Fig. 1 (a) In-plane HAADF image of the film stack Lotus NXT glass |Ta(5)|Cr(40)|MgO(6)|FePt-38vol.% BN(2)|FePt-35vol.%SiOx with its corresponding (b) grain size distribution and (c) grain center-to-center pitch distance. Its XRD pattern and magnetic properties are in (d) and (e) respectively.

 Fabrication of FePt-BN/FePt-SiOx dual-layer structure for HAMR media on Corning Lotus™ NXT glass substrate

I. INTRODUCTION In recent years, spin-torque transfer magnetic random access memory (STT-MRAM) has received tremendous attention due to its low switching energy, fast read/write speed, and high scalability [1]. However, thermal fluctuation and process variation have a detrimental effect on the data recovery of STT-MRAM, leading to both read errors and write errors [2]. Error correction codes (ECCs), such as the Hamming codes and Bose-Chaudhuri-Hoquenghem (BCH) codes have been employed to improve the reliability of STT-MRAM [2, 3]. Meanwhile, the channel quantizer that quantizes the signal read back from the STT-MRAM cell is critical to support the above ECCs, since high-precision analog-to-digital converters (ADCs) are not applicable for STT-MRAM. Various criteria have been proposed for designing the quantizer for STT-MRAM, including the Maximizing-Mutual-Information (MMI) criterion, the Maximizing-Cutoff-Rate (MCR) criterion, and the Optimizing- Polyanskiy-Poor-Verdu -Bound (PPVB) criterion [4]. However, the final choice of the quantization scheme is still relying on the decoding error rate performance of ECCs. It is typically evaluated by using computer simulations, which are too slow to reach the target error rate level of 10-12 or below of data storage systems. In this work, we propose a union bound analysis which can accurately predict the word error rates (WERs) of ECCs with maximum-likelihood (ML) decoding over the quantized STT-MRAM channel. The derived bound provides a theoretical tool for comparing different quantization schemes at the targeted low error rate levels of data storage systems. Moreover, we also present a new criterion to design the quantizer by minimizing the WERs of ECC decoding that are obtained from the union bound analysis. Numerical results show that the union bound optimized quantizer can achieve better WER performance than the state-of-art quantizers for STT-MRAM. II. UNION BOUND ANALYSIS AND CHANNEL QUANTIZATION The union bound analysis is a theoretical technique that is used for bounding the error rate of ML decoding of ECCs. It was mainly developed for codes over symmetric channels [5]. In [6] and [7], more sophisticated union bound techniques were proposed for simple asymmetric channels, i.e. the Z-channel and the general binary asymmetric channel (BAC). In this work, we consider the quantized STT-MRAM channel with both write errors and read errors, which can be modelled as a concatenation of a BAC and a binary-input multiple-output discrete memoryless channel. Our proposed union bound analysis first utilizes a function of a predefined multi-dimensional distance between two codewords to calculate the pairwise error probability (PEP) [7] of the quantized STT-MRAM channel. Note that this is different from the cases of the symmetric channels where the PEP is uniquely determined by the Hamming distance of the code. Based on the PEP, we can derive a union bound of the WER of ML decoding as a function of the weight distributions of ECC. Next, we further propose to use the WER obtained from the above union bound analysis as the criterion to design the channel quantizer of STT-MRAM. We also develop effective differential evolution algorithm to determine the optimum quantization boundaries for the multi-bit quantizers. Since our proposed union bound optimized quantizer takes into consideration the weight spectrum of ECC, it can achieve better error rate performance than the prior-art quantizers. III. NUMERICAL AND SIMULATION RESULTS The system parameters of STT-MRAM are taken from [2]. In the quantized STT-MRAM channel model, we assume the write error rate of 10-5, and vary the mean normalized resistance spreads σ0/μ0=σ1/μ1 of the low and high resistances to account for the influence of different process variations. The (72,64) extended Hamming code [3] is adopted to validate our analysis, and the simulated ML decoding performance is obtained using the Bahl, Cocke, Jelinek and Raviv (BCJR) decoder [5]. In Fig.1, we compare the decoding WERs provided by the union bound with those achieved by the BCJR decoder through simulations, with the proposed union bound optimized quantizer with different number of quantization bits q. Observe that there is a noticeable gap between the union bound and simulated WERs for the case of q=1. However, with two or more quantization bits, the performance gap becomes negligible, and when the WER is less than 10-6, the union bound is almost identical to the simulated WER. In Fig. 2, we fix the quantization bit to be q=2, and compare the WER performance with different types of quantizers. A nice agreement is observed again between the WERs predicted by the union bound and those obtained from simulations, for the various types of quantizers. Moreover, our proposed union bound optimized quantizer outperforms all the other quantizers. There is a larger performance improvement over the MMI quantizer, which is most widely adopted in the literature. This demonstrates the potential of our proposed union bound analysis in predicting the decoding error rate performance and in guiding the design of channel quantizer for STT-MRAM. Acknowledgement: This work is supported by RIE2020 Advanced Manufacturing and Engineering (AME) programmatic grant A18A6b0057 and Singapore MOE Tier 2 fund MOE2019-T2-2-123.

**References:**

[1] M. Marinella, “The future of memory,” in Proc. Aerospace Conf, Big Sky, MN, USA, Mar. 2012, pp. 1–11. [2] K. Cai, and K. A. S. Immink, “Cascaded channel modeling, analysis, and hybrid decoding for spin-torque transfer magnetic random access memory (STT-MRAM),” IEEE Trans. Magn., vol. 53, no. 11, pp. 1–11, 2017. [3] K. Cai, Z. Qin, and B. Chen, “Channel capacity and soft-decision decoding of LDPC codes for spin-torque transfer magnetic random access memory (STT-MRAM),” in Proc. Int. Conf. Comput., Netw., Commun. (ICNC), San Diego, CA, USA, Jan. 2013, pp. 550–554. [4] Z. Mei, K. Cai and L. Shi, “Information Theoretic Bounds Based Channel Quantization Design for Emerging Memories,” in Proc. IEEE Information Theory Workshop (ITW), Guang Zhou, China, Nov. 2018, pp. 1–5. [5]W. E. Ryan and S. Lin, Channel Codes: Classical and Modern, Cambridge, Cambridge University Press, 2009. [6] A. Barbero, P. Ellingsen, S. Spinsante, and O. Ytrehus, “Maximum likelihood decoding of codes on the Z-channel,” in Proc. IEEE International Conference on Communications (ICC), Istanbul, Turkey, Jun. 2006, pp. 1–5. [7] G. Song, K. Cai and J. Cheng, “A union bound analysis for codes over binary asymmetric channels,” in Proc. IEEE International Conference on Communications (ICC), Paris, France, May. 2017, pp. 1–5.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7687adc035569fbf9f2d0102c1f4556f.jpg)
Fig. 1. Comparison between analytical and simulation WERs, with union bound optimized quantizer with q= 1,2,3.

![](https://assets.underline.io/uploads/markdown_image/1/image/ff97a646ffd6d77b07f4e57f875be682.jpg)
Fig. 2. Comparison between analytical and simulation WERs with different types of quantizers, for q=2.

 Union Bound Analysis for Spin-Torque Transfer Magnetic Random Access Memory with Channel Quantization

Two-dimensional magnetic recording (TDMR) with laterally-displaced multiple read heads has been developed to alleviate the impact of inter-track interference (ITI) and track edge effects. However, the cross-track (XT) position of the displaced 2nd head varies significantly with the skew angle of head assembly from ID to OD across disk radius [1]. As a result, each disk platter is divided into hundreds of groups of sectors, or zones, to accommodate the skew angle variations. The 2-dimentional equalization technique used in conventional data detection channels requires different channel parameters at different skew angles/zones for channel optimization, and the number of different channel parameter sets across the disk platter are in hundreds. Furthermore, resulting performance gain is further diminished by random fluctuations such as non-repeatable disk runout. In this situation, if we employ machine learning technique on TDMR data detection, one could imagine the possibility of achieving optimal performance in resolving ITI and track edge effects across the entire disk surface while using “learning” to replace relatively complex parameterization of physical modeling. In our previous work, we have developed deep neural network (DNN) for disk drive data detection channels with performance (detection error-rate vs. signal-to-noise ratio) slightly more superior than the state-of-the-art disk drive channels [2,3]. In the work presented here, we train a convolution neural network (CNN) in TDMR system to detect data under a wide range of ITI from different head skew angles. We demonstrate that in the medium noise dominant situation, CNN can learn all ITI in the training dataset and completely recover ITI-free BER without any physical modeling. Our eventual goal is to explore if we can train a single CNN detector to learn and optimize for all head skew angles/zones automatically, thereby lifting the complexity of designing different channel parameter sets at each head skew angle. The recorded tracks and CNN detection scheme are shown in Fig. 1. Two adjacent data tracks are written with random data and arbitrary phase. The width of the track is denoted TW, and no erase-band nor transition curvature is included. Two XT overlapped heads of width greater than TW are used. Here we simplify the modeling and assume each head only captures signals under its XT coverage. Since the relative positions of head-1 and head-2 are locked, we characterize ITI of the reader array with a single variable: the ratio between head-1 coverage of Track-II (Δx1) versus the track width (TW): δ1=Δx1/TW. Here we assume the ITI stays fixed within each zone, and different zones will have different ITI. In this work, we only investigate the medium noise dominated situation: the jitter noise is modeled as the uncertainty of the transition locations following a Gaussian distribution. Since both heads “see” the same magnetic patterns from the two tracks, the jitter noise is correlated noise. A CNN is used as the data detector in this work. It receives signals from both heads as input, and we only train it to detect data for Track-I. The rest of the parameters are listed in Fig. 1 caption. To simulate reading data at different skew angles, we evaluate the CNN detection BER with signals of 11 different ITI from δ1=0.2 to 0.8 as in Fig. 2. The black dashed line benchmarks the ITI-free BER. For the blue curve, the CNN detector is trained using signals from one skew angle/zone with a fixed ITI, δ1=0.5 . In this case, CNN can only eliminate the trained ITI, and the detection accuracy degrades significantly whenever the testing ITI is different. In contrast, the red curve plots the BER when we train the CNN using signals with mixed ITI same as the testing dataset. This time CNN can successfully eliminate ITI for all testing head skew angles/zones. Our results suggest that CNN has the capacity to learn very complicated correlations and is solely data-driven. With the learning process, the CNN-based ML channel presented here is capable of resolving the interference from ITI infested signals, automatically rejecting them, and arriving at correct detection. This approach is fundamentally different from the conventional channel design that relies on sophisticated physical modeling and channel parametrization. In addition, the fact that a single CNN can learn a wide range of ITI states that it can optimize the channel performance for head skew angles using a single CNN eliminating the need to use multiple channel parameter sets. Not only this machine learning channel can eliminate the complex physical characterization process required for conventional approach, more importantly, the TDMR performance gain can be fully realized without compromising. The potential of fully eliminating ITI also presents the possibility to have reader width wider than track width which could be critically important as track pitches in HDDs continue to decrease.

**References:**

[1] Suzuto R, Nakamura Y, Osawa H, et al. Effect of reader sensitivity rotation in TDMR with head skew. IEEE Transactions on Magnetics, 2016, 52(7): 1-4. [2] Qin Y, Zhu J G. Deep Neural Network: Data Detection Channel for Hard Disk Drives by Learning. IEEE Transactions on Magnetics, 2020, 56(2): 1-8. [3] Qin Y, Zhu J G. Automatically Resolving Inter-Track Interference with Convolution Neural Network Detection Channel in TDMR. IEEE Transactions on Magnetics, 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1636e831501326557b33b2a856085d21.jpg)
CNN detector in TDMR. The heads have DT sensitivity of PW50/bit-length = 2.5. The green(yellow) signals are from head-1(head-2), and they are sampled 1 bit/period. The jitter width is assumed 1.4nm in this work. The CNN channel has 3 hidden layers (blue) with 50 filters each. The kernel sizes are 3-3-3-1. ReLU is used as the non-linear activation function, and cross-entropy is the loss function.

![](https://assets.underline.io/uploads/markdown_image/1/image/3a69ad272e492b195d37c70a85e1048b.jpg)
Detection BER at different zone/ITI. Black dashed curve: ITI-free detection BER. Blue: CNN is only trained with signals of fixed ITI δ1=0.5 . Red: CNN is trained with signals with 11 different ITI (same as the testing dataset).

 Enable TDMR Gain with Convolution Neural Network Based Machine Learning Algorithm

I. Introduction Track misregistration (TMR) and two-dimensional (2-D) interference that consists of an inter-track interference (ITI) and inter-symbol interference (ISI) are the significant problems in an ultra-high bit-patterned media recording system (BPMR) which easily degrade the bit-error-rate (BER) performance of the system, because of the extremely narrow distance between bit-islands. It very challenges to control the reader to fly above the center of the desired track. Normally the TMR effect can be controlled by servomechanism [1] which required extra area to store the redundancy bits for tracking the data track. Instead, several works use only readback signals to estimate and correct the TMR effect [2-4]. For example, we proposed a TMR prediction method by using the energy ratio of readback signals, and then the TMR effect can be dealt with utilizing the appropriate 2-D equalizers together with the use of soft-information adjustment (SIA) technique [5]. II. Proposed Methods To improve the TMR estimation accuracy and BER performances of BPMR system; therefore, we propose to use the neural network models called a multi-layer perceptron (MLP) in both TMR level prediction and TMR effect correction processes. We consider the dual-reader two-track reading under BPMR media at an areal density (AD) of 3.0 Tbits/in2, which track-pitch, Tz and bit-period, Tx are set to be 14.5 nm. In the reading process, 2 readers simultaneously read the medium of upper- and lower-tracks, while the sidetracks located above and below two main tracks will be also read, which denoted as r-1,k, r0,k, r1,k, and r2,k. Then, 4 readback signals are equalized by 1-D (one-dimensional) equalizers which are designed according to signal with no TMR effect. The equalized data sequences will then be multiplied with their absolute value for each data sample to extend their amplitude before sending them to the TMR level prediction and TMR effect correction processes, respectively. In TMR level prediction, four modified readback signals, u-1,k, u0,k, u1,k, and u2,k with the size of 4×32,760 bits will then be grouped into 4×3 bits in each group before sending to the TMR level prediction process. That means each considered group consists of 12 data bits and so there are 10,920 groups in one set of readback sequence, the number group represented by j ∈ {1, 2, 3, …, 10920}. Fig. 1(a) shows the structure of the MLP TMR estimator which consists of 1 input layer and 12 input nodes, 5 hidden layers consist of 100 hidden nodes, and 1 output layer with a single node. This MLP TMR estimator receives a group of readback signals at a time for predicting the estimated TMR level, TMR'j of the jth group. Then, the estimated TMR levels of all groups were averaged to obtain the estimated TMR level, TMR' of the entire sequence. Here, the accuracy percentage of TMR' is measured as accuracy (%) = 100 – (|TMR'-TMR| / TMR × 100) [5]. we also propose to use the MLP data detector which may be employed instead of the conventional detectors-based PRML system. Fig. 1(b) shows the structure of the MLP data detector, which is identical to MLP TMR estimator except for the number of input and output nodes. The MLP data detector receives a group of modified readbacks similar to the MLP TMR estimator, but it also receives an additional estimated TMR level, TMR' that was produced from MLP TMR estimator. Here, it is fixed as one of the input data of the MLP data detector. Finally, we can obtain the estimated user bits of both upper- and lower-tracks, i.e., a'0,k and a'1,k, in the size of 2×3 bits for all 10,920 groups. In this study, the leaky rectified linear unit (ReLU) is used as an activation function for the hidden nodes and linear function in the output nodes for both MLP models. The linear regressions are then adopted for calculating their outputs. The Adam algorithm is used to optimize the weights and bias of both MLP models. III. Results and Discussion In this study, we start with the consideration of an accuracy percentage of TMR level estimation in various TMR and SNR levels where the position jitter is given to be 0%. The TMR level is varied from 0% to 15% of a track pitch as mentioned above. The signal-to-noise ratio (SNR) that is defined as 10log10(1/σ2), where σ is a standard deviation of electronics noise, is first considered at 10, 15, 20, and 25 dBs. We found that the proposed MLP TMR estimator can provide an accuracy percentage higher than 80% for all 4 considered SNRs and all considered TMR levels. Especially, at the higher SNR, e.g., 15, 20, and 25 dBs, we can get more than 90% accuracy for all TMR levels. Moreover, we also investigate the BER of our proposed MLP detector, which is compared with the convention partial response maximum likelihood (PRML) system that performs based on 2-D equalizers and 2-D Viterbi detectors together with the SIA technique [5] where it is represented with “conventional”. As shown in Fig. 2, it seems that at higher SNR, our proposed system can provide better performances for all TMR levels. For example, at BER = 10-4 and TMR level is 0%, our proposed system can provide more than 5 dB over the conventional system. The system performance implies that it is possible to use the MLP neural networks for signal processing in BPMR system.

**References:**

[1] Y. B. Chang, D. K. Park, and N. C. Park, IEEE Trans. Magn., Vol. 38, no. 2, p. 1441 (2002) [2] C. Warisarn, IEEE Trans. on Magn., Vol. 55, no. 7, p. 1 (2019) [3] W. Busyatras, C. Warisarn, and Y. Okamoto, AIP Adv., Vol. 7, p. 056501 (2016) [4] S. Han, G. Kong, and S. Choi, IEEE Transactions on Magnetics, Vol. 55, no. 7, p. 1 (2019) [5] K. Kankhunthod, W. Busyatras, and C. Warisarn, 17th ECTI-CON., p. 735 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/09de0a5a9c8f4396146c47ebd77277d5.jpg)
Fig. 1: MLP structures of the TMR level estimator and TMR detector.

![](https://assets.underline.io/uploads/markdown_image/1/image/fd1a13ccd5cbab14c903baba723d02af.jpg)
Fig. 2: BER performance comparison between the proposed MLP based TMR correction method versus the conventional method at the AD of 3.0 Tbits/in2, here the position jitter is fixed to be 0%.

 Multilayer Perceptron Based Method for Track Misregistration Correcting in Dual-reader Two-track Reading BPMR Systems

I. INTRODUCTION In the head-disk interface (HDI) of heat-assisted magnetic recording (HAMR), a laser is employed over the read/write area to locally heat the recording media to its Curie temperature to facilitate data writing. During this process, the lubricant on the disk undergoes harsh cyclic thermal processes so that the lubricant is partially depleted by the laser [1]. Thus, the lubricant thickness is locally reduced during the writing, but afterwards it recovers gradually due to lubricant reflow [2]. In this study, the effect of the lubricant thickness on the nanoscale heat transfer across the HDI is studied using a thermal fly-height control (TFC) heater and an embedded contact sensor (ECS). The dR/dP, the rate of change in the ECS resistance with respect to the TFC power, was measured to indicate the HDI heat transfer coefficient [3]. It is demonstrated that the ECS is a good thermal sensor for the lubricant thickness through the contact cooling effect. II. EXPERIMENT SETUP Experiments were performed on a component-level spin-stand stage. When flying over the HAMR disks with the lubricant thickness from 8.0 Å to 12.5 Å, the TFC heater was energized until head-disk touchdown occurred. During the touchdown process, the ECS, biased with a constant DC current, was used to monitor the head temperature. An acoustic emission (AE) sensor was used to detect the head-disk contact. The ECS resistance versus the TFC power relation (R-P) was measured. Then the R-P curve’s derivative, dR/dP, was obtained to indicate the head-disk nanoscale heat transfer. III. RESULTS AND DISCUSSION Fig. 1 shows the results of dR/dP versus backoff TFC power using different ECS bias currents, where zero backoff power is the TFC power at the head-disk contact onset detected by the AE sensor. The figure presents the contact cooling effect around +1 mW backoff TFC power, which appears as the local minimum. It is seen from the figure that the cooling effect is stronger with a higher ECS bias current, since the hotter ECS undergoes a larger temperature drop when touching the rotating disk surface. Thus, the ECS biased with a higher current delivers better sensitivity for the experiments. Fig. 2 shows the dR/dP curves for the disks with the lubricant thickness varying from 8.0 Å to 12.5 Å. As the lubricant thickness increases, the dR/dP local minimum rises and hence the contact cooling effect weakens. Therefore, the lubricant behaves as a thermal barrier to the head-disk heat transfer and its effect can be quantified by the ECS. IV. CONCLUSIONS In this digest, touchdown experiments are introduced to quantify the effect of the lubricant on the nanoscale heat transfer at the head-disk interface. The experimental results show that a higher ECS bias current ensures a better sensitivity for the experiments and that the lubricant layer weakens the head-disk heat transfer. Taking advantage of this effect, the ECS can be further used to measure the local lubricant thickness depletion and reflow during HAMR operations.

**References:**

[1] M. Kryder, E. Gage, T. McDaniel, Proc. IEEE, 96(11), 1810-1835 (2008). [2] H. Wu, A. Mendez, S. Xiong, J. Appl. Phys., 117(17), 17E310 (2015). [3] N. Zuckerman, J. Kiely, M. Anaya-Dufresne, IEEE Trans. Magn., 55(3), 1-5 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/90768b5c5efe6453870c0a23b326801e.jpg)
Fig. 1. The dRdP versus backoff TFC power using different ECS bias currents.

![](https://assets.underline.io/uploads/markdown_image/1/image/3d1ddabf5d889ce0eb44baa841bc9121.jpg)
Fig. 2. The dRdP versus backoff TFC power using different lubricant thicknesses (ECS bias: 2.50 mA).

 Effect of Lubricant Thickness on the Nanoscale Heat Transfer at the Head-Disk Interface

The current exponential growth in data in combination with the slow-down in areal density and cost scaling of hard disk drives (HDDs) is fueling demand for cost effective storage technology. Magnetic tape storage has a very low total cost of ownership and is suited for the storage of less frequently accessed data where tape's higher access latency is an acceptable trade-off for the reduced cost. Today's best of breed tape drives provide a 20 TB native cartridge capacity at an areal density of 11.7 Gbit/in2. This is about two orders of magnitude lower than the areal density of state-of-the-art HDDs and implies that tape has significant potential for continued scaling. This is in line with the projections of the Information Storage Industry Consortium (INSIC) Tape Roadmap that projects a 34% annual growth in tape areal density leading to a predicted 278 Gb/in2 in 2029 [1]. In this work we describe a tape areal density demonstration using a prototype perpendicularly oriented strontium ferrite (SrFe) tape that shows the potential of recording at 317 Gbit/in2. Key properties of the media include: a particle volume of 950 nm3, a particle coercivity of Hc=208 kA/m, a perpendicular squareness ratio of 0.87, a surface roughness Ra=1.1 nm and Rz=17 nm measured by AFM, and a tape thickness of 4.3 μm. We investigated the recording potential of the SrFe media by writing repeating 255-bit pseudo-random binary sequences (PRBS) at linear densities ranging from 500 to 768 kbpi. The data was read back using a 29 nm side shielded tunneling magneto resistive (TMR) reader from an HDD and the captured readback signal was processed offline using a software read channel. Fig. 1(a) shows the average SNR of the captured data measured at the input of an EPR4 detector and plotted versus linear density. Fig. 1(b) plots the byte-error rate (BER) versus linear density, obtained by processing the data using three detection algorithms: 1) 8-state EPR4 detection, 2) adaptive 16-state noise-predictive maximum-likelihood (NPML) detection and 3) extended 64-state data-dependent NPML detection that tracks the first and second order statistics of the data-dependent noise (D3-NPML). Each data point results from processing about five million bits. To set a target threshold for the BER at the output of the detector, we analyzed the performance of the Reed-Solomon product code used in state-of-the-art tape drives combined with the iterative decoding scheme described in [2]. This analysis indicates a post-error-correction-coding byte-error rate (UBER) of less than 1e-20, equivalent to that of an enterprise class tape drive, can be achieved with two full decoding iterations if the BER at the output of the detector is &lt; 4.5e-2. Hence, we take a BER &lt; 4.5e-2 as the target threshold. The D3-NPML detector provides significantly better performance than the NPML detector and crosses the BER threshold of 4.5e-2 at a linear density of 750 kbpi. At a linear density of 702 kbpi the D3-NPML detector provides a BER of 2.8e-2 and the NPML detector also has a BER performance below the target threshold. The average SNR at 750 kbpi and 702 kpbi are 9.9 dB and 10.6 dB, respectively. Thus, the D3-NPML detector achieves our target 1e-20 UBER at an operating point of 702 kbpi with an SNR margin of about 0.7 dB. In the area of track following, we made a set of advances to enable the rapid track-density scaling projections of the INSIC roadmap. First, we developed a new timing-based servo pattern that is shown in Fig. 2(a). Second, we developed a field programmable gate array prototyping board that implements four servo channels and a quad channel averaging scheme where the tape head position is calculated by combining position estimates from the readback signals of four servo patterns, see Fig. 2(b). Third, we enhanced the tape transport described in [2] with two 20 mm diameter air bearing tape guides and a prototype track-following actuator that enables a lower spacing between the tape guides adjacent to the head. This decreased tape guide spacing reduces compressional wave disturbances that can degrade the track-following performance. Fourth, we developed a low friction tape head that reduces friction by about 75% compared to the heads used in our previous work [2],[3] and further reduces compressional wave disturbances. Finally, we used the H-infinity framework to design a set of tape velocity optimized track-following controllers. Combining these technologies, we achieved a position error signal (PES) characterized by its standard deviation of σPES ≤ 3.18 nm over the tape velocity range of 1.2 to 4.1 m/s as shown in Fig. 2(c). We estimate the minimum reliable track width supported by this tracking accuracy with the INSIC model used in our previous work [2], [3], i.e.: track width = 2 x (2)0.5 x 3σPES + reader width. Taking the 29nm width of the reader used for the recording experiments and a worst case σPES = 3.2 nm results in a 56.2 nm track width and a track density of 451.9 ktpi. Combined with the linear density of 702 kbpi demonstrated with the 29 nm reader enables a potential areal recording density of 317 Gb/in2.

**References:**

[1] Information Storage Industry Consortium (INSIC) 2019-2029 Tape Roadmap, http://www.insic.org/wp-content/uploads/2019/07/INSIC-Technology-Roadmap-2019.pdf [2] S. Furrer et al., "85.9 Gb/in2 recording areal density on barium ferrite tape ", IEEE Trans. Magn., vol. 51, no. 4, Apr. 2015, Art. ID 3100207. [3] M. A. Lantz et al., "123 Gb/in2 recording areal density on barium ferrite tape ", IEEE Trans. Magn., vol. 51, no. 11, Nov. 2015, Art. ID 3101304.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ea49499647aa7c96c27439679edc4096.jpg)
Fig 1. (a) SNR vs. linear density, (b) BER vs. linear density for three detectors. The dashed line in the BER plot indicates the 4.5e-2 target byte-error rate threshold.

![](https://assets.underline.io/uploads/markdown_image/1/image/1705d36ba0e3724ce22ce7522c845fd5.jpg)
Fig 2. (a) Geometry of the new servo pattern, (b) Read back signals from four servo tracks formatted with the new servo pattern, at 2.15m/s tape velocity, (c) Standard deviation of the PES versus tape velocity.

 317 Gb/in2 Recording Areal Density on Strontium Ferrite Tape INVITED

Introduction and Background 60 Zettabytes (ZB or 10^21 Bytes) will be created in 2021 and grow to 160 ZB by 2025.(1) To store this data, Hard Disk Drives (HDD) areal density must continue to increase from current products near 1.1Tbpsi (2) to the demonstrated AD of 2.77Tbpsi (3) and beyond. To support this growth, reader technology must also advance to higher AD with manufacturable solutions. Remarkably, HDD reader technology still utilizes the Spin Valve reader concept that was first introduced in 1997 at ~ 1 Gbpsi. This 1000x increase in reader AD capability has been achieved by scaling of critical dimensions, the introduction of TMR, advances in stack materials/ processing and utilization of multiple read sensors. The extendibility of the SV TMR design and supporting innovations has been remarkable - but likely not without limits. The HDD industry’s Advanced Storage Research Consortium (ASRC, http://asrc.idema.org/) has sought to understand and address read sensor requirements for HDD Areal Densities (AD) up to 4Tbpsi and higher. In this paper we release the ASRC reader roadmap. We identify critical challenges and key gaps for the SV TMR type reader to support 4Tbpsi. We then outline what may be required for &gt; 4Tbpsi and explore how to proceed. Approach and Methods We begin by seeking to understand the potential extendibility of the Reader Spin Valve design with TMR stack. We partition the problem between Resolution and SNR. Multiple reader design geometries are considered. (Figure 1.) The reader design resolution capabilities were determined using a new 2D micromagnetic reciprocity approach. The Bottom SV and derivative Recessed AFM design appear to be sufficient for 4Tbpsi. To understand the reader SNR requirements, one must begin with the recorded data that one needs to readback. A top-down system level approach and bottom-up micromagnetic modeling approach are combined and iterated to identify the suitable reader requirements. A RSS model is used to estimate reader requirements between 2 and 6 Tbpsi.(4) A combined finite difference micromagnetic model and analytical reader signal-noise model is used to perform DOE’s to determine the closest fit solutions. Results and Discussion The results of this study show that reader widths must shrink to near 10nm and shield-to-shield spacing approach 15nm to provide cross-track and down-track resolution to support track densities near 1130 kTPI and linear densities &gt; 3600 kFCI for ~ 4Tbpsi. Meeting these targets will demand improved process capabilities and new innovations in device designs. SNR requirements are used to project TMR reader stack magnetoresistance (MR) and resistance-area (RA) product targets. Within reasonable assumptions for sensor bias, stability and material properties, we show stack requirements are well in excess of 100% MR at 0.10 uOhm-cm RA. (Figure 2) This requirement is significantly more challenging than previously projected and exceeds best reports to date for TMR readers (5). In addition to seeking high signal, it is also vital to understand and manage the noise components. We show thermal magnetic noise is a growing concern but we further show that other contributions such as preamp noise could dominate as reader dimensions shrink and resistance grows. Roadmap Challenges and Gaps An overall reader spec is provided with proposed geometric, magnetic, and electronic targets. We also explore potential future designs to meet requirements &gt; 4Tbpsi. A summary of key issues, possible solutions and important research topics is reviewed. We hope this study can illuminate and motivate critical research into these key reader technologies. Meeting these challenges will be critical to continued HDD AD growth to 4Tbpsi and beyond.

**References:**

 1) Data Age 2025, Dec 2018 https://www.seagate.com/our-story/data-age-2025/ 2) Forbes, July 2020 https://www.forbes.com/sites/tomcoughlin/2020/07/08/western-digital-data-center-16-20-tb-hdds/?sh=4f56c3f87ba9 3) TMRC 2020, Paper A7, S. Grantz et al, "Heat Assisted Magnetic Recording Dependence on Reader for Conventional and Shingled Magnetic Recording" see https://blog.seagate.com/enterprises/energy-assisted-magnetic-recording-will-solve-the-need-for-capacity/ 4) S. Hernandez, et. al, "Geometrical Scaling Limits of Heat-Assisted Magnetic Recording", IEEE Trans. Magn., 2020 (accepted). 5) Nakatani et al, “Read sensor technology for ultrahigh density magnetic recording” MRS Bulletin 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f9d9c340bac329ce8b71e72a67697970.jpg)
A range of reader designs were considered to satisfy the down-track and cross-track resolution requirements. The Bottom SV and derivative Recessed AFM design may be sufficient near 4Tbpsi.

![](https://assets.underline.io/uploads/markdown_image/1/image/0ed76210a04117fadf5171ea35378555.jpg)
Reader stack requirements at 4Tbpsi for BAR 2.4 (left) and 3.2 (right). MR requirement varies with free layer damping constant alpha as illustrated. The best fit is shown by design point circle on graph .

 HDD Reader Technology Roadmap to an Areal Density of 4 Tbpsi and Beyond INVITED

The development of high-density magnetic recording media is limited by the superparamagnetism in very small ferromagnetic crystals. Hard magnetic materials with strong perpendicular anisotropy offer stability and high recording density. To overcome the difficulty of writing media with a large coercivity, heat assisted magnetic recording (HAMR) has been developed, rapidly heating the media to the Curie temperature Tc before writing, followed by rapid cooling. Requirements are a suitable Tc, coupled with anisotropic thermal conductivity and hard magnetic properties. Here we introduce Rh2CoSb as a new hard magnet with potential for thin film magnetic recording. A magnetocrystalline anisotropy of 3.6 MJm-3 is combined with a saturation magnetization of μ0Ms = 0.52 T at 2 K (2.2 MJm-3 and 0.44 T at room-temperature). The magnetic hardness parameter of 3.7 at room temperature is the highest observed for any rare-earth free hard magnet. The anisotropy is related to an unquenched orbital moment of 0.42 µB on Co, which is hybridized with neighbouring Rh atoms with a large spin-orbit interaction. Moreover, the pronounced temperature-dependence of the anisotropy that follows from its Tc of 450 K, together with a high thermal conductivity of 20 Wm-1K-1, makes Rh2CoSb a candidate for development for heat assisted writing with a recording density in excess of 10 Tb/in2.

**References:**

Adv. Mater. 2020, 32, 2004331

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e4f78a1c92343bbb531bc8b98bb97109.png)
Magnetic properties of Rh2CoSb.

![](https://assets.underline.io/uploads/markdown_image/1/image/bd747b83e3690c6f8fce758097e85b48.png)
Comparison of the magnetic hardness parameter κ with other hard magnets.

 New Highly-Anisotropic Rh-Based Heusler Compound for Magnetic Recording New Highly-Anisotropic Rh-Based Heusler Compound for Magnetic Recording

Magnetic field sensors in a rigid format have been typically associated with recording heads, hard disk drives and the automotive industry. Unlocking new application scenarios requires changing the intrinsic properties of these sensors to make them adaptable to new challenges. One way to accomplish this goal, is to allow these sensors to change shape and be flexible, stretchable or solution-processable, what we call shapeable magnetoelectronics [1]. This technology relies on the smart combination of inorganic thin films prepared directly on flexible or elastomeric substrates. Shapeable magnetoelectronics resulted from the cooperative effort of fundamental and application-oriented communities in the field of curvilinear magnetism [2], and the involvement of fabrication methods for flexible electronics [3], [4]. The combination of these research fields has resulted in a variety of flexible [5], [6], printable [7]–[9], stretchable [10]–[12] and imperceptible17,35–37 magnetic field sensing elements. Stemming from these developments, various applications like automotive [19], consumer electronics and point of care [6], [13], [14], and virtual reality [15]–[17], have emerged. For automotive purposes, shapeable magnetic sensors can be useful to monitor the magnetic field profile the nonplanar and narrow gaps inside electrical motors, to minimize losses and improve the overall efficiency [5]. In point-of-care applications, they can enable fast biosensing methods for wearable health monitoring based on magnetofluidics [6], [13]. For virtual reality they allow a whole new set of touchless interaction possibilities using the ambient magnetic fields as input stimuli [15]–[17]. One example of this application is an on-skin sensor, which can dim the intensity of a virtual lightbulb based on the relative angle between the sensor and the magnetic field of a permanent magnet [16]. This idea was further improved to remove the need for permanent magnets and instead use the earth’s magnetic field as input stimulus. Reaching this level of sensitivity required the use of barber pole [18] modified anisotropic magnetoresistive (AMR) sensors, which allowed detecting magnetic fields of µT with a flexible on-skin patch. Aside from enable artificial magnetoception, the patch can be used as an interactive device for virtual reality which only uses the geomagnetic field [15] (Fig. 1). Further works have improved the sensitivity to about 200 nT, which could have applications for highly sensitive point-of-care devices [14]. In recent works, we have demonstrated shapeable magnetoelectronics which are multimodal, so that they transduce and discriminate both tactile (via mechanical pressure) and touchless (via magnetic field) stimuli in real time [17]. Such a feat is attained by fabricating a magnetic microelectromechanical platform (m-MEMS), which combines flexible magnets based on polymer composites and mechanically compliant magnetic sensors. These m-MEMS e-skins enable complex interactions with magnetically functionalized objects in the real world, which supplement the content data appearing in virtual reality. For example, an augmented reality menu with multiple layers of interaction can be operated with one single sensor using its embedded multidimensional touch (Fig. 2, top). A challenging aspect for shapeable magnetoelectronics is the fact that output signals are usually amplified by rigid components outside the flexible supports. This readout scheme can introduce substantial noise through the cabling which is then amplified together with the signals. Eliminating this noise requires including amplifying elements directly on the flexible support, which implies using intrinsically flexible, thin-film transistor technologies. We have demonstrated such an approach, by combining highly sensitive magnetic field sensorics with high performance InGaZnO based readout electronics, on the same flexible support [19] (Fig. 2, bottom). Although entirely flexible, this platform outperforms commercial rigid magnetic sensor systems in responsivity by at least one order of magnitude. This noteworthy performance is achieved by designing a giant magnetoresistive sensor bridge connected to a cascade of differential and power amplifiers acting as readout circuity. Combining all these features in robust on-skin devices will propel this field beyond exploratory research and towards full-fledged applications, where shapeable magnetic sensors can be crucial for maximizing device performance.

**References:**

[1] D. Makarov, M. Melzer, D. Karnaushenko, and O. G. Schmidt, “Shapeable magnetoelectronics,” Applied Physics Reviews, vol. 3, no. 1, p. 011101, Mar. 2016, doi: 10.1063/1.4938497. [2] R. Streubel et al., “Magnetism in curved geometries,” J. Phys. D: Appl. Phys., vol. 49, no. 36, p. 363001, Aug. 2016, doi: 10.1088/1751-8113/48/12/125202. [3] S. Huang, Y. Liu, Y. Zhao, Z. Ren, and C. F. Guo, “Flexible Electronics: Stretchable Electrodes and Their Future,” Advanced Functional Materials, vol. 29, no. 6, p. 1805924, 2019, doi: https://doi.org/10.1002/adfm.201805924. [4] Y. Liu, M. Pharr, and G. A. Salvatore, “Lab-on-Skin: A Review of Flexible and Stretchable Electronics for Wearable Health Monitoring,” ACS Nano, vol. 11, no. 10, pp. 9614–9635, Oct. 2017, doi: 10.1021/acsnano.7b04898. [5] M. Melzer et al., “Wearable Magnetic Field Sensors for Flexible Electronics,” Advanced Materials, vol. 27, no. 7, pp. 1274–1280, Feb. 2015, doi: 10.1002/adma.201405027. [6] G. Lin, D. Makarov, M. Melzer, W. Si, C. Yan, and O. G. Schmidt, “A highly flexible and compact magnetoresistive analytic device,” Lab Chip, vol. 14, no. 20, pp. 4050–4058, 2014, doi: 10.1039/C4LC00751D. [7] D. Karnaushenko, D. Makarov, C. Yan, R. Streubel, and O. G. Schmidt, “Printable Giant Magnetoresistive Devices,” Advanced Materials, vol. 24, no. 33, pp. 4518–4522, Aug. 2012, doi: 10.1002/adma.201201190. [8] D. Karnaushenko, D. Makarov, M. Stöber, D. D. Karnaushenko, S. Baunack, and O. G. Schmidt, “High-Performance Magnetic Sensorics for Printable and Flexible Electronics,” Adv. Mater., vol. 27, no. 5, pp. 880–885, Feb. 2015, doi: 10.1002/adma.201403907. [9] D. Makarov, D. Karnaushenko, and O. G. Schmidt, “Printable Magnetoelectronics,” ChemPhysChem, vol. 14, no. 9, pp. 1771–1776, 2013, doi: 10.1002/cphc.201300162. [10] M. Melzer et al., “Stretchable Magnetoelectronics,” Nano Letters, vol. 11, no. 6, pp. 2522–2526, Jun. 2011, doi: 10.1021/nl201108b. [11] M. Melzer, D. Karnaushenko, G. Lin, S. Baunack, D. Makarov, and O. G. Schmidt, “Direct Transfer of Magnetic Sensor Devices to Elastomeric Supports for Stretchable Electronics,” Advanced Materials, vol. 27, no. 8, pp. 1333–1338, Feb. 2015, doi: 10.1002/adma.201403998. [12] M. Melzer, D. Makarov, and O. G. Schmidt, “A review on stretchable magnetic field sensorics,” J. Phys. D: Appl. Phys., vol. 53, no. 8, p. 083002, Feb. 2020, doi: 10.1088/1361-6463/ab52cf. [13] G. Lin, D. Makarov, and O. G. Schmidt, “Magnetic sensing platform technologies for biomedical applications,” Lab Chip, vol. 17, no. 11, pp. 1884–1912, May 2017, doi: 10.1039/C7LC00026J. [14] P. N. Granell et al., “Highly compliant planar Hall effect sensor with sub 200 nT sensitivity,” npj Flexible Electronics, vol. 3, no. 1, p. 3, Feb. 2019, doi: 10.1038/s41528-018-0046-9. [15] G. S. Cañón Bermúdez, H. Fuchs, L. Bischoff, J. Fassbender, and D. Makarov, “Electronic-skin compasses for geomagnetic field-driven artificial magnetoreception and interactive electronics,” Nature Electronics, vol. 1, no. 11, p. 589, Nov. 2018, doi: 10.1038/s41928-018-0161-6. [16] G. S. Cañón Bermúdez et al., “Magnetosensitive e-skins with directional perception for augmented reality,” Science Advances, vol. 4, no. 1, p. eaao2623, Jan. 2018, doi: 10.1126/sciadv.aao2623. [17] J. Ge et al., “A bimodal soft electronic skin for tactile and touchless interaction in real time,” Nat Commun, vol. 10, no. 1, p. 4405, Dec. 2019, doi: 10.1038/s41467-019-12303-5. [18] K. Kuijk, W. van Gestel, and F. Gorter, “The barber pole, a linear magnetoresistive head,” IEEE Transactions on Magnetics, vol. 11, no. 5, pp. 1215–1217, Sep. 1975, doi: 10.1109/TMAG.1975.1058886. [19] N. Münzenrieder et al., “Entirely Flexible On-Site Conditioned Magnetic Sensorics,” Advanced Electronic Materials, vol. 2, no. 8, p. 1600188, Aug. 2016, doi: 10.1002/aelm.201600188.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3ba71cee33031382721e1689312e1f2a.jpg)
Fig. 1 Shapeable magnetic sensors as touchless interactive devices for virtual reality. (left) Human hand wearing the on-skin magnetic sensor and approaching a permanent magnet. (center) As the user turns it hands over the magnet, the intensity of virtual lightbulb is dimmed. This two panels are adapted from reference [18]. (right) Applying the same concept but changing the sensing principle allows controlling a virtual character on screen using only the earth's magnetic field. This panel is adapted from reference [17]

![](https://assets.underline.io/uploads/markdown_image/1/image/c1fa368c68af4887c7567f763724f9c8.jpg)
Fig. 2 Multimodal shapeable magnetoelectronics and fully flexible conditioning electronics. (top left) Schematic of a m-MEMS. (top center) Approaching an object using the touchless mode of the m-MEMS activates the first layer of interaction. (top right) Touching the object activates a second layer of interaction and opening a new menu. (center) Entirely flexible and on-site conditioned magnetic field sensing platform containing a power amplifying cascade (bottom left) and a giant magnetoresistive sensor Wheatstone bridge (bottom right).

 Mechanically shapeable magnetic field sensor technologies INVITED

In recent years, magnetoelectric ΔE-effect sensors have been investigated for the detection of small amplitude and low-frequency magnetic fields that typically occur in many biomedical and diagnostic applications. Such sensors are based on magnetoelectric composite resonators, which consist of mechanically coupled magnetostrictive and piezoelectric materials. They can be processed on a large scale by microelectromechanical system (MEMS) technology with dimensions of a few millimeters down to a few micrometers and are compatible with complementary metal-oxide-semiconductor (CMOS) electronics. Furthermore, they can be operated at room temperature with a broad-bandwidth and a large dynamic range and are robust against microphony and mechanical noise. Such sensors utilize the ΔE-effect of the magnetostrictive material, i.e. the change of the mechanical stiffness tensor with magnetization and hence, with an applied magnetic field. Since our first publication of this sensor concept in 2011 [1], much progress has been made in understanding the complex interplay of magnetic, mechanical, and electrical properties and their influence on signal and noise of the sensor system. This holds for different designs of magnetoelectric MEMS cantilevers, but also for surface acoustic wave devices [2]. Here, we present recent experimental and theoretical results on the ΔE-effect, the sensitivity, and the noise of magnetoelectric ΔE-effect sensors. The sensors consist of magnetoelectric MEMS resonators with sputter-deposited AlN or Al73Sc27N as a piezoelectric material and soft-magnetic (Fe90Co10)78Si12B10-based single or multilayers. A magnetoelastic macrospin model of the ΔE-effect in all stiffness tensor components is presented and combined with a finite element electro-mechanical model of the resonator. First and higher order torsion (Fig. 1) and bending modes are compared and analyzed regarding the sensitivity and the ΔE-effect [3]. Measurements and simulations reveal the dependency of the sensitivity on the mode number, caused by the geometry, mode shape, and the ΔE-effect in different stiffness tensor components. Specific rules for the resonator design are derived as a result. Besides the geometric and magnetic material properties, we find that the resonator loss and the piezoelectric material have a decisive impact on signal and noise. The influence of the quality factor Q [4] and the piezoelectric material [5] on signal and noise are investigated experimentally and explained by combining the previous model with a signal-and-noise equivalent circuit model (Fig. 2). Both quantities, Q and the piezoelectric material show the promising potential of significantly increasing the sensitivity and improving the limit of detection (LOD). Yet, an improvement in the LOD is currently limited by magnetic noise that becomes dominant at large operating voltage amplitudes [6]. Hence, understanding the specific origins of magnetic noise in such magnetostrictive resonant structures is crucial for sensor improvement in the future. A physical magnetic noise model is presented to identify the origin of stress-amplified, thermal-magnetic noise. It combines large scale finite differences micromagnetism with the mechanical equations of motion to capture magnetostrictive self-energy and frequency effects. Including the piezoelectric constitutive relation and the operating electronics the sensor’s output voltage noise density can be estimated. With the model, we evaluate and discuss experimental results and explain the dependency of magnetic noise on the excitation amplitude and the magnetic bias field. The model provides detailed insights into general noise limits, which arise from using the ΔE-effect as the sensing principle. Finally, we briefly present first applications in cell imaging [7] and show that small signal measurements with simultaneous localization are enabled by a dual-mode operation scheme with compact self-biased ΔE-effect sensors [8]. This is of particular interest for typical biomedical inverse solution problems where the precise knowledge of the sensor’s position and orientation is essential. Such applications could benefit from sensor arrays that provide many measurements with a high spatial resolution. The noise equivalent model is extended to arrays of parallel sensor elements and compared with measurements. Implications and prospects for sensor developments in the future are discussed in a conclusion.

**References:**

[1] B. Gojdka, R. Jahns, K. Meurisch, et al., APL Vol. 99, p.1-4 (2011); Nature Vol. 480, p.150 (2011) [2] J. Schmalz, A. Kittmann, P. Durdaut, et al., Sensors, Vol. 20, p.1–17 (2020) [3] B. Spetzler, C. Kirchhof, E. Quandt, et al., Phys. Rev. Appl., Vol. 12, p.1-13 (2019) [4] B. Spetzler, C. Kirchhof, J. Reermann, et al, APL., Vol. 114, p.183504 (2019) [5] B. Spetzler, J. Su, R.-M. Friedrich, et al., APL Materials., invited, submitted (2021) [6] P. Durdaut, E. Rubiola, J. Friedt, et al., J. Microelectromech. Syst., Vol. 29, p.1347 - 1361 (2020) [7] N. Lukat, R. M. Friedrich, B. Spetzler, et al., Sensors Actuators A Phys., Vol. 309, 1–8 (2020) [8] B. Spetzler, C. Bald, P. Durdaut, et al., Sci. Rep., accepted, (2021)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1ddee42922239ae2a14790371e63be23.jpg)
Normalized resonance frequencies fr/fr,max of the first three torsion modes (TM1-3) as functions of the magnetic flux density µ0H applied along the long axis of the cantilever; inset: top photograph of the MEMS cantilever with visible electrodes. A soft magnetic FeCoSiB-Cr multilayer is sputter deposited on the other side.

![](https://assets.underline.io/uploads/markdown_image/1/image/9c28120fbc2c2f322ee01c1b390d8acb.jpg)
Measured and simulated limit of detection (LOD) of two sensors of identical design that differs only in the piezoelectric material, which is AlN and AlScN, respectively. At large excitation voltage amplitudes ûex magnetic noise imparis the LOD.

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