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The electric field manipulation of magnetization [1,2] became a subject of acute interest, since it provides a low energy consumption and sub-nanosecond switching time. The yield of such process depends on the anisotropy energy variation in response to the applied electric field and therefore a wide variety of studies have been dedicated to this topic.&lt;br/&gt;In this work we present a combined experimental-theoretical study of the perpendicular magnetic anisotropy (PMA) electric field modulation in magnetron-sputtered epitaxial Pt(111)/Co/MgO type systems.&lt;br/&gt;&lt;i&gt;Ab-initio&lt;/i&gt; calculations of voltage-controlled PMA have been performed using the &lt;i&gt;Full Potential Linear Augmented Plane Wave&lt;/i&gt; &lt;i&gt;FP-LAPW&lt;/i&gt; code &lt;i&gt;Wien2k &lt;/i&gt;[3]. A supercell model has been used to describe the multilayer configuration and the electric field has been applied using a zig-zag additional potential in the Hamiltonian. The anatomy of PMA and its electric field dependence has been theoretically analyzed within the framework of two main mechanisms: the surface charge doping which alters the relative occupation of electronic orbitals at the interface and the intrinsic interfacial dipole field. The main issue of our calculation is the prediction that the adjunction of Pt at top Co/MgO interface in Pt/Co/MgO ultrathin structures enhances the perpendicular anisotropy by about 84% and its electric field variation rate (Fig.1 (a), (b)).&lt;br/&gt;These theoretical predictions have been further used to design, grow by sputtering samples and pattern spintronic devices dedicated for the experimental analysis of the voltage response of magnetic anisotropy. As expected, in both standard Pt/Co(1nm)/MgO and top interface tailored Pt/Co(1nm)/Pt/MgO samples, the room-temperature magnetometry experiments demonstrated the out-of-plane remanent magnetization configuration related to surface PMA. The electric field influence on the PMA has been then studied on Hall-bridge patterned samples with a top-gating insulator (Fig.2 (a)), suitable for Anomalous Hall Effect magnetometry. In these devices, a qualitative agreement between the theoretical predictions and experimental results has been observed. The asymmetric variation of the anisotropy energy dependent on the polarity of the electric field, which was deduced from the ab-initio calculations is also reflected in the asymmetric variation of the coercive field as a response to the applied voltage (Fig.2 (b)). Supplementary insight into the anatomy of the mechanisms involved in the electric field effect on the coercive field, driven by the electric field modulation of the surface anisotropy, is further provided within a macrospin approach.

**References:**

References:&lt;br/&gt;[1] W-G. Wang et al, Nature Mater., vol. 11, pp. 64-68, 2012.&lt;br/&gt;[2] Y. Shiota et al, Nature Mater., vol. 11, pp. 39-43, 2012.&lt;br/&gt;[3] P. Blaha et al, J. Chem. Phys., vol. 152, p. 074101, 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8aa1914679751d7ed802354b310f9987.jpg)
Fig.1 &lt;i&gt;Ab-initio calculation of electric field variation of the surface perpendicular anisotropy Ks for Pt/Co/MgO (a) and Pt/Co/Pt(1ML)/MgO (b) supercells&lt;/i&gt;

![](https://assets.underline.io/uploads/markdown_image/1/image/6a2fc3c369a03e3f0c26127a23d3fb4c.jpg)
Fig.2 &lt;i&gt;(a) Hall-bridge UV lithographically patterned devices; (b) Variation of coercive field, surface anisotropy with the applied electric field.&lt;/i&gt;

INTERMAG 2021

 Electric field modulation of interfacial magnetic anisotropy in magnetron-sputtered Pt/Co/MgO ultra-thin structure with chemically tailored top Co interface

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The electric field manipulation of magnetization [1,2] became a subject of acute interest, since it provides a low energy consumption and sub-nanosecond switching time. The yield of such process depends on the anisotropy energy variation in response to the applied electric field and therefore a wide variety of studies have been dedicated to this topic. In this work we present a combined experimental-theoretical study of the perpendicular magnetic anisotropy (PMA) electric field modulation in magnetron-sputtered epitaxial Pt(111)/Co/MgO type systems. Ab-initio calculations of voltage-controlled PMA have been performed using the Full Potential Linear Augmented Plane Wave FP-LAPW code Wien2k [3]. A supercell model has been used to describe the multilayer configuration and the electric field has been applied using a zig-zag additional potential in the Hamiltonian. The anatomy of PMA and its electric field dependence has been theoretically analyzed within the framework of two main mechanisms: the surface charge doping which alters the relative occupation of electronic orbitals at the interface and the intrinsic interfacial dipole field. The main issue of our calculation is the prediction that the adjunction of Pt at top Co/MgO interface in Pt/Co/MgO ultrathin structures enhances the perpendicular anisotropy by about 84% and its electric field variation rate (Fig.1 (a), (b)). These theoretical predictions have been further used to design, grow by sputtering samples and pattern spintronic devices dedicated for the experimental analysis of the voltage response of magnetic anisotropy. As expected, in both standard Pt/Co(1nm)/MgO and top interface tailored Pt/Co(1nm)/Pt/MgO samples, the room-temperature magnetometry experiments demonstrated the out-of-plane remanent magnetization configuration related to surface PMA. The electric field influence on the PMA has been then studied on Hall-bridge patterned samples with a top-gating insulator (Fig.2 (a)), suitable for Anomalous Hall Effect magnetometry. In these devices, a qualitative agreement between the theoretical predictions and experimental results has been observed. The asymmetric variation of the anisotropy energy dependent on the polarity of the electric field, which was deduced from the ab-initio calculations is also reflected in the asymmetric variation of the coercive field as a response to the applied voltage (Fig.2 (b)). Supplementary insight into the anatomy of the mechanisms involved in the electric field effect on the coercive field, driven by the electric field modulation of the surface anisotropy, is further provided within a macrospin approach.

**References:**

References: [1] W-G. Wang et al, Nature Mater., vol. 11, pp. 64-68, 2012. [2] Y. Shiota et al, Nature Mater., vol. 11, pp. 39-43, 2012. [3] P. Blaha et al, J. Chem. Phys., vol. 152, p. 074101, 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8aa1914679751d7ed802354b310f9987.jpg)
Fig.1 Ab-initio calculation of electric field variation of the surface perpendicular anisotropy Ks for Pt/Co/MgO (a) and Pt/Co/Pt(1ML)/MgO (b) supercells

![](https://assets.underline.io/uploads/markdown_image/1/image/6a2fc3c369a03e3f0c26127a23d3fb4c.jpg)
Fig.2 (a) Hall-bridge UV lithographically patterned devices; (b) Variation of coercive field, surface anisotropy with the applied electric field.

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A Factor graph-based detector (FGB) is one of the promising for the two-dimensional (2-D) detection which can mitigate the 2-D interference channel. In this paper, we present the modified FGB (MFGB) detection of a 2-D interference channel on bit patterned media recording (BPMR) system. The 2-D interference channel with 3×3 matrix is separated into the three sub-windows with 1×3 matrix in horizontal direction and three sub-windows with 3×1 matrix in vertical direction. After that, the joint outputs are averaged of each sub-window in horizontal and vertical directions. This simulation results show that compared with MFGB method achieves lower bit error rate (BER) performances than the original FGB detector and generalized belief propagation (GBP) algorithm on BPMR system at an areal density of 4 Tb/in2. In currently, because of an enlargement in data growth thus the requirement for high areal density storage system has increased. Bit patterned media recording (BPMR) system is one of the most promising choices to continue magnetic recording storage density [1]. The significant issue for very high areal density of BPMR system is the small grain sizes with thermal fluctuation effect of magnetic grains. However, the reduction of grain sizes in both across track and along track directions has become the 2-D interference in read channel of BPMR system that constitute inter-symbol interference (ISI) and inter-track interference (ITI) from the adjacent tracks [2]. More recently, the researchers have works on the method of the impairments in the 2-D interference channel and mitigating their effects using signal processing for communication techniques. A graph based detector has received much attention due to its intrinsic 2-D detection, particularly, for multihead multitrack processing [3], as an alternative to the soft-output Viterbi algorithm (SOVA) method. In this system model, the write head of BPMR syetem with multihead multitrack processing assumes the five input bit sequences recorded on five adjacent tracks. such the read head will be received three readback signal sequences which are caused by combination of noiseless received signal with additive white Gaussian noise. After that, the readback signal sequences are sent to two 2-D equalizer with horizontal and vertical directions. The output bits of horizontal equalizer and vertical equalizer are processed for two FGB detectors with horizontal and vertical directions of the summation which then produce the estimated input bits, as shown in Figure 1. In this paper, we consider the 2-D interference channel 3 by 3 matrix arrays into three sub-windows for horizontal direction and vertical direction. The coefficients of 2-D interference channel represent the weight of the current pixel. Thus, the MFGB detector in the 2-D interference channel separates the 3×3 matrix arrays into two sections for message passing on factor graph. Section one is three sub-windows with 1×3 matrix in horizontal direction. Section two is three sub-windows with 3×1 matrix in vertical direction. After that, the output of each FGB detectors in horizontal and vertical directions are determined the summation of joint outputs detections. The method of the MFGB detector divides the factor graph into three steps. The first step, the 2-D interference channel separates the 3×3 matrix array into 1×3 matrix for sub-window fh1 = [hk-1,l-1, hk,l-1, hk+1,l+1] of the first horizontal direction and the first vertical direction with 3×1 matrix for sub-window fv1 = [hk-1,l-1, hk-1,l, hk-1,l+1], as shown in Figure 2. As for, the second step is the sub-window sliding in second horizontal direction fh2 = [hk-1,l, hk,l, hk+1,l] and the vertical direction fv2 = [hk,l-1, hk,l, hk,l+1], as shown in Figure 3. Finally, the third step is similar to the both previous steps. The sub-window slides to the third horizontal direction fh3 = [hk-1,l+1, hk,l+1, hk+1,l+1] and the vertical direction fv3 = [hk+1,l-1, hk+1,l, hk+1,l+1], as shown in Figure 4. In this simulation, we consider the BPMR system at areal density of 4 Tb/in2. Corresponding to bit period and track pitch are 12.7 nm, PW50 of along-track and PW50 across-track are considered with 4.2 nm and 8.4 nm, respectively [4]. Therefore, the 2-D interference channel resultant of coefficients matrix H with a size of 3×3 can be written as H4Tb = [0.0163 0.4008 0.0163; 0.0408 1.0000 0.0408; 0.0163 0.4008 0.0163]. In this work, we compare BER performance of the MFGB detector, the original FGB detector [5], and generalized belief propagation (GBP) algorithm detector [6]. From the graph considerations in Figure 5, BER performance of the MFGB detector performs better than the original FGB detector. Furthermore, the MFGB detector achieves the gain of about 3.6 dB over the GBP algorithm detector at BER =10-4 after three iterations of all detectors.

**References:**

[1] G. F. Hughes, IEEE Transactions on Magnetics, vol.35, no.5, pp. 2310-2312, (1999) [2] P. W. Nutter, I. T. Ntokas, B. K. Middleton and D. T. Wilton, IEEE Transactions on Magnetics, vol.41, no.10, pp. 3214-3216, (2005) [3] J. Hu, T.M. Duman and M.F. Erden, EURASIP Journal on Advances in Signal Processing, vol.2008. 10.1155/2008/738281, (2009) [4] Y. Wang and B. V. K. Vijaya Kumar, IEEE Transactions on Magnetics, vol.53, no.10, ID.3000710, (2017) [5] T. Sopon, P. Supnithi and K. Vichienchom, IEEE Transactions on Magnetics, vol.50, no.11, ID. 3101704, (2014) [6] J. S. Yedidia, W. T. Freeman and Y. Weiss, IEEE Transactions on Information Theory, vol. 51, no. 7, pp. 2282-2312, (2005)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0831563d918f2f15bb81b7901eff87b9.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/7bcc7ab9eef766aac91272047d37be35.jpg)

 An Improvement to Factor Graph-Based Detector for Bit Patterned Media Recording

Introduction We study the low-density parity-check (LDPC) coding [1] and iterative decoding system, as signal processing for the shingled magnetic recording (SMR) [2] in two-dimensional magnetic recording (TDMR). Previously we have reported waveform equalization using a two-dimensional finite impulse response (TD-FIR) filter [3] and an inter-track interference (ITI) canceler [4] and showed the influence of ITI is reduced. Also, we have proposed a neural network detector (NND) and evaluated the performance of the first decoding by the NND [5]. In this study, the NND iteratively calculates the log-likelihood ratio (LLR) as the decoding reliability using the returned sum-product (SP) decoder [6] output sequence as well as using TD-FIR filter [3] output sequence. Furthermore, we compare the iterative decoding using an NND with a soft-output Viterbi algorithm (SOVA) detector with the signal-dependent noise predictor [7], [8]. Read/write system The input sequence passes through a 128/130 (0, 16/8) run-length limited (RLL) encoder and a (3, 30)-regular LDPC encoder to be changed into the recording sequence and is recorded on a granular medium model [4] under the specification of 4 Tbit/inch2. In the reading process, the decoding target track and both adjacent tracks are read composed by the array head with three readers at the same time [1], [2], and the different additive white Gaussian noise (AWGN) sequence is added to each waveform as the system noise. The signal-to-noise ratio (SNRS) for the system noise at the reading point is defined as SNRS = 20log10(A/σS) [dB], where A is the positive saturation level of the waveform reproduced from an isolated magnetic transition and σS is the root-mean-square (RMS) value of the system noise in the bandwidth of the channel bit rate fc. A channel bit response including read/write (R/W) process on the intended track is equalized to the partial response class-I (PR1) target by the equalizer composed of three low-pass filters (LPFs) having cut-off frequency xh normalized by the fc and TD-FIR filter with Nt taps, where Nt is the number of taps [3] for a reader. We assume that these parameters are set to xh = 0.4 and Nt = 15. Then, the output waveform from the PR1 channel is iteratively decoded by the turbo equalization performed between an NND and an SP decoder [6]. The SP decoder also iteratively decodes using the constraint of LDPC code until the maximum iteration number isp times. Furthermore, the SP decoder returns the reliability sequence including the parity bits of LDPC code to the NND again. In this way, the turbo equalization for the target track is performed with the maximum iteration number iglobal times. After the given number of iterations in the turbo equalization, the output sequence is obtained by the posterior probability sequence except parity passing through a hard decision unit and the RLL decoder. Then, the bit error rate (BER) is calculated by comparing the input sequence with the output sequence. Neural network detector Figure 1 shows the block diagram of the turbo equalization. In the figure, D is the delay operator for a bit interval, Nm (m = 1∼3) is the number of elements in the mth layer. We adopt N1 = 30, N2 = 10 and N3 = 1. The NND consists of the neural network, the memory, the selector, and the LLR calculator. The neural network provides outputs for 3-bit patterns in the down-track direction for the TD-FIR filter and the returned SP decoder outputs, and stores the output in the memory. In the training process by back-propagation algorithm, we set the training signal to be “1” for the target bit pattern and “0” for the others, in order to obtain connection weight sets wij(m)(n) between the ith element at the mth layer and the jth (j = 1∼Nm-1) element at the (m - 1)th layer for the nth pattern (n = 1∼8). Furthermore, the LLR calculator provides the logarithmic ratio of the maximum values for the center bit “1” and “0” from the selector. Performance evaluation Figure 2 shows the BER performances for SNRS. The marks of circle and triangle show the performances of the NND and the SOVA detector, respectively. Here, the LLR of the SOVA detector is provided by the metric of the PR1 channel, where the metric is calculated considering the external LLR obtained by the SP decoder output [5]-[7]. The turbo equalization parameters isp and iglobal adopt the optimum values for minimizing the BER in each detector. As can be seen from the figure, the system with the NND improves about 5.5 dB in the required SNR to achieve no-errors compared to the system with the SOVA detector. Acknowledgments This work was supported in part by the Advanced Storage Research Consortium (ASRC).

**References:**

[1] R. G. Gallager, IRE Trans. Inform. Theory, Vol.IT-8, pp.21-28 (1962). [2] R. Wood, M. Williams, A. Kavcic, and J. Miles, IEEE Trans. Magn., Vol.45, No.2, pp.917-923 (2009). [3] R. Suzuto et al., IEEE Trans. Magn., Vol.52, No.7, 3001604 (2016). [4] M. Yamashita et al., IEICE Trans. Electron., Vol. E96-C, No.12, pp.1504−1507 (2013). [5] M. Nishikawa, Y. Nakamura, Y. Kanai, H. Osawa, and Y. Okamoto, IEEE Trans. Magn., Accepted. [6] P. Robertson et al., Proc. IEEE Int. Conf. Commun. (ICC 1995), pp.1009–1013, Seattle, USA (1995). [7] J. Hagenauer et al., in Proc. IEEE Global Telecommun. Conf. 1989, Dallas, Texas, pp. 1680−1686 (1989). [8] Y. Okamoto et al., IEEE Trans. Magn., Vol.38, No.5, pp.2349−2351 (2002).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7bba5f5ade9f24186c6fa6c6b6b83370.jpg)
Fig. 1 Block diagram of turbo equalization.

![](https://assets.underline.io/uploads/markdown_image/1/image/a29f76c209b5fd1c3bfd4943b298e847.jpg)
Fig. 2 BER performances for SNRS.

 A Study on Iterative Decoding by Neural Network Detector in SMR System

I. INTRODUCTION To further increase areal recording density in hard disk drives, we study a three-dimensional magnetic recording system with double recording layers and the magnetoresistive (MR) read-sensors [1]. We constructed the read/write channel model which combines double recording layers with MR reading sensors to evaluate a three-dimensional magnetic recording. In this study, we evaluate the bit error rate (BER) performance of the generalized partial response (GPR) maximum likelihood (ML) (GPRML) system [2] under each areal recording density of 4 Tbits/inch2 on a dual recording layers medium. II. READ/WRITE CHANNEL MODEL WITH DOUBLE RECORDING LAYERS The two input sequences for 1st and 2nd recording layers are recorded on double recording layers medium without the jitter like medium noise, phase error, grain size fluctuation, and so on. The R/W simulations are started at each areal density corresponding to 4 Tbit/inch2 with bit length lc of 7.3 nm and track pitch ltp of 22.1 nm. The full-shielded reader [3] is assumed. The width between side shields, the shield gap of the individual reader are set to 30 nm and 22 nm, and the width and thickness of the magneto-resistive element are set to 17 nm and 2 nm, respectively. We define the magnetic spacing between the bottom of the reader and the top of each recording layer as Δ1 and Δ2, respectively. In this study, we assume the Δ1 = 2.0 nm and Δ2 = 5.0 nm. Figure 1 shows the distributions of reproducing waveforms from 1st and 2nd recording layers at the reading point without the system noise obtained by the sensitivity functions of the MR read sensor. In this figure, the dotted and solid lines show the distributions of samples captured at phases of the bit center and boundary, respectively. As can be seen from the figure, the distribution at the phase of the bit boundary is clearer than that at the bit center. A channel bit response on the double recording layer medium is adjusted to the GPR-target by the equalizer composed of a low-pass filter (LPF) having cut-off frequency xh = 0.4 normalized by the channel bit rate fc, a finite impulse response (FIR) filter with Nt = 15 taps, and an Mth (M : 0～3) order noise predictor [2]. The GPR channel output is decoded by the Viterbi detector for double recording layers. III. SIMULATION RESULTS AND DISCASSION Figure 2 shows BER performances of the GPRML systems for the double recording layer medium. The open and filled symbols show the performances for samples at phases of the bit center and boundary, respectively. The horizontal axis shows the correlation length for the signal given by the GPR system. As can be seen from the figure, the performance improves by the introduction of GPR for the samples at the bit boundary. It is certified that the GPRML system for the reproducing waveforms captured at phases of the bit boundary offers better BER performance compared with that of the bit center.

**References:**

[1] S. Greaves, K. S. Chan, and Y. Kanai, '' Optimization of dual-structure recording media for microwave-assisted magnetic recording,'' IEEE Trans. Magn., vol.55, no.7, 3001305, July 2019. [2] N. Shinohara, H. Osawa, Y. Okamoto, Y. Nakamura, K. Miura, H. Muraoka, and Y. Nakamura, “Performance of GPRML-AR system in perpendicular magnetic recording channel with thermal decay,” J. Magn. Magn. Mat., vol.320, no.22, pp.3140-3139, Nov. 2008. [3] Y. Nakamura, H. Osawa, Y. Okamoto, Y, Kanai, and H. Muraoka, “Bit error rate performance for head skew angle in shingled magnetic recording using dual reader heads,” J. Appl. Phys., vol.117, no.17, pp.17A901-1-17A901-4, May 2015.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3be7ced0647e926480ea7c7c00c0672b.jpg)
Fig.1 Distributions of reproducing waveforms.

![](https://assets.underline.io/uploads/markdown_image/1/image/e5827a74eed35c6f4665dced82f47344.jpg)
Fig.2 BER performances.

 A study of multi-dimensional magnetic recording system with double recording layers

Magnetic domain wall (DW) manipulation has been widely investigated because of its potential applications for information processing, storage, and transport. Probably the best-known concept device is the racetrack memory, which was proposed by IBM based on the current induced domain wall motion (CIDM) effect [1]. Recently, experimental investigations on GdFeCo exhibits fast domain wall motion (DWM) in the vicinity of the angular momentum compensation temperature [2]. To date, most of the achievements of DWM and the dynamic of DW are based on the Magneto-optical Kerr effect (MOKE) technique. In this work, we investigate ferrimagnetic DWM behavior in GdFeCo by anomalous Hall signal. Multilayers of Hf(4nm)/GdFeCo(7nm)/SiN(4nm) are deposited by means of a high vacuum RF magnetron sputtering method on the thermally oxidized silicon substrate. Using the X-Ray Fluorescence (XRF) spectroscopy technique, we determine that the GdFeCo composition of our sample is 25% of Gd and 75% of FeCo by content. As displayed in Fig.1(a), at room temperature (RT), the magnetic compensation point is observed at a composition of higher Gd content (27%), indicating that the sample possesses TM-rich ferrimagnetic properties. The square-shaped hysteresis loop in the inset of Fig.1(a) measured by the Alternating Gradient Magnetometer (AGM) exhibits high bulk PMA. The Hall bar with a width of 10 μm and length of 65 μm is fabricated using standard photolithography, electron-beam lithography, and Ar ion-beam etching technique. A 150 nm copper (Cu) wire thickness is deposited as probing pads. The experimental setup and Hall bar device schematic is shown in Fig.1(b). The measurements are performed simultaneously with two nanovoltmeters: Voltmeter 1 measures the anomalous Hall voltage at cross PQ, whereas voltmeter 2 measures the longitudinal voltage along the current channel. The AHE resistance and magnetoresistance of the sample are examined as a function of the perpendicular magnetic field with various input DC currents (DCs). As displayed in Fig. 2(a), Fig. 2. (b), and Fig. 2. (c), the magnetoresistance (MR) varies significantly ( resulting in MR peaks) as AHE resistance crosses the switching path of the hysteresis loop. Unlike well known MR effects such as the anisotropy MR (AMR) [3], giant MR (GMR) [4], spin Hall MR (SMR) [5], and Rashba MR [6], the anomalous MR observed here exhibits only two sharp peaks that are asymmetric with respect to the applied field and relates to switching path. It should be noted that the magnitude of the MR peak is equal to the AHE resistance (RH ≈ 8.23 Ω). Therefore, the curve switching path ( Fig. 2(c)) relates to the origin of the MR peak ( Fig. 2(a) and Fig. 2(b)) and is attributed to the magnetization switching behavior of the sample. We further investigate the magnetization reversals by MOKE and observe that as the DW runs along the Hall bar, as shown in Fig. 2(d)), it divides the area of the bar into 2 domains with opposite magnetization alignment which generates intermediate AHE resistances increasing along the curve switching path. Utilizing this fact, we propose a new approach to measuring the DW motion velocity over the hall bar channel. We first realize that the average DW velocity measured at crossbar of width w is given |vDW| =w/(tS - tN), where tN, tS are time corresponding to the nucleation and saturation points detected by AHE hysteresis, respectively. Our measurement results indicate that the external field sweeping speed changes |vDW| significantly. The DW propagation can be manipulated in the wide range from a low rate of 0.09 μm/s (corresponding to field sweep of 0.24 Oe/s) to a high rate of 138.6 μm/s (corresponding to field sweep of 200 Oe/s). The measurement results exhibit the trend that average DW velocity increases linearly with increasing field sweep speed. Furthermore, from the experiment data, we deduce that DW velocity displays an exponential growth function of H-Hn, thus: VDW = αVsweep field × (e(β(H-Hn) - γ). Fitting the expression to experimental data we deduce α, β, and γ. The linear dependence of DW velocity on the field sweep speed and exponential growth of it in the field suggest that DWs have effective mass and thus have inertia. These findings provide further insight into the DWM behavior at the nucleating stage.

**References:**

[1] S. S. P. Parkin, M. Hayashi, and L. Thomas, Science 320 (2008) 190-194. [2] K. J. Kim, S. K. Kim, Y. Hirata, and S. H. Oh, Nat. Mater. 16, 1187 (2017). [3] T. McGuire, R. Potter, IEEE Trans. Magn. 11 (1975) 1018. [4] M.N. Baibich, J.M. Broto, and A. Fert, Phys. Rev. Lett. 61 (1988) 2472. [5] H. Nakayama, M. Althammer, and Y.-T. Chen, Phys. Rev. Lett. 110 (2013) 206601. [6] K. Narayanapillai, G. Go, R. Ramaswamy, and K. Gopinadhan, Phys. Rev. B 96 (2017) 064401.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b2a2d44a83dfaec8ac480270197bf853.jpg)
Figure 1: (a) Coercive field Hc as a function of Gd content in the GdFeCo composition. Inset: the out-of-plane hysteresis loops of the sample, measured by an AGM; (b) Optical image of Hall bar devices and schematic illustration of the measurement setup.

![](https://assets.underline.io/uploads/markdown_image/1/image/f6f1280b4e2b5344da139f6ec18bc652.jpg)
Figure 2: MR as a function of the perpendicular field at (a) lower edge across N and Q, and (b) upper edge across M and P. (c) the AHE resistance measured at the transverse cross bar. The inset illustrates the reversal domain mechanism corresponding to the switching path of hysteresis. (d) the MOKE image of DW motion on Hall bar.

 Investigation of ferrimagnetic domain wall motion behavior in GdFeCo through the anomalous Hall effect.

Current induced domain wall motion is a crucial part of spintronics that has received large attention in the last 15 years and has resulted in memory as well as logic applications. Spin tranfer torques(STT) and Spin orbit torques(SOT) are the two mechanism through which the current induced domain wall motion takes place. In the case of STT, the electron spins get polarized through exchange interaction within the ferromagnetic layer and then transfers its angular momentum into the local magnetic moment of the domain walls thereby resulting in its motion. On the other hand, in the case of spin orbit torque, the spin current is generated by Spin Hall effect and Rashba effect in an adjacent heavy metal layer or interface and then diffuses into the magnetic layer applying a torque on the domain wall magnetic moments. Here, we will focus on spin transfer torque driven domain wall motion in ferrimagnetic Ni doped Mn4N thin films. Recent work on domain wall motion has focused on ferrimagnets in which angular or spin moment compensation can be obtained by either changing the temperature of the material or the composition. Very fast domain wall velocities has been shown at the angular momentum compensation point where the precessional motion of the local spin is neglible thus resulting in faster domain wall motion. Mn4N is a class of rare-earth free ferrimagnetic material with a low magnetization and a high perpendicular magnetic anisotropy. It has an anti-perovskite crystal structure with antiferromagnetically coupled magnetic Mn atoms at the corner sites Mn(I) and at the face centered sites Mn(II). Very high current driven domain wall velocities has already been demostrated in thin Mn4N films epitaxially grown on SrTiO3 [1]. Since in these system domain walls have Bloch internal structure, the driving mechanism is the classical spin-transfer torque. The compensation point is not achieved by varying the temperature of the material. However, by doping of Ni in Mn4N the magnetic compensation can be achieved at room temperature [2]. The Ni atoms replace the Mn(I) atom at the corner sites and their moments align parallel to that of Mn(II) leading to a decrease in the net magnetization and a magnetic compensation or around 3.6% of Ni concentration [3]. On these epitaxially grown Mn4-xNixN thin films on SrTiO3 substrates, due to the reduction of the angular momentum originating from the Ni doping and the large spin-polarization of conduction electrons, very high velocities approaching 3000 m/s have been achieved for compositions close to the magnetic compensation point. Moreover, a reversal of the domain wall motion direction was observed after crossing the angular momentum (and magnetization) compensation point where the domain walls move in the opposite to the electron flow. This unique phenomenon is in agreement with the analytical 1D model applied to ferrimagnetic systems and is due to the switch of the sign of the angular moment with respect to that of the spin polarization after the compensation point. This is supported by the results of ab-initio calculations.

**References:**

1. T. Gushi, M.J. Klug, J.P. Garcia, NanoLetters.,19, 8716–8723(2019) 2. T. Komori, A. Anzai, T. Gushi, Journal of Crystal Growth., 507, 163-167 (2019) 3. T. Komori, T. Hirose, T Gushi, Journal of Applied Physics 127, 043903 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/987f325efaa3e71c344195d0784bddf9.jpg)
Fig 1: Anomalous Hall Effect curves showing a change of sign from negative to positive when crossing the magnetic compensation point. The magnetization decreases towards the compensation point and has been shown as negative after the crossing the compensation point.

![](https://assets.underline.io/uploads/markdown_image/1/image/5aa6153307025ed27b85f769a243db10.jpg)
Fig 2: Domain wall velocity vs current density for Mn4-xNixN thin films of different compositions below and above the compensation point; full symbol show velocities parallel to the electron flow before the compensation point and empty symbols show velocity after the compensation point in the opposite direction. Here, the highest velocity of 3000 m/s is achieved for the lowest magnetization with a composition after the compensation point.

 Very fast current driven and reverse domain wall motion in a rare-earth free compensated ferrimagnetic Mn4-xNixN.

Reconfigurable logic device represented by field-programmable gate array (FPGA) has been widely used in various fields of applications including digital signal processing, image processing, cryptography and so on [1]. The logic programmability makes it possible to deal with varieties of different computing tasks with limited number of devices. Because SRAM-based FPGA suffers from static power dissipation and volatility issues, numerous studies have been conducted on nonvolatile reconfigurable spintronic logic devices [2][3]. Although the logic devices proposed in these studies could perform multiple Boolean logic operations, they could not cover all logic functions. In order to perform all combinational logic functions in a reconfigurable way, look-up tables (LUTs) are used in FPGA and the function of LUT could be realized by cascading multiplexers. Hence, reconfigurable spin logic covering all combinational logic functions could be realized if spintronic multiplexers are demonstrated. Here, we proposed a nonvolatile spintronic 2-to-1 multiplexer based on propagation of domain wall in Ta/CofeB/MgO multilayer with perpendicular magnetic anisotropy (PMA). The device could operate at room temperature with no external magnetic field required for the function of multiplexer. The schematics of the nonvolatile spintronic multiplexer were shown in the inset of Fig. 1 and Fig. 2. Ta/CoFeB/MgO multilayer with PMA was patterned with “H” shape. The magnetization of the magnetic multilayer located at the vertical wires of “H” was manipulated by external out-of-plane magnetic field. The magnetization of the H-shaped magnetic film was first saturated by an external magnetic field applied on all parts of the film. After removing the saturation field, magnetic field of opposite direction was applied only on the left vertical wire of “H” to reverse the magnetization. Thus, a domain wall was generated. When current was applied in the horizontal wire, the domain wall would propagate and the direction of the domain wall movement was determined by the direction of the applied current. No external field was required for the current-driven domain wall motion. When the domain wall propagated from one end to the other end of the horizontal wire, the magnetization of the magnetic multilayer passed through by the domain wall would be reversed. Thus, the magnetization of the horizontal wire was determined by two factors: the initial magnetization state of the device and the direction of the write current applied. The experiment results of the device were shown in Fig. 1 and Fig. 2. The magnetization of the horizontal wire was represented by anomalous Hall voltage. When the write current flew leftwards, the magnetization of the horizontal wire would be the same with the left vertical wire, and vise versa when the write current flew rightwards. If the magnetization states of the two vertical wires were considered as two data inputs and the direction of write current as the selection input, the magnetization of the horizontal wire would be the output of the 2-to-1 multiplexer. In our proposed device, both the data inputs and the output were in the form of spin directions of ferromagnetic multilayer which would retain after power off. Such property not only made this device nonvolatile, but also provided the possibility for cascading because the output could be used as the data input of the multiplexer in the next step. The cascadable feature was necessary for reconfigurable combinational logic. Above all, the proposed device consisted of H-shape ferromagnetic multilayer Ta/CoFeB/MgO with PMA realized the function of nonvolatile 2-to-1 multiplexer experimentally at room temperature and was expected to performing full sets of combinational logic with programmability by cascading.

**References:**

[1] C. Katherine and H. Scott, ACM Computing Surveys., Vol. 34, p.171-210 (2002) [2] Z. Luo, Z. Lu, X. Zhang, et al., Advanced Materials., Vol. 29, p.1605027(2017) [3] X. Wang, C. H. Wan and X. F. Han, et al., Advanced Materials., Vol. 30, p.6 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/298fb3102649d4def3b1ad1ad77ebeac.jpg)
Fig. 1 Current-driven domain wall propagation when the left vertical wire was magnetized downward and right vertical wire magnetized upward. When current flew leftwards in the horizontal wire, the domain wall moved rightwards and the magnetization of the horizontal wire was reversed to downward. When current flew rightwards, the propagation of domain wall and the reversal of magnetization in the horizontal wire were both in the opposite direction.

![](https://assets.underline.io/uploads/markdown_image/1/image/de61849619a96fd5b196fad6e633e902.jpg)
Fig. 2 Current-driven domain wall propagation when the left vertical wire was magnetized upward and right vertical wire magnetized downward. Compared with the case in Fig. 1, the direction of applied write current was still opposite to the direction of domain wall propagation. As a result, the chirality of magnetization switching was reversed. The magnetization state of the horizontal wire was determined by both write current and the magnetization of vertical wires on the left and right side.

 Nonvolatile Spintronic 2-to-1 Multiplexer Based on Current-driven Domain Wall Propagation

We report simulation results of vortex domain wall (VDW) dynamics pinning behavior magnetic wire with 20-nm-thick 100-nm, 200-nm, and 300-nm-wide wires with a triangular notch that depth ratio(Rd) is 30%. The Rd is the depth of notch divide by wire width. The transverse domain wall(TDW) dynamics pinning behavior in 100-nm wide wire has reported by Ref. [2]. Ref. [2] shows the pinning and depinning of DW in the Walker breakdown state(WB). Therefore we are interested in VDW depinning behavior and probability. The method of our study are running the simulation software Mumax3. Our simulation parameters of saturation magnetization(Ms), damping constant, exchange stiffness (A), and cell size of simulation parameters are 860 kA/m, 0.01, 13 pJ/m, and 5*5*5 nm3, respectively. Our results show the width of wire influence dynamic pinning probability, as shown in Fig. 1 and Fig. 2. Figure 1 and Fig. 2 show the relation between dynamics VDW pinning probability and applied field. We employed the different separations from notch sharp to VDW staring positions to simulate the DW initial states in the WB. The data points of Figures 1 and 2 are averaged fields per 5 Oe, this averaged fields mean DW passing notch probability in a field range. The insert of Fig. 1 shows the type of DW pinning at notch. The type of DW pinning is influenced by pinning potential energy barrier or side well of the notch. It indicates that the shape of the notch influences the DW dynamics pinning probability. The applied field gives the magnetic energy to overcome the notch pinning potential. Figure 1 shows VDW in the 100-nm-wide wire is easier pinning as TDW type than 200-nm and 300-nm wide wire. The wire width influences the DW energy density, DW structure, and notch pinning potential energy. To make compassion with Fig. 1, we run the simulation with different wire widths, as shown in Fig. 2. Figure 2 shows the VDW type pinning probability of 200-nm and 300-nm wide wire has more than 100-nm-wide wire. It is caused by the wire width influences. The DW energy density influences by wire width and DW energy density also influences by a notch. The DW potential energy landscape is different at the differently wide wire. The wide wire has more space to release DW energy, and more space can lead DW to transform the structure of itself. In figure 2, 200-nm-wide wire shows unique behavior in the range of 200 Oe. In 200-nm-wide wire and 300-nm-wide wire, wide wires caused by wire width is not large enough to lead DW release metastable state DW energy, the DW energy is lower in the VDW chirality. The topological defects moving are also important for DW chirality changing in DW depinning behavior. The pinning potential of notch also influenced the DW depinning behavior. Those results show the applications of DW structures controlling and placing using notch.

**References:**

[1]. L. J. Chang, Y.D.Yao, Pang Lin, IEEE Transactions on Magnetics., Vol. 47, No 10, (2011) [2]. Burn, D. M., & Atkinson, D. Scientific reports, 6, 34517 (2016). [3]. L. K. Bogart and D. Atkinson, Physics Review B., Vol. 79, p.054414 (2009) [4]. Y. Gao, B. You, X. Z. Ruan, Scientific Reports., Vol. 6, Article number: 32617 (2016) [5]. J. Brandão, R. L. Novak, H. Lozano., Journal of Applied Physics., Vol. 116, p.193902 (2014) [6]. D. M. Burn, D. Atkinson, Scientific Reports., Vol. 6, Article number: 34517 (2016) [7]. K. A. Omari, T. J. Hayward, Scientific Reports., Vol. 7, Article number: 17862 (2017) [8]. Y. Li a, Z. Lu, C. Chen, M. Cheng, Journal of Magnetism and Magnetic Materials., Vol. 456, p.341 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3af7b314acd1d21a2cc7c1fff5262cbc.jpg)
Fig. 1. Dynamics domain wall pinning probability of 100-nm-wide and 200-nm-wide wires. Insert shows the pinning types image of vortex domain wall(VDW) pinning and transverse domain wall(TDW).

![](https://assets.underline.io/uploads/markdown_image/1/image/f8fdc5b72b6336859504ed83f1e68734.jpg)
Fig. 2. The curve shows VDW and TDW types pinning probability in 200-nm-wide wire and 300-nm-wide. The square symbol shows the 200-nm-wide wire simulation results. The circle symbol shows the 300-nm-wide wire simulation results. The open symbols show the probability of DW depinning.

 Domain wall pinnning probability in different width of sub-micron-wire with a notch

Antiferromagnetic spintronics have been blooming in both fundamental science and practical application in recent few years due to the low sensitivity to external perturbation and ultrafast spin dynamics in antiferromagnetic materials. How to detect and manipulate the magnetic state of antiferromagnets efficiently has been a long-term outstanding question (1, 2). Among various regulation methods, electric-field control of antiferromagnetism is a promising way for realizing ultrafast and high density antiferromagnetic spintronics without considering Joule heating effect. Based on ferroelectric P(VDF-TrFE) copolymer, low-voltage-pulse modulation of ferromagnetic La0.7Sr0.3MnO3 (FM-LSMO) thin films via oxygen vacancy has been demonstrated (3, 4). Here, we investigated low-voltage-pulse modulation of antiferromagnetic La1-xSrxMnO3 (x = 0.65) (AFM-LSMO) thin films. Positive 10-volt pulses can increase the resistance at low temperature (Fig. 1), which is ascribed to the oxygen vacancies induced by positive voltage pulses at 300K. This effect was further demonstrated to be related with oxygen vacancy by x-ray photoelectron spectra (XPS) results (Fig. 2). The XPS results suggest that positive pulses can induce more oxygen vacancy and reduce the valence state of Mn ions in AFM-LSMO thin films, thus changing the electrical and magnetic properties of antiferromagnetic layer. Exchange bias effect was established in bilayer FM-LSMO/AFM-LSMO structure and regulated by low-voltage pulses. Both exchange bias field and coercivity show voltage-polarity dependence, suggesting that low-voltage-pulse induced oxygen vacancy dominates the tuning process. Our findings provide a new way for exploring electric-field modification of antiferromagnetic spintronics.

**References:**

1. T. Jungwirth, X. Marti, P. Wadley, J. Wunderlich. Nat Nanotechnol 11, 231-241 (2016). 2. P. Němec, M. Fiebig, T. Kampfrath, A. V. Kimel. Nat Phys 14, 229-241 (2018). 3. H. F. Wong, S. M. Ng, W. F. Cheng et al. Solid-State Electronics 138, 56-61 (2017). 4. H. F. Wong, S. M. Ng, W. Zhang et al. ACS Appl Mater Interfaces 12, 56541-56548 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1ee895f3894fb907fdfc80dbd9e20a61.jpg)
Fig. 1 Temperature dependent resistance of 7-nm AFM-LSMO thin film at pristine, positive pulses gated and negative pulses gated states, respectively. Inset: resistance change as a function of temperature. Rpulses and Rpristine represent the resistance of pulses gated state and pristine state, respectively. Note that all pulses are applied at 300K in vacuum by Kiethley 2400 multimeter and the resistance is recorded after removing pulses.

![](https://assets.underline.io/uploads/markdown_image/1/image/01c793136ea4c47a9354e2b42e0791eb.jpg)
Fig. 2 Mn 2p core-level spectra of AFM-LSMO thin films at pristine, positive pulses gated and negative pulses gated states, respectively.

 Low-voltage-pulse control of the transport properties of antiferromagnetic La0.35Sr0.65MnO3 thin film via ferroelectric P(VDF-TrFE) copolymer

Using LaAlO3 (100) substrates and a 17-nm thick Ca0.96Ce0.04MnO3 (CCMO) buffer layer, we grew BiFeO3 (BFO) thin films with various thicknesses (18nm, 23nm, and 44nm) via pulsed laser deposition (PLD). X-Ray diffraction (XRD), Reciprocal Space Mapping (RSM) and Atomic Force Microscopy (AFM) techniques are employed to characterize the thickness, structure and surface morphology of the films. The large misfit of lattice constants between BFO films and LAO substrates exerts a large compressive strain on the BFO film, which initially stabilizes BFO in the tetragonal (T-) phase. A mixture of T-phase and rhombohedral (R-) phase emerges when the BFO thickness exceeds 20nm. As the BFO film thickness increases, the proportion of R-phase BFO increases as verified by AFM and XRD. Using DC magnetron sputtering, magnetic multilayers of Pt(4nm)/Co(0.8nm)/Pt(1.5nm) were deposited on top of these BFO films. Both Anomalous Hall Effect (AHE) and SQUID-VSM measurements reveal that the mixed-phase BFO favours a perpendicular magnetic anisotropy (PMA) of the upper Pt/Co/Pt multilayers, while the pure T-phase BFO film with smaller thickness suppresses the PMA (Fig.1 and Fig.2). Considering the R-phase BFO at the surface of the mixed-phase BFO film can change reversibly to T-phase BFO when applying electric field across BFO, this finding may provide a new route for realizing the electrical control of PMA in hybrid ferromagnetic-multiferroic structures.

**References:**

[1] Zuhuang Chen, et al., Phys. Rev. B 84, 094116 (2011). [2] He, Q., et al., Nat Commun 2, 225 (2011). [3] R. J. Zeches, et al., Science 326, 977-980 (2009) [4] Huang, Y., et al., Nat Commun 11, 2836 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fbcd28badc4d5c9e655779a945f8e454.jpg)
Room temperature anomalous Hall resistance Rxy for Co(0.8nm)/Pt(1.5nm)/BFO(44nm), Co(0.8nm)/Pt(1.5nm)/BFO(23nm), and Co(0.8nm)/Pt(1.5nm)/BFO(18nm).

![](https://assets.underline.io/uploads/markdown_image/1/image/3c1ebadb60c428cb21edc6d8984bc5f5.jpg)
Room temperature out-of-plane hysteresis curves for Co(0.8nm)/Pt(1.5nm)/BFO(44nm), Co(0.8nm)/Pt(1.5nm)/BFO(23nm), and Co(0.8nm)/Pt(1.5nm)/BFO(18nm).

 Influence of BiFeO3 phase on perpendicular magnetic anisotropy in Co/Pt

Rare earth iron garnets (REIGs) are magnetic insulators that can be grown as nanometer thickness films with perpendicular magnetic anisotropy (PMA), making them attractive for studies of spin orbit torques (SOT) and chiral spin textures. PMA has been achieved in epitaxial films of several REIGs on garnet substrates due to magnetoelastic anisotropy from epitaxial lattice mismatch strain1-2. However, it is of interest to develop PMA garnet films on non-garnet substrates, such as silicon for practical spintronic devices and piezoelectric substrates to investigate the effects of modulating the piezoelectric strain. PMA garnet has been grown directly on silicon, enabling integration of garnet-based spintronics into a conventional CMOS ecosystem. The films are polycrystalline, and PMA is due to the thermal expansion mismatch between the film and substrate following a high temperature anneal to crystallize the film3. Here, we report the growth of garnet films on Si and on piezoelectric substrates. Piezoelectric substrates allow modulation of the film strain through application of a voltage. This allows for tuning of the film anisotropy through magnetoelastic anisotropy, which may be used to manipulate domain walls with voltage-induced strain4. Dysprosium iron garnet (DyIG) was chosen because its two magnetostriction coefficients have the same sign. Pulsed laser deposition is then used to deposit the DyIG, which is then crystallized by a rapid thermal anneal (850 °C/5 min). DyIG grown on Si crystallized without a seed layer for thicknesses over 25nm. Atomic force microscopy of the DyIG/Si films indicates sub-nanometer surface roughness with large grain sizes on the order of 10 µm in a 41 nm thick film. DyIG on Si has a large in plane tensile strain leading to PMA with a coercivity of 4.5kOe at 41 nm thickness compared with 2.5kOe at 75nm thickness, and a room temperature saturation magnetization of 20 emu cm-3. The film coercivity can be tuned from 2.5-6 kOe by varying the annealing temperature. The anisotropy was reduced while retaining PMA by substitution of yttrium for dysprosium. We show that thinner films of DyIG may be crystallized using an underlayer of a nonmagnetic garnet Gd3Ga5O12 coated with ~2nm Pt to prevent interdiffusion. This allowed 10 nm polycrystalline DyIG films to be formed on Si with bulk-like magnetization and PMA. Films were also grown on PMN-PT (011) substrates by first sputtering a thin layer of Pt onto the substrates to prevent interdiffusion. The modulation of the magnetic properties of DyYIG/Pt/PMN-PT will be described as a function of voltage applied to the PMN-PT which produces a strain in the garnet. Fig. 1. Out of plane VSM hysteresis loop for a 75 nm DyIG/Si film substituting the dysprosium with varying amounts of yttrium. Fig. 2. AFM image of large grains in a 41 nm DyIG/Si film. Grain boundaries are indicated by the arrows.

**References:**

1. A. Quindeau, C. Avci, W. Liu, Adv. Elec. Mater., Vol. 3, 1600376 (2017). 2. E. Rosenberg, L. Beran, C. Avci, Phys. Rev. Mater., Vol. 2, 094405 (2018). 3. J. Bauer, E. Rosenberg, C. Ross, APL, Vol. 114, 052403 (2019). 4. M. Azam, et al. Nanotechnology, Vol. 31, 145201 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2391572cbd85d2f4dbab48fca73870b8.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/21c847133e550ecabc6425cc4ad545ca.jpg)

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