France



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(R&lt;sub&gt;d&lt;/sub&gt;) is 30%. The R&lt;sub&gt;d &lt;/sub&gt;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 Mumax&lt;sup&gt;3&lt;/sup&gt;. 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 nm&lt;sup&gt;3&lt;/sup&gt;, 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)&lt;br/&gt;[2]. Burn, D. M., &amp; Atkinson, D. Scientific reports, 6, 34517 (2016).&lt;br/&gt;[3]. L. K. Bogart and D. Atkinson, Physics Review B., Vol. 79, p.054414 (2009)&lt;br/&gt;[4]. Y. Gao, B. You, X. Z. Ruan, Scientific Reports., Vol. 6, Article number: 32617 (2016)&lt;br/&gt;[5]. J. Brandão, R. L. Novak, H. Lozano., Journal of Applied Physics., Vol. 116, p.193902 (2014)&lt;br/&gt;[6]. D. M. Burn, D. Atkinson, Scientific Reports., Vol. 6, Article number: 34517 (2016)&lt;br/&gt;[7]. K. A. Omari, T. J. Hayward, Scientific Reports., Vol. 7, Article number: 17862 (2017)&lt;br/&gt;[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.

INTERMAG 2021

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

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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.

poster

As a next-generation technology for heat-assisted magnetic recording (HAMR), L10 typed FePt-based granular film with a c-plane sheet texture deposited on a flat MgO underlayer is a promising candidate [1]. Although it has been reported that there existed FePt grains whose c-axes are parallel to the film plane (in-plane grains) with FePt grains whose c-axes are normal to the film plane (normal grains) in a FePt granular film [2 - 4], a dominant factor affecting the c-axis orientation of FePt grains with cubic (disorder) and/or tetragonal (order) system was not clarified yet. Therefore, we evaluated the volume ratio of in-plane grains to normal grains in the FePt granular films with various GBMs (GBMs: B2O3, MoO3, SnO, WO3, Nb2O5, TiO2, MnO, Y2O3, MgO, C) and discussed about an effect of the volume ratio and degree of order on perpendicular magnetic anisotropy for the granular films. First of all, we have proposed a new approach to the evaluation of the volume ratio of in-plane grains to normal grains, Rparallel, using in-plane XRD profiles. Rparallel is defined as follows; Rparallel = (I002Meas / I002Calc) / (I200Meas / I200Calc + I002Meas / I002Calc). (1) Here, IhklMeas and IhklCalc are experimentally obtained and calculated values of the integrated intensity of the (hkl) diffractions from FePt phase, respectively. In in-plane XRD profiles, I200 and I002 were observed, which meant there existed not only normal grains but also in-plane grains in the granular films. Fig. 1 (a) shows the dependence of Rparallel on lattice constant of the MgO layer just under the FePt granular layer in the films with various GBMs. There was negative correlation between Rparallel and the lattice constant of the MgO underlayer. Especially in the FePt-C granular film, Rparallel is about 0. The lattice constants were expanded and contracted from literature value (4.213 Å) depending on GBMs. These results mean that the stack of the FePt granular layer with the GBM causes the lattice strain of the MgO underlayer since the lattice constant of MgO underlayer is the same before the FePt-GBM granular layer stacking, which suggests interdiffusion of GBM elements to the MgO underlayer. Fig. 1 (b) shows Rparallel as a function of the degree of order (Sin) for the FePt granular films with various GBMs. The negative correlation between Rparallel and Sin was observed. This result indicates that ordering into L10 structure results in c-axis orientation of FePt grains. From the results of Fig. 1 (a) and (b), the lattice constant of the MgO underlayer has the positive correlation with Sin, which suggests that the lattice strain affects Sin. Fig. 2 shows (a) L2θsat / (L2θsat + L4θsat) and (b) L4θsat / (L2θsat + L4θsat) plotted against Rparallel. Here, L2θsat and L4θsat are the saturated torque coefficient of the twofold components and the fourfold components measured by 90 kOe torquemetry [5], respectively. We considered that the fourfold components of the torque curves were induced by an overlap of the torque curve with a 90° phase shift which was due to in-plane grains [5]. Therefore, L4θsat is index for in-plane grains and L4θsat / (L2θsat + L4θsat) reflects the volume ratio of in-plane grains, while L2θsat / (L2θsat + L4θsat) reflects that of normal grains. L2θsat / (L2θsat + L4θsat) and L4θsat / (L2θsat + L4θsat) had negative and positive correlation with Rparallel, which means L2θsat / (L2θsat + L4θsat) and L4θsat / (L2θsat + L4θsat) also had correlation with Sin. This result is consistent with the relationship between Rparallel and Sin and it indicates that there is a significant correlation with c-axis orientation and degree of order.

**References:**

[1] D. Weller, O. Mosendz, G. Parker, S. Pisana, and T. S. Santos, Phys. Status Solidi A, 210, 1245 (2013). [2] T. Saito, K. K. Tham, R. Kushibiki, T. Ogawa, and S. Saito, Jpn. J. Appl. Phys., 59, 045501 (2020). [3] T. Shiroyama, T. Abe, Y. Takahashi, and K. Honoet, IEEE Trans. Magn., 49, 3616 (2013). [4] J. Wang, H. Sepehri-Amin, H. Tajiri, T. Nakamura, K. Masuda, Y.K. Takahashi, T. Ina, T. Uruga, I. Suzuki, Y. Miura, and K. Hono, Acta Materialia, 166, 413 (2019). [5] T. Saito, K. K. Tham, R. Kushibiki, T. Ogawa, and S. Saito, IEEE Trans. Magn. (in press) (DOI: 10.1109/TMAG.2020.3015515).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f3bbd5dfa832c6c518a87adc258db30c.jpg)
Fig.1 Volume ratio of FePt grains with the c-axes parallel to the film plane, Rparallel plotted against (a) lattice constant of the MgO layer under the FePt granular layer with various GBMs and (b) degree of order of FePt grain.

![](https://assets.underline.io/uploads/markdown_image/1/image/151ea1f0d248ff743aabeab6908843f6.jpg)
Fig. 2 (a) L2θsat / (L2θsat + L4θsat) and (b) L4θsat / (L2θsat + L4θsat) plotted against Rparallel. L2θsat is the saturated torque coefficient of the twofold components and L4θsat is that of fourfold component.

 Correlation among lattice strain of MgO underlayer at hetero-interface between MgO/ FePt, degree of order, and ratio of c-axis parallel to normal for FePt granular film

I. INTRODUCTION It is expected that a heated-dot magnetic recording (HDMR) is a significant future technology to attain the areal density over 5 Tdpsi with bit-patterned media (BPM) [1], [2]. In this research, a two-stage signal processing scheme for the HDMR system with polar coding schemes and double-layered BPM is proposed. This approach assumes to be applicable to a HDMR system with areal density of up to 5Tdpsi. This proposed scheme uses two independent log-likelihood ratio (LLR) detectors which are cascaded and able to detect each recoded data sequence recoded on each layer in order. A high rate polar encoding scheme is used for the error-correcting scheme for the second layer. In generally, the effective rate of the HDMR system with double-layered BPM can be improved twice of that of a HDMR system with single-layered BPM. II. TWO-STAGE SIGNAL PROCESSING SCHEME FOR HDMR Fig.1 shows the block diagram of the proposed signal processing scheme for a HDMR system using double-layered BPM. In Fig.1, double-layered recording is assumed for the HDMR system. In this read/write system, a raw data sequence {ak} is input into each modulation encoder which gives a run length limited (RLL) constraint sequence {bi,k'} for the down-track direction. One of the RLL constraint sequence is transformed into the precoded sequence {c0,k0'} and is recorded on the first layer. The other RLL constraint sequence is encoded into the polar codeword sequence and transformed into the precoded sequence{c1,k1'} with 16 CRC bits. The sequence {c1,k1'} is recorded on the second layer. The sequence {ci,ki'} is NRZ-recorded on islands made of the discrete double layered perpendicular magnetic medium with a soft under layer. These islands are arranged on a circular grid in the surface of recording media. We assume head/medium conditions and modeling with FePt granular magnetic media to achieve areal density of 2.5Tdpsi using micro-magnetic simulation [3],[4]. Both of magnetic dots are called "upper dot" and "lower dot" in this research. In the recording process, it is assumed that magnetization is calculated by use of the Landau-Lifshitz-Gilbert equations for both of magnetic dots. For the readback HDMR channel, the readback signal of BPM is represented by our evaluated 2D pulse response and the normalized peak amplitude is Ap. In this system, the parallel readback signal sequence {r'k'} is obtained by combining readback signal sequences from the pair of upper and lower dots. In Fig. 1, r'k' = r0,k' + r1,k’ + nk' , where the sequence{ri,k'}is the readback signal sequence from the k-th dot of the i+1-th layer and the noise sequence {nk’} is added at the reading point. The sequence {nk’} is additive white Gaussian noise (AWGN) with zero mean and variance . The reproducing waveform corresponding to the recording sequences readback by the reading head is input into the equalizer which consists of a 2D low-pass filter (LPF) and the 2D transversal filter (TVF). The equalization is performed so that the overall characteristic between the input of recording head and the output of the equalizer is equal to the aimed 2D generalized partial response (GPR) targets. The equalizer output sequence {yk'} is obtained which sums equalizer output sequences from the pair of two upper and lower dots. In the equalizing process, tap-gain coefficients in the 2D TVF are evaluated by minimizing the expectation of the mean square error (MSE) E({ek’}), where the sequence {ek’}is the equalized error sequence between the ideal GPR target output sequence {dk’} and the sequence {yk’}. The signal-to-noise ratio (SNR) at the reading point is defined as the ratio of Ap and the noise power of AWGN. In decoding process, the equalizer output sequence {yk'} is decoded by the one-dimensional (1D) multi-level LLR detector. Both of the estimated RLL codeword sequence {b'0,j} and readback signal waveforms corresponding to the sequence {c'0,k0'}are given as the detector output. Using this estimated readback signal waveforms {r0,k'}, it is able to estimate the readback signal waveforms{r'1,k'}. The estimated readback signal waveforms {r1,k'} is input into 1D TVF and equalized to generate the aimed 1D GPR target output sequence and detected by the 1D LLR detector and CRC-aided successive cancellation list (SCL) decoder [5]. The output sequence form this decoder is the estimated RLL codeword sequence {b'1,j}. The sequences {b'i,j} are decoded by RLL decoders and we get the estimated the data sequence {a'k} is obtained after demodulation. The block error rate (BER) performance is evaluated by computer simulation between the sequences {ak} and {a'k}. III. ERROR RATE PERFORMANCES In Fig.2, the solid line shows the BER performance of the proposed coding GPR scheme with the double-layered BPM. The dashed and dotted lines show the performances of the compared 64/65(0,8) coding schemes using the single-layered, double-layered BPM. These coding schemes have the effective transmission rate reff = 1.96, 1.97, 0.985, respectively. The recording condition of the proposed scheme corresponds to the areal density of 5.0Tdpsi. As can be seen Fig.2, the proposed scheme outperforms that of the compared 1D scheme by about 6.0 dB of SNR gains at a BER of 10-6. IV. CONCLUSIONS In this digest, we propose a two-stage signal processing scheme for a HDMR system with polar coding and double-layered BPM. Our proposed scheme shows the possibility of development of the advanced signal processing scheme with multi-layered recording.

**References:**

[1] T. R. Albrecht, et al., IEEE Trans. Magn., 51, 5, 0800342, May 2015. [2] J. K. W. Yang, et al., Nanotechnology, 38501, Aug. 2011. [3] F. Akagi, et al., J. Appl. Phys., 101, 09H5011, Apr. 2007. [4] F. Akagi, et al., J. Magn. Magn. Mater., 324, pp.309–313, Apr. 2012. [5] I. Tal and A. Vardy, IEEE Trans. Inf. Theory, 61, 5, 2213–2226, May 2015.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d4b5304e77b82acb027a65f955783467.jpg)
Fig.1 Block diagram of the proposed HDMR system.

![](https://assets.underline.io/uploads/markdown_image/1/image/55db71732ce3c89119188afb2e622de2.jpg)
Fig.2 BER performances.

 Two-Stage Signal Processing Schemes for Heated Dot Magnetic Recording with Polar Coding and Double-layered Bit Patterned Media

1) Introduction: Low-density parity-check (LDPC) codes have been known to exhibit good error-correcting performance by using the belief propagation (BP) decoding algorithm. The BP algorithm commonly updates all variable nodes simultaneously, known as “flooding BP” schedule. However, the flooding BP schedule has drawback on convergence speed required in high-speed applications. Alternatively, the “sequential” schedules of variable node updates, e.g., Shuffled-BP (S-BP) [1], V-to-C Residual BP (VCR-BP) [2], and Reliability-based-Layered BP (RBL-BP) [3] are shown that the convergence speed is twice faster than flooding BP schedules. Previously, the S-BP schedule is applied in the turbo equalization of magnetic recording system [4], the results on bit patterned media (BPM) system show that the S-BP schedule can achieve some coding gains over the flooding BP schedule. The paper [5] also proposed the stopping criterion of S-BP schedule in BPM system to reduce the number of updated variable nodes per iteration. Motivated by the fact that the previous works [4,5] utilize the S-BP schedule straightforwardly in BPM systems, in this work, we then propose the sequential schedules, namely the “Reliability ratio-based BP (RR-BP)” schedule in the turbo equalization of BPM system. The update sequences of RR-BP schedule may differ at each iteration according to the extrinsic LLR. Our results show that the RR-BP schedule applied in BPM system gives better performance than the S-BP [1,4,5] and RBL-BP [3]. 2) Turbo equalization of BPM system: The read channel of BPM system is shown in Fig. 1. The encoded bits vj are modulated and recorded on the patterned media. On the receiver side, the readback rj is passed to 2D MMSE equalizer to handle the 2D interference effect, and the output LLR Lch(vj) will be sent to the turbo equalization consisting of BCJR detector and LDPC decoder. The BCJR detector is performed corresponding to the received LLR Lch(vj), and extrinsic LLR LA(vj) from LDPC decoder. Then, the extrinsic LLR LE(vj) is sent to LDPC decoder. The LDPC decoder consists of N variable nodes, v = [v1,v 2, ..vj, ..vN], representing the codeword bits, and M check nodes, c = [c1,c2, ..ci, ..cM], representing the parity-check equation. The LDPC decoder uses the BP algorithm to exchange the variable-to-check message L(qji) and check-to-variable message L(rij) at each iteration. The flooding BP schedule is a conventional schedule of BP algorithm, whereby the simultaneous update of all L(qji) is followed by simultaneous update of L(rij) at each iteration. After the maximum number of iteration is reached, the LDPC decoder will send back the extrinsic LLR LA(vj) to the BCJR detector. 3) Sequential schedule: 3.1) Previous schedules: S-BP [1] introduced the ordering of message updates resulting in the best convergence speed and/or decoding performance. An iteration consists of the sequential update of all L(qji) by ascending or descending order. For each variable node vj to generate the message L(qji), the message L(rij) from its connected check nodes is required. Even though the convergence speed of S-BP schedule is twice as fast as that of the flooding BP schedule, the convergence speed can be further increased by using dynamic schedules. The VCR-BP updates have been presented in [2] to update the messages according to the difference between the message L(qji) in current and previous iterations. The drawback of VCR-BP schedule is the high complexity of the residual operations. Therefore, in paper [3], the RBL-BP schedule is proposed to omit the residual computations, the absolute of LLR values from the channel |Lch(vj)| is used to measure the reliability of variable nodes instead of the residual values. The variable nodes with low |Lch(vj)| will start to update at early iterations, and those with high |Lch(vj)| will start later. The performances of RBL-BP schedule is comparable to VCR-BP schedule. However, in MR systems, only the fixed schedule, such as S-BP, is studied [4-5]. In this work, we then propose the dynamic schedules for BPM system with high-level interferences and media noise in which the ordering of message updates will be generated based on the reliability ratio of extrinsic LLR. 3.2) Proposed RR-BP schedule: Based on our observation and study in the recent works, the received |Lch(vj)| introduced in [3] cannot indicate the reliabilities of variable nodes in the MR system due to the high-level interferences and media noise. Therefore, in this work, we then propose the RR-BP schedule which utilizes the extrinsic LLR LA(vj) combined with syndrome checking to indicate the reliability of each variable node instead of channel information. Here we will introduce the update criterion in terms, Ej = (1/|LA(vj)|)∑i∈N(j)((2si -1)∑j’∈M(i)|LA(vj’)|), where si is the syndrome bit associated with the ith check node, the set N(j) denotes the ith check nodes connected to the variable node vj and the set M(i) denotes the jth variable nodes connected to the check node ci. The variable node has a large Ej, which means that it has not converged yet (may be in error). Hence, at any iteration, the variable nodes with the largest Ej will be firstly updated and followed by the remaining variable nodes. Fig. 2 shows the BER performance comparisons of the RR-BP, RBL-BP, S-BP, and flooding BP schedules in BPM system with 2Tb/in2. The results show that the RR-BP schedule offers about 0.13, 0.14, and 0.25 dB coding gains compared to RBL-BP, SBP, and flooding BP schedules, respectively.

**References:**

[1] J. Zhang, and et.al, “Shuffled iterative decoding,” IEEE Transactions on Communications, vol. 53, no. 2, pp. 209–213, 2005. [2] J. H. Kim, and et.al, “Variable-to-check residual belief propagation for ldpc codes,” Electronics Letters, vol. 45, no. 2, pp. 117–119, 2009. [3] R. Sun, and et.al, "Reliability-Based-Layered Belief Propagation for Iterative Decoding of LDPC Codes," 2018 IEEE International Symposium on Information Theory (ISIT), Vail, CO, 2018, pp. 1156-1160 [4] W. Phakphisut, and et.al, "Serial Belief Propagation for The High-Rate LDPC Decoders and Performances in The Bit Patterned Media Systems with Media Noise," in IEEE Transactions on Magnetics, vol. 47, no. 10, pp. 3562-3565, Oct. 2011. [5] X. Liu, and et.al, "Improved Decoding Algorithm of Serial Belief Propagation with a Stop Updating Criterion for LDPC Codes and Applications in Patterned Media Storage," in IEEE Transactions on Magnetics, vol. 49, no. 2, pp. 829-836, Feb. 2013.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/93430bbcb9a6b2f1482542343b1014dd.jpg)
Read channel of BPM systems.

![](https://assets.underline.io/uploads/markdown_image/1/image/901241dccd9305eb37888381a6a15d4b.jpg)
BER performance comparisons.

 Reliability Ratio-Based Serial Scheduling of LDPC Decoder for Turbo Equalization Schemes

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

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.

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

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