France



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 &lt;i&gt;extrinsic &lt;/i&gt;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].&lt;br/&gt;&lt;br/&gt;2) Turbo equalization of BPM system: The read channel of BPM system is shown in Fig. 1. The encoded bits &lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt; are modulated and recorded on the patterned media. On the receiver side, the readback &lt;i&gt;r&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt; is passed to 2D MMSE equalizer to handle the 2D interference effect, and the output LLR &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;ch&lt;/sub&gt;(&lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;) will be sent to the turbo equalization consisting of BCJR detector and LDPC decoder. The BCJR detector is performed corresponding to the received LLR &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;ch&lt;/sub&gt;(&lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;), and &lt;i&gt;extrinsic&lt;/i&gt; LLR &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;A&lt;/sub&gt;(&lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;) from LDPC decoder. Then, the &lt;i&gt;extrinsic&lt;/i&gt; LLR &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;E&lt;/sub&gt;(&lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;) is sent to LDPC decoder. The LDPC decoder consists of &lt;i&gt;N&lt;/i&gt; variable nodes, v = [&lt;i&gt;v&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;,&lt;i&gt;v&lt;/i&gt;&lt;sub&gt; 2&lt;/sub&gt;, ..&lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;, ..&lt;i&gt;v&lt;sub&gt;N&lt;/sub&gt;&lt;/i&gt;], representing the codeword bits, and &lt;i&gt;M&lt;/i&gt; check nodes, c = [&lt;i&gt;c&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;,&lt;i&gt;c&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;, ..&lt;i&gt;c&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt;, ..&lt;i&gt;c&lt;sub&gt;M&lt;/sub&gt;&lt;/i&gt;], representing the parity-check equation. The LDPC decoder uses the BP algorithm to exchange the variable-to-check message &lt;i&gt;L&lt;/i&gt;(&lt;i&gt;q&lt;sub&gt;ji&lt;/sub&gt;&lt;/i&gt;) and check-to-variable message &lt;i&gt;L&lt;/i&gt;(&lt;i&gt;r&lt;sub&gt;ij&lt;/sub&gt;&lt;/i&gt;) at each iteration. The flooding BP schedule is a conventional schedule of BP algorithm, whereby the simultaneous update of all &lt;i&gt;L&lt;/i&gt;(&lt;i&gt;q&lt;sub&gt;ji&lt;/sub&gt;&lt;/i&gt;) is followed by simultaneous update of &lt;i&gt;L&lt;/i&gt;(&lt;i&gt;r&lt;sub&gt;ij&lt;/sub&gt;&lt;/i&gt;) at each iteration. After the maximum number of iteration is reached, the LDPC decoder will send back the &lt;i&gt;extrinsic&lt;/i&gt; LLR &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;A&lt;/sub&gt;(&lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;) to the BCJR detector.&lt;br/&gt;&lt;br/&gt;3) Sequential schedule:&lt;br/&gt;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 &lt;i&gt;L&lt;/i&gt;(&lt;i&gt;q&lt;sub&gt;ji&lt;/sub&gt;&lt;/i&gt;) by ascending or descending order. For each variable node &lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt; to generate the message &lt;i&gt;L&lt;/i&gt;(&lt;i&gt;q&lt;sub&gt;ji&lt;/sub&gt;&lt;/i&gt;), the message &lt;i&gt;L&lt;/i&gt;(&lt;i&gt;r&lt;sub&gt;ij&lt;/sub&gt;&lt;/i&gt;) 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 &lt;i&gt;L&lt;/i&gt;(&lt;i&gt;q&lt;sub&gt;ji&lt;/sub&gt;&lt;/i&gt;) 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 |&lt;i&gt;L&lt;/i&gt;&lt;sub&gt;ch&lt;/sub&gt;(&lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;)| is used to measure the reliability of variable nodes instead of the residual values. The variable nodes with low |&lt;i&gt;L&lt;/i&gt;&lt;sub&gt;ch&lt;/sub&gt;(&lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;)| will start to update at early iterations, and those with high |&lt;i&gt;L&lt;/i&gt;&lt;sub&gt;ch&lt;/sub&gt;(&lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;)| 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.&lt;br/&gt;3.2) Proposed RR-BP schedule: Based on our observation and study in the recent works, the received |&lt;i&gt;L&lt;/i&gt;&lt;sub&gt;ch&lt;/sub&gt;(&lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;)| 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 &lt;i&gt;extrinsic&lt;/i&gt; LLR &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;A&lt;/sub&gt;(&lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;) 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, &lt;i&gt;E&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt; = (1/|&lt;i&gt;L&lt;/i&gt;&lt;sub&gt;A&lt;/sub&gt;(&lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;)|)∑&lt;i&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt;&lt;sub&gt;∈&lt;/sub&gt;&lt;i&gt;&lt;sub&gt;N&lt;/sub&gt;&lt;/i&gt;&lt;sub&gt;(&lt;i&gt;j&lt;/i&gt;)&lt;/sub&gt;((2&lt;i&gt;s&lt;sub&gt;i &lt;/sub&gt;&lt;/i&gt;-1)∑&lt;i&gt;&lt;sub&gt;j’&lt;/sub&gt;&lt;/i&gt;&lt;sub&gt;∈&lt;/sub&gt;&lt;i&gt;&lt;sub&gt;M&lt;/sub&gt;&lt;/i&gt;&lt;sub&gt;(&lt;i&gt;i&lt;/i&gt;)&lt;/sub&gt;|&lt;i&gt;L&lt;/i&gt;&lt;sub&gt;A&lt;/sub&gt;(&lt;i&gt;v&lt;sub&gt;j’&lt;/sub&gt;&lt;/i&gt;)|), where &lt;i&gt;s&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt; is the syndrome bit associated with the &lt;i&gt;i&lt;/i&gt;&lt;sup&gt;th&lt;/sup&gt; check node, the set &lt;i&gt;N&lt;/i&gt;(&lt;i&gt;j&lt;/i&gt;) denotes the &lt;i&gt;i&lt;/i&gt;&lt;sup&gt;th&lt;/sup&gt; check nodes connected to the variable node &lt;i&gt;v&lt;sub&gt;j&lt;/sub&gt; &lt;/i&gt;and the set &lt;i&gt;M&lt;/i&gt;(&lt;i&gt;i&lt;/i&gt;) denotes the &lt;i&gt;j&lt;/i&gt;&lt;sup&gt;th&lt;/sup&gt; variable nodes connected to the check node &lt;i&gt;c&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt;. The variable node has a large &lt;i&gt;E&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;, which means that it has not converged yet (may be in error). Hence, at any iteration, the variable nodes with the largest &lt;i&gt;E&lt;/i&gt;&lt;sub&gt;j &lt;/sub&gt;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/in&lt;sup&gt;2&lt;/sup&gt;. 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 &lt;i&gt;et.al&lt;/i&gt;, “Shuffled iterative decoding,” &lt;i&gt;IEEE Transactions on Communications&lt;/i&gt;, vol. 53, no. 2, pp. 209–213, 2005.&lt;br/&gt;[2] J. H. Kim, and &lt;i&gt;et.al&lt;/i&gt;, “Variable-to-check residual belief propagation for ldpc codes,” &lt;i&gt;Electronics Letters&lt;/i&gt;, vol. 45, no. 2, pp. 117–119, 2009.&lt;br/&gt;[3] R. Sun, and &lt;i&gt;et.al&lt;/i&gt;, &quot;Reliability-Based-Layered Belief Propagation for Iterative Decoding of LDPC Codes,&quot; 2018 &lt;i&gt;IEEE International Symposium on Information Theory (ISIT)&lt;/i&gt;, Vail, CO, 2018, pp. 1156-1160&lt;br/&gt;[4] W. Phakphisut, and &lt;i&gt;et.al&lt;/i&gt;, &quot;Serial Belief Propagation for The High-Rate LDPC Decoders and Performances in The Bit Patterned Media Systems with Media Noise,&quot; in &lt;i&gt;IEEE Transactions on Magnetics&lt;/i&gt;, vol. 47, no. 10, pp. 3562-3565, Oct. 2011.&lt;br/&gt;[5] X. Liu, and &lt;i&gt;et.al&lt;/i&gt;, &quot;Improved Decoding Algorithm of Serial Belief Propagation with a Stop Updating Criterion for LDPC Codes and Applications in Patterned Media Storage,&quot; in &lt;i&gt;IEEE Transactions on Magnetics&lt;/i&gt;, 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.

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

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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.

poster

Permanent micro-magnets are widely used in many devices such as MEMS and diverse biological applications. However, their fabrication typically includes several complex processing steps. MnBi is an intermetallic ferromagnetic alloy that possesses good permanent magnet properties such as a high Curie temperature of 711 K, a high magnetocrystalline anisotropy of 1.6 MJ/m3 at room temperature, a relatively high (BH)max of around 20 MGOe and, remarkably, an unusual positive temperature coefficient of the coercivity [1,2], which makes MnBi an attractive rare earth-free alternative for high temperature applications. In this study, a one-step route has allowed for the fabrication of highly crystalline hexagonal MnBi micro-islands (lateral dimension of 30 µm and thickness of 0.2 – 2.1 µm), by RF-sputtering of a composite target onto glass substrates at different deposition temperatures (TD) [3]. A strong impact of TD on the magnetic properties has been proven. Specifically, magnetic anisotropy could be tuned from out-of-plane (TD &lt; 375 K) to in-plane (TD = 475 K), remarkably, without applying any external magnetic field during the deposition. High values of coercivity have been obtained: 13.1 kOe at 400 K along the out-of-plane direction for the sample grown at 375 K and 14.1 kOe at 400 K along the in-plane direction for the sample grown at 475 K. The sample topography and the magnetic domain structure have been studied, observing a strong perpendicular anisotropy in micro-islands with a crater-like shape as shown in the scheme of Figure 1. It has been observed that the periodicity of stripe domains obeys the D = 1.18 * sqrt (T) law [4] in good agreement with theoretical predictions (data points and red line in Figure 1). We have validated the dependency of D vs T in MnBi thin films previously reported in literature, which has been possible through the MFM study (Fig. 1) of the crater-like shape of our MnBi micro-islands [3]. Moreover, this study has allowed us to extend the dependency of D vs T for MnBi in a thickness range well beyond previously published results. Acknowledgements IMDEA acknowledges financial support from the EU M-ERA.NET Network and MINECO through "NEXMAG" (Project Success Case at H2020 M-era.Net, Ref. PCIN-2015-126) and "3D-MAGNETOH "(Ref. MAT2017-89960-R); and from CM through "NANOMAGCOST" (Ref. P2018/NMT-4321).

**References:**

[1] K. Patel et al., Nanoscale 10, 11701 (2018) [2] E. Céspedes et al., J. Alloys Compd. 729, 1156 (2017); M. Villanueva et al., AIP Adv. 9, 035325 (2019) [3] M. Villanueva et al., Submitted for publication (2021) [4] C. Kittel, Physical Review 70, 11-12 (1946)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/65afd49c6f719bdfe8463c50b2dc14a0.jpg)
Figure 1. Dependence of domain width (D/2) on the thickness (T) of the MnBi micro-islands from MFM images (inset) measured at remanence after sample demagnetization. The D = 1.18 * sqrt (T) law is obtained by fitting the data points (red line).

 High-coercive hexagonal MnBi micro-islands with tunable magnetic anisotropy and stripe magnetic domain patterns

The III-nitride family of wide bandgap semiconductors GaN, AlN, and their alloys are important for diverse applications ranging from solid-state lighting to RF and power electronics [1]. The long spin lifetimes in nitride semiconductor platform [2] makes it attractive for exploiting the spin degree of freedom of conducting electrons. The ferromagnet/semiconductor heterostructure is crucial for fundamental spin-related device building blocks such as spin injection, spin transport, spin detection [3] and spin to charge conversion [4]. Memory devices utilizing spin-orbit torques require smooth interfaces between ferromagnets and the heavy metal or topological insulator layers on top for efficient spin transmission [5]. Epitaxial growth of magnetic layers with smooth surfaces on GaN hosting desirable properties for spintronic applications will provide a path towards spintronic devices for energy-efficient memory applications, and its integration with GaN-based RF, photonic, and wide-bandgap CMOS platforms [6]. Mn4N, a metallic nitride ferrimagnet, is an attractive candidate for direct epitaxial integration with GaN and AlN for all-nitride ferromagnet/semiconductor heterostructures. MBE grown Mn4N thin films on cubic substrates such as MgO and SrTiO3 (STO) exhibit desirable properties for spintronic applications such as a high critical temperature (TN ∼ 740 K), large spin polarization (P ∼ 70 %), strong perpendicular magnetic anisotropy (Ku = 1.1×105 J/m3), low saturation magnetization (Ms = 7.1×104 A/m on STO), large domains (∼ millimeter size on STO) and high domain wall velocities (up to 900 m/s) [7, 8]. Through exploration of nucleation and growth conditions, we uncover plasma-assisted MBE growth conditions needed for significantly improved epitaxial growth of c-axis aligned Mn4N on GaN with smooth surface morphologies. A series of four samples were grown in which the growth temperature of the 80 nm Mn4N layer was varied from Ts = 150 C to Ts = 375 C, after the deposition of 100 nm homoepitaxial undoped GaN buffer layers at Ts = 670 C, as shown in Fig. 1. Instead of out-of-plane [111] orientation of Mn4N on GaN as found in reactive MBE [9], Mn4N layers grown using plasma-assisted MBE in this work are dominated by [001] orientation, and exhibit 12-fold in-plane symmetry in the diffraction pattern. Smooth Mn4N layers are obtained at low growth temperatures of Ts &lt;= 300 C, though deep pits with depth ~ 10 nm measured by atomic force microscopy are present in the film grown at Ts = 300 C. The magnetic properties of Mn4N grown on hexagonal GaN are comparable to those in earlier reports on cubic substrates such as MgO, and can be tailored by varying the growth temperature. For example, with the increase of growth temperature, the anomalous Hall resistance hysteresis loop (Fig. 2) not only becomes squarer but also exhibits an interesting sign-flip from n-type to p-type between Ts = 225 C and Ts = 300 C. Details about the structural and magnetic properties of Mn4N on GaN will be presented.

**References:**

[1]. D. Jena, et al., Japanese Journal of Applied Physics 58, SC0801 (2019). [2]. S. Krishnamurthy, et al., Applied physics letters 83, 1761 (2003). [3]. A. Song, et al., Applied Physics Express 13, 043006 (2020). [4]. W. Stefanowicz, et al., Physical Review B 89, 205201 (2014). [5]. Q. Shao, et al., Nature communications 9, 1 (2018). [6]. S. J. Bader, et al., IEEE Electron Device Letters 39, 1848 (2018). [7]. T. Gushi, et al., Nano Letters 19, 8716 (2019). [8]. T. Gushi, et al., Japanese Journal of Applied Physics 57, 120310 (2018). [9]. S. Dhar, et al., Applied Physics Letters 86, 112504 (2005).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/99cbce60474038d00770cf3b06e8bed4.jpg)
Fig. 1 (a) Schematic of the epitaxial structures in this study and (b) Crystal and magnetic structure of Mn4N.

![](https://assets.underline.io/uploads/markdown_image/1/image/48b511882754c881e1a60b3bbff1eba4.jpg)
Fig. 2 Anomalous Hall resistance hysteresis loops at 300 K for Mn4N layers grown on MgO at (a) 450 C and on GaN at (b) 150 C (c) 225 C (d) 300 C and (e) 375 C. Note the flip in the loop orientation from (c) to (d), indicating n-type to p-type conversion.

 Epitaxial Ferrimagnetic Mn4N Thin Films on GaN by Molecular Beam Epitaxy

Ability to control the spin orientation in antiferromagnets (AFMs) has recently attracted a lot of attention [1]. In our recent work we performed systematic studies on magnetic properties of NiO in Fe/NiO/Cr/MgO multilayers for various Cr thicknesses [2]. We proved existence of a continuous strain-induced spin reorientation transition (SRT) in NiO from nearly out-of-plane direction in Fe/NiO/MgO to the in-plane direction in Fe/NiO/Cr. For ultrathin NiO layers the in plane direction of AFMs spins was determined to be perpendicular to Fe spins due to spin-flop interaction. In this contribution we studied magnetic properties of NiO in NiO/MgO(dMgO)/Cr(20 nm)/MgO(001) for different MgO thicknesses, dMgO. We also investigated how the adjacent ferromagnetic coverage layer influence the spin structure in NiO. X-ray Magnetic Linear Dichroism (XMLD) technique was used to determine magnetic ordering in NiO. The XAS spectra were collected using a linearly polarized x-ray beam for the Ni2+ L2 edge at normal (γ = 0°) and grazing (γ = 60°) x-ray incident angles. The XAS spectra were measured as a function of MgO buffer layer thickness for NiO/MgO/Cr, MgO/NiO/MgO/Cr and Fe/NiO/MgO/Cr. Figure 1 shows L2 ratio difference, defined as ΔRL2= RL2(γ = 0°) – RL2(γ = 60°), as a function of dMgO for NiO with different capping layers. For both, capped and non-capped NiO layers we noted an increase in ΔRL2 with an increase in dMgO. According to the previous studies [3] increase of ΔRL2 can be interpreted as enhancement of the out-of-plane component of NiO spins. Thus, our results show that insertion of MgO layer between NiO and Cr leads to development of out-of-plane NiO spin direction, which can be understand in terms of tensile strain exerted by MgO buffer layer on NiO. Interestingly, while there are no significant differences between ΔRL2(dMgO) dependences for MgO-capped and uncapped NiO layers (Fig. 1, circles, triangles), a change of ΔRL2 as a function of MgO thickness is much more pronounced for Fe/NiO/MgO/Cr (Fig. 1, stars). Moreover, only for Fe/NiO/MgO/Cr ΔRL2 changes a sign with an increase of dMgO which indicates that NiO spins undergo an SRT from in-plane to out-of-plane direction. To investigate the influence of Fe/NiO interactions on SRT in NiO a dedicated sample was prepared. Wedge-shaped Fe layer was grown on NiO(2 nm)/MgO(8.5 nm)/Cr(20 nm)/MgO(001), where the dMgO layer was chosen to be near the critical thickness of MgO for which SRT in NiO was observed. To elucidate if modulation of magnetic structure in NiO is influenced by magnetic properties of Fe or rather by strains from capping layer, half of the sample was capped with wedge-shaped Cr. Due to the small lattice mismatch between Cr and Fe (1.5%) strain-induced changes in magnetic properties of NiO should be similar for Cr/NiO/MgO and Fe/NiO/MgO. Prior to XAS measurement the sample was magnetized along the Fe[001] (NiO[110]) in-plane direction (φ = 0°) to study the influence of Fe magnetization on NiO spin structure. Figure 2(a) shows ΔRL2 dependence on dFe(Cr) for two azimuthal angles, φ. In case of Cr/NiO, for both φ = 0° and φ = 90° we noted no considerable ΔRL2 changes as a function of Cr thickness (dCr) (Fig. 2(a) circles, triangles). For Fe/NiO we noted a drastic difference in ΔRL2(dFe) dependence for φ = 0° and φ = 90°. Strong ΔRL2 dependence on dFe observed for φ = 90° and a lack of change in ΔRL2 as a function of dFe for φ = 0° was noted for Fe/NiO/MgO/Cr, which brings two conclusions. First, a change of sign in ΔRL2(dFe) obtained for φ = 90° proves that SRT from in-plane to out-of-plane direction in NiO can be obtained as a function of Fe thickness. Dependence of ΔRL2(dFe) on azimuthal angle in Fe/NiO/MgO together with a lack of ΔRL2 dependence on dCr in Cr/NiO/MgO prove that reorientation of NiO spins is not related to the strains exerted by capping layer, but to the magnetism of Fe layer. Second, a difference between ΔRL2(dFe) for φ = 0° and φ = 90° indicates that together with an increase in Fe thickness an in-plane anisotropy of NiO is developed. This conclusion was confirmed in XAS measurements collected as a function of φ (γ was set to 0) for different Fe thicknesses (Fig. 2(b)). While for dFe= 2 Å no change in the RL2(φ) was observed, for dFe≥8 Å we noted well-pronounced extrema in the RL2(φ) dependence for the NiO[110] and [1–10]. According to the previous studies [3], if the RL2 reaches an extremum when the polarization vector is parallel to the [110] NiO direction, the AFM spin alignment is determined from the maximum of the RL2. Thus, an in-plane component of NiO spins is perpendicular to the spins of Fe. Our results show that spin structure of antiferromagnet can be modulated by strain induced by the buffer layer and emphasize the role of adjacent ferromagnetic layer on the magnetic structure in AFM. This work was supported by the “Antiferromagnetic proximity effect and development of epitaxial bimetallic antiferromagnets – two routes towards next-generation spintronics” project, which is carried out within the Homing programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund.

**References:**

[1] C. Song, Y.You and X.Chen, Nanotechnology, Vol.29, p.112001(2018) [2] A. Koziol-Rachwal, M. Slezak, M. Zajac, APL Mater., Vol.8, p.061107 (2020) [3] W. Kim, E. Jin, J. Wu, Phys. Rev. B., Vol.81, p.174416 (2010)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3eb02b9b080b4178806eb96c5dd60035.jpg)
Fig. 1. XLD magnitudes of NiO in the NiO/MgO/Cr, MgO/NiO/MgO/Cr, Fe/NiO/MgO/Cr.

![](https://assets.underline.io/uploads/markdown_image/1/image/b44441a561c3ec343508212ae55e0015.jpg)
Fig. 2. a) XLD magnitudes of NiO in the Fe/NiO and Cr/NiO as a function of dFe(Cr), b) Ni RL2 (φ) as a function of polarization angle φ for Fe(2 Å)/NiO ,Fe(8 Å)/NiO, Fe(18 Å)/NiO and Fe(30 Å)NiO.

 Strain and ferromagnetic proximity induced spin reorientation transition in NiO

The ability to modify the magnetic anisotropy and to control spin state of AFM materials is interesting from both a fundamental and an application point of view. By taking advantage of AFM/FM coupling, magnetic anisotropy of AFM sublayer can be tailored either by appropriate choice of FM thickness or in uniform thickness system by temperature induced processes [1]. Additionally, magnetic state of the AFM can be controlled by small external magnetic field. Here, we follow the magnetic properties of epitaxial NiO(111)/Fe(110) bilayers on W(110) substrate using XMCD and XMLD spectroscopy together with PEEM microscopy. We find that the magnetic spins in NiO are rotatable within the NiO(111) plane and both NiO magnetic anisotropy and orientation of AFM spins are determined by the magnetic properties of underlying ferromagnetic Fe layer. Specifically, magnetic state and anisotropy of antiferromagnetic NiO can be modified by tuning the thickness of Fe, changing the temperature or applying small external magnetic field. A special sample was prepared for X-PEEM measurements in order to image the magnetic domain pattern below and above the critical Fe thickness of in-plane Spin Reorientation Transition (SRT). The sample consisted two 50Å and 200Å thick Fe(110) regions, covered by homogeneous (40Å) layer of NiO(111). Fig.1 a shows XMCD-PEEM and XMLD-PEEM images of the border spot between the two Fe thicknesses. The photon helicity k is aligned parallel to the Fe[1-10] direction which is easy axis of thin Fe and perpendicular to the bulk-like Fe[001] easy axis of 200Å thick Fe(110) region. The zig-zag pattern indicates the 90° in-plane rotation of Fe magnetization across the Fe (50/200Å) boundary. XMLD-PEEM image acquired at the Ni L2 edge (Fig.1 a, middle panel, “XMLD Ni L2V POL”), with the linear polarization of incoming X-rays oriented in the Fe(110) || NiO(111) surface plane shows that magnetic domain structure of Fe in the vicinity of SRT is directly imprinted into the antiferromagnetic NiO overlayer. The transition between orthogonally oriented ferromagnetic Fe regions is reflected in the shape of the magnetic domain structure of AFM NiO. In XMLD-PEEM image acquired with horizontal polarization of incoming beam (bottom panel of Fig.1a, “Ni L2 H POL”) magnetic contrast totally vanishes because the X-ray polarization is along the surface normal. This confirms that the NiO spins are confined within NiO(111) plane and no out-of-plane magnetic components are present. In case of NiO, the magnitude of XMLD effect is usually defined by the ratio of the two characteristic peaks at L2 absorption edge of Ni (RL2). We define RL2 as the higher-energy peak intensity divided by the intensity of the lower one. RL2 ratios were determined for both normal (γ = 0○) and grazing (γ = 60○) incidence geometries and we define their difference as |ΔR L2| = |RL2(γ = 0○) − R L2 (γ = 60○)|. Fig.1 b shows polar plots ΔR L2(φ) of ΔRL2 as a function of the azimuthal in-plane angle φ between polarization and Fe[1-10] direction. Instead of three-fold in-plane symmetry observed for bulk NiO(111) in pioneering works [2], exchange coupling with neighboring Fe layer makes the in-plane magnetic anisotropy of NiO two-fold with its easy axis determined by the magnetic anisotropy of ferromagnet. Specifically, NiO and Fe spins couple collinearly at the interface and so the easy axis of NiO is parallel to Fe[1-10] or Fe[001] on 50 and 200Å thick regions, respectively. In Fig. 1 c we show element sensitive magnetic hysteresis loops measured by means of XMCD and XMLD for ferromagnetic Fe and antiferromagnetic NiO sublayers, respectively. Typical square hysteresis curve is observed for thin Fe region which is below SRT critical thickness, while hard axis loop with almost zero magnetization in remanent state is presented for 200Å thick Fe. In case of NiO, on 50Å thin Fe region, external magnetic field makes no changes in XMLD as it is insensitive to 180° reversal of AFM spins. Contrary, on thick Fe one can clearly see a change of RL2 as a function of small external magnetic field (~ 500 Oe). Recently we showed that in a uniform thickness NiO(111)/Fe(110) epitaxial bilayer system, at given temperature near 300 K, two magnetic states with orthogonal spin orientations can be stabilized in antiferromagnetic NiO [1]. Field-free, reversible switching between these two AFM states was demonstrated. Here we present results of systematic investigations of such field-free, temperature induced switching of AFM NiO spins. A sample prepared for that purpose contained several 300 µm wide Fe stripes with different thickness in the range of (92Å – 113Å). Fig. 2 shows temperature dependence of RL2 ratio for various thicknesses of Fe (only heating branch is shown for clarity). It is clear that depending on the Fe thickness a critical temperature of SRT in AFM NiO can be tuned. With increasing Fe thickness the critical temperature, at which NiO spins rotate in-plane by 90○ towards Fe[1-10] direction, continuously increases. This provides possibility to cover wide temperature window ~ (250 – 380 K) for field-free, reversible switching of AFM spins.

**References:**

References: [1] M. Slezak, P. Drozdz, W. Janus, H. Nayyef, A. Koziol-Rachwal, M. Szpytma, M. Zajac, T.O. Mentes, F. Genuzio, A. Locatelli and T. Slezak. Nanoscale 2020, 12, 18091. [2] K. Kurosawa, M. Miura, S. Saito, J. Phys. C: Solid St. Phys. 13 (1980) 1521-7

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4219bb73c0734141604e4caa280a32fd.jpg)
Fig. 1 (a) XMCD-PEEM and XMLD-PEEM images at the border between thick (up) and thin (down) Fe (110) regions (200 and 50Å). (b) polar plot of XMLD for NiO (111) sublayer as a function of azimuthal in-plane angle (c) XMCD and XMLD magnetic hysteresis loops for Fe and NiO respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/7cf20ee7c47f47142b421c6a84a02f0c.jpg)
Fig. 2. Temperature dependence of XMLD (RL2) shows SRT in AFM NiO during heating process for various Fe(110) thicknesses.

 Tailoring the magnetic anisotropy and controlling the spin orientation in antiferromagnetic NiO(111) films on Fe(110).

In the last decades, transition metal oxides are growing in importance in spintronic applications. There are many different magnetic oxides, all of them very stable, with a wide range of properties that could allow broadening the range of spintronic applications [1]. Furthermore, the physical properties of these materials can be tuned by reducing the material to the nanoscale, tuning the composition, and/or incorporating it to heterostructures. However, in many cases, growth defects such as antiphase boundaries can strongly affect their magnetic properties, acting as pinning centers for magnetic domain walls. Considering their potential, it is essential to develop growth methods that allow engineering high quality oxide-based epitaxial nanostructures with customizable functionalities [2], as well as to develop the tools to fully characterize them. Extremely high-quality oxide films can be obtained by depositing metals by molecular beam epitaxy on a hot substrate, while the sample is exposed to an oxidizing agent such as molecular oxygen. We have used this method to fabricate ultrathin spinel islands of up to 100 µm2 area, with nanometer thickness and atomically flat surfaces. By this method many spinel islands (CoFe2O4 [3], Fe3O4 [4] and NiFe2O4 [5]) grow from single crystallographic nuclei and are thus expected to be antiphase boundaries-free. The extremely low defect concentration leads to a robust magnetic order and exceptionally large magnetic domains. Different microscopy techniques can be used to explore the magnetic configuration of these nanoobjects but few provide information about the vector configuration of the magnetic moments. In this work we use PhotoEmission Electron Microscopy with X-Ray Magnetic Circular Dichroic contrast (XMCD-PEEM) in order to obtain 3D information of the magnetic configuration of in-situ grown single crystal nanometer-thick islands, by acquiring images at different photon beam incidence angles. The 3D magnetization maps were used as the initial magnetization configuration for micromagnetic simulations of islands with the same lateral and vertical dimensions as the experimental ones. A careful analysis of the magnetic configuration was done by combining XMCD-PEEM with atomic force microscopy and Low Energy Electron Microscopy (LEEM) maps in order to tackle which effects might be responsible for the differences between measured and simulated experimental domain landscape. We will show how the combination of XMCD-PEEM, LEEM and modelling is a very powerful tool for the study of magnetic configurations of nanometer sized objects, and how the atomic steps in the Ru substrate give rise to efficient pinning sites for the domain walls in the particular case of ultrathin CoFe2O4 ferrites.

**References:**

[1] S. Gariglio, et al. Rep. Prog. 82, 012501, (2019) [2] S. Farokhipoor et al. Nature, 515, 379, (2015). [3] L. Martín-García et al. Adv. Mater. 27, 5955, (2015) [4] S. Ruiz-Gómez, et al. Nanoscale 10, 5566 (2018). [5] A. Mandziak et al. Scientific reports 8, 1, (2018).

**Images:**

 Domain wall pinning in epitaxial spinel ferrites grown on Ru

Large spin orbit coupling (SOC) is at the heart of many magnetic phenomena important for spintronic systems such as magnetic anisotropy, the spin Hall effect (SHE), and the Dzyaloshinskii-Moriya interaction. In a simple picture, the SOC of a material increases ∼ Z4, where Z is the atomic number [1]. Therefore there has recently been intense focus on systems containing heavy non-magnetic metals such as Pt, Au and Ir. However, heavy metals may also result in undesirable effects within these systems, such as enhanced spin damping in the ferromagnetic layer [2], and proximity-induced magnetism, which may inhibit the efficiency of spin current detection through the inverse SHE [3]. Understanding the influence of the interfacial induced moment and the large SOC is an important challenge. To understand and disentangle the roles of induced moment and large SOC, the study of uranium - with the largest Z for a naturally occurring element - may be of considerable interest. Earlier X-ray magnetic circular dichroism studies of U/FM (FM = Fe, Ni,Co) superlattices observed negligible induced moment in U when grown on FM = Ni, Co, but a relatively large moment when U is grown on Fe [4,5]. Through comparing and contrasting studies of Fe/U and Ni/U, the phenomena related to proximity induced moment and SOC may potentially be identified. Bilayer films with the structure glass/Fe(∼8 nm)/U(0-6.5 nm)/Nb(∼10 nm) were fabricated by dc magnetetron sputtering. Both the in-plane and out-of-plane magnetic anisotropy was investigated through vibrating sample magnetometry. The average in-plane coercive field for each sample provides a quantitative measure of the in-plane magnetic anisotropy and the effect uranium has. Fig.1 illustrates the non-monotonic behaviour of the average coercive field of each sample as a function of uranium thickness (triangles). Given that the iron layers thicknesses are not in the ultra-thin limit, it is not expected that any perpendicular magnetic anisotropy (PMA) would be observed. However, as seen in Fig.1 (squares), a small subset of samples do exhibit PMA. It does not appear that there is significant correlation between the in-plane anisotropy and the samples which display out-of-plane behaviour. Out-of-plane measurements revealed perpendicular magnetisation for samples with thicknesses dU =1.7, 4.4 and 5.0 nm. The unexpected presence of PMA in these relatively thick films can not be easily explained and significant further study would be required to pinpoint its origin. This non-monotonic behaviour of the in-plane anisotropy is likely linked to quantum well states which form in the uranium overlayers.Computational calculations of the Bloch spectral functions for $\alpha$-U indicate possible regions in the electronic structure which might drive this behaviour. Magnetometry studies on Ni/U also reveal non-monotonic behaviour in the in-plane anisotropy with uranium thickness, though on a smaller scale, most likely due to the weaker hybridisation of Ni and U.

**References:**

[1] Y. Tserkovnyak, et al. Rev.Mod. Phys., 77, 1375 (2005) [2] S. Mizukami, Y. Ando, and T. Miyazaki., Phys. Rev. B., 66, 104413 (2002) [3] S. Y. Huang, et al., Phys. Rev. Lett., 109, 107204 (2012) [4] R. Springell, et al., Phys. Rev. B., 77, 064423 (2008) [5] F. Wilhelm, et al., Phys. Rev. B., 76, 024425 (2007)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0e7d641a1bb8fad1d3f7f271573dc697.jpg)
Average in-plane coercive field (triangles) as a quantitative measure of in-plane magnetic anisotropy in comparison with the out-of-plane coercive field measurements (squares).}

 Uranium-Based Spintronics

The future sensing and data storage technologies will be based on the exploitation of the spin-orbit physics in ferromagnetic-heavy metal systems. Graphene (Gr), a single atomic layer of graphite, is considered an ideal material for room temperature spintronics because of its unique and intrinsically tuneable electronic properties [1]. However, its technological development for this purpose relies on the capability to engineer high-quality interfaces in which the negligible intrinsic spin-orbit interaction in Gr would be modified to allow for efficient room-temperature spin injection, detection, manipulation, or gating [2]. We have introduced a novel methodology based on the combined use of ultrahigh vacuum growth, metal intercalation, spectroscopy, and tunneling microscopy to fabricate and characterize in situ high-quality Gr-based, perpendicular magnetic anisotropy systems [3]. By combining a collection of surface science ultra-high vacuum techniques, including XPS, LEED and STM, and performing experiments as functions of the annealing temperature, the team has discerned the processes of Co intercalation underneath Gr grown epitaxially on two different heavy metal surfaces, Pt and Ir, which were deposited onto (111)-oriented insulating oxides. The experiments show that the thermally activated Co intercalation occurs in two steps in which the deposited atoms penetrate in Gr either via direct Co-C exchange or through surface defects and edges. The intercalated atoms diffuse then in 2D underneath Gr and form flat, homogeneous, and crystalline layers. These processes are characterized by a low activation temperature. The Co intercalation occurs at lower temperature and is more efficient in Gr/Pt interfaces than Gr/ Ir. Higher temperatures promote the intermixing between the FM and the metallic buffer. This research demonstrated that the metal intercalation allows for efficient tuning of the structural and electronic properties of Gr and enables the growth of high-quality flat layers with tailored magnetic properties.

**References:**

[1] W. Han, R.K. Kawakami, M. Gmitra and J. Fabian, Graphene Spintronics, Nat. Nanotech. 9, 794 (2014). [2] F. Ajejas, et al., Unravelling Dzyaloshinskii–Moriya interaction and chiral nature of Graphene/Cobalt interface, Nano Lett. 18(9), 5364-5372 (2018). [3] F. Ajejas, et al. ACS Applied Materials & Interfaces 12 (3), 4088-4096 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/078919cc2ed25c235b4d5656e631f0ab.jpg)
Figure 1. The thermally activated Co intercalation underneath Graphene occurs in two steps in which the deposited atoms penetrate in Gr either via direct Co-C exchange or through surface defects and edges. The intercalated atoms diffuse then in 2D underneath Gr and form flat, homogeneous and crystalline layers [3].

 Thermally Activated Processes for Ferromagnet Intercalation in Graphene-Heavy Metal Interfaces

1. Background Heat assisted magnetic recording technology combining L10-FePt-based bit-patterned media (BPM) has been investigated to realize terabit data storage density in hard disk drives. This technology has been referred to as heated dot magnetic recording (HDMR). The size of the magnetic dot of the BPM must be reduced to no greater than 5 nm to achieve areal recording density of 8.0 Tbpsi or more [1]. However, the critical size for L10-ordering of FePt layers was evaluated as 3 nm, below which the respective long-range order parameter degraded [2]. Then, 3D magnetic storage technology, where data are written in multi-recording layers in the depth direction of a magnetic medium, can be employed to increase the areal recording density. This technology could enable magnetic recording over10 Tbpsi, even if the dot size is large. Some recording methods that use this technology have been proposed, including a method in which data are written in order from the lower layer with the higher Curie temperature to the upper layer with the lower Curie temperature in the multi-layers. Here, the intensities of the static magnetic fields between multi-layers and rise temperatures in the layers via near-field optics are important factors for writing different data in each layer. Thus, in this study, the effects of static magnetic fields and temperatures on 3D magnetic storage in HDMR was investigated using micromagnetic simulation. 2. Calculation Method and Conditions The recording process was calculated using the Landau-Lifshitz-Gilbert equation [1] while considering thermal fluctuations as a first-stage analysis. In this study, the magnetic media had double recording layers with 8-nm dot arrays and 16-nm dot pitch corresponding to areal recording density of 5.0 T bpsi. The saturation magnetizations (Ms) of the upper and lower layer were 1.1 T and 1.2 T, and the anisotropy fields (Hk) were 3374 kA/m and 3965 kA/m at room temperature, respectively. The Curie temperatures of the upper and lower layers were 550 K and 600 K, respectively. Here the temperature (T) dependence of Ms was calculated by the Brilloiun function. The temperature dependence of the magnetic anisotropy constant (Ku(T)) was Ku(T)/Ku(0) ={Ms(T)/Ms(0)}2.1. The spacing between the recording head and medium was 4 nm, and the thickness of the recording layers was 4 nm. The thermal profiles in the recording layers were assumed to be the same as the Gaussian distribution with a full-width at half-maximum of 20 nm. The head-field strengths of the upper and lower layers were 926 and 810 kA/m at the center of the thermal profile and were constant regardless of the spacing value between the recording layers. The relative velocity between the head and medium was set to 10 m/sec. 2. Results Figure 1 shows the temperature dependence of the bit error rate (BER) in the upper layer. Here, the BER was determined as the ratio of the number of error bits to the number of on-track bits. The upper layer was recorded after the lower layer was recorded at 260 K. The spacing between the upper and lower layers was changed from 3 to 8 nm. As shown, the BER was very small (less than 0.1%) when the spacing between layers was 4 nm or greater and the temperature was approximately 175 K. As mentioned previously, the minimal spacing depends on the static magnetic fields between the recording layers. The magnetization directions in the upper layer are determined by the static magnetic fields from the lower layer during the cooling process of the medium. Therefore, the magnetization directions in the upper layer when the lower layer was recorded according to the change of the head fields were examined. Then, the temperature dependence of the matching percentage of the magnetization directions in the upper and lower layers was calculated by changing the spacing between layers. We found that the matching percentage decreased as the spacing between layers increased but did not change when the spacing was greater than 8 nm, as shown in Fig. 2. Therefore, the static magnetic fields between layers become nearly zero at the 8-nm spacing. We also found that the matching percentage of the magnetizations was the highest at 230 K. The differences in the matching percentage among temperatures were due to thermal fluctuations. At 230 K, thermal stability was high; however, the lower layer could not be recorded due to the poor temperature. Note that the lower layer was recorded without errors at 260 K. 3. Conclusion The minimal spacing for recording nearly without error was 4 nm for 3D magnetic storage in HDMR. This gives the critical value of the static magnetic fields for recording different data in each layer. Acknowledgment We thank Hitachi Corporation for the use of the simulator. We also thank Dr. Yamakawa from the Akita Industrial Technology Center for calculating the head fields.

**References:**

[1] J. Ushiyama, F. Akagi, A. Ando, and H. Miyamoto: IEEE Trans. Magn. 49(7), pp. 3612-3615 (2013). [2] T. Miyazaki, O. Kitakami, S. Okamoto, and Y. Shimada: PHYSICAL REVIEW B 72, 144419 (2005).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3eeb27ef25add13729d29a2ebe124797.jpg)
Temperature dependence of BER in upper layer

![](https://assets.underline.io/uploads/markdown_image/1/image/bd86d8e18000dd2dc5a9f7c3e2fe33d5.jpg)
Matching percentage of magnetization directions in upper and lower layers

 Effects of Static Magnetic Fields and Temperature on 3D Magnetic Storage in Heated Dot Magnetic Recording

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

L10 FePt has drawn attention from a lot of researches as the most probable material for the next generation magnetic recording media due to its high magnetocrystalline anisotropy of ~5–7×107 erg/cm3 at room temperature. Realization of columnar small magnetic grains with granular structure and good isolation, strong perpendicular (001) texture, and high degree of ordering still remain challenging for its commercial applications. In order to achieve these requirements, many studies regarding the addition of various grain boundary materials (GBMs), such as C 1,2), MgO 3), TiO2 4), Ta2O5 5), and SiO2 6) into the FePt magnetic thin films which is expected to separate the magnetic grains to promote the exchange decoupling have been done. To obtain columnar growth magnetic grains, the employment of FePt-C as a granular nucleation layer (NL) due to well separated in-plane granular structure has been widely studied.7) Furthermore, it was reported that the in-plane (001) texture component was observed when FePt-oxide granular film was directly deposited on MgO underlayer.8,9) One of the methods to reduce the in-plane (001) texture component is by introducing a granular NL in between MgO underlayer and FePt-oxide granular layer. However, the effect of the granular NL on nanostructure, including the heteroepitaxial growth and crystal orientation in relation with magnetic properties has not been clarified. Therefore, in this paper, we have quantitatively evaluated grain diameter (GD), degree of ordering (Sin), and size effect of FePt-GBM granular films with various thickness deposited on FePt-C granular film as the granular NL. As a typical FePt-oxide granular film, Fig. 1(a) shows in-plane XRD profile of FePt-SnO (0-8 nm) deposited on FePt-C (2 nm) granular NL. For references, powder pattern diffractions of FePt, and MgO are shown in the figure. In the in-plane XRD profile, at diffraction angle of around 33° and 69°, FePt(110) and FePt(220) diffractions, respectively, are observed which indicates that the granular films have c-plane sheet texture with ordered phase. Furthermore, at angle of around 24° FePt(001) diffraction is observed which reveals that the granular films have in-plane (001) texture component. Dependence of FePt(001) diffraction integral intensity of the granular films with granular NL against the film thickness is shown in Fig. 1(b). For the reference, the integral intensity of FePt(001) diffraction for FePt-SnO granular film without granular NL are also shown in the figure. There is almost no integral intensity of FePt(001) diffraction observed for FePt-C (2 nm) granular NL. Integral intensity of FePt(001) diffraction for FePt-SnO granular film with granular NL is reduced linearly against granular layer thickness and the amount the reduction increases with thicker granular layer thickness. FePt-oxide granular films with other GBM also show the same tendency with different amount of reduction which suggests that in-plane (001) texture component in the FePt-oxide / FePt-C stacked media depends on the GBM. Fig. 2 shows dependence of degree of ordering (Sin) on the grain diameter (GD) of FePt granular layers of various GBMs with and without granular NL. The GBMs are B2O3, MoO3, SnO, GeO2, WO3, Nb2O5, SiO2, TiO2, MnO, Y2O3, ZrO2, and MgO. Sin is evaluated from in-plane X-ray diffraction from the L10 FePt(110) and FePt(220) diffractions.10) GD is determined from the translation of crystal lattice along an in-plane direction in a FePt grain and was evaluated according to Scherrer’s equation 9) derived by the L10 type FePt (200) diffraction of the in-plane XRD profiles. Depends on the GBM, GD for FePt-GBM granular film, becomes smaller or larger with range changes from around 3-8 to 5-8 nm when the granular NL is introduced which indicates that magnetic grain of the stacked media is not growing in one-on-one mode. Focusing on the Sin, Sin enhancement is observed for FePt-GBM granular film with the granular NL. From the film thickness dependence analysis, it was found that from the disordered and ordered part of the film, the Sin for the ordered part was improved. In the conference, the detail analysis of Sin and magnetic properties will be discussed.

**References:**

1) J. S. Chen, B. C. Lim, J. F. Hu, B. Liu, G. M. Chow, and G. Ju, Appl. Phys. Lett., 91, 132506 (2007). 2) A. Perumal, Y. K. Takahashi, and K. Hono, J. Appl. Phys., 105, 07B732 (2009). 3) Y. Peng, J.-G. Zhu, and D. E. Laughlin, J. Appl. Phys., 99, 08F907 (2006). 4) Y. F. Ding, J. S. Chen, B. C. Lim, J. F. Hu, B. Liu, and G. Ju, Appl. Phys. Lett., 93, 032506 (2008). 5) B. C. Lim, J. S. Chen, J. F. Hu, P. W. Lwin, Y. F. Ding, K. M. Cher, and B. Liu, J. Appl. Phys., 105, 07A730 (2009). 6) E. Yang and D. E. Laughlin, J. Appl. Phys., 104, 023904 (2008). 8) B. S. D. Ch. S. Varaprasad, M.Chen, Y. K. Takahashi, and K. Hono, IEEE Trans. Magn., 49, 718 (2013). 8) J. Wang, S. Hata, Y. K. Takahashi, H. Sepehri-Amin, B. S. D. Ch. S. Varaprasad, T. Shiroyama, T. Schrefl, and K. Hono, Acta Mater., 91, 41 (2015). 9) T. Saito, K. K. Tham, R. Kushibiki, T. Ogawa, and S. Saito, Jpn. J. Appl. Phys., 59, 045501 (2020). 10) P. Scherrer, Göttinger Nachr. Ges. 2, 98 (1918).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5c6d827366f9a10189af9bc51824d85e.jpg)
Fig.1 (a) In-plane XRD profile for Sub./ CoW(80 nm)/ MgO (5 nm)/ FePt-C (2 nm)/ FePt-SnO (0-8 nm)/ C (7 nm) and (b) dependence of FePt(001) diffraction integral intensity of the granular films on the film thickness.

![](https://assets.underline.io/uploads/markdown_image/1/image/2c38656cae81f4c67005b703bee658d8.jpg)
Fig. 2 Dependence of degree of ordering (Sin) on the grain diameter (GD) of FePt granular layers of various GBMs with and without granular NL.

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