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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.&lt;br/&gt;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.&lt;br/&gt;It should be noted that the magnitude of the MR peak is equal to the AHE resistance (R&lt;sub&gt;H ≈&lt;/sub&gt; 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 |v&lt;sub&gt;DW&lt;/sub&gt;| =w/(t&lt;sub&gt;S &lt;/sub&gt;- t&lt;sub&gt;N&lt;/sub&gt;), where t&lt;sub&gt;N&lt;/sub&gt;, t&lt;sub&gt;S &lt;/sub&gt;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 |v&lt;sub&gt;DW&lt;/sub&gt;| 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-H&lt;sub&gt;n&lt;/sub&gt;, thus: V&lt;sub&gt;DW&lt;/sub&gt; = αV&lt;sub&gt;sweep field&lt;/sub&gt; × (e&lt;sup&gt;(β(H-H&lt;sub&gt;n&lt;/sub&gt;)&lt;/sup&gt; - γ). Fitting the expression to experimental data we deduce α, β, and γ.&lt;br/&gt;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 H&lt;sub&gt;c&lt;/sub&gt; 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.

INTERMAG 2021

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

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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.

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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.

 Effect of FePt-C nucleation layer on magnetic properties and nanostructure for FePt-oxide / FePt-C stacked media

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.

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