Combinatorial dependence of magnetic printing characteristics in double magnet master media for energy-assisted magnetic recording

The amount of information handled by society is increasing explosively due to the development of information and communication technology. Because the demand for hard disk drives (HDDs), especially in data centers, is increasing, the problem of information storage becomes more serious. One solution is to increase the areal recording density of HDDs by overcoming the trilemma, which is arising from the conflicting requirements between signal-to-noise ratio, writeability, and stability.¹ Energy-assisted magnetic recording (EAMR) such as heat-assisted magnetic recording (HAMR)² and microwave-assisted magnetic recording (MAMR)^3–5 is feasible to overcome the trilemma by improving writability and enhancing areal recording density. The commercialization of EAMR also begins recently. Two-dimensional magnetic recording with shingled writing^6,7 has also been proposed for increasing track density, which is enabled by partial overlapping of recorded tracks.

On the other hand, servo signal writing is one of serious problems for high areal recording density HDDs in order to supply the demand for HDDs. The self-servo track writing technology, which regenerated from previous written servo patterns, has been adopted during head-disk assembly.^8,9 However, since the servo signal writing in the present hard disks takes a few days per one drives on manufacturing process, and the supply of HDDs can not keep up with the social demand.

Magnetic printing technique is a strong candidate for servo track writing with extremely high speed and low cost.^10,11 Recently, the double magnet printing technique was proposed for EAMR media with high coercivity of recording layer.^12,13 The double magnet master (DMM) can enhance the recording field to improve servo-writing characteristics due to two different magnets. However, the influence of combination of two magnets has not been clarified yet. In this study, the combinatorial dependence in double magnet master was investigated by the micromagnetic simulation.

For comparison, the conventional master is called single magnet master in this study. Two kinds of magnetic materials in the conventional master are considered. One of feasible materials is FeCo alloy with a large saturation magnetization, which is hereafter called soft single magnet (SSM). The other material is CoPt alloy which has a perpendicular anisotropy and moderately sufficient saturation magnetization,¹¹ which is hereafter called hard single magnet (HSM). The schematic illustrations of these single magnet master were shown in Figs. 1(a) and 1(b), respectively.

On the other hands, the DMM media consists of two magnetic materials with different magnetic properties. Two magnetic materials have no exchange interaction between these materials by insertion of non-magnetic separation layer.¹³ One material has a coercivity higher than the coercivity of the recording layer, while the other has a lower coercivity. The promising material of high coercivity magnet in DMM is L1₀ − FePt ordered alloy with extremely high magnetocrystalline anisotropy K_u of 7 × 10⁷ erg/cm³.^2,14 This hard magnetic materials has the extremely large coercivity of up to 70 kOe by fabricating nano-scaled patterns. Thus, during application of printing field H_p in double magnet printing, the magnetization of lower coercivity parts orients to the direction of printing field while high coercivity pars is not subject to magnetization reversal. The candidates of lower coercivity part are also the above described FeCo and CoPt alloys. Thus, two combination of double magnet are considered. The lower coercivity magnet of FeCo alloy in DM master media is called soft double magnet (SDM) while the lower coercivity magnet of CoPt alloy is called hard double magnet (HDM). Therefore, in this study, four kinds of master media were considered as shown in Figs. 1(a)–(d). The magnetic parameters in SSM, HSM, SDM, and HDM media as shown in Table I are used for calculating recording field H^r during the application of printing field H_p.

Figure 1(e) shows the schematic illustrations of DMM medium and recording layer during printing process. The bit length was set to 10 or 20 nm. The magnetic pattern thickness was fixed to be 10 nm, and the magnetic spacing between master and recording layer was also fixed to be 2 nm in each case.

The exchange coupled composite media, which consists of hard- and soft-magnetic layers with granular structure, were utilized as the recording layer. In this study, the hexagonal column grains with the grain size of 4.6 nm, the grain spacing of 0.2 nm, the height of 12 nm were assumed as shown in Fig. 1(f). This is an ideal granular structure but the purpose of this study is to confirm magnetic printing characteristics. The thicknesses of soft- and hard-layers are 4 and 8 nm, respectively. The material parameters in recording layer are shown in Table II. The intergranular exchange coupling constant is 1.0 × 10⁻⁶ erg/cm, the interlayer exchange coupling constant is 70 erg/cm², and the intergrain exchange coupling constant is 1.0 erg/cm². These parameters showed the coercivity of recording layer is about 10 kOe which is the representative value of EAMR HDDs.

The test pattern of master media was assumed to be line/space (L/S), which is similar to automatic gain control part in servo-signals. First, the recording field H^r generated from the master medium was calculated by micromagnetic simulation.¹⁰ By utilizing the recording field distribution, the printed magnetization in recording layer was also calculated, and the printing characteristics in each case was discussed.

Figure 2(a) shows the recording field distributions of L/S patterns with pattern length of 20 nm, which corresponds to bit length, by utilizing four kinds of master media. The effective switching fields H^eff,

are also shown in Fig. 2(b). The printing field H_p is 10.0 kOe. In SSM and HSM, the recording field H_r is the sum of the printing field H_p and the magnetostatic field generated from soft or hard magnet, while in SDM and HDM, the recording field H_r is the sum of the magnetostatic fields generated from low-coercivity magnet and high-coercivity magnet parts. The recording field difference $ΔHzr$ of about 11 kOe for double magnet master is about twice as that for single magnet master. It is clearly found that the recording field can be enhanced in both cases of SDM and HDM. Moreover, the $ΔHzr$ of SDM is slightly larger than that of HDM. In case of SSM and SDM, the recording field underneath at the center of soft magnet slightly decreases comparing with hard magnet in HSM and HDM, since the magnetization of soft magnet patterns does not saturate in the application of printing field of 10 kOe, which is related to the effective switching field distribution. Since the saturation field for the soft magnet is associated with the demagnetizing factor N of magnetic patterns, the increase in pattern thickness improves the recording field strength.

Figure 3 shows the recording field difference $ΔHzr$ as a function of printing field. The printing field dependence of HDM is quite different from that of SDM because of different magnetic anisotropy in low-coercivity magnet. The $ΔHzr$ of HDM is almost constant even if the printing field increases, while the $ΔHzr$ of SDM increases as the printing field increases and saturates for the printing field of about 13 kOe. This saturation field is determined from the demagnetizing factor N of magnetic pattern related to the pattern width and the pattern thickness of master media. The maximum value $ΔHzr$ of SDM is larger than that of HDM because of different saturation magnetization of low-coercivity magnet. Moreover, the saturation field of SDM is less than that of SSM since the demagnetizing factor of SDM is effectively reduced by the magnetostatic field from high-coercivity magnet as shown in Fig. 4. In case of SSM, the saturation field H_s is about 16 kOe and the demagnetizing factor is about 0.6 from estimating the demagnetizing field $Hdsoft=4πNMssoft$⁠. On the other hand, in case of SDM, the saturation field H_s is about 13 kOe. This difference is related to the stray field from high-coercivity magnet, $Hdhard$⁠. The effective demagnetizing field at the low-coercivity magnet is $Hd′=Hdsoft−Hdhard$⁠, thus, the saturation field of SDM media is smaller than that of SSM media. The lower saturation field effectively causes the large saturation magnetization of low-coercivity magnet, FeCo alloy.

Figure 5 shows the printed magnetization distribution by utilizing four kinds of master media. The printing field of 8.5 kOe is applied, which gives the maximum printing characteristics in each master media. The optimum printing field is slightly less than the coercivity of recording layer. In each case, the magnetization reversal occurs underneath low-coercivity magnetic pattern, and the printed magnetization pattern has the almost bit length. In case of single magnet master media, the printing performance of HSM is superior to that of SSM due to larger ΔH^r for the application of printing field of 8.5 kOe. However, there are many unreversed regions and non-straight transition in single magnet master cases, and these unreversed region and non-straight transition cause the error during servo tracking. On the other hands, the double magnet master media can clearly print L/S patterns comparing with single magnet although there are a few unreversed regions underneath only the center of low-coercivity magnetic pattern. As the previous report,¹³ the printed magnetization pattern is affected by the effective recording field as shown in Fig. 2(b), and the magnetization reversal is likely to occur at the magnetic pattern edge of master media.

Figure 6 also shows the recording field distributions of L/S patterns with pattern length of 10 nm by utilizing four kinds of master media. The printing field H_p is 10 kOe. The recording fields H_r of SDM and HDM are also enhanced comparing with these of SSM and HSM. The recording field difference $ΔHzr$ of about 11 kOe for double magnet master is about twice as that for single magnet master. Moreover, the $ΔHzr$ of SDM is larger than that of HDM due to larger saturation magnetization of low-coercivity magnet in SDM.

Figure 7 shows the recording field difference $ΔHzr$ as a function of printing field. The recording field difference $ΔHzr$ of double magnet is larger than that of single magnet. The printing field dependence of $ΔHzr$ is similar to the case of bit length of 20 nm. The saturation field of SDM is about 10 kOe and is smaller than that of pattern width of 20 nm due to the aspect ratio of magnetic pattern. Moreover, the saturation field of SDM is also less than that of SSM because of effective reduction of the demagnetizing factor.

Figure 8 shows the printed magnetization distribution by utilizing four kinds of master media. The printing field of 10 kOe is applied. The double magnet master media can clearly print L/S patterns comparing with single magnet. The magnetization printed by SDM is superior to that of HDM. This is because the recording field difference of SDM is larger than that of HDM as shown in Fig. 3. If the printing field corresponding to the coercivity of recording field is less than about 6 kOe, the superiority is reversed. But, since the next generation EAMR media has more than 10 kOe, the SDM is more adequate for writing servo-signals onto EAMR media.

As a result, the larger recording field difference $ΔHzr$ improves the printing characteristics, and the double magnet master is clearly superior to the single magnet master. Moreover, the saturation field of low-coercivity magnet in double magnet master is desirable less than the optimal printing field, which is slightly less than the coercivity of recording layer. In order to reduce the saturation field of low-coercivity magnet in double magnet master, the magnetic pattern thickness becomes thicker to reduce the demagnetizing factor of low-coercivity magnet. The thicker magnetic pattern enhances the recording field difference $ΔHzr$ as the previous report.¹³ Especially, since the demagnetizing factor in case of long bit pattern is larger than that of short bit pattern, the whole pattern thickness should be optimized according to the long bit pattern. The other ways to reduce the saturation magnetization is to find out the magnetic materials with larger saturation magnetization and larger perpendicular anisotropy. In any case, the double magnet master media is superior to the conventional master media.

For higher coercivity EAMR media, the magnetization distributions printed by SDM and HDM were also calculated. As the previous report,¹³ the coercivity of recording layer can be varied by adjusting soft- and hard-layer thicknesses of grains. The soft layer has 2 nm thickness and the hard layer has 10 nm thickness resulting to the coercivity of about 27 kOe. The printing field is 25.5 kOe in this case. Figure 9 shows the printed magnetization distributions by utilizing two kinds of DMM media. The DMM printing could write the L/S patterns onto the EAMR media with more-than 20 kOe. The larger printing field causes larger recording field difference ΔH^r in case of SDM, while in case of HDM, the recording field difference ΔH^r is almost constant. Thus, the recording field difference ΔH^r of SDM is larger than that of HDM, and can write the servo signals onto higher coercivity EAMR media. It was confirmed that the potential of DMM printing was revealed for writing the servo-signals onto the next generation EAMR media. Especially, the printing characteristics of SDM is superior to that of HDM due to larger saturation magnetization of low-coercivity magnet.

In this study, the combinatorial dependence in double magnet master was investigated by the micromagnetic framework. Compared to the single magnet, more details of double magnet master media were discussed. The HSM, SDM, and HDM media can write L/S pattern in case of L/S pattern with bit length of 20 nm. The double magnet master media can clearly print L/S patterns comparing with single magnet in case of 10 nm. The maximum value of recording field difference, $ΔHzr$⁠, in SDM is larger than that of HDM because of different saturation magnetization of low-coercivity magnet parts. The saturation field of SDM is less than that of SSM since the demagnetizing factor of SDM is effectively reduced by the magnetostatic field from high-coercivity magnet. For higher coercivity EAMR media, the larger printing field causes larger recording field difference ΔH^r in case of SDM, while in case of HDM the recording field difference ΔH^r is almost constant. Thus, the recording field difference ΔH^r of SDM is larger than that of HDM, and can write the servo signals onto higher coercivity EAMR media. The printing characteristics of SDM is superior to that of HDM due to larger saturation magnetization of low-coercivity magnet.

This research was supported in part by a Grant-in-Aid for Scientific Research (B) from the Japan Society for the Promotion of Science (Grant No. 20H02196), and by a Grant-in-aid from the KDDI Foundation.

The author has no conflicts to disclose.

Takashi Komine: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.