- Email: [email protected]
in2 patterned media
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 320 (2008) 2195–2200 www.elsevier.com/locate/jmmm
Design and recording simulation of 1 Tbit/in2 patterned media Naoki Hondaa,, Shingo Takahashia, Kazuhiro Ouchia,b a
Research Institute of Advanced Technology, Akita Prefectural R & D Center, 4-21 Sanuki, Araya, Akita-shi 010-1623, Japan Faculty of Systems Science and Technology, Akita Prefectural University, 84-4 Ebinokuchi, Tsuchiya, Yurihonjo-shi 015-0055, Japan
b
Received 4 October 2006; received in revised form 7 May 2007 Available online 4 April 2008
Abstract Design of patterned media for an areal density of 1 Tbit/in2 with thermal stability is presented based on perpendicular M–H loops of the media. Required perpendicular magnetic anisotropy was estimated to be achieved with known materials. However, it is indicated that magnetostatic interaction between the dots becomes a limiting factor for achieving higher densities. Recording simulation using a Karlqvist pole head on the designed media exhibited possibility of the recording of 1 Tbit/in2. Shift margin of the write head in the crosstrack direction was found to be increased with elongated dots in the down-track direction. Recording simulation with an FEM-analyzed field of a side-shielded multi-surface pole head exhibited successful recording with increased cross-track shift margins as well as the effect of the elongated dot shape. r 2008 Elsevier B.V. All rights reserved. PACS: 85.70.Li Keywords: Patterned magnetic recording media; Medium design; Recording simulation; 1 Tbit/in2 recording; Dot shape and size
1. Introduction Perpendicular magnetic recording [1] is expected to dominate over the magnetic storage technology in the near future. However, an areal density of 1 Tbit/in2 would be achieved only by introducing additional technologies for perpendicular magnetic recording to overcome the thermal instability of the recorded bits. Among the candidates, patterned media technology is the most promising one because it is highly consistent with conventional magnetic recording. The idea of patterned media was firstly proposed by Nakatani et al. [2] in 1991 followed by a demonstration of fabrication of 65 Gbit/in2 dots by Chou et al. [3] in 1994. However, since the new method was mainly based on high preciseness of the lithography technology, the superiority of the method in areal density was soon overtaken by the advancement of conventional magnetic recording. At the same period, Nakamura [4] proposed a ‘‘terabit spinic storage’’, which stores bits per grain, indicating preferred perpendicular anisotropy in Corresponding author. Tel.: +81 18 866 5800; fax: +81 18 866 5803.
E-mail address: [email protected] (N. Honda). 0304-8853/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.03.048
terms of magnetostatic interactions between bits, but with no suggestions for fabrication and design of the media. Reattention of patterned media in terms of thermal stability was made by White et al. [5] in 1997 after the suggestion of thermal stability limit of conventional magnetic recording by Charap et al. [6]. Therefore, the works that followed early studies of patterned media [7–9] were not focused on the media with perpendicular anisotropy. Although many papers on the fabrication of magnetic dots were reported [10,11], few have reported on either the thermal stability design or the recording condition of the patterned media. In this paper, design and recording properties were studied using a micromagnetic simulation for patterned media with perpendicular anisotropy aiming at an areal density of 1 Tbit/in2.
2. Design of patterned media The required condition for the thermal stability of patterned magnetic recording media with perpendicular anisotropy was evaluated, using a method similar to that for granular perpendicular recording media based on
ARTICLE IN PRESS N. Honda et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2195–2200
perpendicular M–H loop [12]. As the M–H loop for a magnetic dot array consists of small S–W like square M–H loops of each magnetic dot, even one step change in the M–H loop directly corresponds to a magnetic reversal of a dot. The thermal stability condition for a magnetic dot array should be based on the condition for a dot that is the easiest to reverse. Regarding the beginning field of the reversal or the nucleation field of the magnetic dot array, Hn, as the effective anisotropy field, the condition is presented as E m =kB T ¼ ð1=2ÞH n M s V =kB T460,
(1)
where Em, Ms, V, kB, T represent the magnetic energy, saturation magnetization, volume of a dot, Boltzmann constant, and the temperature in K, respectively. Here, Hn is represented as a zero time value. Eq. (1) assures the error of less than 107 in 30 years for the weakest dot according to the thermal decay property of magnetic particles proposed by M. P. Sharrock [13]. The energy ratio, Em/kBT, was set to 70 for T ¼ 300 K so that it can maintain the value to be greater than 60 at 70 1C. The simplicity of condition (1) comes from the fact that all the complicated background phenomena are represented with Hn. Relatively large Ms was chosen so that reduced Hn was required for the thermal stability. The value of Hn is always smaller than the coercivity, Hc, for a dot array due to (i) dispersion in Hc of each dot and (ii) the magnetostatic interaction between dots. In the case (i), the estimation of the magnetic energy in Eq. (1) is correct. But in the case (ii), the estimation includes error as the magnetic energy should be reduced by (1Hd/Hc)2, where Hd is the demagnetizing field from the neighboring magnetization, according to Ref. [13]. However, the error is less than 10% in the present case because Hd/Hco1/10 as described later. The other case of error may be incoherent rotation of the magnetization in dots. The extreme incoherent rotation indicated for exchange-coupled composite (ECC) media by Victora and Shen [14] causes 50% error in the estimation of the magnetic energy. However, it was estimated that the error is less than +10% when a magnetic dot is assumed to have a sub-volume with half anisotropy. Because the two sources have opposite contribution to the error, it is safe to say that the error in the estimation of Eq. (1) is less than 10%. A typical estimated example of the dot placed on a soft magnetic underlayer (SUL) is a square column with a size of 7.5 7.5 10 nm3 having magnetic properties Hn of 11 kOe with Ms of 1000 emu/cm3. Using a simple M–H loop simulation including magnetostatic interaction between the dots, the Hn value of 12 kOe was obtained with a perpendicular anisotropy field, Hk, of 15 kOe. The required Hk value indicates a small value of about 7.5 106 erg/cm3 for the anisotropy constant, Ku, of the material. Since we can use dense and continuous structure for each dot of patterned media, these magnetic properties are easily obtainable with presently known high-Ku materials such as FePt [15] and Co–Pt alloy [16]. The simulation study
also indicated that decreased spacing between the dots less than about the thickness causes substantial decrease in Hn and increase in the saturation field, Hs, while the coercivity, Hc, is little affected by the spacing. This means that the media become thermally less stable while hard to be recorded when the areal density of the dot array is increased. This would impose a severe condition on the allowable minimum spacing between the dots; thus it would limit the achievable areal density for a limited write head field. 3. Simulation model Recording simulations for dot patterns arranged in a square lattice with a dot pitch of 25 nm (areal density of 1 Tbit/in2) were performed using a Karlqvist-type single pole head with a pole of 25 nm-size square, where the magnetic charge is assumed to be uniformly distributed on the top pole surface. The perpendicular field, Hy, exhibited a half-height width of 42.5 nm in both down- and crosstrack directions as shown in Fig. 1 when the spacing between the head pole surface and the soft underlayer (SUL) was 25 nm. A 3D-FEM-analyzed head field was also used for comparison with the Karlqvist-type head. Each magnetic dot of the patterned media was modeled with exchange-coupled 2.5 nm-size cubic elements so that it could include incoherent rotation mode in the recording process. Each element has saturation magnetization, Ms ¼ 1000 emu/cm3, and the elements are exchange coupled with an exchange stiffness of 0.98 106 erg/cm. Dispersions in Hk and perpendicular orientation of 15% and 1.51 of the standard deviation, respectively, were
20 3D pole head 25x25 nm Separation = 25 nm
15 Head field, Hy [kOe].
2196
Hy(x) at 3.8 nm Hmax =12.5 kOe
10
H50 =42.5 nm
5
0 50
100
150 x, z [nm]
200
Fig. 1. Perpendicular field distribution of a Karlqvist pole head at the storage layer.
ARTICLE IN PRESS N. Honda et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2195–2200
introduced between the elements that make up a dot. Since the dispersion was defined to whole elements, not in each dot, a switching field distribution in a dot array was obtained. A non magnetic interlayer of 5 or 1 nm thick was assumed between the dots and the analytic SUL. The recording simulation was done using an advanced recording model (ARM) of Euxine Technologies, LLC. with an energy equilibrium method [17]. Although the present simulation cannot describe dynamic properties of the media, the result well exhibits basic properties of the recording process. Size and magnetic properties of patterned media used in the present recording simulation are listed in Table 1. D1 and D2 represent the dot size in crossand down-track directions, respectively. The dot size was changed from 7.5 to 22.5 nm, and 2.5 to 10 nm in the thickness so that effect of the dot shape could be seen. Required values of Hn, which satisfies Em/kBT470 at room temperature, were obtained by choosing Hk using perpendicular M–H loop simulation for dot arrays. Note that remanence coercivities, Hcr, are substantially smaller than the average anisotropy field, Hk, in Table 1. This was mainly caused by the shape anisotropy of the dots and dispersions in the orientation.
2197
4. Recording simulation 4.1. Recording with Karlqvist head field When the reverse or switching timing of the recording head field was properly chosen, a 1 Tbit/in2 pattern was successfully recorded on the center track without affecting adjacent tracks, as shown in Fig. 2, where the medium M-2 (the dot size is 12.5 nm square with a thickness of 5 nm) was used. The error rates for 25 recorded bits with a dot pitch of 25 nm were investigated for various square dots. NRZ signal of a 1016 kFCI was recorded by shifting the reverse timing in the down-track direction. Although the recording simulation was done on the center track for DC magnetized media, the recording process involves the effect of demagnetizing field with almost maximum and minimum. The result is shown in Fig. 3 for the media M-1 to M-4. As the volumes of the dots were chosen to be about the same, the required Hn values of the dot arrays for thermal stability were not so different from each other. The optimum recording field was used for each dot array. The optimum field was obtained using DC field recording as the middle field between the minimum field that could reverse
Table 1 Size and magnetic properties of patterned media used in the recording study Media
D1 (nm)
D2 (nm)
t (nm)
M-1 M-2 M-3 M-4
7.4 12.5 15 17.5
7.5 12.5 15 17.5
10 5 2.5 2.5
M-5 M-6 M-7 M-8 M-9
7.5 7.5 7.5 7.5 7.5
12.5 15 17.5 20 22.5
M-10 M-11 M-12 M-13
12.5 12.5 12.5 15
12.5 15 20 15
Volume (nm3)
Hk (kOe)
Hnr (kOe)
Hcr (kOe)
Hsr (kOe)
563 781 563 766
15 15 22 19
12.0 8.4 11.4 8.4
14.8 9.9 13.2 9.9
18.0 12.0 15.0 11.7
10 5 5 5 5
938 563 656 750 844
10 19 18 17 16
7.2 11.4 10.2 9.6 8.1
8.4 13.8 12.4 11.0 9.7
10.5 16.5 15.0 13.5 12.3
5 5 5 5
781 938 1250 1125
15 15 13 13
8.7 7.8 5.1 6.0
10.2 9.5 6.3 7.3
12.6 11.1 8.7 9.9
Magnetization, (L1)
0.00 0.02 0.04 0.06 0.08
Cross-Track Position (μm)
D1 and D2 represent the dot size in cross and down track directions, respectively.
0.00
0.16
0.32
0.48
0.64
Down-Track Position (μm)
-1500
My (EMU/cc)
1500
Fig. 2. An example of recorded magnetization pattern with a density of 1 Tbit/in2 (medium M-2).
ARTICLE IN PRESS N. Honda et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2195–2200
1
D / t =7.5/10 nm D / t =12.5/5 nm D / t =15/2.5 nm D / t =17.5/2.5 nm
M-3 D = 15 nm
0.8 D = 7.5-17.5 nm
Write bit error rate
Ms = 1000 emu/cm3 Hk = 15-22 kOe (σ = 15 %)
0.6
= 2 deg. M-2 D=12.5 nm
0.4 M-4 D = 17.5 nm
M-1 D = 7.5 nm
0.2
0 0
5
10 15 20 Down track shift [nm]
25
30
Fig. 3. Error rates for 25 recorded bits on the reverse timing shift in the down-track direction for patterned media with various dot sizes.
all the center track dots and the maximum field that did not reverse the adjacent track dots. The maximum values of the recording fields were 9.6–13.7 kOe, which were near to the remanence coercivity, Hcr, of each dot array. A write shift margin or write window of 17.5 nm was obtained for smaller dots less than 12.5 nm. The ideal write window should be equal to the down-track period of the dots, Dp. But the write position would be shifted between two downtrack locations where head field H ¼ Hnr and H ¼ Hsr; then this width of the position shift could be the source of the squeezing length for the write window. Since the head field gradient is roughly constant between H ¼ Hnr and H ¼ Hsr, the write shift margin, Ww, is roughly estimated using (HsrHnr) and perpendicular write field gradient, dHy/dx, as Ww ¼ Dp(HsrHnr)/(dHy/dx). As (HsrHnr) ¼ 3.6 kOe, dHy (eff)/dx ¼ 370 Oe/nm, and Dp ¼ 25 nm for M-2, where effective field, Hy (eff), compensated for the angle dependence of the switching field of a S–W particle [18] was used for Hy, Ww ¼ 15.3 nm is estimated. The difference between the estimated and simulated values would be caused by the reduced saturation field in the recording process. Although the head field exhibited decreased field gradient at cross-track positions apart from the center, reduction in the field gradient with averaging over the dot width was estimated to be only about 10%. Therefore, the large decrease in Ww observed for larger dots would be attributed to enhanced incoherent rotation in larger dots. The magnetization reverse rates at both the adjacent tracks when the head filed was shifted in the crosstrack direction were also investigated for the dot arrays. It was found that the shift margin in the crosstrack direction was less than 1/3 of that in the down-track direction. The decreased shift margin in the cross-track
direction is mainly attributed to the wide field distribution. The shift margin in the cross-track direction, Wt, is estimated as Wt ¼ 2TpW(Hn), where Tp is the crosstrack period of dots and W(Hn) is the effective head field width for H ¼ Hnr. The present case for M2 estimates Wt ¼ 4 nm with Tp ¼ 25 nm and W(Hn) ¼ 46 nm. It can be said that only the write field gradient at the trailing edge defines the write shift margin in the down-track direction no matter how the field is spreading in the down-track direction, while the field width defines the write shift margin in the cross-track direction. It is essential to use a write field with a high field gradient in the down-track direction and a narrow distribution in the cross-track direction. It should be noted that the worst error rate detectable in the present study is only one 1/25, but it is obvious from the above discussion that the small tail of the error rate less than the present case depends on the small tail of the distribution in Hnr and Hsr of the dot array. Similar shift margins are investigated for other media in Table 1, including dots with elongated shapes in the downtrack direction. The summary is shown in Fig. 4. It was also found that less decreased or even increased shift margin in the down- and cross-track directions was obtained for the dots with an elongated shape. The dot size in down-track direction, D2, could be elongated to over 20 nm with less degraded shift margins for dots with the size in cross-track direction, D1, of less than 12.5 nm. The elongated shape could increase the dot volume so that required Hn for thermal stability can be reduced. The cause of the effect is explained with the anisotropic switching field or remanence coercivity, Hcr, of such anisotropic dots, as shown in Fig. 5. The Hcr value for inclined applied field angle in y (cross-track direction) is larger than that in f 20
D1, D2 =7.5- 22.5 nm t=2.5- 10 nm
15 Shift margin [nm]
2198
(D1 = 7.5 nm)
Ms =1000 emu/cm3 Hk =10 - 22 kOe (σHk =15 %)
(D1 =D2 )
σ=2 deg.
10
3D pole head Tw /Tm =25/25 nm Head- SUL= 25 nm
(D1 =7.5 nm)
5 (D1 =D2) DT shift margin CT shift margin
0 0
5
10 15 Dot size, D2 [nm]
20
25
Fig. 4. Shift margin in the down- and cross-track directions for patterned media with various dot sizes and shapes.
ARTICLE IN PRESS N. Honda et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2195–2200
elongated dot shapes are useful for obtaining patterned media with larger shift margins for a write head.
(down-track direction). Although this asymmetric behavior in Hcr was obtained for an asymmetric location of the dots as shown in the inset of the figure, no appreciable asymmetric behavior was observed for square dots with the same location. Moreover, almost the same asymmetry in Hcr was observed even for a symmetric location of the elongated dots. Therefore, this asymmetric behavior in Hcr should be explained by the shape anisotropy of the elongated dots. It could be concluded that down track
4.2. Recording with multi-surface pole head To confirm the effectiveness of the above recording study using Karlqvist head fields, recording simulation was done using a more realistic head field. A 3D-head field was obtained using FEM analysis for a multi-surface pole head [19] with front shields [20]. Only the side shields were introduced to minimize the field distribution in the crosstrack direction with less decreased maximum field. A saturation magnetic flux of 2.4 T was assumed for the head core and the side shields in the FEM analysis. The perpendicular field distribution of the head at the medium is shown in Fig. 6, where the bump core of 14 nm (W) 45 nm (L) 10 nm (H) was placed on a 231-tapered base core of 1000 nm (W) 300 nm (L) with 10 nm-thick side shields placed with a separation of 12 nm from the bump core. As the field width does not affect the shift margin in the down-track direction, the present multisurface pole head was designed to have a rectangular pole shape in the down-track direction so that it can produce larger field than that of a square pole with the same track width. A maximum perpendicular field of 12.5 kOe was obtained under the bump core at the storage layer position with a broad boosting field from the main core. A reduced half-height width of the field in the cross-track direction of 34 nm was also obtained under the bump core. Fig. 7 shows the shift margin in the down- and cross-track directions for recording with the head on patterned media with various dot shapes (M-2, M-10, M-11 and M-3 with t ¼ 5 nm in Table 1), where a reduced non-magnetic interlayer thickness of 1 nm and a head-medium spacing of 6 nm were assumed to obtain a high field for the small bump core pole
15 Hcr (Theta) Hcr (Phi)
θ
10 φ
S-W Hsw() =Hsw(0)(sin2/3+cos2/3)−3/2
5 Cross-Track Position (μm)
Remanence coercivity, Hcr [kOe]
Hsw (S-W)
D=7.5x15 nm t=5 nm tIL=5 nm
Magnetization, (L1)
0.00
0.32
0.16
0.48
0.64
Down-Track Position (μm)
Ms=1000 emu/cm3
Hk=19 kOe
0 90
60 30 Applied field angle, , [deg]
2199
0
Fig. 5. Difference in the applied field angle dependence of the switching field, Hcr, between the applied field directions for the anisotropic medium M-6.
14000 12000
Hy [Oe]
Bump core
Side shield
10000 8000 6000 4000
121
111
101
91
71
x (5 nm step, 600 nm)
81
61
51
41
31
11
21
0
1
2000
S1
z (100 nm)
Fig. 6. Perpendicular component of the head field for a multi-surface pole head with front side shields shown in the inset; x and z denote down- and crosstrack directions, respectively.
ARTICLE IN PRESS N. Honda et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2195–2200
2200
with 1 Tbit/in2 using a Karlqvist pole head exhibited possibility of the high density recording. Shift margin of the write head in the cross-track direction was found to be increased with elongation of the dots in the down-track direction. Recording simulation with an FEM-analyzed field for a side-shielded multi-surface pole head exhibited successful recording of 1 Tbit/in2 with increased cross-track shift margins due to decreased cross-track field distribution as well as the effect of the elongated dot shape.
20 DT shift margin CT shift margin (D 1=12.5 nm) (D1 =D2 )
Shift margin [nm]
15
(D 1=12.5 nm)
D1=12.5, 15 nm t=5 nm D2=12.5-20 nm
10
Ms =1000 emu/cm3 Hk=13-15 kOe (σ =15 %)
Acknowledgments (D 1=D 2 )
We would like to thank Dr. S. Iwasaki, President of Tohoku Institute of Technology, for his stimulating guidance. This work was partially supported by Akita Prefecture CREATE, JST and the Special Coordination Funds for Promoting Science and Technology, MEXT.
σ=2 deg.
5
Multi-surface pole head Tw /Tm=14/45 nm Head-SUL=12 nm
0 0
5
10 15 Dot size, D2 [nm]
20
25
Fig. 7. Shift margin in the down- and cross-track directions for recording with a multi-surface pole head on patterned media with various dot shapes.
size. To obtain the optimum field for each medium, the original head field was proportionally changed by +10% for M-2, 20% for M-12, and 10% for M-13, except for M-11. Required maximum head fields for write were around the saturation field, Hsr, of each medium in the case of FEM-analyzed head fields. The cause of the difference from that of the Karlqvist head field comes from a smaller inclination of the field at the trailing edge for the FEM-analyzed head field. Successful recording of 1 Tbit/in2 and the similar increase in the shift margins with down track elongated dots were also confirmed for the head field. It can be said that the multi-surface structure of the head is beneficial to obtain a sufficient field with a small pole size corresponding to the recording of 1 Tbit/in2. 5. Conclusion Design of patterned media for recording of an areal density of 1 Tbit/in2 with thermal stability was presented based on perpendicular M–H loops of the dot array. The perpendicular magnetic anisotropy required was estimated to be achieved with known materials. However, it was indicated that magnetostatic interaction between the dots becomes a severe limiting factor for achieving higher areal recording densities. Recording simulation on the media
References [1] S. Iwasaki, Y. Nakamura, IEEE Trans. Magn. 13 (1977) 1272. [2] I. Nakatani, T. Takahashi, M. Hijikata, T. Furubayashi, K. Ozawa, H. Hanaoka, Japan Patent 1888363, Publication JP03-022211A, 1991. [3] S.Y. Chou, M.S. Wei, P.R. Krauss, P.B. Fischer, J. Appl. Phys. 76 (1994) 6673. [4] Y. Nakamura, J. Magn. Soc. Japan 18 (S1) (1994) 161. [5] R.L. White, R.M.H. New, R.F.W. Pease, IEEE Trans. Magn. 33 (1) (1997) 990. [6] S.H. Charap, P.-L. Lu, Y. He, IEEE Trans. Magn. 33 (1) (1997) 978. [7] B.D. Terris, L. Folks, D. Weller, J.E.E. Baglin, A.J. Kellock, H. Rothuizen, P. Vettiger, Appl. Phys. Lett. 75 (1999) 403. [8] C.A. Ross, H.I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M. Hwang, M. Walsh, M.C. Abraham, R.J. Ram, J. Vac. Sci. Technol. B 17 (1999) 3168. [9] G.F. Hughes, IEEE Trans. Magn. 36 (2) (2000) 521. [10] C.T. Rettner, M.E. Best, B.D. Terris, IEEE Trans. Magn. 37 (2001) 1649. [11] T. Aoyama, I. Sato, S. Ishio, Oyo Butsuri 72 (2003) 298. [12] N. Honda, K. Ouchi, S. Iwasaki, IEEE Trans. Magn. 38 (2002) 1615. [13] M.P. Sharrock, IEEE Trans. Magn. 26 (1990) 193. [14] R.H. Victora, X. Shen, IEEE Trans. Magn. 41 (2) (2005) 537. [15] T. Suzuki, N. Honda, K. Ouchi, J. Magn. Soc. Japan 21 (S2) (1997) 177. [16] T. Shimatsu, H. Sato, T. Oikawa, Y. Inaba, O. Kitakami, S. Okamoto, H. Aoi, H. Muraoka, Y. Nakamura, IEEE Trans. Magn. 40 (2004) 2483. [17] J.R. Hoinville, J. Appl. Phys. 91 (2002) 8010. [18] J. Miles, D. McKirdy, R. Chantrell, R. Wood, IEEE Trans. Magn. 39 (2003) 1876. [19] S. Takahashi, K. Yamakawa, K. Ouchi, J. Appl. Phs. 93 (10) (2003) 6546. [20] S. Takahashi, K. Yamakawa, N. Honda, K. Ouchi, in: Abstracts of the International Symposium on Creation of Magnetization Recording Materials with Nano-interfacial Technology, Tokyo, 2005, p. 27.
Journal of Magnetism and Magnetic Materials 320 (2008) 2195–2200 www.elsevier.com/locate/jmmm
Design and recording simulation of 1 Tbit/in2 patterned media Naoki Hondaa,, Shingo Takahashia, Kazuhiro Ouchia,b a
Research Institute of Advanced Technology, Akita Prefectural R & D Center, 4-21 Sanuki, Araya, Akita-shi 010-1623, Japan Faculty of Systems Science and Technology, Akita Prefectural University, 84-4 Ebinokuchi, Tsuchiya, Yurihonjo-shi 015-0055, Japan
b
Received 4 October 2006; received in revised form 7 May 2007 Available online 4 April 2008
Abstract Design of patterned media for an areal density of 1 Tbit/in2 with thermal stability is presented based on perpendicular M–H loops of the media. Required perpendicular magnetic anisotropy was estimated to be achieved with known materials. However, it is indicated that magnetostatic interaction between the dots becomes a limiting factor for achieving higher densities. Recording simulation using a Karlqvist pole head on the designed media exhibited possibility of the recording of 1 Tbit/in2. Shift margin of the write head in the crosstrack direction was found to be increased with elongated dots in the down-track direction. Recording simulation with an FEM-analyzed field of a side-shielded multi-surface pole head exhibited successful recording with increased cross-track shift margins as well as the effect of the elongated dot shape. r 2008 Elsevier B.V. All rights reserved. PACS: 85.70.Li Keywords: Patterned magnetic recording media; Medium design; Recording simulation; 1 Tbit/in2 recording; Dot shape and size
1. Introduction Perpendicular magnetic recording [1] is expected to dominate over the magnetic storage technology in the near future. However, an areal density of 1 Tbit/in2 would be achieved only by introducing additional technologies for perpendicular magnetic recording to overcome the thermal instability of the recorded bits. Among the candidates, patterned media technology is the most promising one because it is highly consistent with conventional magnetic recording. The idea of patterned media was firstly proposed by Nakatani et al. [2] in 1991 followed by a demonstration of fabrication of 65 Gbit/in2 dots by Chou et al. [3] in 1994. However, since the new method was mainly based on high preciseness of the lithography technology, the superiority of the method in areal density was soon overtaken by the advancement of conventional magnetic recording. At the same period, Nakamura [4] proposed a ‘‘terabit spinic storage’’, which stores bits per grain, indicating preferred perpendicular anisotropy in Corresponding author. Tel.: +81 18 866 5800; fax: +81 18 866 5803.
E-mail address: [email protected] (N. Honda). 0304-8853/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.03.048
terms of magnetostatic interactions between bits, but with no suggestions for fabrication and design of the media. Reattention of patterned media in terms of thermal stability was made by White et al. [5] in 1997 after the suggestion of thermal stability limit of conventional magnetic recording by Charap et al. [6]. Therefore, the works that followed early studies of patterned media [7–9] were not focused on the media with perpendicular anisotropy. Although many papers on the fabrication of magnetic dots were reported [10,11], few have reported on either the thermal stability design or the recording condition of the patterned media. In this paper, design and recording properties were studied using a micromagnetic simulation for patterned media with perpendicular anisotropy aiming at an areal density of 1 Tbit/in2.
2. Design of patterned media The required condition for the thermal stability of patterned magnetic recording media with perpendicular anisotropy was evaluated, using a method similar to that for granular perpendicular recording media based on
ARTICLE IN PRESS N. Honda et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2195–2200
perpendicular M–H loop [12]. As the M–H loop for a magnetic dot array consists of small S–W like square M–H loops of each magnetic dot, even one step change in the M–H loop directly corresponds to a magnetic reversal of a dot. The thermal stability condition for a magnetic dot array should be based on the condition for a dot that is the easiest to reverse. Regarding the beginning field of the reversal or the nucleation field of the magnetic dot array, Hn, as the effective anisotropy field, the condition is presented as E m =kB T ¼ ð1=2ÞH n M s V =kB T460,
(1)
where Em, Ms, V, kB, T represent the magnetic energy, saturation magnetization, volume of a dot, Boltzmann constant, and the temperature in K, respectively. Here, Hn is represented as a zero time value. Eq. (1) assures the error of less than 107 in 30 years for the weakest dot according to the thermal decay property of magnetic particles proposed by M. P. Sharrock [13]. The energy ratio, Em/kBT, was set to 70 for T ¼ 300 K so that it can maintain the value to be greater than 60 at 70 1C. The simplicity of condition (1) comes from the fact that all the complicated background phenomena are represented with Hn. Relatively large Ms was chosen so that reduced Hn was required for the thermal stability. The value of Hn is always smaller than the coercivity, Hc, for a dot array due to (i) dispersion in Hc of each dot and (ii) the magnetostatic interaction between dots. In the case (i), the estimation of the magnetic energy in Eq. (1) is correct. But in the case (ii), the estimation includes error as the magnetic energy should be reduced by (1Hd/Hc)2, where Hd is the demagnetizing field from the neighboring magnetization, according to Ref. [13]. However, the error is less than 10% in the present case because Hd/Hco1/10 as described later. The other case of error may be incoherent rotation of the magnetization in dots. The extreme incoherent rotation indicated for exchange-coupled composite (ECC) media by Victora and Shen [14] causes 50% error in the estimation of the magnetic energy. However, it was estimated that the error is less than +10% when a magnetic dot is assumed to have a sub-volume with half anisotropy. Because the two sources have opposite contribution to the error, it is safe to say that the error in the estimation of Eq. (1) is less than 10%. A typical estimated example of the dot placed on a soft magnetic underlayer (SUL) is a square column with a size of 7.5 7.5 10 nm3 having magnetic properties Hn of 11 kOe with Ms of 1000 emu/cm3. Using a simple M–H loop simulation including magnetostatic interaction between the dots, the Hn value of 12 kOe was obtained with a perpendicular anisotropy field, Hk, of 15 kOe. The required Hk value indicates a small value of about 7.5 106 erg/cm3 for the anisotropy constant, Ku, of the material. Since we can use dense and continuous structure for each dot of patterned media, these magnetic properties are easily obtainable with presently known high-Ku materials such as FePt [15] and Co–Pt alloy [16]. The simulation study
also indicated that decreased spacing between the dots less than about the thickness causes substantial decrease in Hn and increase in the saturation field, Hs, while the coercivity, Hc, is little affected by the spacing. This means that the media become thermally less stable while hard to be recorded when the areal density of the dot array is increased. This would impose a severe condition on the allowable minimum spacing between the dots; thus it would limit the achievable areal density for a limited write head field. 3. Simulation model Recording simulations for dot patterns arranged in a square lattice with a dot pitch of 25 nm (areal density of 1 Tbit/in2) were performed using a Karlqvist-type single pole head with a pole of 25 nm-size square, where the magnetic charge is assumed to be uniformly distributed on the top pole surface. The perpendicular field, Hy, exhibited a half-height width of 42.5 nm in both down- and crosstrack directions as shown in Fig. 1 when the spacing between the head pole surface and the soft underlayer (SUL) was 25 nm. A 3D-FEM-analyzed head field was also used for comparison with the Karlqvist-type head. Each magnetic dot of the patterned media was modeled with exchange-coupled 2.5 nm-size cubic elements so that it could include incoherent rotation mode in the recording process. Each element has saturation magnetization, Ms ¼ 1000 emu/cm3, and the elements are exchange coupled with an exchange stiffness of 0.98 106 erg/cm. Dispersions in Hk and perpendicular orientation of 15% and 1.51 of the standard deviation, respectively, were
20 3D pole head 25x25 nm Separation = 25 nm
15 Head field, Hy [kOe].
2196
Hy(x) at 3.8 nm Hmax =12.5 kOe
10
H50 =42.5 nm
5
0 50
100
150 x, z [nm]
200
Fig. 1. Perpendicular field distribution of a Karlqvist pole head at the storage layer.
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introduced between the elements that make up a dot. Since the dispersion was defined to whole elements, not in each dot, a switching field distribution in a dot array was obtained. A non magnetic interlayer of 5 or 1 nm thick was assumed between the dots and the analytic SUL. The recording simulation was done using an advanced recording model (ARM) of Euxine Technologies, LLC. with an energy equilibrium method [17]. Although the present simulation cannot describe dynamic properties of the media, the result well exhibits basic properties of the recording process. Size and magnetic properties of patterned media used in the present recording simulation are listed in Table 1. D1 and D2 represent the dot size in crossand down-track directions, respectively. The dot size was changed from 7.5 to 22.5 nm, and 2.5 to 10 nm in the thickness so that effect of the dot shape could be seen. Required values of Hn, which satisfies Em/kBT470 at room temperature, were obtained by choosing Hk using perpendicular M–H loop simulation for dot arrays. Note that remanence coercivities, Hcr, are substantially smaller than the average anisotropy field, Hk, in Table 1. This was mainly caused by the shape anisotropy of the dots and dispersions in the orientation.
2197
4. Recording simulation 4.1. Recording with Karlqvist head field When the reverse or switching timing of the recording head field was properly chosen, a 1 Tbit/in2 pattern was successfully recorded on the center track without affecting adjacent tracks, as shown in Fig. 2, where the medium M-2 (the dot size is 12.5 nm square with a thickness of 5 nm) was used. The error rates for 25 recorded bits with a dot pitch of 25 nm were investigated for various square dots. NRZ signal of a 1016 kFCI was recorded by shifting the reverse timing in the down-track direction. Although the recording simulation was done on the center track for DC magnetized media, the recording process involves the effect of demagnetizing field with almost maximum and minimum. The result is shown in Fig. 3 for the media M-1 to M-4. As the volumes of the dots were chosen to be about the same, the required Hn values of the dot arrays for thermal stability were not so different from each other. The optimum recording field was used for each dot array. The optimum field was obtained using DC field recording as the middle field between the minimum field that could reverse
Table 1 Size and magnetic properties of patterned media used in the recording study Media
D1 (nm)
D2 (nm)
t (nm)
M-1 M-2 M-3 M-4
7.4 12.5 15 17.5
7.5 12.5 15 17.5
10 5 2.5 2.5
M-5 M-6 M-7 M-8 M-9
7.5 7.5 7.5 7.5 7.5
12.5 15 17.5 20 22.5
M-10 M-11 M-12 M-13
12.5 12.5 12.5 15
12.5 15 20 15
Volume (nm3)
Hk (kOe)
Hnr (kOe)
Hcr (kOe)
Hsr (kOe)
563 781 563 766
15 15 22 19
12.0 8.4 11.4 8.4
14.8 9.9 13.2 9.9
18.0 12.0 15.0 11.7
10 5 5 5 5
938 563 656 750 844
10 19 18 17 16
7.2 11.4 10.2 9.6 8.1
8.4 13.8 12.4 11.0 9.7
10.5 16.5 15.0 13.5 12.3
5 5 5 5
781 938 1250 1125
15 15 13 13
8.7 7.8 5.1 6.0
10.2 9.5 6.3 7.3
12.6 11.1 8.7 9.9
Magnetization, (L1)
0.00 0.02 0.04 0.06 0.08
Cross-Track Position (μm)
D1 and D2 represent the dot size in cross and down track directions, respectively.
0.00
0.16
0.32
0.48
0.64
Down-Track Position (μm)
-1500
My (EMU/cc)
1500
Fig. 2. An example of recorded magnetization pattern with a density of 1 Tbit/in2 (medium M-2).
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1
D / t =7.5/10 nm D / t =12.5/5 nm D / t =15/2.5 nm D / t =17.5/2.5 nm
M-3 D = 15 nm
0.8 D = 7.5-17.5 nm
Write bit error rate
Ms = 1000 emu/cm3 Hk = 15-22 kOe (σ = 15 %)
0.6
= 2 deg. M-2 D=12.5 nm
0.4 M-4 D = 17.5 nm
M-1 D = 7.5 nm
0.2
0 0
5
10 15 20 Down track shift [nm]
25
30
Fig. 3. Error rates for 25 recorded bits on the reverse timing shift in the down-track direction for patterned media with various dot sizes.
all the center track dots and the maximum field that did not reverse the adjacent track dots. The maximum values of the recording fields were 9.6–13.7 kOe, which were near to the remanence coercivity, Hcr, of each dot array. A write shift margin or write window of 17.5 nm was obtained for smaller dots less than 12.5 nm. The ideal write window should be equal to the down-track period of the dots, Dp. But the write position would be shifted between two downtrack locations where head field H ¼ Hnr and H ¼ Hsr; then this width of the position shift could be the source of the squeezing length for the write window. Since the head field gradient is roughly constant between H ¼ Hnr and H ¼ Hsr, the write shift margin, Ww, is roughly estimated using (HsrHnr) and perpendicular write field gradient, dHy/dx, as Ww ¼ Dp(HsrHnr)/(dHy/dx). As (HsrHnr) ¼ 3.6 kOe, dHy (eff)/dx ¼ 370 Oe/nm, and Dp ¼ 25 nm for M-2, where effective field, Hy (eff), compensated for the angle dependence of the switching field of a S–W particle [18] was used for Hy, Ww ¼ 15.3 nm is estimated. The difference between the estimated and simulated values would be caused by the reduced saturation field in the recording process. Although the head field exhibited decreased field gradient at cross-track positions apart from the center, reduction in the field gradient with averaging over the dot width was estimated to be only about 10%. Therefore, the large decrease in Ww observed for larger dots would be attributed to enhanced incoherent rotation in larger dots. The magnetization reverse rates at both the adjacent tracks when the head filed was shifted in the crosstrack direction were also investigated for the dot arrays. It was found that the shift margin in the crosstrack direction was less than 1/3 of that in the down-track direction. The decreased shift margin in the cross-track
direction is mainly attributed to the wide field distribution. The shift margin in the cross-track direction, Wt, is estimated as Wt ¼ 2TpW(Hn), where Tp is the crosstrack period of dots and W(Hn) is the effective head field width for H ¼ Hnr. The present case for M2 estimates Wt ¼ 4 nm with Tp ¼ 25 nm and W(Hn) ¼ 46 nm. It can be said that only the write field gradient at the trailing edge defines the write shift margin in the down-track direction no matter how the field is spreading in the down-track direction, while the field width defines the write shift margin in the cross-track direction. It is essential to use a write field with a high field gradient in the down-track direction and a narrow distribution in the cross-track direction. It should be noted that the worst error rate detectable in the present study is only one 1/25, but it is obvious from the above discussion that the small tail of the error rate less than the present case depends on the small tail of the distribution in Hnr and Hsr of the dot array. Similar shift margins are investigated for other media in Table 1, including dots with elongated shapes in the downtrack direction. The summary is shown in Fig. 4. It was also found that less decreased or even increased shift margin in the down- and cross-track directions was obtained for the dots with an elongated shape. The dot size in down-track direction, D2, could be elongated to over 20 nm with less degraded shift margins for dots with the size in cross-track direction, D1, of less than 12.5 nm. The elongated shape could increase the dot volume so that required Hn for thermal stability can be reduced. The cause of the effect is explained with the anisotropic switching field or remanence coercivity, Hcr, of such anisotropic dots, as shown in Fig. 5. The Hcr value for inclined applied field angle in y (cross-track direction) is larger than that in f 20
D1, D2 =7.5- 22.5 nm t=2.5- 10 nm
15 Shift margin [nm]
2198
(D1 = 7.5 nm)
Ms =1000 emu/cm3 Hk =10 - 22 kOe (σHk =15 %)
(D1 =D2 )
σ=2 deg.
10
3D pole head Tw /Tm =25/25 nm Head- SUL= 25 nm
(D1 =7.5 nm)
5 (D1 =D2) DT shift margin CT shift margin
0 0
5
10 15 Dot size, D2 [nm]
20
25
Fig. 4. Shift margin in the down- and cross-track directions for patterned media with various dot sizes and shapes.
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elongated dot shapes are useful for obtaining patterned media with larger shift margins for a write head.
(down-track direction). Although this asymmetric behavior in Hcr was obtained for an asymmetric location of the dots as shown in the inset of the figure, no appreciable asymmetric behavior was observed for square dots with the same location. Moreover, almost the same asymmetry in Hcr was observed even for a symmetric location of the elongated dots. Therefore, this asymmetric behavior in Hcr should be explained by the shape anisotropy of the elongated dots. It could be concluded that down track
4.2. Recording with multi-surface pole head To confirm the effectiveness of the above recording study using Karlqvist head fields, recording simulation was done using a more realistic head field. A 3D-head field was obtained using FEM analysis for a multi-surface pole head [19] with front shields [20]. Only the side shields were introduced to minimize the field distribution in the crosstrack direction with less decreased maximum field. A saturation magnetic flux of 2.4 T was assumed for the head core and the side shields in the FEM analysis. The perpendicular field distribution of the head at the medium is shown in Fig. 6, where the bump core of 14 nm (W) 45 nm (L) 10 nm (H) was placed on a 231-tapered base core of 1000 nm (W) 300 nm (L) with 10 nm-thick side shields placed with a separation of 12 nm from the bump core. As the field width does not affect the shift margin in the down-track direction, the present multisurface pole head was designed to have a rectangular pole shape in the down-track direction so that it can produce larger field than that of a square pole with the same track width. A maximum perpendicular field of 12.5 kOe was obtained under the bump core at the storage layer position with a broad boosting field from the main core. A reduced half-height width of the field in the cross-track direction of 34 nm was also obtained under the bump core. Fig. 7 shows the shift margin in the down- and cross-track directions for recording with the head on patterned media with various dot shapes (M-2, M-10, M-11 and M-3 with t ¼ 5 nm in Table 1), where a reduced non-magnetic interlayer thickness of 1 nm and a head-medium spacing of 6 nm were assumed to obtain a high field for the small bump core pole
15 Hcr (Theta) Hcr (Phi)
θ
10 φ
S-W Hsw() =Hsw(0)(sin2/3+cos2/3)−3/2
5 Cross-Track Position (μm)
Remanence coercivity, Hcr [kOe]
Hsw (S-W)
D=7.5x15 nm t=5 nm tIL=5 nm
Magnetization, (L1)
0.00
0.32
0.16
0.48
0.64
Down-Track Position (μm)
Ms=1000 emu/cm3
Hk=19 kOe
0 90
60 30 Applied field angle, , [deg]
2199
0
Fig. 5. Difference in the applied field angle dependence of the switching field, Hcr, between the applied field directions for the anisotropic medium M-6.
14000 12000
Hy [Oe]
Bump core
Side shield
10000 8000 6000 4000
121
111
101
91
71
x (5 nm step, 600 nm)
81
61
51
41
31
11
21
0
1
2000
S1
z (100 nm)
Fig. 6. Perpendicular component of the head field for a multi-surface pole head with front side shields shown in the inset; x and z denote down- and crosstrack directions, respectively.
ARTICLE IN PRESS N. Honda et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2195–2200
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with 1 Tbit/in2 using a Karlqvist pole head exhibited possibility of the high density recording. Shift margin of the write head in the cross-track direction was found to be increased with elongation of the dots in the down-track direction. Recording simulation with an FEM-analyzed field for a side-shielded multi-surface pole head exhibited successful recording of 1 Tbit/in2 with increased cross-track shift margins due to decreased cross-track field distribution as well as the effect of the elongated dot shape.
20 DT shift margin CT shift margin (D 1=12.5 nm) (D1 =D2 )
Shift margin [nm]
15
(D 1=12.5 nm)
D1=12.5, 15 nm t=5 nm D2=12.5-20 nm
10
Ms =1000 emu/cm3 Hk=13-15 kOe (σ =15 %)
Acknowledgments (D 1=D 2 )
We would like to thank Dr. S. Iwasaki, President of Tohoku Institute of Technology, for his stimulating guidance. This work was partially supported by Akita Prefecture CREATE, JST and the Special Coordination Funds for Promoting Science and Technology, MEXT.
σ=2 deg.
5
Multi-surface pole head Tw /Tm=14/45 nm Head-SUL=12 nm
0 0
5
10 15 Dot size, D2 [nm]
20
25
Fig. 7. Shift margin in the down- and cross-track directions for recording with a multi-surface pole head on patterned media with various dot shapes.
size. To obtain the optimum field for each medium, the original head field was proportionally changed by +10% for M-2, 20% for M-12, and 10% for M-13, except for M-11. Required maximum head fields for write were around the saturation field, Hsr, of each medium in the case of FEM-analyzed head fields. The cause of the difference from that of the Karlqvist head field comes from a smaller inclination of the field at the trailing edge for the FEM-analyzed head field. Successful recording of 1 Tbit/in2 and the similar increase in the shift margins with down track elongated dots were also confirmed for the head field. It can be said that the multi-surface structure of the head is beneficial to obtain a sufficient field with a small pole size corresponding to the recording of 1 Tbit/in2. 5. Conclusion Design of patterned media for recording of an areal density of 1 Tbit/in2 with thermal stability was presented based on perpendicular M–H loops of the dot array. The perpendicular magnetic anisotropy required was estimated to be achieved with known materials. However, it was indicated that magnetostatic interaction between the dots becomes a severe limiting factor for achieving higher areal recording densities. Recording simulation on the media
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