ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 321 (2009) 566–571
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Current Perspectives
Perpendicular recording write process modeling issues Michael Mallary a,, Mourad Benakli a, Apalkov Dmytro b a b
Seagate Research Center, 1251 Waterfront Pl, Pittsburgh, PA 15222, USA Grandis Corporation, USA
a r t i c l e in f o
a b s t r a c t
Available online 6 September 2008
An optimal write process is essential for realizing the high-density potential of perpendicular recording. An analytic Williams–Comstock-type model of transition width is derived, which is based on a linear transition shape. This model is used to explore the effect of system parameters on transition width. In order to preserve high write field gradient during high-speed recording it is essential to have fast head switching. The role of magnon processes in providing high damping for fast switching is discussed and micromagnetic simulation results are presented. & 2008 Elsevier B.V. All rights reserved.
Keywords: Perpendicular recording Transition width Switching speed Modeling
1. Introduction Perpendicular recording has now displaced longitudinal recording due to its ability to write sharper transitions on finer grained media without loss of thermal stability. However, as areal density increases perpendicular recording will start to reach its limits of thermal stability and it will become more important to obtain the sharpest possible transitions. In pursuit of this goal, the shielded pole write head [1] illustrated in Fig. 1 has become the standard for all head manufacture. The advantage of the shielded pole head is primarily its higher write field gradient and greater in-plane field relative to an unshielded pole. This comparison is provided in Fig. 2 for the field components for a design close to the 1 Tb/in2 conceptual design [1] (i.e. the pole tip to the top of the media spacing is 4 nm here, the gap is 18 nm, the media thickness is 14 nm, and there is no non-magnetic under layer between the media layer and the soft under layer, SUL). Fig. 3 shows the effective Stoner–Wolfarth switching field given by n
2=3
Heff ¼ H2=3 perp þ H long
o3=2
(1)
With the parameters quoted above it should be possible to demonstrate recording at about 1 Tb/in2 [1]. Optimization of the system parameters to achieve this density requires good analytic tools. To this end, we have developed a Williams–Compstock-type [2] model of the perpendicular recording process. This enables rapid analysis of the impact of these variables on transition width and SNR. Of course write field gradient is an important variable. However, at high data rates the high effective gradient of a Corresponding author.
E-mail address:
[email protected] (M. Mallary). 0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.08.105
shielded pole head can be degraded by slow write field rise time [3]. Numerous micromagnetic simulations have established the need for a Landau–Lifshitz–Gilbert damping parameter of about 0.2 in order to achieve rapid head switching [4–7]. However, intrinsic damping is expected to be only 0.005 [8]. Very slow head switching would be the result if this is the case. However, Ref. [8] reports measuring large damping at large rotation angles (i.e. greater than about 51) and has attributed this to multi-magnon processes. This has been confirmed in the time domain for thin films for large rotation angles [9]. We show below that the failure of previous modeling attempts to achieve fast switching with low damping is due to the use of element sizes that are too large to model magnon processes. By using element sizes that are significantly smaller than magnon wave lengths, we have simulated fast switching even when low intrinsic damping is assumed. This is detailed below.
2. Transition width model In order to develop an analytic model of transition width, we use a linear approximation to the transition shape. Comparison between this model and the more realistic hyperbolic tangent model [10] is provided in Fig. 4. From this, it can be seen that the linear approximation agrees fairly well with the hyperbolic tangent (with the same slope at the origin). The maximum error is 28% at the saturation point. These errors can be minimized (to 7% and 13%) by reducing the linear model slope to 75% of that of the Tanh model, but we are interested in the self-demagnetization fields of these models near x ¼ 0. This will be dominated by the slope there; so matching the slopes near x ¼ 0 is a better approach (see discussion below). Note that the arguments of these models have been normalized by a factor of 2/p so that they have the
ARTICLE IN PRESS M. Mallary et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 566–571
Pancake Write Coils
Effective Fields normalized to upstream values 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -30nm
Perpendicular Write Pole Read Shields
Media Motion
Media SUL
GMR Sensor
567
Monopole Shielded Pole
Pole Edge
30nm
Write Field Flux in SUL Fig. 3. Calculated Stoner–Wolfarth effective switching field vs down track position of a perpendicular monopole and a shielded pole writer [1].
Pancake Coils Write Pole
Transition Shape Models 3x/2πa 2x/πa 1.1
Shield Pole Media
Tanh(2x/πa)
0.9 SUL
0.7
Shields
0.5
Motion
M/Mr
0.3
Write Field Flux in SUL
GMR
Fig. 1. Cross-sectional diagram of a perpendicular monopole writer (a) and a shielded pole writer (b).
(2/π)Tan-1(x/a)
0.1 -3
-2. 5
-2
-1. 5
-1
-0.1
0
0.5
1
1.5
2
2.5
3
0-0.3 5-0.5 -0.7 -0.9
Fields normalized to maximum perpendicular field 1 Pole 0.9 Corners 0.8
-1.1 x/a
Perpendicular Fields
Fig. 4. Comparison of transition shapes.
Monopole Shielded Pole
0.7 Longitudinal Fields
0.6 0.5
Shielded Pole Monopole
0.4 0.3 0.2 0.1
-25
-15
0 -5 5 15 Horizontal Position, x (nm)
25
35
Fig. 2. Calculated perpendicular and longitudinal fields vs down track position of a perpendicular monopole and a shielded pole writer [1].
same slope as the Williams–Comstock model (i.e. M ¼ Mr(2/ p)tan1(x/a) with media remanence Mr). Though the forms in Fig. 4 use the conventional slope definition of the width parameter, a, it is algebraically messy. Therefore, we will temporarily use a different parameter, a0 , such that a0 ¼ pa=2
(2)
and the linear model is M ¼ M r ð2x=paÞ ¼ M r x=a0 ;
jxjopa=2 ¼ a0
(3)
For this linear transition shape the virtual current distribution in
Fig. 5. Uncancelled virtual current sheet in media for a small displacement, D, from the origin.
the media is uniform (i.e. JdM/dx ¼ constant). For a displacement of D the self-demagnetization field, Hd, is due only to the part of the virtual current sheet at the most negative values of x, which is not balanced by a corresponding region at the most positive values (see Fig. 5).
ARTICLE IN PRESS 568
M. Mallary et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 566–571
Trans. Width, a, vs Field Gradient u=20nm, Mr=477 emu/cc, t=15nm, Hc=10kOe 16 14
TransWidth, a (nm)
12 S*=.7
10
S*=.8 S*=.9
8
S*=.99
6 4
Fig. 6. Self-demagnetizing field with SUL.
2 0 0
The field from a thin current sheet (e.g. Karlqist field) is proportional to the opening angle, y, divided by p. Also noting that H ¼ B4pM and that current is the source of B, we get the demagnetizing field from the data layer as Hdd ¼ fM r ðD=a0 Þ þ Mr ð2D=2a0 Þ½tan1 ðt=2a0 Þ½2=pg4p
(4)
The gradient is then dHdd =dx ¼ ½8M r =a0 ½tan1 ð2a0 =tÞ
(6)
A numeric study of the gradient of the self-demagnetizing field of a tanh(x/a0 ) function yields results that are 4.6–10.5% less than that predicted by Eq. (6) for the interesting range of t/4oa0 o4t. Therefore, if we introduce a correction factor of F ¼ 0.925 the discrepancy will be o3%. That is dHdd =dx ¼ ½8FMr =a0 ½tan1 ð2a0 =tÞ
(7)
For simplicity here we will always use F ¼ 1 in the analysis that follows but carry F in the equations. All perpendicular media used today has an SUL that is separated from the data layer by a non-magnetic underlayer that has a thickness, u. The image of the data layer current sheet appears in the SUL starting at a depth of 2u (see Fig. 6); the gradient of the net demagnetizing field is then dHd =dx ¼ f8FM r =a0 gftan1 ½2a0 =t tan1 ½2a0 =ð4u þ tÞ þ tan1 ½2a0 =ð4u þ 3tÞg
(8)
Now in the classic Williams–Comstock approach dM=dx ¼ ðdM=dHÞðdH=dxÞ
(9)
(10)
and combining Eqs. (3), (9) and (10) gives M r =a0 ¼ ðdH=dxÞfM r =½Hc ð1 S Þg So dH=dx ¼ dHp =dx þ dHd =dx ¼ Hc ð1 S Þ=a0
(11)
where Hp is the perpendicular component of the pole tip field, S* is the coercive squareness and Hc is the coercivity (note that Hc(1S*) is the change in field that causes M to become 0 from Mr
1500
1750
2000
0.16 0.14 0.12 0.1 0.08 0.06 0.04 y = -0.3501x + 0.3925
0.02 0 0.7
0.8 0.9 S*, Coercive Squareness
1
Fig. 8. Normalized head field gradient to obtain a ¼ 2 nm.
for high remanent squareness, S). Combining this with Eq. (8) gives the transcendental equation: a0 ¼ ½Hc ð1 S Þ þ f8FMr gftan1 ½2a0 =t tan1 ½2a0 =ð4u þ tÞ þ tan1 ½2a0 =ð4u þ 3tÞg=½dHp =dx
Defining the coercive squareness by 1 S ¼ ðMr =Hc Þ=dM=dH
750 1000 1250 dH/dx (Oe/nm)
Normalized Gradient at a=2 nm vs S* (media t=15, u=20)
Normalized Grad (dH/dx/Hc)
(5)
500
Fig. 7. Transition width, a, vs field gradient (Hc ¼ 10 kOe so Hk18 kOe).
for small displacement D (Mr is in emu/cc). The first term is the magnetization at x ¼ D and the second is B due to the unbalanced current sheet with width 2D. This simplifies to Hdd ¼ ½8M r D=a0 ½tan1 ð2a0 =tÞ
250
(12) 0
Eq. (12) has been solved graphically for a and then converted to the standard transition width parameter, a (see Eq. (2)). The calculated transition width vs field gradient for various values of coercive squareness is plotted in Fig. 7 (for Hc ¼ 10 kOe, Mr ¼ 477 emu/cc, u ¼ 20 nm and t ¼ 15 nm). For finite grain size the minimum obtainable value of a is about 32% of the average grain diameter [1] (see below). Taking this to be 2 nm for 6 nm grains then sets a maximum field gradient beyond which the transition width cannot be improved significantly. Fig. 8 plots this value vs the S* (taken from Fig. 7). The values of S* and Hc used in these calculations are assumed to reflect the switching field distribution of non-exchangecoupled grains on a nanosecond time scale. Hc can be obtained
ARTICLE IN PRESS M. Mallary et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 566–571
Transition Width vs Mr (0.03
