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ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 320 (2008) 2880–2884
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Micromagnetic simulations for terabit/in2 head/media systems Manfred E. Schabes Hitachi San Jose Research Center, Hitachi GST, San Jose, CA 95135, USA
a r t i c l e in f o
a b s t r a c t
Available online 5 August 2008
Bit-patterned (BP) recording is a candidate for extending magnetic data storage towards 10 Tb/in2 bit densities. An analysis of the design tolerances is carried out using dynamic micromagnetic simulations and statistical models. The effects of distributions of the magnetic material properties on phase margin and addressability error-rate during writing are investigated. At 1.3 Tb/in2 a rapid increase of the errorrate is observed when the write-synchronization deviates from the optimum phase f0. Estimates of the fabrication and write-synchronization tolerances are derived from the phase margins. It is shown that the switching-field distribution (from intra-island variations and inter-island interactions) as well as the fabrication and synchronization tolerances must be tightly controlled for Tb/in2 applications. At ultrahigh densities, BP media may need to be combined with energy-assisted writing, which is referred to as second-generation BP recording. & 2008 Elsevier B.V. All rights reserved.
PACS: 75.50.Ss 75.75.+a 85.70.Ay 85.70.Kh 85.70.Li Keywords: Micromagnetic simulation Bit-patterned medium Magnetic recording
1. Introduction Magnetic data storage technology has made significant progress towards increasing areal densities using continuous-granular (CG) perpendicular magnetic recording media as well as advanced transducers for writing and reading [1]. If progress continues at present rates, it is expected that commercial magnetic disk drives at 1 Tb/in2 will be realized in a few years’ time. Aspects of the recording physics at Tb/in2 densities have been discussed previously for CG media in Ref. [2] and for bitpatterned (BP) media in Refs. [3,4]. BP media circumvent the increasingly difficult task of reducing the size of thin-film grains and of magnetic clusters while maintaining thermal stability. However, BP media need to cope with many novel challenges not only in terms of media manufacture but also in terms of the recording physics, in particular, due to the need of synchronized writing, i.e. the phase of the record current needs to be accurately synchronized with the geometry of the BP media islands [5]. The challenge of write-synchronization is exacerbated by the distribution of the magnetic media properties of the islands and the interaction fields between the islands [6,7]. I have previously introduced the notion ‘‘addressability’’ [4] to refer to the ability of synchronously writing BP-media islands. In the current paper, I will expand on the work of Ref. [4] and further quantify the notion of addressability by calculating phase margins F and addressability error-rates BERw as a function of the distribution of Corresponding author at: Hitachi San Jose Research Center, Hitachi GST, 3403 Yerba Buena Rd, San Jose, California 95135, USA. Tel.: +1 408 717 5181. E-mail address: [email protected]
0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.07.035
magnetic materials properties of the islands. Dynamic micromagnetic simulations [8] are used for this purpose at 1.3 Tb/in2 in Section 3. The results serve then to motivate analytical approaches to survey a larger design space in terms of the BP island fabrication tolerances, the write-synchronization jitter, the gradient of the effective write-field and the bit-pattern-dependent fluctuations of the interactions between islands at densities up to about 10 Tb/in2 (Sections 4–8). It is clear that BP recording at such densities poses also many (as-of-now unsolved) problems for the write and read heads (e.g. magnetic write-width o8 nm, at 10 Tb/in2, see Section 7). However, these questions are beyond the scope of this paper. Here scaled effective head-field profiles from conventional perpendicular pole heads are used for writing. Advanced write heads based on planar designs have been discussed recently [9] with field profiles that will be of interest for BP recording. In this paper, the write head is assumed to be laterally centered on a track of islands neglecting off-track fluctuations as well as temporal fluctuations of the write-field in the rest frame of the write head [10].
2. Recording on BP media BP recording is different from magnetic recording on CG media in many important aspects. BP recording partitions the write process into two steps: (1) spatial patterning and (2) magnetic addressing. In the first step (‘‘patterning’’), the spatial components of each bit-cell are written by creating precisely placed features (‘‘islands’’). In the second step (‘‘magnetic addressing’’), the magnetic components of each bit-cell are written by
ARTICLE IN PRESS M.E. Schabes / Journal of Magnetism and Magnetic Materials 320 (2008) 2880–2884
magnetizing the islands in one of several (typically two) magnetic configurations. In contradistinction, recording on CG media considers the medium to be translational invariant during placement of magnetic domains (bit-cells), and thus writes bits in a manifestly asynchronous fashion relative to the grains. As a consequence, local fluctuations of the shape, phase and magnetic uniformity of magnetic bit-cells result during writing and reading, leading to granular media noise. An increase of the recording density at constant media signal-to-noise ratio requires reducing the magnetic cluster sizes (which often means also smaller physical grains) and possibly tighter distributions of the granular material’s properties. The difficulty of further improving granular properties at reduced magnetic correlation size and sufficient thermal stability is the main motivator for attempting synchronous approaches, like BP recording, for Tb/in2 systems. The patterning step of BP media typically involves lithography, nano-imprinting and possibly self-organized processes [11]. There are many different geometries of BP media possible. For simplicity, I consider here a certain class of BP media (Fig. 1) with islands of the shape of rectangular orthogonal parallelepipeds arranged along orthogonal axes with down-track period l1 and cross-track period l2. The widths of the trenches in the downtrack and cross-track directions are g1 and g2, respectively. The ability to address precisely the island that is to be written is affected by a number of variables, in particular, the fabrication tolerances of the islands sprint, the write-synchronization jitter ssynch, the gradient of the effective write-field and the patterndependent fluctuations of the interactions between islands. Fig. 2 depicts a schematic of a write head moving from right to left above stationary media islands. The micromagnetic calculations of the following section will show that the probability of an
Fig. 1. Parameterization of BP-media class.
Fig. 2. Definition of down-track phase f relative to optimum phase f0; v indicates the direction of head motion.
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addressability error is minimized for a certain optimum phase f0 of the head relative to the islands as has been observed in recording experiments [5]. In the current paper, also the effects of fluctuations of the magnetic material properties of the islands are studied.
3. Calculations of the addressability error-rate BERw directly from micromagnetic dynamics In this section, a dynamic micromagnetic model [8] is used to quantify the impact of fluctuations of the magnetic material’s properties on the probability of error during magnetic addressing of islands at a bit density of 1.3 Tb/in2. The BP media have spatial periods l1 ¼ 15, l2 ¼ 33 nm, and trench widths g1 ¼ 5 and g2 ¼ 12 nm. The resulting bit aspect-ratio of the island is wisland ¼ 2.1, and of the bit-cell wcell ¼ 2.2, with an areal fill-factor r ¼ 42%. The magnetization of the islands is allowed to be nonuniform during reversal by discretizing each island into approximately 28 first-order tetrahedral finite elements. The magnetic material parameters (anisotropy, exchange, moment density and damping) are uniform within each island but vary from island to island by drawing from Gaussian distributions that are truncated at 73 standard deviations. In particular, the crystalline (or interfacial anisotropy in the case of multi-layers) is uniaxial and has a mean value of /K1S ¼ 2.7 105 J/m3 with standard deviation sK1 in the range of 0–8.0% for different BP media samples. The corresponding easy axes are on average perpendicular to the plane of the substrate with a standard deviation of 1.21. The magnetic polarization of the island has an expectation value of /JsS ¼ 0.7 T with sJs ¼ 2.0%. The intra-island exchange of the islands is centered at /AS ¼ 1.0 1011 J/m, with sA ¼ 2.0%. The gyromagnetic damping has a mean of /aS ¼ 0.1, and standard deviation sa ¼ 2.0%. The island thickness is fixed at 12 nm, giving a thermal stability ratio /b1S ¼ K1V/kBT ¼ 141, at the center of the K1 distribution at temperature T ¼ 350 K, where kB is the Boltzmann constant kB ¼ 1.38 1023 J/K. In the micromagnetic simulations thermal fluctuations are not included (T ¼ 0). Note that thermal stability criteria for BP islands and CG-media grains are expected to be different because each island represents a bit whereas multiple grains constitute a bit in CG media. Optimal design of energy barriers of BP islands requires additional study (the above large /b1S has therefore not been optimized by e.g. varying the island thickness). The micromagnetic calculations of the probability of an addressability error use ensembles of BP media with 240 members, each member being drawn from the distributions described above. For every ensemble member a square wave is recorded along a path of 21 islands in the down-track direction. The write head is a shielded perpendicular pole head, whose write-field profile has been calculated with a commercial magnetostatic finite element code and then scaled with risetimes of 60 ps (zero-to-peak). The maximum Stoner–Wohlfarth effective write-field [9], averaged over 30 nm near the trackcenter, is about 1.6 T, for example, when dmag ¼ 7 and dHUS ¼ 22 nm, where dmag is the magnetic spacing from the top surface of the media to the bottom surface of the write pole, and dHUS is the spacing between the soft underlayer and the write pole. In this case, the gradient of the similarly averaged effective field is about 0.066 T/nm at about 1.277 T, for example. In the cross-track direction the nearest-neighbor tracks are also included in the simulations. The BP media are uniformly magnetized prior to the start of the write process. The magnetization of the islands after writing is then compared with the target square wave to compute the ratio of the number of incorrectly written islands to the total number of written islands (all on the center track).
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M.E. Schabes / Journal of Magnetism and Magnetic Materials 320 (2008) 2880–2884
No addressability errors are committed on the adjacent tracks when the write head is centered on the target track because the cross-track trench width g2 ¼ 12 nm is sufficiently wide for the chosen head–media combination. Fig. 3 plots the logarithm of BERw (i.e. the probability of an addressability error) as a function of the down-track phase f for the case of sK1 ¼ 4% and the head centered on the track. At f ¼ 40 nm, the optimum write phase is apparent in Fig. 3 as a pronounced minimum. The value of the minimum error-rate at f ¼ f0 is taken to be the inverse of the total number of targeted islands even though no addressability error was observed in the ensemble at f ¼ f0. Detuning the phase from f0 quickly produces significant numbers of addressability errors. In general,
I define the addressability phase margin F to give the range of permissible phases relative to f0 such that the addressability error-rate is below a specified level BERw,F, i.e. BERwoBERw,F for (f0F)pfp(f0+F). Figs. 3 and 4 show that the phase margin and the addressability error-rate are quite sensitive to the dispersion of the island anisotropy. For instance, the phase margin at a write-error-rate of BERw ¼ 102.5 is given by F ¼ 73.5 nm for BP media with sK1 ¼ 4% (Fig. 3). For comparison, Fig. 4 shows that an increase of sK1 by 2–6% significantly raises the addressability error-rate even at optimum phase alignment f0. The increase is about half an order, with BERw ¼ 102.9 at f ¼ f0. Furthermore, the phase margin at BERw ¼ 102.5 is reduced to F72.0 nm. Another increase of sK1 by 2–8% increases BERw for all values of f beyond 102.5, as shown in Fig. 4. If the K1 distribution cannot be tightened, other systems parameters will need to be improved (e.g. the head-field gradient) in order to regain an adequate phase margin (see Section 6).
4. Estimation of fabrication tolerances from the phase margin Let F0 be the phase margin for vanishing lithography jitter
sprint and vanishing synchronization jitter ssynch. Assuming uncorrelated Gaussian distributions for the lithography and synchronization jitters, an upper bound for the fabrication tolerances can be estimated from F0 by requiring that a certain multiple of the pooled standard deviations be smaller than the phase margin: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi bw s2print þ s2synch pF0 , (1) with bw obtained from 1 b BERw ¼ erfc pwffiffiffi , 2 2
Fig. 3. Probability of an addressability error as a function of down-track phase f for sK1 ¼ 4%. Filled symbols are micromagnetic data, open symbols are interpolated as a guide for the eye.
(2)
where erfc is the error-function complement. Combining Eqs. (1) and (2) gives the following bound for the fabrication tolerance: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 uF (3) sprint pt 20 s2synch .
bw
Note that sprint implicitly is (via F0) a function of the magnetic distributions smag ¼ {sK1, sA, y} and the effective head-field gradient. Taking the micromagnetic results of the previous section for 1.3 Tb/in2 BP media with sK1 ¼ 4%, BERw ¼ 102.5, and ssynch ¼ 0.8 nm, an upper bound for the fabrication tolerance is given by sprinto1.0 nm.
5. Calculation of fabrication tolerances from pooled Gaussian fluctuations In this section, the general case is discussed, where the phase margin is not known a priori. The required fabrication tolerances are estimated by pooling geometrical and magnetic fluctuations assuming uncorrelated Gaussian distributions. A similar approach has been discussed in Ref. [3]. Let the quantity u be defined by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 sHs u ¼ bw (4) þ s2print þ s2synch , qHeff =qx Fig. 4. Probability of an addressability error as a function of f for sK1 ¼ 6% and 8%, respectively. Filled symbols are micromagnetic data, open symbols are interpolated as a guide for the eye.
where sHs is the standard deviation of the switching-field distribution (including contributions from pattern-dependent interactions between islands) and bw is given by Eq. (2).
ARTICLE IN PRESS M.E. Schabes / Journal of Magnetism and Magnetic Materials 320 (2008) 2880–2884
If the islands are spaced in the down-track direction such that the down-track period l1 satisfies the constraint (5)
l1 X2u,
the probability of making an addressability error is given by BERw of Eq. (2). The factor of 2 in Eq. (5) arises from the fact that both islands which are neighbors in the down-track direction are allowed to fluctuate independently. Eq. (5) indicates that the islands need to have a center-to-center distance larger than 2u if the addressability error-rate is to be better than BERw (i.e. the upper bound of the addressability error-rate). On the other hand, if l1o2u, an upper bound for the addressability error-rate is no longer known. I therefore call 7u the ‘‘uncertainty zone’’. Note that the above equations require an effective write-field profile that is approximately linear within the required operating range (due to SFD and interaction fields). Furthermore, the islands are assumed to be sufficiently small to reverse quasi-uniformly and are characterized by their center-to-center separation, neglecting effects due to possible variation of the trench size relative to the island period. Similarly, temporal variations (e.g. rise-time fluctuations [10]) of the effective field profile are not included. Additional motivation for Eq. (5) can also be found in Ref. [3]. For given fabrication and magnetic tolerances the achievable areal density can now be calculated from A¼
A0 2 l1 cell
w
,
(6)
where A is the areal density in Tb/in2, A0 is 645.16, wcell ¼ l1/l2 is the aspect ratio of the bit-cell; l1 is measured in nm and given by the lower bound of Eq. (5).
6. Design scenarios for 1 Tb/in2 The parameter space for a systems design is large and it is important to focus on the leading order terms. The charting methods developed in this section are based on Eq. (6) and highlight the importance of switching-field distribution, field gradient, and thermal stability for fixed values of the fabrication tolerance, write-synchronization tolerance, and bit aspect-ratio,
Fig. 5. Design chart for sprint ¼ ssynch ¼ 1 nm, wcell ¼ 1, Ms ¼ 430 emu/cm3, K1 ¼ 2.7 106 erg/cm3, BERw ¼ 106. The gray scale encodes the areal density in Tb/in2. The dashed contours with labels in bold font are areal-density contours in Tb/in2. Other contours are thermal energy-barrier contours of the islands at the underlying areal density and temperature T ¼ 350 K.
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respectively. An example of such a chart for the design space of about 0.7–2.0 Tb/in2 is shown in Fig. 5 for g1/l1 ¼ g2/l20.29. The gray scale encodes the areal density in Tb/in2. Contours of constant areal density (labeled with bold font) are included in Fig. 5 as a guide for the eye. While the areal density is a non-linear function of sHs and grad(Heff) (see Eq. (6)), the areal density contours display a linear shape. The linearity of the density contours can easily be explained from the fact that the expression for u (Eq. (4)) depends on the ratio of sHs and grad(Heff). The other contours (with regular type-face labels) in Fig. 5 give the thermal stability ratio b2 ¼ (K12p/MS2)V/(kBT), where V is the volume of the island at the underlying areal density, /MS is the mean magnetic moment density averaged over the islands and trenches, and T is the temperature. The design chart of Fig. 5 shows that 1 Tb/in2 can be achieved with an addressability error-rate BERw ¼ 106, if the switchingfield distribution is on the order of 1000 Oe, head-field gradient is about 430 Oe/nm, fabrication tolerance sprint ¼ 1 nm, and writesynchronization tolerance ssynch ¼ 1 nm. The BP periods are l1 ¼ l2 ¼ 25.4 nm, with island size of 17.9 17.9 8 nm3, and trench widths g1 ¼ g2 ¼ 7.5 nm; mean energy barrier /b2S is 113 at T ¼ 350 K. The chart makes visible the inherent trade-off between larger switching-field distributions and increased headfield gradients. In Fig. 5, the bit aspect-ratio is one and equally distributes lithography requirements in the down-track and cross-track directions. Generally, a larger bit aspect-ratio wcell would be preferred for larger write fields (due to larger pole size) and less stringent servo tolerances. However, larger wcell requires tighter fabrication and synchronization tolerances. Conversely, if these tolerances are kept constant, a narrower switching-field distribution or a sharper head-field gradient is needed. For example, increasing the bit aspect-ratio from 1 to 2 in Fig. 5 and keeping sprint ¼ ssynch ¼ 1 nm requires a reduction of the switching-field distribution sHs to less than about 500 Oe (unless the write-field gradient is increased).
7. Extendibility of BP recording It is interesting to ask whether technologies developed for BP recording at 1 Tb/in2 can be extended to even higher densities. The answer to this question is especially significant since it is not clear at present where the cross-over density from CG to BP recording is located. Fig. 6 shows a design chart spanning areal densities of about 2–10 Tb/in2 at fabrication and synchronization tolerances sprint ¼ ssynch ¼ 0.4 nm, and bit aspect-ratio wcell ¼ 1, attempting an addressability error-rate BERw ¼ 106. At 10 Tb/in2 and g1/l1 ¼ g2/l2 ¼ 0.25, the island size is about 6 nm for trench widths of 2 nm. Note that in this case the BP island is of similar size as an average grain in current CG media. The write-field gradient would need to be of order 700–800 Oe/nm to accommodate a switching-field distribution of about 450 Oe. However, the interaction fields would need to be tightly controlled to have any margin for the K1 distribution (since sHs includes the fluctuation of the interaction fields). In Fig. 6 Ms ¼ 430 emu/cm3, K1 ¼ 1.8 107 erg/cm3, and island thickness is 4.5 nm, implying the use of exchange-spring effects [12] or other techniques, e.g., energy-assisted methods (see below), to render the islands writeable since the nominal anisotropy field, Hk ¼ 2K1/Ms, is 8.4 T. The fact that neither the required exchange-spring materials nor the write heads at write-widths of about 8 nm are available at present points to some of the formidable challenges ahead when extending magnetic data storage towards 10 Tb/in2.
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trenches break lateral exchange, whereas it needs to be controlled by grain-boundaries in CG media. Furthermore, combinations of CG media with energy-assisted writing (CGTAR, CGMAMR) still require small grains to achieve low media noise and to fully leverage improvements of write gradients. For these reasons, BP media appear to offer more extendibility than CG media.
9. Conclusions A theoretical analysis of the geometrical and magnetic tolerances of BP recording has been presented. Magnetic switching-field distributions, fabrication tolerances, write-synchronization tolerances, as well as the gradient of the effective write-field profile need to be well controlled in a balanced BP recording systems design. Larger bit aspect-ratios of the islands allow the use of larger write poles with higher write fields, yet exacerbate the lithography and write-synchronization tolerances. Second-generation BP-recording avoids the granular challenges of energy-assisted recording on CG media, and thus represents a pathway into the deep Tb/in2 domain. Fig. 6. Design chart for sprint ¼ ssynch ¼ 0.4 nm, wcell ¼ 1, Ms ¼ 430 emu/cm3, K1 ¼ 1.8 107 erg/cm3, BERw ¼ 106. See Fig. 5 for the definition of gray scale, labels, and contours.
8. Differential extendibility The challenges at 10 Tb/in2 suggest that advanced approaches should be considered whereby BP media are combined with various forms of energy-assisted writing. Thermally assisted recording (TAR) [13] and microwave-assisted recording (MAMR) [14,15] have been considered for CG recording and will also be of interest in combination with BP recording. [16] I call such combined techniques ‘‘2nd generation BPR’’, in contradistinction to approaches where the writing of BP media is done primarily with Zeeman fields at clock-frequencies fw ¼ v/(2l1) (‘‘1st generation BPR’’). Second-generation BPR may include thermally assisted writing of islands (BPTAR) or the addition of an auxiliary high-frequency (HF) magnetic field to provide resonantly assisted switching (BPMAMR). The frequency of the auxiliary HF field is typically significantly larger than the fundamental frequency of the main write current (depending on the resonance frequency of the magnetic materials used [14,15]). In the absence of energy-assisted writing, exchange-spring media [12] are considered to be important factors in extending both BP and CG media for the following reasons. In the case of BP media, exchange-springs facilitate designs with smaller bit aspect-ratio (less write-field) and thus relax the lithography tolerances. For CG media, exchange-springs could make possible grain sizes sufficiently small for ultra-high densities. Recent simulations [17] projected 42 Tb/in2 on CG media. However, considerable challenges exist to develop materials with the required properties for BP and CG media, respectively. A significant advantage of BP media stems from the fact that
Acknowledgements I wish to thank T. Albrecht and X. Wu for many fruitful discussions. I am grateful to T. Olson for providing scaled FEM head-field profiles, which I used as input for the micromagnetic simulations. References [1] C. Tsang, et al., IEEE Trans. Magn. 42 (2006) 145. [2] R. Wood, IEEE Trans. Magn. 36 (2000) 36. [3] H.J. Richter, A.Y. Dobin, O. Heinonen, K.Z. Gao, R.J.M.v.d. Veerdonk, R.T. Lynch, J. Xue, D. Weller, P. Asselin, M.F. Erden, R.M. Brockie, IEEE Trans. Magn. 42 (2006) 2255. [4] M.E. Schabes, The write process and thermal stability in bit-patterned recording media, Paper DA-05, 10th Joint MMM/Intermag Conference, Baltimore, 2007. [5] M. Albrecht, A. Moser, C.T. Rettner, S. Anders, T. Thomson, B.D. Terris, Appl. Phys. Lett. 80 (2002) 3409. [6] T. Thomson, G. Hu, B.D. Terris, Phys. Rev. Lett. 96 (2006) 257204. [7] J.M. Shaw, W.H. Rippard, S. Russek, T. Reith, C.M. Falco, J. Appl. Phys. 101 (2007) 023909. [8] M.E. Schabes, T. Schrefl, D. Suess, O. Ertl, IEEE Trans. Magn. 41 (2005) 3073. [9] K. Ise, S. Takahashi, K. Yamakawa, N. Honda, IEEE Trans. Magn. 42 (2006) 2224. [10] T. Schrefl, private communication, 2007. [11] B.D. Terris, T. Thomson, J. Phys. D—Appl. Phys. 38 (12) (2005) R199. [12] D. Suess, T. Schrefl, S. Faehler, M. Kirschner, G. Hrkac, F. Dorfbauer, J. Fidler, Appl. Phys. Lett. 87 (2005) 012504. [13] T.W. McDaniel, W.A. Challener, K. Sendur, IEEE Trans. Magn. 39 (2004) 1972. [14] H.T. Nembach, P.M. Pimentel, S.J. Hermsdoerfer, B. Leven, B. Hillebrands, S.O. Demokritov, Appl. Phys. Lett. 90 (2007) 062503. [15] J.G. Zhu, X. Zhu, Y. Tang, Microwave assisted magnetic recording (MAMR), Digests of PMRC 2007, 15pA-05, Tokyo, 2007. [16] INSIC, Workgroups on 10 Tb/in2 magnetic recording, 2007. [17] A. Dobin, Micromagnetic simulations of the domain wall assisted magnetic recording at ultra-high densities, Paper FC-02, 52nd Conference on Magnetism and Magnetic Materials, Tampa, 2007.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Micromagnetic simulations for terabit/in2 head/media systems Manfred E. Schabes Hitachi San Jose Research Center, Hitachi GST, San Jose, CA 95135, USA
a r t i c l e in f o
a b s t r a c t
Available online 5 August 2008
Bit-patterned (BP) recording is a candidate for extending magnetic data storage towards 10 Tb/in2 bit densities. An analysis of the design tolerances is carried out using dynamic micromagnetic simulations and statistical models. The effects of distributions of the magnetic material properties on phase margin and addressability error-rate during writing are investigated. At 1.3 Tb/in2 a rapid increase of the errorrate is observed when the write-synchronization deviates from the optimum phase f0. Estimates of the fabrication and write-synchronization tolerances are derived from the phase margins. It is shown that the switching-field distribution (from intra-island variations and inter-island interactions) as well as the fabrication and synchronization tolerances must be tightly controlled for Tb/in2 applications. At ultrahigh densities, BP media may need to be combined with energy-assisted writing, which is referred to as second-generation BP recording. & 2008 Elsevier B.V. All rights reserved.
PACS: 75.50.Ss 75.75.+a 85.70.Ay 85.70.Kh 85.70.Li Keywords: Micromagnetic simulation Bit-patterned medium Magnetic recording
1. Introduction Magnetic data storage technology has made significant progress towards increasing areal densities using continuous-granular (CG) perpendicular magnetic recording media as well as advanced transducers for writing and reading [1]. If progress continues at present rates, it is expected that commercial magnetic disk drives at 1 Tb/in2 will be realized in a few years’ time. Aspects of the recording physics at Tb/in2 densities have been discussed previously for CG media in Ref. [2] and for bitpatterned (BP) media in Refs. [3,4]. BP media circumvent the increasingly difficult task of reducing the size of thin-film grains and of magnetic clusters while maintaining thermal stability. However, BP media need to cope with many novel challenges not only in terms of media manufacture but also in terms of the recording physics, in particular, due to the need of synchronized writing, i.e. the phase of the record current needs to be accurately synchronized with the geometry of the BP media islands [5]. The challenge of write-synchronization is exacerbated by the distribution of the magnetic media properties of the islands and the interaction fields between the islands [6,7]. I have previously introduced the notion ‘‘addressability’’ [4] to refer to the ability of synchronously writing BP-media islands. In the current paper, I will expand on the work of Ref. [4] and further quantify the notion of addressability by calculating phase margins F and addressability error-rates BERw as a function of the distribution of Corresponding author at: Hitachi San Jose Research Center, Hitachi GST, 3403 Yerba Buena Rd, San Jose, California 95135, USA. Tel.: +1 408 717 5181. E-mail address: [email protected]
0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.07.035
magnetic materials properties of the islands. Dynamic micromagnetic simulations [8] are used for this purpose at 1.3 Tb/in2 in Section 3. The results serve then to motivate analytical approaches to survey a larger design space in terms of the BP island fabrication tolerances, the write-synchronization jitter, the gradient of the effective write-field and the bit-pattern-dependent fluctuations of the interactions between islands at densities up to about 10 Tb/in2 (Sections 4–8). It is clear that BP recording at such densities poses also many (as-of-now unsolved) problems for the write and read heads (e.g. magnetic write-width o8 nm, at 10 Tb/in2, see Section 7). However, these questions are beyond the scope of this paper. Here scaled effective head-field profiles from conventional perpendicular pole heads are used for writing. Advanced write heads based on planar designs have been discussed recently [9] with field profiles that will be of interest for BP recording. In this paper, the write head is assumed to be laterally centered on a track of islands neglecting off-track fluctuations as well as temporal fluctuations of the write-field in the rest frame of the write head [10].
2. Recording on BP media BP recording is different from magnetic recording on CG media in many important aspects. BP recording partitions the write process into two steps: (1) spatial patterning and (2) magnetic addressing. In the first step (‘‘patterning’’), the spatial components of each bit-cell are written by creating precisely placed features (‘‘islands’’). In the second step (‘‘magnetic addressing’’), the magnetic components of each bit-cell are written by
ARTICLE IN PRESS M.E. Schabes / Journal of Magnetism and Magnetic Materials 320 (2008) 2880–2884
magnetizing the islands in one of several (typically two) magnetic configurations. In contradistinction, recording on CG media considers the medium to be translational invariant during placement of magnetic domains (bit-cells), and thus writes bits in a manifestly asynchronous fashion relative to the grains. As a consequence, local fluctuations of the shape, phase and magnetic uniformity of magnetic bit-cells result during writing and reading, leading to granular media noise. An increase of the recording density at constant media signal-to-noise ratio requires reducing the magnetic cluster sizes (which often means also smaller physical grains) and possibly tighter distributions of the granular material’s properties. The difficulty of further improving granular properties at reduced magnetic correlation size and sufficient thermal stability is the main motivator for attempting synchronous approaches, like BP recording, for Tb/in2 systems. The patterning step of BP media typically involves lithography, nano-imprinting and possibly self-organized processes [11]. There are many different geometries of BP media possible. For simplicity, I consider here a certain class of BP media (Fig. 1) with islands of the shape of rectangular orthogonal parallelepipeds arranged along orthogonal axes with down-track period l1 and cross-track period l2. The widths of the trenches in the downtrack and cross-track directions are g1 and g2, respectively. The ability to address precisely the island that is to be written is affected by a number of variables, in particular, the fabrication tolerances of the islands sprint, the write-synchronization jitter ssynch, the gradient of the effective write-field and the patterndependent fluctuations of the interactions between islands. Fig. 2 depicts a schematic of a write head moving from right to left above stationary media islands. The micromagnetic calculations of the following section will show that the probability of an
Fig. 1. Parameterization of BP-media class.
Fig. 2. Definition of down-track phase f relative to optimum phase f0; v indicates the direction of head motion.
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addressability error is minimized for a certain optimum phase f0 of the head relative to the islands as has been observed in recording experiments [5]. In the current paper, also the effects of fluctuations of the magnetic material properties of the islands are studied.
3. Calculations of the addressability error-rate BERw directly from micromagnetic dynamics In this section, a dynamic micromagnetic model [8] is used to quantify the impact of fluctuations of the magnetic material’s properties on the probability of error during magnetic addressing of islands at a bit density of 1.3 Tb/in2. The BP media have spatial periods l1 ¼ 15, l2 ¼ 33 nm, and trench widths g1 ¼ 5 and g2 ¼ 12 nm. The resulting bit aspect-ratio of the island is wisland ¼ 2.1, and of the bit-cell wcell ¼ 2.2, with an areal fill-factor r ¼ 42%. The magnetization of the islands is allowed to be nonuniform during reversal by discretizing each island into approximately 28 first-order tetrahedral finite elements. The magnetic material parameters (anisotropy, exchange, moment density and damping) are uniform within each island but vary from island to island by drawing from Gaussian distributions that are truncated at 73 standard deviations. In particular, the crystalline (or interfacial anisotropy in the case of multi-layers) is uniaxial and has a mean value of /K1S ¼ 2.7 105 J/m3 with standard deviation sK1 in the range of 0–8.0% for different BP media samples. The corresponding easy axes are on average perpendicular to the plane of the substrate with a standard deviation of 1.21. The magnetic polarization of the island has an expectation value of /JsS ¼ 0.7 T with sJs ¼ 2.0%. The intra-island exchange of the islands is centered at /AS ¼ 1.0 1011 J/m, with sA ¼ 2.0%. The gyromagnetic damping has a mean of /aS ¼ 0.1, and standard deviation sa ¼ 2.0%. The island thickness is fixed at 12 nm, giving a thermal stability ratio /b1S ¼ K1V/kBT ¼ 141, at the center of the K1 distribution at temperature T ¼ 350 K, where kB is the Boltzmann constant kB ¼ 1.38 1023 J/K. In the micromagnetic simulations thermal fluctuations are not included (T ¼ 0). Note that thermal stability criteria for BP islands and CG-media grains are expected to be different because each island represents a bit whereas multiple grains constitute a bit in CG media. Optimal design of energy barriers of BP islands requires additional study (the above large /b1S has therefore not been optimized by e.g. varying the island thickness). The micromagnetic calculations of the probability of an addressability error use ensembles of BP media with 240 members, each member being drawn from the distributions described above. For every ensemble member a square wave is recorded along a path of 21 islands in the down-track direction. The write head is a shielded perpendicular pole head, whose write-field profile has been calculated with a commercial magnetostatic finite element code and then scaled with risetimes of 60 ps (zero-to-peak). The maximum Stoner–Wohlfarth effective write-field [9], averaged over 30 nm near the trackcenter, is about 1.6 T, for example, when dmag ¼ 7 and dHUS ¼ 22 nm, where dmag is the magnetic spacing from the top surface of the media to the bottom surface of the write pole, and dHUS is the spacing between the soft underlayer and the write pole. In this case, the gradient of the similarly averaged effective field is about 0.066 T/nm at about 1.277 T, for example. In the cross-track direction the nearest-neighbor tracks are also included in the simulations. The BP media are uniformly magnetized prior to the start of the write process. The magnetization of the islands after writing is then compared with the target square wave to compute the ratio of the number of incorrectly written islands to the total number of written islands (all on the center track).
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No addressability errors are committed on the adjacent tracks when the write head is centered on the target track because the cross-track trench width g2 ¼ 12 nm is sufficiently wide for the chosen head–media combination. Fig. 3 plots the logarithm of BERw (i.e. the probability of an addressability error) as a function of the down-track phase f for the case of sK1 ¼ 4% and the head centered on the track. At f ¼ 40 nm, the optimum write phase is apparent in Fig. 3 as a pronounced minimum. The value of the minimum error-rate at f ¼ f0 is taken to be the inverse of the total number of targeted islands even though no addressability error was observed in the ensemble at f ¼ f0. Detuning the phase from f0 quickly produces significant numbers of addressability errors. In general,
I define the addressability phase margin F to give the range of permissible phases relative to f0 such that the addressability error-rate is below a specified level BERw,F, i.e. BERwoBERw,F for (f0F)pfp(f0+F). Figs. 3 and 4 show that the phase margin and the addressability error-rate are quite sensitive to the dispersion of the island anisotropy. For instance, the phase margin at a write-error-rate of BERw ¼ 102.5 is given by F ¼ 73.5 nm for BP media with sK1 ¼ 4% (Fig. 3). For comparison, Fig. 4 shows that an increase of sK1 by 2–6% significantly raises the addressability error-rate even at optimum phase alignment f0. The increase is about half an order, with BERw ¼ 102.9 at f ¼ f0. Furthermore, the phase margin at BERw ¼ 102.5 is reduced to F72.0 nm. Another increase of sK1 by 2–8% increases BERw for all values of f beyond 102.5, as shown in Fig. 4. If the K1 distribution cannot be tightened, other systems parameters will need to be improved (e.g. the head-field gradient) in order to regain an adequate phase margin (see Section 6).
4. Estimation of fabrication tolerances from the phase margin Let F0 be the phase margin for vanishing lithography jitter
sprint and vanishing synchronization jitter ssynch. Assuming uncorrelated Gaussian distributions for the lithography and synchronization jitters, an upper bound for the fabrication tolerances can be estimated from F0 by requiring that a certain multiple of the pooled standard deviations be smaller than the phase margin: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi bw s2print þ s2synch pF0 , (1) with bw obtained from 1 b BERw ¼ erfc pwffiffiffi , 2 2
Fig. 3. Probability of an addressability error as a function of down-track phase f for sK1 ¼ 4%. Filled symbols are micromagnetic data, open symbols are interpolated as a guide for the eye.
(2)
where erfc is the error-function complement. Combining Eqs. (1) and (2) gives the following bound for the fabrication tolerance: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 uF (3) sprint pt 20 s2synch .
bw
Note that sprint implicitly is (via F0) a function of the magnetic distributions smag ¼ {sK1, sA, y} and the effective head-field gradient. Taking the micromagnetic results of the previous section for 1.3 Tb/in2 BP media with sK1 ¼ 4%, BERw ¼ 102.5, and ssynch ¼ 0.8 nm, an upper bound for the fabrication tolerance is given by sprinto1.0 nm.
5. Calculation of fabrication tolerances from pooled Gaussian fluctuations In this section, the general case is discussed, where the phase margin is not known a priori. The required fabrication tolerances are estimated by pooling geometrical and magnetic fluctuations assuming uncorrelated Gaussian distributions. A similar approach has been discussed in Ref. [3]. Let the quantity u be defined by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 sHs u ¼ bw (4) þ s2print þ s2synch , qHeff =qx Fig. 4. Probability of an addressability error as a function of f for sK1 ¼ 6% and 8%, respectively. Filled symbols are micromagnetic data, open symbols are interpolated as a guide for the eye.
where sHs is the standard deviation of the switching-field distribution (including contributions from pattern-dependent interactions between islands) and bw is given by Eq. (2).
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If the islands are spaced in the down-track direction such that the down-track period l1 satisfies the constraint (5)
l1 X2u,
the probability of making an addressability error is given by BERw of Eq. (2). The factor of 2 in Eq. (5) arises from the fact that both islands which are neighbors in the down-track direction are allowed to fluctuate independently. Eq. (5) indicates that the islands need to have a center-to-center distance larger than 2u if the addressability error-rate is to be better than BERw (i.e. the upper bound of the addressability error-rate). On the other hand, if l1o2u, an upper bound for the addressability error-rate is no longer known. I therefore call 7u the ‘‘uncertainty zone’’. Note that the above equations require an effective write-field profile that is approximately linear within the required operating range (due to SFD and interaction fields). Furthermore, the islands are assumed to be sufficiently small to reverse quasi-uniformly and are characterized by their center-to-center separation, neglecting effects due to possible variation of the trench size relative to the island period. Similarly, temporal variations (e.g. rise-time fluctuations [10]) of the effective field profile are not included. Additional motivation for Eq. (5) can also be found in Ref. [3]. For given fabrication and magnetic tolerances the achievable areal density can now be calculated from A¼
A0 2 l1 cell
w
,
(6)
where A is the areal density in Tb/in2, A0 is 645.16, wcell ¼ l1/l2 is the aspect ratio of the bit-cell; l1 is measured in nm and given by the lower bound of Eq. (5).
6. Design scenarios for 1 Tb/in2 The parameter space for a systems design is large and it is important to focus on the leading order terms. The charting methods developed in this section are based on Eq. (6) and highlight the importance of switching-field distribution, field gradient, and thermal stability for fixed values of the fabrication tolerance, write-synchronization tolerance, and bit aspect-ratio,
Fig. 5. Design chart for sprint ¼ ssynch ¼ 1 nm, wcell ¼ 1, Ms ¼ 430 emu/cm3, K1 ¼ 2.7 106 erg/cm3, BERw ¼ 106. The gray scale encodes the areal density in Tb/in2. The dashed contours with labels in bold font are areal-density contours in Tb/in2. Other contours are thermal energy-barrier contours of the islands at the underlying areal density and temperature T ¼ 350 K.
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respectively. An example of such a chart for the design space of about 0.7–2.0 Tb/in2 is shown in Fig. 5 for g1/l1 ¼ g2/l20.29. The gray scale encodes the areal density in Tb/in2. Contours of constant areal density (labeled with bold font) are included in Fig. 5 as a guide for the eye. While the areal density is a non-linear function of sHs and grad(Heff) (see Eq. (6)), the areal density contours display a linear shape. The linearity of the density contours can easily be explained from the fact that the expression for u (Eq. (4)) depends on the ratio of sHs and grad(Heff). The other contours (with regular type-face labels) in Fig. 5 give the thermal stability ratio b2 ¼ (K12p/MS2)V/(kBT), where V is the volume of the island at the underlying areal density, /MS is the mean magnetic moment density averaged over the islands and trenches, and T is the temperature. The design chart of Fig. 5 shows that 1 Tb/in2 can be achieved with an addressability error-rate BERw ¼ 106, if the switchingfield distribution is on the order of 1000 Oe, head-field gradient is about 430 Oe/nm, fabrication tolerance sprint ¼ 1 nm, and writesynchronization tolerance ssynch ¼ 1 nm. The BP periods are l1 ¼ l2 ¼ 25.4 nm, with island size of 17.9 17.9 8 nm3, and trench widths g1 ¼ g2 ¼ 7.5 nm; mean energy barrier /b2S is 113 at T ¼ 350 K. The chart makes visible the inherent trade-off between larger switching-field distributions and increased headfield gradients. In Fig. 5, the bit aspect-ratio is one and equally distributes lithography requirements in the down-track and cross-track directions. Generally, a larger bit aspect-ratio wcell would be preferred for larger write fields (due to larger pole size) and less stringent servo tolerances. However, larger wcell requires tighter fabrication and synchronization tolerances. Conversely, if these tolerances are kept constant, a narrower switching-field distribution or a sharper head-field gradient is needed. For example, increasing the bit aspect-ratio from 1 to 2 in Fig. 5 and keeping sprint ¼ ssynch ¼ 1 nm requires a reduction of the switching-field distribution sHs to less than about 500 Oe (unless the write-field gradient is increased).
7. Extendibility of BP recording It is interesting to ask whether technologies developed for BP recording at 1 Tb/in2 can be extended to even higher densities. The answer to this question is especially significant since it is not clear at present where the cross-over density from CG to BP recording is located. Fig. 6 shows a design chart spanning areal densities of about 2–10 Tb/in2 at fabrication and synchronization tolerances sprint ¼ ssynch ¼ 0.4 nm, and bit aspect-ratio wcell ¼ 1, attempting an addressability error-rate BERw ¼ 106. At 10 Tb/in2 and g1/l1 ¼ g2/l2 ¼ 0.25, the island size is about 6 nm for trench widths of 2 nm. Note that in this case the BP island is of similar size as an average grain in current CG media. The write-field gradient would need to be of order 700–800 Oe/nm to accommodate a switching-field distribution of about 450 Oe. However, the interaction fields would need to be tightly controlled to have any margin for the K1 distribution (since sHs includes the fluctuation of the interaction fields). In Fig. 6 Ms ¼ 430 emu/cm3, K1 ¼ 1.8 107 erg/cm3, and island thickness is 4.5 nm, implying the use of exchange-spring effects [12] or other techniques, e.g., energy-assisted methods (see below), to render the islands writeable since the nominal anisotropy field, Hk ¼ 2K1/Ms, is 8.4 T. The fact that neither the required exchange-spring materials nor the write heads at write-widths of about 8 nm are available at present points to some of the formidable challenges ahead when extending magnetic data storage towards 10 Tb/in2.
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trenches break lateral exchange, whereas it needs to be controlled by grain-boundaries in CG media. Furthermore, combinations of CG media with energy-assisted writing (CGTAR, CGMAMR) still require small grains to achieve low media noise and to fully leverage improvements of write gradients. For these reasons, BP media appear to offer more extendibility than CG media.
9. Conclusions A theoretical analysis of the geometrical and magnetic tolerances of BP recording has been presented. Magnetic switching-field distributions, fabrication tolerances, write-synchronization tolerances, as well as the gradient of the effective write-field profile need to be well controlled in a balanced BP recording systems design. Larger bit aspect-ratios of the islands allow the use of larger write poles with higher write fields, yet exacerbate the lithography and write-synchronization tolerances. Second-generation BP-recording avoids the granular challenges of energy-assisted recording on CG media, and thus represents a pathway into the deep Tb/in2 domain. Fig. 6. Design chart for sprint ¼ ssynch ¼ 0.4 nm, wcell ¼ 1, Ms ¼ 430 emu/cm3, K1 ¼ 1.8 107 erg/cm3, BERw ¼ 106. See Fig. 5 for the definition of gray scale, labels, and contours.
8. Differential extendibility The challenges at 10 Tb/in2 suggest that advanced approaches should be considered whereby BP media are combined with various forms of energy-assisted writing. Thermally assisted recording (TAR) [13] and microwave-assisted recording (MAMR) [14,15] have been considered for CG recording and will also be of interest in combination with BP recording. [16] I call such combined techniques ‘‘2nd generation BPR’’, in contradistinction to approaches where the writing of BP media is done primarily with Zeeman fields at clock-frequencies fw ¼ v/(2l1) (‘‘1st generation BPR’’). Second-generation BPR may include thermally assisted writing of islands (BPTAR) or the addition of an auxiliary high-frequency (HF) magnetic field to provide resonantly assisted switching (BPMAMR). The frequency of the auxiliary HF field is typically significantly larger than the fundamental frequency of the main write current (depending on the resonance frequency of the magnetic materials used [14,15]). In the absence of energy-assisted writing, exchange-spring media [12] are considered to be important factors in extending both BP and CG media for the following reasons. In the case of BP media, exchange-springs facilitate designs with smaller bit aspect-ratio (less write-field) and thus relax the lithography tolerances. For CG media, exchange-springs could make possible grain sizes sufficiently small for ultra-high densities. Recent simulations [17] projected 42 Tb/in2 on CG media. However, considerable challenges exist to develop materials with the required properties for BP and CG media, respectively. A significant advantage of BP media stems from the fact that
Acknowledgements I wish to thank T. Albrecht and X. Wu for many fruitful discussions. I am grateful to T. Olson for providing scaled FEM head-field profiles, which I used as input for the micromagnetic simulations. References [1] C. Tsang, et al., IEEE Trans. Magn. 42 (2006) 145. [2] R. Wood, IEEE Trans. Magn. 36 (2000) 36. [3] H.J. Richter, A.Y. Dobin, O. Heinonen, K.Z. Gao, R.J.M.v.d. Veerdonk, R.T. Lynch, J. Xue, D. Weller, P. Asselin, M.F. Erden, R.M. Brockie, IEEE Trans. Magn. 42 (2006) 2255. [4] M.E. Schabes, The write process and thermal stability in bit-patterned recording media, Paper DA-05, 10th Joint MMM/Intermag Conference, Baltimore, 2007. [5] M. Albrecht, A. Moser, C.T. Rettner, S. Anders, T. Thomson, B.D. Terris, Appl. Phys. Lett. 80 (2002) 3409. [6] T. Thomson, G. Hu, B.D. Terris, Phys. Rev. Lett. 96 (2006) 257204. [7] J.M. Shaw, W.H. Rippard, S. Russek, T. Reith, C.M. Falco, J. Appl. Phys. 101 (2007) 023909. [8] M.E. Schabes, T. Schrefl, D. Suess, O. Ertl, IEEE Trans. Magn. 41 (2005) 3073. [9] K. Ise, S. Takahashi, K. Yamakawa, N. Honda, IEEE Trans. Magn. 42 (2006) 2224. [10] T. Schrefl, private communication, 2007. [11] B.D. Terris, T. Thomson, J. Phys. D—Appl. Phys. 38 (12) (2005) R199. [12] D. Suess, T. Schrefl, S. Faehler, M. Kirschner, G. Hrkac, F. Dorfbauer, J. Fidler, Appl. Phys. Lett. 87 (2005) 012504. [13] T.W. McDaniel, W.A. Challener, K. Sendur, IEEE Trans. Magn. 39 (2004) 1972. [14] H.T. Nembach, P.M. Pimentel, S.J. Hermsdoerfer, B. Leven, B. Hillebrands, S.O. Demokritov, Appl. Phys. Lett. 90 (2007) 062503. [15] J.G. Zhu, X. Zhu, Y. Tang, Microwave assisted magnetic recording (MAMR), Digests of PMRC 2007, 15pA-05, Tokyo, 2007. [16] INSIC, Workgroups on 10 Tb/in2 magnetic recording, 2007. [17] A. Dobin, Micromagnetic simulations of the domain wall assisted magnetic recording at ultra-high densities, Paper FC-02, 52nd Conference on Magnetism and Magnetic Materials, Tampa, 2007.