reversal in bit patterned media with vertical and lateral exchange

REVERSAL IN BIT PATTERNED MEDIA WITH VERTICAL AND LATERAL EXCHANGE M. V. Lubarda, S. Li, B. Livshitz, E. E. Fullerton, V. Lomakin Center for Magnetic Recording Research, Department of Electrical and Computer Engineering, University of California, San Diego, California 92093, USA ABSTRACT The extent to which dipolar interactions affect switching field distributions and thermal stability, and subsequently system performance, depends closely on the areal density, materials properties, and the architecture of the media, as well as the recording scheme and field profiles. This paper assesses, via micromagnetic simulations, the potential of heterogeneous capped bit patterned media and other proposed patterned media designs for ultra-high density magnetic recording with respect to writability, switching field distributions, and thermal stability at different areal densities. Such media is comprised of an array of homogeneous or exchange coupled composite elements with vertical anisotropy that is ferromagnetically or antiferromagnetically coupled to a continuous horizontal layer. It is shown that such systems, characterized by lateral and vertical exchange, enable ultra-high density recording at low switching fields while ensuring high thermal stability and low switching field distributions. Mechanisms leading to improved performance in capped systems are investigated. Structural and material considerations are provided for all media models. I.

INTRODUCTION

Magnetic recording on continuous granular media has reached areal densities on the level of 500 Gb/in 2 [1]. The areal density limit for convention perpendicular recording is estimated around 1 Tb/in 2 [2]. Reducing the grain size beyond this mark, in order to achieve yet higher storage capacity, may compromise the thermal stability due to the superparamagnetic effect [3-5]. In response, much research has been focused on alternative media architectures and recording schemes. Foremost among these are bit patterned media (BPM) magnetic recording [6-11] and energy assisted magnetic recording [12-13]. We focus attention on BPM. BPM consists of an arranged array of magnetic islands, fabricated using lithography techniques and/or self-assembly methods [14] (Fig. 1a). Separation between the islands ensures a large signal to noise ratio (SNR), while increased magnetic volume of bits in BPM increases thermal stability of the stored data. Various extensions of BPM allow using high anisotropy materials for high thermal stability that can be switched with sufficiently low head field. For example, composite BPM consisting of exchange coupled composite (ECC) elements [15] [16] [17] or ledge elements [18] has been shown to significantly reduce switching fields, without compromising thermal stability [15] [19] [20] (Fig. 1b, c). The switching field distribution (SFD) poses another serious problem that can considerably limit recording performance [21-22]. SFDs appear due to intrinsic distributions of the media properties as well as due to distributions of dipolar fields caused by the magnetization of recorded bits [23-24]. Dipolar interactions may also significantly reduce the thermal stability. Dipolar interactions are most significant between neighboring elements. In principle one can partially account for such interactions in a recording method by tuning the head field or time synchronization. However, while such an approach could reduce SFDs it may significantly complicate the recording process and it would not address the problem of reduced thermal stability caused by dipolar interactions. Capped BPM (CBPM), which is comprised of magnetically hard patterned islands coupled to continuous low anisotropy film, was recently introduced to address the magnetostatically induced SFD problem [25] [26] (Fig. 1d). In this design the continuous capping layer enables compensation of dipolar interactions through lateral exchange between the bits, which is tuned to counterbalance the effects of the magnetostatic fields and reduce SFDs. These media also can reduce the switching fields. However, due to optimization towards minimum SFDs, the potential of the capping layer in explicitly reducing switching fields may be not fully exploited [25]. Moreover, the domain walls in the capping layer can reduce media stability for certain parameter ranges. 4

In this work we investigate the potential of heterogeneous CBPM (and other recently proposed BPM designs) for ultra-high density magnetic recording in terms of writability, SFDs, and thermal stability. Mechanisms leading to reduced switching fields and SFDs in different BPM designs are described. Effects of the capping layer on media stability and its optimization are examined. To achieve a maximum reduction in switching fields at minimal SFDs, ECC elements can be used in concert with the continuous capping layer [27] (Fig. 1e). The capping layer may be coupled ferromagnetically or antiferromagnetically to the patterned bits. We show that in such media a simultaneous optimization for reduced SFDs and improved thermal stability is possible. In the AFC-composite-CBPM (AFCCCBPM) design, the capping layer may also be optimized to suppress magnetostatic interference effects in the readback response [27]. II.

WRITABILITY AND SWITCHING FIELD DISTRIBUTIONS

A. MAGNETOSTATICALLY INDUCED SFDs Though media performance depends on a number of factors, such as the head design (e.g. integration with energy delivery mechanisms [12]) and recording scheme (e.g. shingled writing), we will focus on switching fields and SFDs obtained assuming conventional recording systems. The procedure used here will allow for generalized conclusions, which can be extended to a more elaborate description of the recording system and process. Presuming a uniform two dimensional array of identical magnetic islands, the width of the SFD is due to dipolar interactions exclusively, and can be evaluated as the difference in switching fields between a bit surrounded by bits of the same magnetization direction (parallel configuration: Fig. 2a) and oppositely magnetized bits (antiparallel configuration: Fig. 2b). Generally, the dipolar contribution of the first and second nearest-neighbor bits accounts for most of the spread in switching fields. Hence, the third nearest neighbors can typically be omitted from the calculation of magnetostatically induced SFDs. A model consisting of only several nearest array elements surrounding the element to be switched is used. In Fig. 5-8, 11 an array of only 3 elements is considered as it is sufficient to study the behavior and trends. For more complete media characterization in Figs. 3 and 9, a five-by-five square array of bits is used to quantify the magnetostatically induced SFDs. Square and staggered arrays lead to very similar results when the inter-island spacing is comparable to the island dimensions. One solution to limit the extent of dipolar interactions in regular homogeneous or ECC BPM is to lower the saturation magnetization of the magnetic layer(s). Though this would result in a narrower SFD, it would also require a higher anisotropy field to keep the same thermal stability, thus leading to higher switching fields with associated writability problem (especially pronounced for high density media with bits of small magnetic volume). To demonstrate this trade-off between writability and SFDs, we have carried out simulations on homogeneous and CBPM at 4 Tb/in 2 considering five by five element array. The results were obtained by integrating the LandauLifshitz Gilbert equation in time, with all effective fields accurately included (exchange, anisotropy, magnetostatics, Zeeman). The shape anisotropy and dipolar coupling are taken into account via the magnetostatics term. In both the homogeneous and CBPM model the net thickness of the patterned elements was chosen to be 15nm (larger thickness would imply excessive requirements on the write-field gradient [22]) , the anisotropy of the hard element (

H K  5 kOe ) was chosen for KU V / kBT  55 (for T=300K), and the applied field was directed vertically (see caption for details). Figure 3 shows the switching fields for homogeneous (black) and capped BPM (red) versus the P saturation magnetization of the hard layer. The solid and dashed lines correspond to the switching fields, H sw and H swAP , of the central bit obtained for the parallel (Fig. 2a) and antiparallel case (Fig. 2b), respectively. The

discrepancy between the two field values represents the SFD. For homogeneous BPM, the SFD is large for large M s (corresponding to low switching fields for a fixed thermal barrier). For example, for M s  950 emu/cm3 and magnetocrystalline anisotropy energy density

KU  2.38 Merg/cm3 (corresponding to an anisotropy field,

H K  5 kOe ) the SFD for the homogeneous BPM is 70% of the mean switching field. Such a large SFD would pose 5

major restrictions on the write field gradient, synchronization accuracy, and media patterning fidelity [22]. To relax these restrictions, media anisotropy would have to be substantially increased or the saturation magnetization reduced. However, this would increase the writability requirements and could compromise the readback signal intensity. The advantage of the CBPM design, as seen in Figure 3, is that it is able to significantly reduce the SFD, thus allowing reliable recording at low switching fields. Here, the CBPM structure has been optimized towards minimal SFD at a hard layer saturation magnetization of 950 emu/cm3 . The tunability of the material parameters of the capping layer allows optimization towards minimal SFDs for arbitrary hard layer material parameters. We now describe details of the lateral and vertical exchange interactions in CBPM, and analyze the dependence of the switching field and SFD on materials parameters of the capping layer. A single-track capped BPM model consisting of three islands is sufficient to illustrate the main principles and provide understanding of the optimization process. Figure 4a and 4b illustrate the magnetization configurations of a track of capped BPM when the central island is oriented parallel and antiparallel to its neighbor-islands, respectively. The structure is characterized by vertical exchange across the island-cap interface, and lateral exchange across the length of the capping layer. The degree of exchange coupling between adjacent islands can be modulated by tuning the strength of lateral and vertical exchange. Vertical exchange is modulated through the interfacial coupling strength (or energy density), J int , which in practice can be tuned by varying the composition and thickness of a thin spacer layer deposited between the capping layer and the patterned hard layer [28]. The strength of the lateral exchange depends on the exchange length of the capping layer, lexcap  Aexcap / M Scap , where Aexcap is the exchange constant, and M Scap is the saturation magnetization. A large lexcap implies increased stiffness in the capping layer, hence stronger lateral exchange coupling. Because the capping layer stiffness favors uniform magnetization (Fig. 4a), the exchange interaction is seen to oppose the dipolar interaction (Fig. 4b). The magnetocrystalline anisotropy of the capping layer also has an influence on the extent to which magnetostatic interactions are compensated during island reversal and has important implications for the media stability. P Figure 5 illustrates the dependence of the switching fields for the parallel configuration ( H sw , solid line) and

antiparallel configuration ( H swAP , dashed line) on the saturation magnetization, M Scap , for capping layer thickness, tcap  1 nm , 3 nm and 6 nm . When M Scap is large, the exchange coupling between the bits is week, and the dipolar P AP interaction dominates, resulting in H sw . As M Scap is reduced, the exchange interaction becomes dominant, and  H sw P AP P AP . The point of intersection between the solid and dashed lines (when H sw ) indicates that the effect H sw  H sw  H sw

of dipolar interactions on the switching fields has been fully compensated by the exchange interaction. P Figure 6 shows the dependence of H sw and H swAP on the interfacial coupling strength, J h / cap , for three values of

capping layer anisotropy, KUcap  0 , 1 , and 2 Merg/cm3 . As J h / cap increases, so does the inter-island exchange P AP coupling, and hence, for large J h / cap we have H sw . Furthermore, the greater the KUcap , the greater the effect  H sw

of the exchange interaction on switching fields. This is because in the antiparallel configuration the magnetization of the capping layer is not in perfect alignment with the easy axis, and it can under a reduced applied field cross over to the opposite preferential direction, thereafter assisting the applied field in reversing the hard island through an increased exchange field. Another parameter which may serve to tune the exchange interaction is the exchange constant Aexcap . It may be preferable to have a relatively small Aexcap to prevent the exchange interaction from being too strong. The exchange constant can be varied by tuning the Curie temperature through compositional adjustment [26] or by ion-irradiation Aexcap [29] [30] [31] [32]. The entire capping layer can be irradiated, or only parts of the capping layer between patterned islands. The latter method would reduce lateral exchange while preserving vertical exchange, thus 6

enabling significant reduction in both switching fields and SFDs. Reduced lateral exchange would enable large thicknesses of the capping layer. As a result, the capping layer can further be replaced by the soft magnetic underlayer (SUL), thus allowing reducing switching fields, SFDs, controlling the head field and readback, and potentially simplifying the fabrication process. Another possible means to tune lateral exchange is to use a soft granular capping layer (with grains smaller than the BPM elements) and modulate the inter-granular exchange coupling [33]. cap To achieve a maximal reduction in both switching fields and SFDs, assuming Alat . ex. has not been previously

reduced, we introduced a new design, referred to as capped-composite-BPM (CCBPM), in which ECC elements are coupled to the capping layer, instead of homogeneous elements [27] (Fig. 1e). Because the ECC elements ensure low switching fields [15, 19, 34], the capping layer may be coupled either ferromagnetically or antiferromagnetically to the hard layer, in this new design. Figure 7 illustrates that the switching fields for FC and AFC-CCBPM are considerably lower than for CBPM, while the SFD is equally reduced. Conversely, ECC and ledge BPM are shown to have very wide SFDs, represented by the magenta and cyan shading in Fig. 7b, respectively. B. MATERIALS CONTRIBUTION TO SFDs Before moving on to a discussion of thermal stability in the next section, it is useful to inspect the materials contribution to SFD in capped BPM structures. Preceding figures relating the dependence of switching fields on J int , M Scap , KUcap , and tcap already gave some insight to the SFD caused by structural and materials fluctuations in the capping layer. What follows is an investigation of the SFDs caused by materials fluctuations occurring in the hard layer. Figures 8 illustrates the sensitivity of the switching fields for homogeneous BPM, capped BPM, ECC BPM, and AFC-CCBPM on hard layer anisotropy energy density. When interfacial coupling is low, CBPM responds similarly as homogeneous BPM to fluctuations in hard layer material properties (Fig 8a). If the interfacial exchange between a soft and a hard layer is increased, the switching field dependence on hard layer anisotropy is significantly altered due to a change in reversal mode, as seen in Fig. 8b for ECC as well as FC and AFC-CCBPM [19]. The CCBPM designs allow significant reduction in both dipolar and material induced SFDs. III.

THERMAL STABILITY

In order to ensure high thermal stability of recorded data the energy barrier, Eb , separating the up and down magnetization directions is required to be at least 45 kBT , where k B is the Boltzmann constant and T  300 K [35]. In BPM with uncoupled elements dipolar interactions can significantly reduce the thermal stability of the media, because the stray magnetostatic fields emanating from the bits act as an effective applied field, H aeff , reducing the energy barrier between the two stable states by around KV [1  (1  H aeff / H 0 ) ] , where H 0 is the short-time coercivity of the island, and  specifies the angle dependence to the effective applied field [36]. Below we investigate thermal stability of several media types and show that CBPM can lead to increased energy barriers. The energy barriers for all results were computed with the nudge elastic band method [37] [38] taking into account all effective field components, geometrical and material details, and domain processes. Figure 9 illustrates the thermal reversal of a central island in a five-by-five array of homogeneous bits at 4 Tb/in 2 , with thermal stability ratio KU V / kBT  55 , and anisotropy field H K  5 kOe . The energy barrier corresponding to the transition from the parallel to the antiparallel configuration, T P AP , is much smaller than the energy barrier for the reverse transition, T P  AP , and the energy path is asymmetric around the saddle point S (Fig. 9a). This asymmetry is caused by the change in polarity of the dipolar field acting on the central island in the parallel and antiparallel configuration. As a result, the energy barrier associated with T P AP is four times smaller than that of

7

T P  AP , and well below the acceptable limit of 45 kBT . A way to recover stability in homogeneous BPM would be to

increase H K of the media, which would lead to higher switching fields. CBPM provides an alternative means to regain media stability that does not rely on increasing media anisotropy. Figure 9b illustrates the minimum energy path for thermal reversal of the central bit in a five-by-five array of capped bits, with hard layer material and structural parameters identical to those of homogeneous BPM (see caption of Fig. 9 for details). Apart from the improvement in symmetry about the saddle point, the energy barrier for both the T P AP and T P  AP transitions in capped BPM is well above 45 kBT , unlike for homogeneous BPM. The energy barrier corresponding to the T P AP transition is improved in capped BPM because this transition necessitates the formation of domain walls in the capping layer (as in Fig. 4b). To achieve a T P AP transition an added exchange energy that is required to obtain the domain wall needs to be supplied. For the reverse transition T P  AP , the energy barrier which was in homogeneous BPM inflated by the dipolar interaction, in capped BPM is lowered by the energy provided to the system through the expulsion of the domain walls in the capping layer. Because the modes for field-assisted and thermal reversal differ from one another [15], it is not obvious whether capped BPM can resolve the SFD problem and retrieve media stability simultaneously. However, both the simulations leading to the SFD results of Fig. 3 and the stability calculations presented in Fig. 9b involved the same capped BPM model, with identical structural and material parameters, demonstrating that a simultaneous optimization toward minimal SFDs and improved thermal stability is indeed possible. Besides dipolar interactions, long-term storage performance can also be jeopardized by exchange interactions in CBPM systems, even when the media is optimized for minimum SFDs. Therefore, careful consideration is essential in properly optimizing CBPM to prevent possible stability loss. In the following text, we investigate the influence of the capping layer on the thermal stability of capped structures, study the dependence of the energy barriers on materials parameters of the capping layer, and explore means to maximize stability. In order to study thermal stability it is useful to look at the equilibrium states of capped BPM for different media parameters and recorded configurations [39]. Figure 10a shows the expected equilibrium magnetization configuration when all bits are equally oriented (parallel configuration) and the interfacial coupling, J h / cap , between the hard layer and capping layer is strong, and/or when the capping layer has a moderate anisotropy, KUcap . If J h / cap and KUcap are on the low end, and the saturation magnetization of the capping layer, M Scap , is high, the magnetization in the capping layer has a tendency to point in plane due to magnetostatic interactions (Fig. 10b). Figures 10c-f illustrate the equilibrium magnetization states that occur for the antiparallel configuration under different media parameters. For the larger part of the CBPM parameter space, the magnetization configuration in Fig. 10c is prevalent. That is, the magnetization in the capping layer for a state of alternating bits tends to be largely in-plane due to exchange-stiffness [40]. A more symmetric magnetization distribution results (Fig. 10e) when the capping layer is thin, and J h / cap and/or KUcap is increased, or when the exchange constant, Aexcap , is reduced (by irradiation, for example [29]). The domain wall formed between the oppositely oriented bits in single-track CBPM is usually a Néel wall due to dipolar interactions and a relatively large exchange length. However, if M Scap is significantly reduced while maintaining a small exchange length through Aexcap , a Bloch wall is possible (Fig. 10d). Finally, if the capping layer is sufficiently stiff magnetically and/or has too large an anisotropy, the exchange field on the capping layer from the island above may be too weak to influence its magnetization in the same direction, resulting in an adverse stable state as depicted in Fig. 10f. With these possible equilibrium states in mind, we can look at the dependence of the energy barriers separating the parallel and antiparallel configurations on the material parameters of the capping layer. The inset in Fig. 11 shows

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P  AP the transition from the parallel to the antiparallel configuration, Tthermal , indicated by the blue arrow, and the reverse P  AP transition, Tthermal , indicated by the red arrow. The blue and red lines in the plot of Fig. 11 show the dependence of P  AP P  AP cap the energy barriers associated with these transitions, Eb and Eb , on the uniaxial anisotropy, KU , of the

capping layer. The thermal stability for the parallel configuration EbP AP , is seen to grow with KUcap on the interval cap cap 3 from KU  0 to approximately KU  3.5 Merg/cm , and saturating thereafter. This behavior is expected, because, for the parallel configuration, an increase in capping layer anisotropy adds to the net anisotropy of the system, thus the stability initially increases. Once the capping layer anisotropy field exceeds the exchange field provided by the P  AP cap coupling between the island and the capping layer, the energy barrier, Eb , grows no longer with KU . In other

words, the energy required to independently reverse the magnetization in the portion of the capping layer beneath the island becomes greater than the energy of the interfacial domain wall created thereof. Indeed, when the anisotropy field exceeds the exchange field, the state in Fig. 10f becomes a possible equilibrium state for the P  AP cap antiparallel configuration, which further explains the behavior of Eb with KU (red line). Greatest thermal cap stability is obtained, therefore, when KU is relatively small.

Another way to avoid the equilibrium configuration of Fig. 10f, is to increase the coupling strength , J h / cap , between the capping layer and the hard islands. Though this would prevent the state of Fig. 10f form occurring, the energy P  AP barrier for the Tthermal transition would generally suffer. A large J h / cap implies the existence of condensed high-energy domain walls in the antiparallel configuration. During thermal reversal the energy provided by the domain walls as they unfold exceeds the dipolar contribution, and lowers the net energy of the system. Furthermore, as seen in Fig. 10c, the exchange field exerted by the capping layer on the central element at equilibrium causes the moment in the hard island to noticeably deviate from the easy axis. Hence, the anisotropy energy of the island in its initial equilibrium state is reduced in comparison to the full island anisotropy, and the absolute energy barrier for the P  AP 2 2 Tthermal transition is reduced. Overall, increasing J h / cap from 1 erg/cm to 4 erg/cm results in a two-fold reduction in media stability, for the chosen parameters cap cap The thermal stability can also be tuned through the saturation magnetization, M S , and exchange constant, Aex , cap P  AP P  AP of the capping layer. Presuming a relatively small J h / cap and KU , the energy barriers, Eb and Eb , will not be cap cap drastically effected by adjustments in M S or Aex , providing a decent range over which both SFDs and thermal P  AP P  AP cap cap P AP stability may be optimized. The behavior of Eb and Eb with M S and Aex is similar to that of H sw and H sw .

Finally, we mention that thermal stability can also be improved by exploiting domain wall assisted switching. For example, ECC BPM allows much larger hard-layer anisotropies to be used for the same switching fields as in homogeneous BPM [15]. This improves media stability without compromising writability. However, ECC BPM suffers from reduced thermal stability due to dipolar interaction. The FC and AFC-CCBPM designs resolve this issue, allowing increased thermal stability both due to vertical coupling, which permits larger media anisotropies for the same switching fields, and lateral coupling, which enables compensation of the dipolar fields. IV.

COMPARISONS

To compare AFC-CCBPM with other alternatives, similar numerical calculations were performed for other reported and possible BPM designs (listed in the caption to Fig. 3) for equal areal density and optimized values of material parameters. Due to concerns involving planarization and write-field gradients28-29, the net thickness of the pillars (homogenous or composite) was chosen not to exceed 10 nm , except for the tri-layer composite design, with thickness 4 nm  6 nm  4 nm  14 nm . Performance in terms of switching fields and SFDs for the different models is summarized in Fig. 3. 9

Composite BPM is seen (Fig. 3) to be successful at reducing switching fields in comparison to homogeneous BPM, but suffers from a high SFD (33%) due to an increased net moment. Such a high SFD results from the presence of the soft ECC section, which is affected significantly by magnetostatics at high areal densities. AFC-composite-BPM, on the other hand, appreciably lowers SFDs, but with no reduction in switching fields21. The apparent trade-off between the two quantities is partially resolved for the case of capped BPM13, and tri-layer composite BPM with ferromagnetic coupling at one interface and reduced antiferromagnetic coupling at the other. The disadvantage of the latter is the increased aspect ratio of the patterned elements and reduced effectiveness in reducing SFDs at ultrahigh areal densities. Ferromagnetically-coupled-CCBPM (FC-CCBPM) and AFC-CCBPM are most successful at eliminating the trade-off between switching fields and SFDs, achieving a simultaneous and significant reduction in both quantities. Improved performance can be accredited to the wide range of tuning parameters afforded by the multilayer structures, which enable independent reductions in SFDs and switching field strengths through proper optimization of lateral and vertical exchange in the system. The vertical exchange in the ECC elements is tuned to reduce the switching field, while lateral and vertical exchange in the cap is tuned to compensate the magnetostatic interactions between the elements thus reducing the SFD. While FC and AFC-composite-CBPM have a similar recording performance, the AFC design has important advantages in terms of the reading performance, as discusses next. The reciprocity principle30 was used to calculate the readback response for the BPM designs outlined in Fig. 3. The read head was modeled as a finite width MR sensor and infinitely wide shields, based on the procedure outlined in Refs. [31] and [32]. Head width was chosen to be W  15 nm , with a thickness of the MR sensor t  3 nm , and a gap between sensor and shield g  15 nm . The pattern of magnetization states used in the reciprocity calculation is pattern (iii) of Fig. 2a. Such a pattern has been selected to emphasize the magnetostatic interference (or screening) effects neighboring bits can have on the central element during readback when the dimensions of the head, due to technological limitations, do not ideally conform to the media geometry. Plots in Fig. 4a show the calculated readback signal obtained for AFC-CCBPM, FC-CCBPM, as well as ECC-BPM as the head flies over the central track of pattern (iii) in Fig. 2a. The screening effects have a noticeable influence on the readback signal for ECC-BPM and FC-CCBPM, due to the stray fields emanating from the neighboring composite elements, and, in the latter case, from the cap magnetization as well. A more robust signal results from AFC-CCBPM, where interference effects are in part compensated by the AF-coupled capping layer, leading to a more consistent waveform. It is worthwhile noting that the antiferromagnetic coupling in AFC-CCBPM does not necessarily imply that the moments in the capping layer are in antiparallel alignment with the moments in the patterned elements. Rather, the magnetic configuration of the capping layer depends on the specific pattern of magnetization states of patterned bits. The capping layer moments will point to a larger extent out-of-plane as the number of equally oriented bits in a particular region increases. In the case of a random distribution of alternating states, where the screening effects are uncorrelated and cancel out, the magnetization of the capping layer will point largely in-plane33, and not appreciably participate in the readback response. Figure 4b shows the effect of the soft underlayer (SUL) on the readback signal for the three media designs. The influence of magnetostatic interference on the readback signal for ECC and FC-CCBPM is seen to be enhanced due to the SUL30, 34-35. However, the SUL does not have the same effect on the response of AFC-CCBPM indicating that this effect may be moderated through a proper choice of capping layer thickness, saturation magnetization, and other materials parameters.

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IV.

SUMMARY

Dipolar interactions play a significant role in the broadening of SFDs and in deterioration of thermal stability, which significantly limit the performance of magnetic recording on BPM at ultra-high areal densities. For a five-by-five 2 array of homogeneous BPM at 4 Tb/in and media anisotropy H K  5 kOe it was found that the SFD was 70% of the mean switching field, while the stability was reduced to less than 50% of the stability of a single magnetostatically isolated island, having the same material parameters. Use of ECC elements can improve stability for the same switching fields, but does not help with narrowing SFDs. We have shown that CBPM and its extensions can address simultaneously the problem of SFDs and stability loss, leading to significant improvements by offsetting dipolar effects through exchange interactions introduced through the coupling with a continuous capping layer. At larger areal density and media anisotropy, the CCBPM designs (CBPM with ECC elements) demonstrated improved writability over homogeneous and capped BPM, and significantly narrower SFDs in comparison to ECC and ledge BPM. The switching field and energy barrier dependence on capping layer material properties, and, in particular, which parameters most influence these quantities, and in what range, were discussed. The rich range of tuning parameters offered by the capped designs allows optimization leading to minimal SFDs, improved stability, and greater writability, which can be achieved for arbitrary areal density and media geometry. With these characteristics, CBPM presents itself as a promising candidate for ultra-high density magnetic recording applications.

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FIG. 1: Bit patterned media designs: (a) homogeneous BPM (HBPM), (b) exchange coupled composite (ECC) BPM, (c) ledge BPM, (d) capped BPM (CBPM), (e) composite capped BPM (CCBPM).

FIG. 2: Two most magnetostatically extreme environments: (a) all bits in parallel alignment with the central bit, (b) all bits in antiparallel alignment with the central bit.

12

9 8

H

sw

(kOe)

7 6 5 4 3 2 1 600

700

800

900

Msh

1000

1100

1200

1300

3

(emu/cm )

FIG. 3: Plot indicating that the tradeoff between switching fields and SFDs which effects homogeneous BPM can be resolved by the capped BPM structure. The solid and dashed lines indicate the switching field of the central bit in the parallel (Fig. 2a) and antiparallel (Fig. 2a) configuration, respectively, for (black) homogeneous BPM and (red) capped BPM. Structural and material parameters for homogeneous and CBPM are given in Table 1 for 4Tb in 2 .

th (nm) ts (nm) tcap (nm) wxw (nm2) b (nm) MSh (emu/cm3) s MS (emu/cm3) MScap (emu/cm3) HKh (kOe) HKs (kOe) HKcap (kOe) Jh/s (erg/cm2) Jh/cap (erg/cm2)

HBPM CBPM 4 Tb/in2 15 15 2 8x8 8x8 4 4 600-1300 600-1300 400 3.7 – 7.9 3.7 – 7.9 0.1 0.83

HBPM

CBPM

12 5x5 3 900 20 -

12 3 5x5 3 900 900-1300 20 0.32 – 0.45 0.56

ECC

Ledge FC-CCBPM 10 Tb/in2 4 4 4 8 8 8 2 5x5 5x10 5x5 3 3 3 900 900 900 1350 1350 1350 500-900 20 20 20 3.3 3.3 3.3 0.28-0.5 20 20 20 0.75

AFC-CCBPM 4 8 2 5x5 3 900 1350 500-900 20 3.3 0.28-0.5 20 -1.67

Table 1. Summary table listing all structural and material parameters used to model different BPM designs. In all models the exchange constant was Aex  106 erg/cm and the high-damping regime was assumed. The parameters for 4Tb in 2 are used for the results in Figs. 3, 5, 6, and 9. The parameters for 10Tb in 2 are used for the results in Figs. 7, 8, and 11.

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FIG. 4: Magnetization configuration in CBPM for (a) the parallel and (b) antiparallel configuration.

FIG. 5: Switching fields versus saturation magnetization of the capping layer in CBPM for central bit in the parallel (solid lines) and antiparallel (dashed lines) configurations for capping layer thicknesses, tcap  1 nm (black lines),

tcap  3 nm (blue lines), and tcap  6 nm (green lines). Remaining parameters are the same as in Table 1 for 4Tb in 2 , with the exception of M Sh  950 emu/cm3 and interfacial coupling energy density J h / cap  1 erg/cm2 .

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FIG. 6: Switching fields versus interfacial coupling between capping layer and hard island for central bit in the parallel (solid lines) and antiparallel (dashed lines) configurations for capping layer anisotropy, KUcap  0 (black lines), KUcap  1 Merg/cm3 (blue lines), and KUcap  2 Merg/cm3 (red lines). The simulation parameters (apart from the those indicated in the figure above), are the same as the ones listed in Table 1 for 4Tb in 2 , except for M Scap  1050 emu/cm3 .

Fig. 7: Comparison of switching fields and SFDs at 10 Tb/in 2 for (a) homogeneous BPM (gray), CBPM (blue), and for (b) ECC BPM (magenta), ledge BPM (cyan), FC-composite-capped BPM (black), and AFC-composite-capped BPM (red). Solid and dashed lines correspond to the switching field of central bit in the parallel (Fig. 3a) and antiparallel (Fig. 3b) configuration, respectively. The discrepancy between a solid and dashed curve (of the same color) indicates the width of the SFD of the corresponding capped structure. Switching fields for the capped designs are shown at different values of capping layer saturation magnetization, M Scap (horizontal axis). The span of the SFD for BPM designs not consisting of a capping layer is color-shaded for ease of comparison. The range of M Scap in each plot was chosen to capture the balance point in capped designs, where the solid and dashed lines intercept and the SFD is at a minimum. The location of the balance point relative to the M Scap depends on the intensity of dipolar and exchange interactions, which are different for the capped structures in the left and right plot. Corresponding values of structural and material parameters for the different layers in each design are listed in Table 1 for 10Tb in 2 . 15

FIG. 8: Switching field sensitivity on the hard-layer uniaxial magnetocrystalline anisotropy energy density for (a) homogeneous and CBPM ( M Scap  1250 emu/cm3 , J h / cap  1 erg/cm2 ), and (b) for ECC BPM, FC-CCBPM ( M Scap  400 emu/cm3 , J h / cap  1.17 erg/cm2 ), and AFC-CCBPM ( M Scap  350 emu/cm3 , J h / cap  1 erg/cm2 ), with

remaining parameters listed in Table 1 for 10Tb in 2 . The horizontal axis spans a range of 30% of the KUh value for which the thermal stability ratio is equal to KUhV / kBT  55 .

FIG. 9: Minimum energy path (MEP) between the parallel (Fig. 2a) and antiparallel (Fig. 2b) configuration for (a) homogeneous BPM and (b) capped BPM. For homogeneous BPM the energy barriers for the forward and reverse transition are markedly different due to uncompensated dipolar interactions. In CBPM, the stability is improved. Structural and material parameters are listed in Table 1 for 4 Tb/in 2 .

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FIG. 10: Possible equilibrium states for capped BPM. Equilibrium configuration and stability depend both on the geometry and material properties of the patterned islands and the capping layer, as well as the strength of exchange coupling at the interface. Due to the vast space of possible structural and material parameters used for modeling BPM at various areal densities, a discussion of the influence of these parameters on equilibrium and stability is provided in the main body of the article.

FIG. 11: Energy barriers for the transition from the parallel to the antiparallel configuration and vice versa, versus capping layer anisotropy, for M Scap  1050 emu/cm3 , and J h / cap  0.33 erg/cm2 . Remaining parameters, apart from

KUcap which is here a variable, are the same as in Table 1 for CBPM for 10Tb in 2 .

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REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

T. Osaka, et al., "Electrochemical Nanotechnologies," in Nanostructure Science and Technology, ed: Springer New York, 2010. Y. Shiroishi, et al., "Future Options for HDD Storage," IEEE Trans. Magn., vol. 45, 2009. H. N. Bertram and H. J. Richter, "Arrhenius–Néel thermal decay in polycrystalline thin film media," J. Appl. Phys., vol. 85, p. 4991, 1999. A. Moser, et al., "Magnetic recording: advancing into the future," J. Phys. D: Appl. Phys., vol. 35, p. R157, 2002. H. J. Richter, " The transition from longitudinal to perpendicular recording " J. Phys. D, vol. 40, p. R149, 2007. M. Chou, et al., "Study of nanoscale magnetic structures fabricated using electron-beam lithography and quantum magnetic disk," J. Vac. Sci. Technol. B, vol. 12, p. 3695, 1994. M. Albrecht, et al., "Recording performance of high-density patterned perpendicular magnetic media," Appl. Phys. Lett., vol. 81, p. 2875 2002. B. D. Terris, et al., " Patterned media for future magnetic data storage," Microsyst. Technol., vol. 13, p. 189, 2007. S. Li, et al., "Microwave-assisted magnetization reversal and multilevel recording in composite media," J. Appl. Phys., vol. 105, 2009. B. Livshitz, et al., "Precessional reversal in exchange-coupled composite magnetic elements," Appl. Phys. Lett., vol. 91, 2007. B. Livshitz, et al., "Analysis of recording in bit patterned media with parameter distributions," J. Appl. Phys., vol. 105, 2009. T. Matsumoto, et al., "Thermally assisted magnetic recording on a bit-patterned medium by using a nearfield optical head with a beaked metallic plate," Appl. Phys. Lett., vol. 93, 2008. W. A. Challener, et al., "Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer," Nature Photonics, vol. 3, p. 220, 2009. E. A. Dobisz, et al., "PatternedMedia: Nanofabrication Challenges of Future Disk Drives," Proceedings of the IEEE, vol. 96, p. 1836, 2008. D. Suess, et al., "Exchange spring media for perpendicular recording," Appl. Phys. Lett., vol. 87, p. 012504 2005. R. H. Victora and X. Shen, "Composite media for perpendicular magnetic recording," IEEE Trans. Magn., vol. 41, p. 537, 2005. E. E. Fullerton, et al., "Exchange-spring behavior in epitaxial hard/soft magnetic bilayers," Phys. Rev. B, vol. 58, 1998. V. Lomakin, et al., "Dual-layer patterned media "ledge" design for ultrahigh density magnetic recording," Appl. Phys. Lett., vol. 92, 2008. R. H. Victora and X. Shen, "Exchange Coupled Composite Media," Proceedings of the IEEE, vol. 96, p. 11 2008. A. Y. Dobin and H. J. Richter, "Domain wall assisted magnetic recording (invited)," J. Appl. Phys., vol. 101, 2007. B. Livshitz, et al., "Semi-analytical approach for analysis of BER in conventional and staggered bit patterned media," Appl. Phys. Lett., vol. 91, p. 182502 2007. M. E. Schabes, "Micromagnetic simulations for terabit/in2 head/media systems," J. Magn. Magn. Mater., vol. 320, p. 2880, 2008. H.-J. Jang, et al., "Magnetostatic interactions of single-domain nanopillars in quasistatic magnetization states," Appl. Phys. Lett., vol. 86, 2005. V. Repain, et al., "Magnetic interactions in dot arrays with perpendicular anisotropy," J. Appl. Phys., vol. 95, 2004. S. Li, et al., "Capped bit patterned media for high density magnetic recording," J. Appl. Phys., vol. 105, p. 07C121, 2009. T. R. Albrecht and M. E. Schabes, "Patterned Magnetic Media Having An Exchange Bridge Structure Connecting Islands," U.S. Patent, p. 0169731 2009. M. V. Lubarda, et al., "Antiferromagnetically coupled capped bit patterned media for high-density magnetic recording," (submitted, 2010).

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[28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40]

S. S. P. Parkin, et al., "Oscillations in exchange coupling and magnetoresistance in metallic superlattice structures: Co/Ru, Co/Cr, and Fe/Cr," Phys. Rev. Lett., vol. 64, 1990. I. Škorvanek and A. Zetenko, "Effects of Neutron Irradiation on Fe 80B20," Phys. Stat. Sol. (a), vol. 99, 1987. C. Chappert, et al., "Planar Patterned Magnetic Media Obtained by Ion Irradiation," Science, vol. 280, 1998. D. Stanescu, et al., "Tailoring magnetism in CoNi films with perpendicular anisotropy by ion irradiation," J. Appl. Phys., vol. 103, 2008. J. Lee, et al., "Micromagnetic study of recording on ion-irradiated granular-patterned media," J. Magn. Magn. Mater., vol. 319, 2007. G. W. Qin and L. Zuo, "Tailoring exchange coupling between magnetic nano-grains of high density magnetic recording media," Materials Science Forum Vols., vol. 638-642, p. 6, 2010. E. E. Fullerton, et al., "Hard/soft magnetic heterostructures: Model exchange-spring magnets," J. Magn. Magn. Mater., vol. 200, p. 392 1999. D. Weller and A. Moser, "Thermal Effect Limits in Ultrahigh-Density Magnetic Recording," IEEE Trans. Magn., vol. 35, 1999. M. P. Sharrock and J. T. McKinney, "Kinetic effects in coercivity measurements," IEEE Trans. Magn., vol. 17, 1981. R. Dittrich, et al., "A path method for finding energybarriers and minimum energy paths in complex micromagnetic systems," J. Magn. Magn. Mater., vol. 250, 2002. R. Dittrich, et al., "Thermally induced magnetization reversal in antiferromagnetically coupled media," J. Magn. Magn. Mater., vol. 93, 2003. D. Goll and S. Macke, "Thermal stability of ledge-type L10-FePt/Fe exchange-spring nanocomposites for ultrahigh recording densities," Appl. Phys. Lett., vol. 93, p. 152512, 2008. A. Moser, et al., " Magnetic Tuning of Biquadratic Exchange Coupling in Magnetic Thin Films," Phys. Rev. Lett., vol. 91, p. 9, 2003.

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