Exchange spring media are proposed for magnetic-recording systems consisting of a hard/soft ... DUE to the limited head field in perpendicular recording,.
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 10, OCTOBER 2005
Optimization of Exchange Spring Perpendicular Recording Media Dieter Suess1 , T. Schrefl2 , M. Kirschner1 , G. Hrkac1 , F. Dorfbauer1 , O. Ertl1 , and J. Fidler1 Institute of Solid State Physics, Vienna University of Technology, A-1140 Vienna, Austria Department of Engineering Materials, University of Sheffield, Western Bank, Sheffield, U.K. Exchange spring media are proposed for magnetic-recording systems consisting of a hard/soft bilayer. By varying the fraction of thickness for the hard and soft layer and by varying their saturation polarizations, the media properties can be optimized in order to achieve high thermal stability without increase of coercive field. In grains with identical size and coercivity, an optimized bilayer reaches an energy barrier exceeding those of optimized single-phase media by more than a factor of two. Thus, exchange spring media allow to 2. Additionally, the lower angular dependence of coercivity of exchange spring reduce the grain diameter by more than a factor of 1 media improves the signal-to-noise ratio (SNR) by a factor of 2 5. Index Terms—Areal density, composite media, exchange spring, perpendicular recording, thermal stability.
I. INTRODUCTION
II. ANALYTIC MODEL
UE to the limited head field in perpendicular recording, is limthe maximum value of the anisotropy constant ited to about , where is the head field. For uniaxial anisotropy, the energy barrier is proportional to the anisotropy constant and, hence, proportional to the head field. For other anisotropies (e.g., cubic) Usov et al. [1] showed that the ratio of coercive field over energy barrier can be decreased by 40%. Various approaches have been proposed to overcome the writing problem, such as thermally assisted recording [2] and ferromagnetic/antiferromagnetic bilayers [3]. Okamoto et al. [4] prepared epitaxial FePt L nanoparticles covered with a Pt overlayer that has negligible magnetic anisotropy and an induced magnetic polarization. The experimental results suggest that the coercive field is decreased by the Pt overlayer but the energy barrier remains almost constant. Recently, magnetic multilayer structures composed of magnetically hard and magnetically soft layers were proposed in order to address the recording problem [5], [1]. The idea of Victora and Shen [5] is to lower the coercivity of the data layer by applying an effective switching field at an angle of 45 with respect to the film normal. Their model system consists of two weakly exchange coupled singledomain particles with different volume, saturation magnetization, and anisotropy constants. In this paper, micromagnetic simulations are presented for exchange spring bilayers. This differs significantly from the scope of pioneering work on exchange spring systems, aiming at an optimization of energy product of bulk permanent magnets [6], [14] and thin films [7]. In all calculations, the coercivity was fixed at 1.7 T and, if not stated otherwise, the grain size of cylindrical grains was fixed at the dimensions expected for the next media generation (diameter 6 nm, thickness 14 nm).
In the following, a simple analytical model for the optimization of a single-phase data layer is introduced. Starting with a given head design and therefore a fixed head field, one has to optimize the data layer properties. For the optimization of the material parameters such as and , we assume that the film is composed of weakly coupled single-domain grains. The influence of that angle on the media properties has been discussed by Miles et al. [8]. For a single-domain particle, the energy barrier is given by
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Digital Object Identifier 10.1109/TMAG.2005.855284
(1) is the volume, the effective field acting on where is the effective the grain parallel to the easy axis, and anisotropy, which is the sum of the uniaxial anisotropy and the shape anisotropy. For a particle with the ratio and a polarization of 0.4 T, the shape length/diameter [9]. The Stoner–Wohlfarth anisotropy is . The effecswitching field in (1) is given by tive field is composed of the demagnetizing field and the exchange field from the neighboring grains. The worst case concerning the thermal stability is the limit of low data rate where one track is uniformly magnetized. In that case, a demagnetizing factor of is assumed. The exchange field from the neighboring grains stabilizes the grain. It opposes the demagnetizing field. . The effective field can be written as is the demagnetizing field and is the exchange Here field in tesla. The maximum value of the anisotropy is limited . The head field has to be large by the maximum head field enough in order to saturate the film. Assuming all grains except one to be reversed, the switching field of the last grain, which is equal to the saturation field of the film, can be expressed as . The exchange field of the neighboring grains supports the switching of the last grain, whereas the demagnetizing field of the film hinders the switching of the last grain. The minimum head field to record . From this on the data layer is
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SUESS et al.: OPTIMIZATION OF EXCHANGE SPRING PERPENDICULAR RECORDING MEDIA
Fig. 1. Contour plot of the energy barrier for single-phase media as a function of the intergrain exchange field B and the head field B . The grain diameter is 8 nm the film thickness 20 nm.
expression, can be expressed as a function of and and substituted in (1). By setting the first derivative of (1) to zero, the optimum value follows from an with respect to and equation of third order. Thus, we obtain values for that maximize the energy barrier for a given head field. The solution of interest is given by
with
The optimum value of the magnetic polarization is given by and the energy barrier by
(2) Fig. 1 shows a contour plot of the energy barrier as a function of the exchange field and the maximum head field for a grain diameter of 8 nm and a layer thickness of 20 nm. In a first approximation, the isolines can be regarded as straight lines. The energy . Conbarrier is constant for equal values of cerning the energy barrier, the intergranular exchange should be as large as possible, however, negative aspects of the exchange are an increase of the transition width and large cluster size which tends to result in catastrophic reversal once thermal decay starts. III. NUMERICAL RESULTS FOR BILAYERS AND SINGLE LAYERS The finite-element method was used to optimize the magnetic properties of an exchange-coupled bilayer composed of a magnetically hard and soft layers for perpendicular magnetic recording. In the limit of vanishing soft magnetic layer thickness, the numerical results are compared with the analytic model. The thickness of the hard layer and the thickness of the in the soft layer are changed. Furthermore, the values of and , which is assumed as equal in hard layer both layers, are varied.
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Fig. 2. Side view of a bilayer for perpendicular recording. (a)–(d) Magnetization states during the hysteresis cycle for the bilayer with J = = 0.9 T. Configuration (a) shows the remanent state for the 0.26 T and J fully magnetized disc. (e) Here, the saddle-point configuration without external field is shown. This configuration requires the lowest thermal activation energy for domain reversal. (a) H = 0.5 T, (b) H = 0.74 T, (c) H = 1.14 T, (d) H = 1.38 T, (e) H = 0
For each configuration, the value of the crystalline anisotropy in the hard magnetic layer was changed iteratively in order to get a coercive field of the bilayer structure equally to the max1.7 T which is achieved for imum possible head field of the head design proposed in [11]. Instead of using (1), we calculate the energy barrier numerically using the nudged elastic band method [10]. Both the demagnetizing field and the exchange field are taken into account with an effective field . This effective field acts as an external field during the calculation of the saddle-point configuration and saddle-point energy. For every hysteresis loop calculation, the Landau–Lifshitz equation is integrated numerically while the external field is subsequently decreased. The demagnetizing field is taken into . The exaccount via a reduction of the external field by change field helps to reverse the last grain of a bit. Therefore, it is added to the external field. The soft layer which is fully exchange coupled to the hard layer acts as a magnetic spring that initiates the reversal of the hard layer similar to what is observed in composite permanent magnets [6], [14]. A magnetic domain wall is created next to the hard/soft interface. Compared to single-phase media with the magnetic properties of the hard layer the coercive field is significantly reduced (by a factor of ). The numerical results show two distinct reversal modes for switching by an external field and for switching caused by thermal fluctuations. These reversal modes are compared in Fig. 2 for a single grain of exchange spring recording media. The thickness of the hard layer 1 10 J/m, 9.6 10 J/m 0.26 T) and ( 1 10 J/m, 0.9 T) is 8.7 the soft layer ( and 5.3 nm, respectively. Fig. 2(a)–(d) shows the reversal of the grain under the influence of an external field. As the external field reaches coercivity, the domain wall forms at the hard/soft interface and propagates into the hard magnetic part. For zero external field, thermal activation helps the system to cross the energy barrier. Fig. 2(e) depicts the magnetization distribution at the saddle point. The saddle-point configuration is a quasi-uniform state. The reversal process which is induced by thermal
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Fig. 3. Energy barrier as a function of the fraction of the hard layer thickness to the total thickness for a magnetic bilayer structure. Different curves are for different magnetic polarizations which are set to be identical for the hard and soft magnetic layers.
activation is different from the reversal mode under the application of the switching field. Due to different reversal mechanisms, the ratio between the energy barrier and the coercive field is not constant, as it is expected for single-domain particles, but changes with the media properties. It can be tuned by the magnetic properties of the bilayer structure. First, we investigate the influence of the fraction of the hard-layer thickness to the total thickness on the energy barrier. For simplicity, we assume for now that both layers have the same saturation polariza. Later, we will fully optimize all paramtion eters. Fig. 3 shows the calculated energy barrier as a function of . Under the constraint of a coercive field of 1.7 T the highest and for 0.5 T. An energy barrier is obtained for exchange field of 0.20 T was assumed in the calculation. In the , the medium consists only of one hard magnetic limit of layer. The energy barrier of the optimal bilayer is more than two times larger than the energy barrier of the single-phase medium. The finite-element method leads to an optimal value of 0.42 T for single-phase media. This is in excellent agreement 0.41 T. Therefore, one with the analytic model that predicts can see that for single-phase media, the magnetization processes can be described with the Stoner–Wohlfarth model and a subgrain division is not necessary for modeling such single-layer media. In a second step, we are looking at the properties of exchange spring media that maximize the energy barrier for a maximum head field of 1.7 T. The material parameters of the optimal structure are found to be those of the grain in Fig. 2, where different values of in the hard and soft layers are used. Again, an exchange field of 0.2 T is assumed. This is about 12% of the cofor ercive field of the bilayer. The energy barrier is 48 k T the optimized exchange spring media and 19 k T for the optimum single phase media. A small angular dependence of the coercive field is important in order to optimize the signal-to-noise ratio (SNR). For the composite media, the angular dependence of the coercive field . This can be fitted with the expression expression is commonly used for magnetic materials which are
IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 10, OCTOBER 2005
controlled by domain-wall pinning. For an angle between 0 and 40 , the difference between the analytic formula and the finite-element calculation is less than 5%. In contrast to the angular dependence of the coercive field for single-phase media which can be described by the Stoner–Wohlfarth theory, the is considerably weaker for composite systems. change of For a misalignment of 15 , the coercive field increases by a factor of for the composite media, whereas it decreases by for perfectly aligned single-phase media. For a factor of perpendicular recording without intergranular exchange (grain diameter is 10 nm), a change of the anisotropy distribution from to leads to an increase of the transition parameter from about 10 to 18 nm [12]. For the exchange increases from about 10 spring media the same change in to less than 11 nm. The SNR is proportional to SNR [1]. Therefore, for the given easy axis distribution, the SNR for the comcan be improved by more than a factor of posite media. In conclusion, we optimized the magnetic properties for single-phase and composite perpendicular recording media. In particular, it gives the minimum possible grain diameter to achieve a reasonable thermal stability. The introduction of a magnetic soft layer increases the thermal stability by more than a factor of two as compared to optimal single-phase media for a fixed-head field. The SNR can be increased by more than a factor of ACKNOWLEDGMENT Fruitful discussions with H. J. Richter and the financial support of the Austrian Science Fund under Grant Y-132-N02 are acknowledged. REFERENCES [1] N. A. Usov, C. Chang, and Z. Wei, Appl. Phys. Lett., vol. 83, p. 3749, 2003. [2] S. Cumpson, P. Hidding, and R. Coehoorn, IEEE Trans. Magn., vol. 36, no. 5, pp. 2271–2275, Sep. 2000. [3] J. U. Thiele, S. Maat, and E. Fullerton, Appl. Phys. Lett., vol. 82, p. 2859, 2003. [4] S. Okamoto, O. Kitakami, N. Kikuchi, T. Miyazaki1, Y. Shimada1, and T. Chiang, J. Phys.: Condens. Matter, vol. 16, no. 2109, 2004. [5] R. H. Victora and X. Shen, IEEE Trans. Magn., vol. 41, no. 2, pp. 537–542, Feb. 2005. [6] D. Suess et al., J. Magn. Magn. Mat, vol. 551, pp. 290–291, 2005. [7] E. Fullerton, J. Jiang, M. Grimsditch, C. Sowers, and S. Bader, Phys. Rev. B., vol. 58, no. 12 193, 1998. [8] J. Miles, D. McKirdy, R. Chantrell, and R. Wood, IEEE Trans. Magn., vol. 39, no. 4, pp. 1876–1890, Jul. 2003. [9] D.-X. Chen, J. A. Brug, and R. B. Goldfarb, IEEE Trans. Magn., vol. 27, no. 4, pp. 3601–3619, Jul. 1991. [10] R. Dittrich, T. Schrefl, D. Suess, W. Scholz, H. Forster, and J. Fidler, J. Magn. Magn. Mater., vol. 250, p. 12, 2002. [11] Y. Kanai, R. Matsubara, H. Watanabe, H. Muraoka, and Y. Nakamura, IEEE Trans. Magn., vol. 39, no. 4, pp. 1955–1960, Jul. 2003. [12] Y. Shimizu and N. Bertram, IEEE Trans. Magn., vol. 39, no. 3, pp. 1846–1850, May 2003. [13] K. Gao and N. Bertram, IEEE Trans. Magn., vol. 38, no. 6, pp. 3675–3683, Nov. 2002. [14] E. F. Kneller and R. Hawig, IEEE Trans. Magn., vol. 27, no. 4, pp. 3588–3600, Jul. 1991. Manuscript received February 1, 2005.
