Computer Modeling and Simulation of Ultra-High Density Perpendicular Recording Processes LONG HAOHUI (M. Eng., HUST., P. R. China) A DISSERTATION SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2006 Acknowledgements Acknowledgements It is my pleasure to thank the many people who helped to make this thesis possible. Firstly, without the constant encouragement and invaluable guidance from my supervisor, Dr. Z. J. Liu of Data Storage Institute, my completion of this research work would not have been possible. I am grateful to my co-supervisor Dr. E. P. Li of the Institute of High Performance Computing for his support and suggestions over the entire course of my Ph. D project. I would also like to extend my gratitude to Dr. E. T. Ong, and Mr. J. T. Li, who have been generous in sharing their knowledge and research experiences with me. I also want to thank Prof. A. Kav i of Harvard University and Prof. W. C. Ye for taking time to discuss the details of statistic model with me. I would also like to express special thanks to all the staff and students in Data Storage Institute, who have helped me in one way or another. I also want to acknowledge the financial support provided by Data Storage Institute. Finally, I would like to express my most heartfelt thanks and gratitude to my parents, Long Chuyuan and Wu Jin, my younger brother, Long Jianhui, and my girlfriend, for their love and support. Needless to say, mentioning their names here is just the most National University of Singapore I Acknowledgements modest way of showing my gratitude to them. National University of Singapore II Table of Contents Table of Contents Acknowledgements . I Table of Contents .III Summary VIII List of Tables X List of Figures XI List of Symbols XIX Introduction 1.1 Magnetic Recording 1.1.1 Magnetic Recording System .3 1.1.2 Magnetic Recording Physics .5 1.1.2.1 Hysteresis Loop 1.1.2.2 Transition Parameter .6 1.2 Challenges for Predicting the Performance of Recording System .8 1.3 Historical Background of Micromagnetic Modeling 10 1.4 Research Objectives 13 1.5 Organization of Dissertation 18 National University of Singapore III Table of Contents Fundamentals of Micromagnetic Theory .21 2.1 Introduction .21 2.2 Gibbs Free Energy .21 2.2.1 Zeeman Energy .22 2.2.2 Magnetocrystalline Anisotropy Energy .23 2.2.3 Exchange Energy 24 2.2.4 Demagnetizing Energy .25 2.2.5 Effective Field and Energy Minimization 26 2.3 Magnetization Dynamics .28 2.4 Stoner-Wolfarth Single Grain Model .38 Numerical Micromagnetic Model Development 41 3.1 Introduction .41 3.2 Description of Finite Element Micromagnetic Model 43 3.2.1 Mathematical Fundamentals .44 3.2.2 Discretization of the Problem Domain 45 3.2.3 The Discretised Effective Field .49 3.2.4 Demagnetizing Field Calculation 53 3.2.4.1 Direct Approach Method .56 3.2.4.2 Hybrid FEM/BEM Method .58 3.2.5 3.3 Solution of Dynamic Equation 64 Conclusion 67 A New Fast Algorithm for Rapid Calculation of Demagnetizing Field 68 National University of Singapore IV Table of Contents 4.1 Introduction .68 4.2 Fast Fourier Transform on Multipoles Method (FFTM) .69 4.3 4.4 4.2.1 Multipole Approximation Theory 69 4.2.2 FFTM Algorithm Implementation .71 Performance and Error Analysis 75 4.3.1 Permalloy Nanowire Simulation .75 4.3.2 Perpendicular Recording Media Simulation 81 Conclusion 89 Write Field Analysis on Perpendicular Recording Process .91 5.1 Introduction .91 5.2 A New Analytical Model for Perpendicular Write Head .93 5.3 5.2.1 Write Head Model 93 5.2.2 Analytical Solution of Write Field 98 Sensitivity Analysis of Write Field with respect to Design Parameters for Perpendicular Recording Heads 109 5.4 5.3.1 Effect of Soft Underlayer on Write Field Performance 110 5.3.2 Write Field Distribution versus Design Parameters .115 5.3.3 Effect of Write Field Distribution on Media Switching Field .117 5.3.4 Sensitivity Analysis of Write Field Performance .122 Conclusion 126 Distribution of Slanted Write Field for Perpendicular Recording Heads with Shielded Pole .128 National University of Singapore V Table of Contents 6.1 Introduction .128 6.2 Finite Element Analysis of Single Pole Write Field 129 6.3 Effects of Write Head Parameters on the Tilted Field Distribution .134 6.4 Distribution of Slanted Write Field for Perpendicular Recording Heads with Shielded Pole 137 6.5 Conclusion 140 Analysis of Perpendicular Recording Media .141 7.1 Introduction .141 7.2 Finite Element Model of Perpendicular Recording Media 142 7.3 Magnetization Dynamics in Perpendicular Recording Media .146 7.3.1 Micromagnetic Simulations of the Hysteresis Loop 146 7.3.2 Damped Gyro-Magnetic Reversal Process in Perpendicular Recording Media 151 7.4 Conclusion 163 Micromagnetic Simulation for Microtrack Model .165 8.1 Introduction .165 8.2 Microtrack Model 166 8.3 8.2.1 Transition Parameter and Probability Density Function .169 8.2.2 Cross Track Correlation Length 174 8.2.3 Partial Erasure Threshold 175 8.2.4 Simulation Results of System Performance .178 Effect of Media Characteristics on Transition Noise Property 182 National University of Singapore VI Table of Contents 8.4 8.3.1 Exchange Coupling .183 8.3.2 Anisotropy Distribution 185 8.3.3 Saturation Magnetization Distribution 185 Conclusion 187 Conclusions and Discussions 188 References .195 Appendix .211 List of Publications 212 National University of Singapore VII Summary Summary The perpendicular recording system has received attention again in recent years aiming to fulfill market demands for extremely high-level areal densities when the longitudinal recording system reaches its limit. This research work focuses on analyses of ultra-high density perpendicular magnetic recording processes by using finite element micromagnetic modeling and analytical methods. The 3-D micromagnetic model being developed involves finite element micromagnetic modeling based on Laudau-Lifishitz-Gilbert equation. One of the existing obstacles of using the finite element micromagnetic modeling in the study of magnetic recording physics and in building analytical tools for investigation of the signal generation processes, is the low computing speed of such numerical technique. Hence, a fast algorithm – Fast Fourier Transform on Multipoles is proposed to speed up the calculation of the demagnetizing field, and thus the modeling process. As the product development cycles for magnetic recording devices become shorter, it is very essential to predict the performance of the recording system before it is physically built. The combination of the micromagnetic simulation and statistical modeling of the read/write process provides a promising approach towards designing National University of Singapore VIII Summary recording heads and channels. The physics of the microtrack model are studied in this dissertation, and the media characteristic effects on the transition noise are also investigated. Results show that the distributed anisotropy distribution and exchange coupling have important effects on the performance of magnetic recording system. An analytical model for the perpendicular writer field based on vector potential method has been developed to predict the write field distribution. With the analytical solution of magnetic field distributions under the influence of various design parameters, a sensitivity analysis based on the Response Surface Methodology has been carried out to investigate the dominant effect of the design parameters on the write field performance. 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Magn, vol. 41, p. 2911, 2005 157.K. Z. Gao, X. B. Wang, and H. N. Bertram., “Track edge effects in tilted and conventional perpendicular recording,” J. Appl. Phys., vol.93, p. 7840, 2003 National University of Singapore 210 Appendix Appendix Recurrence Formulas Given that x = ( x1 , x , x3 ) , r = x and i = − , the recurrence formulas are: Rmm ( x ) = (− x1 + ix )Rmm−−11 ( x ) 2m (2n − 1)x3 Rnm−1 ( x ) − r Rnm−2 ( x ) Rnm ( x ) = (n − m )(n + m ) S mm ( x ) = S m n (x ) = (A.1) (2m − 1)(− x1 − ix )S mm−−11 ( x ) r2 (2n − 1)x3 S nm−1 ( x ) − (n − m − 1)(n + m − 1)S nm−2 ( x ) (A.2) r2 [ ] [ ] ∂ m m − 1+ m −1 1+ m m − 1− m −1 −1+ m Rn ( x ) = − i Rn −1 ( x ) + i Rn −1 ( x ) ∂x1 ∂ m i m − 1+ m −1 1+ m m − 1− m −1 −1+ m Rn ( x ) = − i Rn −1 ( x ) − i Rn −1 ( x ) ∂x 2 (A.3) ∂ m Rn ( x ) = Rnm−1 ( x ) ∂x3 National University of Singapore 211 List of Publications List of Publications Journal [1] Z. J. Liu, J. T. Li and H. H. Long, “Sensitivity analysis of write field with respect to design parameters for perpendicular recording heads,” Journal of Applied Physics. Vol.97, No.10, p. 515-517 May, 2005 [2] Z. J. Liu, J. T. Li, H. H. Long, H. L. Li and H. T. Wang, “Distribution of slanted write field for perpendicular recording heads with shielded pole,” IEEE Transaction on Magn., Vol.41, No.10, p. 2908-2910 Oct, 2005 [3] T. Liu, Y. H. Wu, H. H. Long, Z. J. Liu, Y. K. Zheng, and A. O. Adeyeye, “Transport properties and micromagnetic modeling of magnetic nanowires with multiple constrictions,” Journal of Thin solid films, Vol.505, No.1-2, p.35-40 May 18, 2006 [4] H. H. Long, E. T. Ong, Z. J. Liu, E. P. Li, “Fast Fourier Transform on Multipole algorithm for demagnetizing Fields,” IEEE Transaction on Magn., Vol.42, No.2, p. 295-300 Feb, 2006 [5] Z. J. Liu, H. H. Long, E. P. Li and J. T. Li, “Dynamic simulation of high density perpendicular recording head and media combination,” IEEE trans on Magn., Vol.42, No.4, p. 943-946 April, 2006 National University of Singapore 212 List of Publications [6] Z. J. Liu, H. H. Long, E. T. Ong, and E. P. Li, “A Fast Fourier Transform on Multipoles algorithm based micromagnetic modeling for perpendicular magnetic recording media,” Journal of Applied Physics., Vol.99, No.8, p. 08B903 April, 2006 [7] Z. J. Liu, H. H. Long, E. P. Li, J. S. Chen, X. X. Zou, W. C. Ye, “Micromagnetic study of transition noise for ultra-high density perpendicular recording,” Journal of Magnetism and Magnetic Materials., Vol.303, No.2, p. e48-e51 Aug, 2006 [8] H. H. Long, E. T. Ong, T. Liu, H. L. Li, Z. J. Liu, E. P. Li, Y. H. Wu, A. O. Adeyeye, “Micromagnetic simulations of magnetic nanowires with constrictions by FIB,” Journal of Magnetism and Magnetic Materials., Vol.303, No.2, p. e299-e303 Aug, 2006 [9] H. H. Long, Z. J. Liu, E. T. Ong and E. P. Li, “Finite element micromagnetic modeling simulations and applications,” submitted to IEEE trans on EMC [10] H. H. Long, E. T. Ong, P. Y. Xiao, Z. J. Liu and K. L. Huang.,“Hybrid finite element and Fast Fourier on Multipole algorithm for micromagnetic modeling of perpendicular SOMA media,” IEEE Transaction on Magn., Vol.42, No.10, p. 32013203 Oct, 2006 Conference [1] H. H. Long, J. T. Li, Z. J. Liu, “Parallelization in 3D finite element micromagnetic simulation of magnetization processes in perpendicular magnetic recording,” Proceedings of the International Conference on Scientific & Engineering Computation(ICSEC), Parallel Session (PS-8), Computational Electronics and Electromagnetics (3), Singapore, June. 30 th –July. th, 2004 National University of Singapore 213 List of Publications [2] L. W. Ruan, D. W. Sun, H. H. Long, Z. J. Liu, “Data streaming for real-time collaboration design,” Proceedings of the International Conference on Scientific & Engineering Computation(ICSEC), PS-11, Industrial Mathematics (2), Singapore, June. 30 th –July. th, 2004 [3] J. T. Li, H. H. Long, Z. J. Liu,, “A 2-D analytical field prediction for perpendicular recording heads,” Proceedings of the Asia-Pacific Magnetic Recording Conference(APMRC), FT-02, Seoul, Korea, Aug. 16 th -19 th, 2004 [4] H. H. Long, J. T. Li, Z. J. Liu, and E. P. Li, “Finite element micromagnetic simulation of switch dynamics of perpendicular media under tilted write field,” Digest accepted by IEEE International Magnetics Conference(INTERMAG), DF-04, Nagoya, Japan, April. th -8 th, 2005 [5] H. H. Long, T. Liu, J. T. Li, H. L. Li and Z. J. Liu, “Finite element micromagnetic simulation of switching dynamic of composite media,” Abstract accepted by 3rd International Conference on Materials for Advanced Technologies(ICMAT), D-6-PO22, Singapore, July. th -8 th, 2005 [6] Z. J. Liu, H. H. Long, J. T. Li, E. P. Li, E. T. Ong and K. S. Chai “Calculation of dynamic write field for perpendicular recording heads,” 17th International Zurich Symposium on Electromagnetic Compatibility(EMC), FSC-231, Singapore, Feb.27 th March. th, 2006 [7] H. H. Long, Z. J. Liu, E. T. Ong and E. P. Li, “Micromagnetic modeling simulations and applications,” 17th International Zurich Symposium on Electromagnetic Compatibility(EMC), FSC-263, Singapore, Feb.27 th - March. th, 2006 National University of Singapore 214 [...]... predict the performance of a recording system and study the optimal write head and media designs for ultra high density and ultra high data rate magnetic recording using micromagnetic simulation National University of Singapore 12 Chapter 1 Introduction 1.4 Research Objectives Bit Sizing Fig 1.6 Historical progress and projection of bit size and number grains per bit with areal density It has been more... the real magnetic recording media, the magnetization reversal modes of grains are different with respect to the geometrical size of grains Therefore, it is necessary to consider the effect of true reversal mode of media grain and grain boundary when conducting computer modeling and simulation for ultra- high density perpendicular recording processes It is expected that micromagnetic simulation based... One of these challenges is the realization of a media, capable of writing and reading, with a high signal-to-noise ratio and thermal stability even at high bit densities For that, a recording layer should consist of fine ferromagnetic grains with volumes as small as possible while with coercivity field as high as possible Fig 1.6 shows the historical progress and projection of bit size and number of. .. University of Singapore X List of Figures List of Figures Fig 1.1 Areal density road map of information storage industry consortium (INSIC) 2 Fig 1.2 (a) Longitudinal magnetic recording (b) type 1: perpendicular recording, using a single pole head and a soft underlayer in the media (c) type 2: perpendicular recording, using a ring head with no soft underlayer 4 Fig 1.3 Typical M-H loop for perpendicular. .. mechanism of LLG[13] 29 Fig 2.3 (a) Spherical components of dM of Landau-Lifshitz equation; (b) asymptotic dt behavior of Landau-Lifshitz equation 30 Fig 2.4 (a) Spherical components of dM of Gilbert equation; (b) asymptotic dt behavior of Gilbert equation 32 National University of Singapore XI List of Figures Fig 2.5 Coordinate system showing polar angle θ and azimuthal angle ϕ of. .. Schematic diagram of functions of micromagnetic simulation Computer simulation is a bridge between theory and experiment Furthermore, it forms a link between microscopic and macroscopic properties As mentioned before, the numerical micromagnetic simulation can provide the fundamental understanding of magnetization processes on the nanometer scale since it predicts the magnetic behavior of magnetic material... for perpendicular recording media 6 Fig 1.4 Plot of three different recorded magnetization distributions 8 Fig 1.5 Schematic diagram of functions of micromagnetic simulation .9 Fig 1.6 Historical progress and projection of bit size and number grains per bit with areal density 13 Fig 2.1 Schematic representation of change in angle between neighboring spins i and j, and position vector... magnetic material from its microstructure and intrinsic magnetic properties.[13][14] National University of Singapore 9 Chapter 1 Introduction Furthermore, micromagnetic simulations provide a suitable and helpful tool in studying the recording performance and optimal design of magnetic recording media 1.3 Historical Background of Micromagnetic Modeling The fundamentals of magnetism have matured for many years... of the perpendicular recording technology will bring about technology challenges to designers attempting to push the physics limits of longitudinal recording on magnetic continuous media, such as the write head, media grain sizes and grain numbers per bits, etc Thus it is necessary to investigate the aspects of recording, signal and channels Fig 1.2 (a) Longitudinal magnetic recording (b) type 1: perpendicular. .. more than 25 years since the father of modern perpendicular recording – Professor Shun-ichi Iwasaki verified distinct density advantages in perpendicular recording, [26] and the perpendicular recording technology in which a single pole write head is combined with a double-layered medium is expected to be able to open up possibilities for achieving areal storage densities of 1 Tbit/in2 However, there are . Computer Modeling and Simulation of Ultra- High Density Perpendicular Recording Processes LONG HAOHUI (M. Eng., HUST., P demands for extremely high- level areal densities when the longitudinal recording system reaches its limit. This research work focuses on analyses of ultra- high density perpendicular magnetic recording. 7 Analysis of Perpendicular Recording Media 141 7.1 Introduction 141 7.2 Finite Element Model of Perpendicular Recording Media 142 7.3 Magnetization Dynamics in Perpendicular Recording Media