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Micromagnetic analysis of transition noise for high-density perpendicular recording
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 303 (2006) e48–e51 www.elsevier.com/locate/jmmm
Micromagnetic analysis of transition noise for high-density perpendicular recording Z.J. Liua, H.H. Longa,b,, W.C. Yea, X.X. Zoua, Z.L. Qina, E.P. Lic, J.S. Chena a
b
Data Storage Institute, DSI Building, 5 Engineering Drive 1, Singapore 117608, Singapore Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576, Singapore c Institute of High Performance Computing, Science Park II, Singapore 117528, Singapore Available online 24 February 2006
Abstract In this paper, specific issues related to high-density perpendicular magnetic recording processes, such as transition noise properties and cross-track correlation lengths, were investigated with the help of micromagnetic analysis. The effects of media parameters were taken into consideration, including intergranular exchange coupling, and exchange distribution, irregular grain shapes, magnetization saturation distribution, and anisotropy distribution. The micromagnetic simulation results showed that the effect of anisotropy distribution on transition noise is more significant than magnetization saturation distribution, and it is crucial to reduce this effect to achieve a high signal-to-noise ratio. Additionally, a new method to further estimate the partial erasure threshold was proposed to approximate the partial erasure effects, and the relation between the microtrack jitter and total track jitter was investigated. r 2006 Elsevier B.V. All rights reserved. Keywords: Perpendicular magnetic recording; Micromagnetics; Cross-track correlation length; Partial erasure threshold
1. Introduction
2. Micromagnetic simulation model
In recent years, the perpendicular recording technology has attracted intensive attention due to their potential to offer higher areal-density beyond the limit of longitudinal recording technology [1]. To achieve ultra-high density recording, it is essential to reduce the medium noise. Over a past few years, a great deal of discussions concentrated on the effects of intergranular exchange coupling on the performance of recording system [2–4]. However, for highdensity magnetic recording head–media combinations, the relation between medium characteristics and recording performance is not sufficiently clear due to lack of systematic study of the transition noise and their interdependence against the media parameters, such as magnetization saturation and anisotropy distribution. Based on micromagnetic analysis, transition noise property related to high-density perpendicular magnetic recording processes were investigated in this paper.
A three-dimensional micromagnetic model solving the LLG equation [4], is used to study the cross-track correlations length and other transition noise parameters for 400 Gbit/in2 perpendicular recording system. The medium anisotropy axis direction is assumed perpendicular to the media plane with 31 deviation and anisotropy constant Ku ¼ 7.4 106 erg/cm3. The saturation magnetization is about Ms ¼ 750 emu/cm3. The intergranular exchange parameter He (He ¼ Aex/KuD2) is varied from 0 to 0.1 and also has a random distribution in the media due to microstructure and irregular shapes of grains. In the simulation, the thickness of media layer and SUL are 12 and 200 nm, respectively. A 128 256 hexagonal lattice is used for modeling the recording media. One hundred independent transitions were obtained. Each transition was written on a media plane with randomly distributed irregular grain plane, which is generated using ‘pseudo Voronoi algorithm’ [5]. To produce media grain plane from such algorithm, grain seeds are scattered in accordance with log-normal distribution whilst keeping an average grain size of 5.5 nm with variation of about 30%. Fig. 1
Corresponding author. Data Storage Institute, DSI Building, 5 Engineering Drive 1, Singapore 117608, Singapore E-mail address: [email protected] (H.H. Long).
0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.01.119
ARTICLE IN PRESS Z.J. Liu et al. / Journal of Magnetism and Magnetic Materials 303 (2006) e48–e51
e49
Transition parameter Cross track correlation length 1.2
Transition noise parameters s/
Nomalized to
1.0
0.8
0.6
0.4
a/
0.2 a2s/3
Fig. 1. Media average grain size distribution from 100 media grain plane.
0.0 0.00
3.1. Transition noise parameters The probability density function of transitions can be obtained from the micromagnetic analysis. In addition, the transition parameter a, cross-track correlation length, s, and transition noise parameter [2] under different intergranular exchange couplings can also be produced, as shown in Fig. 2 when the value of anisotropy distribution ¼ 3%. It can be found that the cross-track correlation length is increased with increasing exchange coupling, which indicates a large media cluster is formed. For a weak intergranular exchange coupling, the transition noise parameter decreases linearly. With continuously increasing exchange coupling, the transition noise parameter changes slightly. The simulation results also show that the effect of exchange coupling on the cross-track correlation length is more pronounced than that on the transition parameter. Fig. 3 gives the exchange dependency of the transition parameter and transition noise parameter with different anisotropy distribution. Simulations show that the transition noise parameter is increased with increasing anisotropy distribution indicating that reducing the medium anisotropy distribution can improve the performance of recording systems. We also investigated the effect of the saturation magnetization distribution on the transition noise. As
0.06
0.08
0.10
Fig. 2. Exchange coupling dependency of transition parameters, crosstrack correlation length and transition noise parameters.
0
0.05
0.1 0.8
0.85 0.7
0.80 0.75
0.6
Ku with 3% distribution Ku distribution with 10% Ku distribution with 20%
0.70 0.65
0.5
Solid line: Transition parameter Dash line: Transition noise parameter
0.60 0.55
0.4 0.3
0.50 0.2
0.45 0.00
0.02
0.04
0.06
0.08
Transition noise parameter a2s/3
3. Transition noise properties and analysis
0.04
He
Transition parameter a/
plots the records of the grain size distribution recorded for the aforementioned media plane distributions. A modified 3D head solution [6] is used to drive the recording process in simulation. The write width is 50 nm and the fly height is 6.5 nm. The return yolk width is 250 nm and the space between write pole and return yolk is 300 nm. For the recording simulations, the head field in the gap region at the air-bearing surface is set to be 29 KOe.
0.02
0.10
He Fig. 3. Dependence of transition parameter and transition noise parameter on exchange with anisotropy distributions of 3%, 10% and 20% case.
shown in Fig. 4, it can be seen that the effect of magnetization saturation distribution is not comparable to that of the anisotropy distribution. For decoupling case, the transition parameter and transition noise parameter increase with increasing deviation of the saturation magnetization distribution. With continuously increasing the exchange coupling, the effect of saturation magnetization distribution becomes insignificant. The above micromagnetic analysis with effect of anisotropy and saturation magnetization taken into consideration indicates that a weak coupling is needed to achieve high SNR. The simulation also shows that the effect of anisotropy distribution is more pronounced and a low anisotropy
ARTICLE IN PRESS Z.J. Liu et al. / Journal of Magnetism and Magnetic Materials 303 (2006) e48–e51
e50
0.05
0
0.1
0.50 Transition parameter a/
0.45 0.5
0.40 0.35
Solid line: Transition parameter Dash line: Transition noise parameter
0.4
0.30 Ms with 3% distribution Ms distribution with 10% Ms distribution with 20%
0.25 0.20
0.3
0.15
0.2
Transition noise parameter a2s/3
0.6
0.10 0.00
0.02
0.04
0.06
0.08
0.10
He Fig. 4. Dependence of transition parameter and transition noise parameter on exchange with magnetization saturation distributions of 3%, 10% and 20% case.
Fig. 5. Partial erasure threshold estimated from micromagnetic simulation and analytical calculation.
distribution can improve the recording system performance. 3.2. Partial erasure threshold and system performance It is known that when two transitions are close to each other for high-density recording they tend to cancel each other. The partial erasure (PE) effect can be included in the microtrack model with the help of PE threshold, which can be estimated through micromagnetic analysis. A new method to estimate the partial erasure threshold is introduced as below. By matching the amount of average magnetization in between two transitions with the one estimated from probability density function of transition jitters, one can determine when to remove a closely placed transition pair in the microtrack. Let us assume the two transitions are written at x ¼ 0 and x ¼ D, respectively. The magnetization at x-D/2 can be expressed as D M ; L ¼ PrðPEÞM r þ PrðnotPEÞðM r Þ, (1) 2 where L is the partial erasure threshold. Here we assume that the magnetization of the media is transited from Mr to Mr, then back to Mr. The probability of occurrence of partial erasure within a single microtrack is denoted by PrðPEÞ, and non-occurrence is by PrðnotPEÞ. This two probabilities are functions of D and L, and highly depends on the probability density function of the transition jitter. The magnetization curves with several predefined values of partial erasure threshold, L, for 400 Gbit/in2 are plotted in Fig. 5. The fully decoupled case is studied here. The best matching curve of the magnetization amount at x ¼ D/2 with the estimation obtained from micromagnetic simulations indicates a suitable L for microtrack simulation. It is
Fig. 6. BER for different SNR.
found the partial erasure threshold is about 3.8 nm in this case. The transition parameter, probability density function, cross-track correlation length and partial erasure threshold obtained from the micromagnetic analysis can be in turn used to predict the system performance with microtrack model [7]. Fig. 6 shows the bit-error-rate (BER) performance of a Viterbi detector based on autoregressive (AR) model [8] for 400 Gbit/In2 channels with 10% jitter. The corresponding channel density DC is 1.0, while the partial erasure threshold L is 0.24B (B is bit length, for 400 Gbit/In2, B ¼ 15.8 nm). It is shown that the detector can achieve the BER of 105 at SNR 30 dB. Fig. 6 shows that it is possible to perform BER analysis and predict the system performance based on microtrack model, where the parameters are extracted from the above micromagnetic simulation.
ARTICLE IN PRESS Z.J. Liu et al. / Journal of Magnetism and Magnetic Materials 303 (2006) e48–e51
e51
4. Conclusion
Fig. 7. Relationship between total track jitter and microtrack jitter noise.
Micromagnetic simulations have been performed to investigate the relation between medium characteristics and transition noise properties for high-density perpendicular recording. The effect of the anisotropy distribution and saturation magnetization distribution were investigated. A new method to estimation of the partial erasure threshold was developed. The simulation results showed that for high-density perpendicular recording, the effects of the anisotropy distribution and intergranular exchange coupling are the dominating factors affecting the transition noise. The noise properties parameters obtained can in turn be used to predict the performance of recording system with microtrack model. It is worth noting that the relationship between microtrack jitter and total jitter is investigated by micromagnetic simulation and theoretical analysis. The results indicate that the total track jitter is proportional to the microtrack jitter with the factor equal to the square root of microtrack numbers.
3.3. Relationship between microtrack jitter and total jitter Acknowledgement To investigate the relationship between microtrack jitter and total jitter, a microtrack jitter sjit is assumed and a series of transition response with jitter generated. Then, summarizing these microtrack transitions, the jitter for each track transition can be measured and the total track transition jitter calculated from the jitter distribution using fitting technique, as shown in Fig. 7. It can be found that for different microtrack numbers, the total track jitter is proportional to the microtrack jitter with the factor equal to the square root of microtrack numbers. This is identical to the theoretical analysis [4]: rffiffiffiffiffiffiffiffiffiffiffi p4 a2 s sjit ¼ , (2) 96W where W is the track width. As shown in Fig. 7, the transition jitter of the total track decreases when microtrack numbers, N, increases.
The authors would like to express their gratitude to Dr. A. Kavcˇic´, Associate Professor in Division of Engineering and Applied Science, Harvard University, for valuable discussions and advices. Reference [1] M. Mallary, A. Torabi, M. Benakli, IEEE Trans. Magn. 38 (2002) 1719. [2] H.N. Bertram, M. Williams, IEEE Trans. Magn. 36 (2000) 4. [3] H. Zhou, H.N. Bertram, M.E. Schabes, IEEE Trans. Magn. 38 (2002) 1422. [4] Y. Shimizu, H.N. Bertram, IEEE Trans. Magn. 39 (2003) 1846. [5] J.R. Hoinville, IEEE Trans. Magn. 37 (2001) 1350. [6] Z.J. Liu, J.T. Li, H.H. Long, J. Appl. Phys. 97 (2005) 515. [7] J.S. Goldberg, J.K. Wolf, IEEE Trans. Magn. 35 (1999) 2256. [8] A. Kavcˇic´, J.M.F. Moura, IEEE Trans. Inform. Theory 46 (2000) 291.
Journal of Magnetism and Magnetic Materials 303 (2006) e48–e51 www.elsevier.com/locate/jmmm
Micromagnetic analysis of transition noise for high-density perpendicular recording Z.J. Liua, H.H. Longa,b,, W.C. Yea, X.X. Zoua, Z.L. Qina, E.P. Lic, J.S. Chena a
b
Data Storage Institute, DSI Building, 5 Engineering Drive 1, Singapore 117608, Singapore Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576, Singapore c Institute of High Performance Computing, Science Park II, Singapore 117528, Singapore Available online 24 February 2006
Abstract In this paper, specific issues related to high-density perpendicular magnetic recording processes, such as transition noise properties and cross-track correlation lengths, were investigated with the help of micromagnetic analysis. The effects of media parameters were taken into consideration, including intergranular exchange coupling, and exchange distribution, irregular grain shapes, magnetization saturation distribution, and anisotropy distribution. The micromagnetic simulation results showed that the effect of anisotropy distribution on transition noise is more significant than magnetization saturation distribution, and it is crucial to reduce this effect to achieve a high signal-to-noise ratio. Additionally, a new method to further estimate the partial erasure threshold was proposed to approximate the partial erasure effects, and the relation between the microtrack jitter and total track jitter was investigated. r 2006 Elsevier B.V. All rights reserved. Keywords: Perpendicular magnetic recording; Micromagnetics; Cross-track correlation length; Partial erasure threshold
1. Introduction
2. Micromagnetic simulation model
In recent years, the perpendicular recording technology has attracted intensive attention due to their potential to offer higher areal-density beyond the limit of longitudinal recording technology [1]. To achieve ultra-high density recording, it is essential to reduce the medium noise. Over a past few years, a great deal of discussions concentrated on the effects of intergranular exchange coupling on the performance of recording system [2–4]. However, for highdensity magnetic recording head–media combinations, the relation between medium characteristics and recording performance is not sufficiently clear due to lack of systematic study of the transition noise and their interdependence against the media parameters, such as magnetization saturation and anisotropy distribution. Based on micromagnetic analysis, transition noise property related to high-density perpendicular magnetic recording processes were investigated in this paper.
A three-dimensional micromagnetic model solving the LLG equation [4], is used to study the cross-track correlations length and other transition noise parameters for 400 Gbit/in2 perpendicular recording system. The medium anisotropy axis direction is assumed perpendicular to the media plane with 31 deviation and anisotropy constant Ku ¼ 7.4 106 erg/cm3. The saturation magnetization is about Ms ¼ 750 emu/cm3. The intergranular exchange parameter He (He ¼ Aex/KuD2) is varied from 0 to 0.1 and also has a random distribution in the media due to microstructure and irregular shapes of grains. In the simulation, the thickness of media layer and SUL are 12 and 200 nm, respectively. A 128 256 hexagonal lattice is used for modeling the recording media. One hundred independent transitions were obtained. Each transition was written on a media plane with randomly distributed irregular grain plane, which is generated using ‘pseudo Voronoi algorithm’ [5]. To produce media grain plane from such algorithm, grain seeds are scattered in accordance with log-normal distribution whilst keeping an average grain size of 5.5 nm with variation of about 30%. Fig. 1
Corresponding author. Data Storage Institute, DSI Building, 5 Engineering Drive 1, Singapore 117608, Singapore E-mail address: [email protected] (H.H. Long).
0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.01.119
ARTICLE IN PRESS Z.J. Liu et al. / Journal of Magnetism and Magnetic Materials 303 (2006) e48–e51
e49
Transition parameter Cross track correlation length 1.2
Transition noise parameters s/
Nomalized to
1.0
0.8
0.6
0.4
a/
0.2 a2s/
Fig. 1. Media average grain size distribution from 100 media grain plane.
0.0 0.00
3.1. Transition noise parameters The probability density function of transitions can be obtained from the micromagnetic analysis. In addition, the transition parameter a, cross-track correlation length, s, and transition noise parameter [2] under different intergranular exchange couplings can also be produced, as shown in Fig. 2 when the value of anisotropy distribution ¼ 3%. It can be found that the cross-track correlation length is increased with increasing exchange coupling, which indicates a large media cluster is formed. For a weak intergranular exchange coupling, the transition noise parameter decreases linearly. With continuously increasing exchange coupling, the transition noise parameter changes slightly. The simulation results also show that the effect of exchange coupling on the cross-track correlation length is more pronounced than that on the transition parameter. Fig. 3 gives the exchange dependency of the transition parameter and transition noise parameter with different anisotropy distribution. Simulations show that the transition noise parameter is increased with increasing anisotropy distribution indicating that reducing the medium anisotropy distribution can improve the performance of recording systems. We also investigated the effect of the saturation magnetization distribution on the transition noise. As
0.06
0.08
0.10
Fig. 2. Exchange coupling dependency of transition parameters, crosstrack correlation length and transition noise parameters.
0
0.05
0.1 0.8
0.85 0.7
0.80 0.75
0.6
Ku with 3% distribution Ku distribution with 10% Ku distribution with 20%
0.70 0.65
0.5
Solid line: Transition parameter Dash line: Transition noise parameter
0.60 0.55
0.4 0.3
0.50 0.2
0.45 0.00
0.02
0.04
0.06
0.08
Transition noise parameter a2s/
3. Transition noise properties and analysis
0.04
He
Transition parameter a/
plots the records of the grain size distribution recorded for the aforementioned media plane distributions. A modified 3D head solution [6] is used to drive the recording process in simulation. The write width is 50 nm and the fly height is 6.5 nm. The return yolk width is 250 nm and the space between write pole and return yolk is 300 nm. For the recording simulations, the head field in the gap region at the air-bearing surface is set to be 29 KOe.
0.02
0.10
He Fig. 3. Dependence of transition parameter and transition noise parameter on exchange with anisotropy distributions of 3%, 10% and 20% case.
shown in Fig. 4, it can be seen that the effect of magnetization saturation distribution is not comparable to that of the anisotropy distribution. For decoupling case, the transition parameter and transition noise parameter increase with increasing deviation of the saturation magnetization distribution. With continuously increasing the exchange coupling, the effect of saturation magnetization distribution becomes insignificant. The above micromagnetic analysis with effect of anisotropy and saturation magnetization taken into consideration indicates that a weak coupling is needed to achieve high SNR. The simulation also shows that the effect of anisotropy distribution is more pronounced and a low anisotropy
ARTICLE IN PRESS Z.J. Liu et al. / Journal of Magnetism and Magnetic Materials 303 (2006) e48–e51
e50
0.05
0
0.1
0.50 Transition parameter a/
0.45 0.5
0.40 0.35
Solid line: Transition parameter Dash line: Transition noise parameter
0.4
0.30 Ms with 3% distribution Ms distribution with 10% Ms distribution with 20%
0.25 0.20
0.3
0.15
0.2
Transition noise parameter a2s/
0.6
0.10 0.00
0.02
0.04
0.06
0.08
0.10
He Fig. 4. Dependence of transition parameter and transition noise parameter on exchange with magnetization saturation distributions of 3%, 10% and 20% case.
Fig. 5. Partial erasure threshold estimated from micromagnetic simulation and analytical calculation.
distribution can improve the recording system performance. 3.2. Partial erasure threshold and system performance It is known that when two transitions are close to each other for high-density recording they tend to cancel each other. The partial erasure (PE) effect can be included in the microtrack model with the help of PE threshold, which can be estimated through micromagnetic analysis. A new method to estimate the partial erasure threshold is introduced as below. By matching the amount of average magnetization in between two transitions with the one estimated from probability density function of transition jitters, one can determine when to remove a closely placed transition pair in the microtrack. Let us assume the two transitions are written at x ¼ 0 and x ¼ D, respectively. The magnetization at x-D/2 can be expressed as D M ; L ¼ PrðPEÞM r þ PrðnotPEÞðM r Þ, (1) 2 where L is the partial erasure threshold. Here we assume that the magnetization of the media is transited from Mr to Mr, then back to Mr. The probability of occurrence of partial erasure within a single microtrack is denoted by PrðPEÞ, and non-occurrence is by PrðnotPEÞ. This two probabilities are functions of D and L, and highly depends on the probability density function of the transition jitter. The magnetization curves with several predefined values of partial erasure threshold, L, for 400 Gbit/in2 are plotted in Fig. 5. The fully decoupled case is studied here. The best matching curve of the magnetization amount at x ¼ D/2 with the estimation obtained from micromagnetic simulations indicates a suitable L for microtrack simulation. It is
Fig. 6. BER for different SNR.
found the partial erasure threshold is about 3.8 nm in this case. The transition parameter, probability density function, cross-track correlation length and partial erasure threshold obtained from the micromagnetic analysis can be in turn used to predict the system performance with microtrack model [7]. Fig. 6 shows the bit-error-rate (BER) performance of a Viterbi detector based on autoregressive (AR) model [8] for 400 Gbit/In2 channels with 10% jitter. The corresponding channel density DC is 1.0, while the partial erasure threshold L is 0.24B (B is bit length, for 400 Gbit/In2, B ¼ 15.8 nm). It is shown that the detector can achieve the BER of 105 at SNR 30 dB. Fig. 6 shows that it is possible to perform BER analysis and predict the system performance based on microtrack model, where the parameters are extracted from the above micromagnetic simulation.
ARTICLE IN PRESS Z.J. Liu et al. / Journal of Magnetism and Magnetic Materials 303 (2006) e48–e51
e51
4. Conclusion
Fig. 7. Relationship between total track jitter and microtrack jitter noise.
Micromagnetic simulations have been performed to investigate the relation between medium characteristics and transition noise properties for high-density perpendicular recording. The effect of the anisotropy distribution and saturation magnetization distribution were investigated. A new method to estimation of the partial erasure threshold was developed. The simulation results showed that for high-density perpendicular recording, the effects of the anisotropy distribution and intergranular exchange coupling are the dominating factors affecting the transition noise. The noise properties parameters obtained can in turn be used to predict the performance of recording system with microtrack model. It is worth noting that the relationship between microtrack jitter and total jitter is investigated by micromagnetic simulation and theoretical analysis. The results indicate that the total track jitter is proportional to the microtrack jitter with the factor equal to the square root of microtrack numbers.
3.3. Relationship between microtrack jitter and total jitter Acknowledgement To investigate the relationship between microtrack jitter and total jitter, a microtrack jitter sjit is assumed and a series of transition response with jitter generated. Then, summarizing these microtrack transitions, the jitter for each track transition can be measured and the total track transition jitter calculated from the jitter distribution using fitting technique, as shown in Fig. 7. It can be found that for different microtrack numbers, the total track jitter is proportional to the microtrack jitter with the factor equal to the square root of microtrack numbers. This is identical to the theoretical analysis [4]: rffiffiffiffiffiffiffiffiffiffiffi p4 a2 s sjit ¼ , (2) 96W where W is the track width. As shown in Fig. 7, the transition jitter of the total track decreases when microtrack numbers, N, increases.
The authors would like to express their gratitude to Dr. A. Kavcˇic´, Associate Professor in Division of Engineering and Applied Science, Harvard University, for valuable discussions and advices. Reference [1] M. Mallary, A. Torabi, M. Benakli, IEEE Trans. Magn. 38 (2002) 1719. [2] H.N. Bertram, M. Williams, IEEE Trans. Magn. 36 (2000) 4. [3] H. Zhou, H.N. Bertram, M.E. Schabes, IEEE Trans. Magn. 38 (2002) 1422. [4] Y. Shimizu, H.N. Bertram, IEEE Trans. Magn. 39 (2003) 1846. [5] J.R. Hoinville, IEEE Trans. Magn. 37 (2001) 1350. [6] Z.J. Liu, J.T. Li, H.H. Long, J. Appl. Phys. 97 (2005) 515. [7] J.S. Goldberg, J.K. Wolf, IEEE Trans. Magn. 35 (1999) 2256. [8] A. Kavcˇic´, J.M.F. Moura, IEEE Trans. Inform. Theory 46 (2000) 291.