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Effect of intergranular interactions on recording characteristics
ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 320 (2008) 2921–2924
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Effect of intergranular interactions on recording characteristics E. Miyashita , K. Kawana, H. Shiino, N. Hayashi NHK Science and Technical Research Laboratories, 1-10-11 Kinuta, Setagaya-ku, Tokyo, Japan
a r t i c l e in fo
abstract
Available online 8 August 2008
The dependence of intergranular exchange interaction on medium SNR was investigated by micromagnetic simulation. It was found that the medium SNR at a high recording density takes its maximum value at the point where the magnitude of the maximum intergranular exchange field is about same as that of the maximum demagnetization field. & 2008 Elsevier B.V. All rights reserved.
Keywords: Simulation SNR Demagnetization field Intergranular exchange field
1. Introduction Intergranular interaction are of two types. One is magnetostatic interaction (demagnetization), and the other is intergranular exchange interaction. The magnetization curve of a medium is determined by both the dispersion of magnetic constants of individual grains in the medium and by the interaction between grains. The recording characteristics of a medium also depend on both of these factors, together with the recording head-field distribution [1,2]. In order to understand the recording process, it is, therefore, necessary to establish how the magnetization process of the medium is affected by these intergranular interactions. In practice, the magnitude of magneto-static interaction does not vary widely if the materials of the recording layer are fixed, because the magneto-static field in a medium is determined by saturation magnetization. On the other hand, the magnitude of intergranular exchange interaction varies considerably according to the underlayer materials, and the conditions of their manufacture. It has also been reported that recording characteristic can be improved by introducing a moderate intergranular exchange interaction [3–6], but no clear reason was given for this. In order to clarify the effect of intergranular interaction on recording characteristics, the magnetization and recording processes were analyzed by using a micromagnetic simulation [7].
2. Calculation parameters Table 1 shows the parameters of the medium and recording head used for a calculation. A cell size of 10 nm is used, and the dimensions are assumed to be cubic. A medium with a thickness of 10 nm is also used. Normal distribution is assumed for the dispersion of each parameter. The magnetization curves and recording patterns are calculated by the LLG equation. The average Corresponding author. Tel.: +81 3 5494 3231; fax: +81 3 5494 3278.
E-mail address: [email protected] (E. Miyashita). 0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.08.035
anisotropy field strength of the medium is fixed at 15 kOe, and only the intergranular exchange stiffness and saturation magnetization are changed. The thermal fluctuation is considered as a random field [6]. The sweep time of the magnetization curve is set to 20 ns, because the recording is performed within the order of nanoseconds. The applied pulse width is 2 ns for the remanent magnetization curve.
3. Results and discussion 3.1. Influence of magneto-static interaction on the magnetization curve Fig. 1 shows the magnetization curves with an anisotropy field dispersion sHk of 10% for several saturation magnetizations Ms, where the intergranular exchange stiffness Aex is roughly zero. The dashed line represents the magnetization curve of the medium with no intergranular interaction. The magneto-static field differs in each curve. The magnetization curve with the smallest Ms has the steepest gradient, because the demagnetization field is smallest in the medium with the smallest Ms. The gradient of the magnetization curve decreases as Ms increases, due to the increase of the demagnetization field. The magnitude of the nucleation field Hn in the medium decreases, and the magnitude of the saturation field Hs increases with higher Ms. Fig. 1(b) shows the remanent curve of a medium when Ms is 500 emu/cm3. The dashed line represents the media with no intergranular interaction. The demagnetization field effectively expands the switching field distribution. 3.2. Influence of intergranular exchange interaction on the magnetization process Fig. 2 shows the magnetization curve of the medium for various intergranular exchange stiffnesses when Ms is 500 emu/cm3. The magnitude of the Hn increases and that of Hs falls as Aex increases.
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Table 1 Calculation parameters Medium parameters Anisotropy field Anisotropy field dispersion Dispersion of easy axis direction Intergranular exchange stiffness Saturation magnetization Soft under layer thickness Saturation flux density Permeability Temperature
15 kOe 1% and 10% 51 0.001–1.5 106 erg/cm 300, 500, 800 emu/cm3 100 nm 1T 250 300 K
Write head parameters Saturation flux density Permeability Pole width/length Magnetic spacing Head to medium relative speed
2T 500 0.2/0.2 mm 20 nm 15 m/s
Normalized magnetization Ms 300 500
0.5
800 no interaction
-30
-20
-10
0 -0.5
10
Fig. 2. Magnetization curves of perpendicular media with saturation magnetization of 500 emu/cm3 and anisotropic field dispersion of 10% at a temperature of 300 K. (a) Magnetization curve of media with various intergranular exchange stiffnesses. (b) Remanence curve of media with and without interaction.
20 30 Applied field [kOe]
Normalized magnetization no interaction
0.5 Ms=500
-30 Applied field [kOe]
-20
-10
0
Saturation field [kOe]
25 20 15 10
Ms [emu/cm3] 300
5
500
-0.5
800
0 0 Fig. 1. Magnetization curves of perpendicular media with weak intergranular exchange interaction and anisotropic field dispersion of 10% at a temperature of 300 K. (a) Magnetization curves of media with various saturation magnetizations. (b) Remanence curves of media with and without interaction.
The gradient of the magnetization curve accordingly increases with Aex. Fig. 2(b) shows the remanent curve. Its gradient is reduced by the effects of demagnetization. The gradient of the remanent curve does, however, approach that of the curve without interaction when Aex is 0.2 106 erg/cm. It seems that the exchange field makes the effective switching field distribution narrower. Fig. 3 shows the dependence of the saturation field on the normalized maximum exchange field Hnex, where the maximum exchange field is normalized to the maximum demagnetization field, 4pMs. In the case of large Ms, Hs is large for small Hnex but decreases rapidly as Hnex increases. All curves intersect around Hnex of 1.0, where the maximum exchange field is same as the maximum demagnetization field. The demagnetization field and the exchange field take the maximum values near the saturation field. All saturation fields of the medium with differing Ms approach the same value as that of the medium without interaction, because the exchange and demagnetization fields
2 4 Normalized exchange field HAmax/Hdmax
6
Fig. 3. Saturation field dependence on a normalized maximum exchange field for anisotropy field dispersion of 10%.
cancel each other out, and the medium behaves, therefore, as if there is no interaction field. However, the nucleation field does not agree with the values found for the medium without interaction. Near the nucleation field, the demagnetization field reaches maximum value, but the exchange field is very small. 3.3. Influence of magneto-static interaction on recording characteristics Fig. 4 shows medium SNR dependence of saturation magnetization at a linear recording density of 1000 kFCI, when the intergranular exchange stiffness is very small. Medium SNR is calculated by the signal output and integration of noise in the expression 0 , 1 sffiffiffiffiffiffiffiffiffiffiffiffiffi X SNR ¼ 20 log @pi p2 A k
kai
ARTICLE IN PRESS E. Miyashita et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2921–2924
2923
with small intergranular exchange stiffness, a reduction not only of sHk but also that of Ms improves the medium SNR.
0 σHk = 1%
SNR [dB]
-5
3.4. Influence of intergranular exchange interaction on recording characteristics
-10 σHk = 10%
-15
-20 200
400
600
Saturation magnetization
800
[emu /cm3]
Fig. 4. Depencence of SNR on saturation magnetization at a linear recording density of 1000 kFCI for small exchange stiffness. (a) SNR at a linear recording density of 1000 kFCI with an anisotropy field dispersion of 1%. (b) SNR at a linear recording density of 1000 kFCI with an anisotropy field dispersion of 10%.
0 Ms [emu/cm3] 300 500
-5 SNR [dB]
800
-10 -15 -20 -25 0
2 4 Normalized exchange field HAmax/Hdmax
6
0 3
Ms [emu/cm ]
SNR [dB]
-5
300 500 800
-10
Fig. 5 shows the dependence of medium SNR on a normalized maximum exchange field. The anisotropy field dispersion is 1% in Fig. 5(a) and 10% in Fig. 5(b). In both cases, the SNR increases with Aex for small Aex. The SNR reaches its maximum value at a moderate Aex and then falls as Aex increases for large Aex. All SNR curves reach their maximum value near the normalized exchange field of 1.0. The maximum values of SNR are almost equal, and none depends on Ms. The decrease of SNR for large Aex is caused by the increase of transition noise. In addition, magnetic cluster size increases with Aex and this impairs recording resolution. Fig. 5 also reveals the tendency of the most suitable SNR range with Aex to become narrower as Ms increases. The SNR decreases rapidly as Aex deviates from the suitable point. A medium with high Ms is better for obtaining low thermal fluctuation than one with low Ms if the SNR is the same. However, it is difficult to optimize the SNR of a medium with high Ms, because the optimal range of the SNR becomes much narrower. For larger anisotropic field dispersion, the peak SNR drops and the peak shifts to a larger Aex. This is because the gradient of the magnetization curve decreases with the increase of sHk in addition to the effect of the demagnetization field. The location of the most suitable exchange field is shifted upwards, but all media take the maximum SNR in the same normalized exchange field. The maximum SNR value is also almost the same for media with various values for Ms. SNR loss due to the demagnetization field can be compensated by adjusting the intergranular exchange field, but SNR loss due to the large sHk cannot be compensated by adjusting the intergranular exchange field. Fig. 6 shows the recorded pattern for a medium with anisotropy dispersion of 1% at a linear recording density of 1000 kFCI. The uppermost pattern represents the medium without intergranular interaction. The pattern near the normalized exchange field of 1.0 is clear, and resembles that without
Normalized exchange field HAmax/Hdmax
-15
no interaction
-20 -25
0.005
-30 0
2 4 Normalized exchange field HAmax/Hdmax
6
Fig. 5. SNR dependence on a normalized maximum exchange field for various saturation magnetizations. (a) SNR at a linear recording density of 1000 kFCI with an anisotropy field dispersion of 1%. (b) SNR at a linear recording density of 1000 kFCI with an anisotropy field dispersion of 10%.
1.02
2.04
3.06 where pk and pi are, respectively, the Fourier component of the read signal and the signal component. The curves for anisotropy dispersions of 1% and 10% reveal a monotonous decrease of SNR as Ms increases. The reduction of SNR for large Ms is due to the demagnetization field. The transition broadening effect due to the demagnetization field occurs because the demagnetization field reduces the gradient of the magnetization curve. For a medium
4.07
Fig. 6. Recorded magnetization patterns of media with saturation magnetization of 500 emu/cm3 and anisotropy field dispersion of 1%.
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interaction. The recorded pattern is disordered for a small normalized exchange field. For a large normalized exchange field, deformation of the bit shape is observed.
4. Conclusion The effect of intergranular interaction of a medium on the magnetization curve and recording characteristic was investigated by micromagnetic simulation. It was found that demagnetization field reduces the gradient of the magnetization curve, and that it reduces the SNR at high linear recording densities. The intergranular exchange field, on the other hand, makes the gradient of
the magnetization curve steeper. The medium SNR is maximized at the normalized exchange field of 1.0, where the magnitude of the maximum exchange field is same as that of the maximum demagnetization field. References [1] [2] [3] [4] [5] [6] [7]
E. Miyashita, et al., JMMM 235 (2001) 413. E. Miyashita, et al., IEEE Trans. Magn. 38 (5) (2002) 2075. Y. Nakamura, JMMM 200 (1999) 634. M. Mallary, IEEE Trans. Magn. 38 (4) (2002) 1719. R.H. Victra, IEEE. Trans. Magn. 39 (2) (2003) 710. E. Miyashita, et al., JMMM 287 (2005) 96. Y. Nakatani, Y. Uesaka, N. Hayashi, Jpn. J. Appl. Phys. 28 (12) (1989) 2485.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Effect of intergranular interactions on recording characteristics E. Miyashita , K. Kawana, H. Shiino, N. Hayashi NHK Science and Technical Research Laboratories, 1-10-11 Kinuta, Setagaya-ku, Tokyo, Japan
a r t i c l e in fo
abstract
Available online 8 August 2008
The dependence of intergranular exchange interaction on medium SNR was investigated by micromagnetic simulation. It was found that the medium SNR at a high recording density takes its maximum value at the point where the magnitude of the maximum intergranular exchange field is about same as that of the maximum demagnetization field. & 2008 Elsevier B.V. All rights reserved.
Keywords: Simulation SNR Demagnetization field Intergranular exchange field
1. Introduction Intergranular interaction are of two types. One is magnetostatic interaction (demagnetization), and the other is intergranular exchange interaction. The magnetization curve of a medium is determined by both the dispersion of magnetic constants of individual grains in the medium and by the interaction between grains. The recording characteristics of a medium also depend on both of these factors, together with the recording head-field distribution [1,2]. In order to understand the recording process, it is, therefore, necessary to establish how the magnetization process of the medium is affected by these intergranular interactions. In practice, the magnitude of magneto-static interaction does not vary widely if the materials of the recording layer are fixed, because the magneto-static field in a medium is determined by saturation magnetization. On the other hand, the magnitude of intergranular exchange interaction varies considerably according to the underlayer materials, and the conditions of their manufacture. It has also been reported that recording characteristic can be improved by introducing a moderate intergranular exchange interaction [3–6], but no clear reason was given for this. In order to clarify the effect of intergranular interaction on recording characteristics, the magnetization and recording processes were analyzed by using a micromagnetic simulation [7].
2. Calculation parameters Table 1 shows the parameters of the medium and recording head used for a calculation. A cell size of 10 nm is used, and the dimensions are assumed to be cubic. A medium with a thickness of 10 nm is also used. Normal distribution is assumed for the dispersion of each parameter. The magnetization curves and recording patterns are calculated by the LLG equation. The average Corresponding author. Tel.: +81 3 5494 3231; fax: +81 3 5494 3278.
E-mail address: [email protected] (E. Miyashita). 0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.08.035
anisotropy field strength of the medium is fixed at 15 kOe, and only the intergranular exchange stiffness and saturation magnetization are changed. The thermal fluctuation is considered as a random field [6]. The sweep time of the magnetization curve is set to 20 ns, because the recording is performed within the order of nanoseconds. The applied pulse width is 2 ns for the remanent magnetization curve.
3. Results and discussion 3.1. Influence of magneto-static interaction on the magnetization curve Fig. 1 shows the magnetization curves with an anisotropy field dispersion sHk of 10% for several saturation magnetizations Ms, where the intergranular exchange stiffness Aex is roughly zero. The dashed line represents the magnetization curve of the medium with no intergranular interaction. The magneto-static field differs in each curve. The magnetization curve with the smallest Ms has the steepest gradient, because the demagnetization field is smallest in the medium with the smallest Ms. The gradient of the magnetization curve decreases as Ms increases, due to the increase of the demagnetization field. The magnitude of the nucleation field Hn in the medium decreases, and the magnitude of the saturation field Hs increases with higher Ms. Fig. 1(b) shows the remanent curve of a medium when Ms is 500 emu/cm3. The dashed line represents the media with no intergranular interaction. The demagnetization field effectively expands the switching field distribution. 3.2. Influence of intergranular exchange interaction on the magnetization process Fig. 2 shows the magnetization curve of the medium for various intergranular exchange stiffnesses when Ms is 500 emu/cm3. The magnitude of the Hn increases and that of Hs falls as Aex increases.
ARTICLE IN PRESS 2922
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Table 1 Calculation parameters Medium parameters Anisotropy field Anisotropy field dispersion Dispersion of easy axis direction Intergranular exchange stiffness Saturation magnetization Soft under layer thickness Saturation flux density Permeability Temperature
15 kOe 1% and 10% 51 0.001–1.5 106 erg/cm 300, 500, 800 emu/cm3 100 nm 1T 250 300 K
Write head parameters Saturation flux density Permeability Pole width/length Magnetic spacing Head to medium relative speed
2T 500 0.2/0.2 mm 20 nm 15 m/s
Normalized magnetization Ms 300 500
0.5
800 no interaction
-30
-20
-10
0 -0.5
10
Fig. 2. Magnetization curves of perpendicular media with saturation magnetization of 500 emu/cm3 and anisotropic field dispersion of 10% at a temperature of 300 K. (a) Magnetization curve of media with various intergranular exchange stiffnesses. (b) Remanence curve of media with and without interaction.
20 30 Applied field [kOe]
Normalized magnetization no interaction
0.5 Ms=500
-30 Applied field [kOe]
-20
-10
0
Saturation field [kOe]
25 20 15 10
Ms [emu/cm3] 300
5
500
-0.5
800
0 0 Fig. 1. Magnetization curves of perpendicular media with weak intergranular exchange interaction and anisotropic field dispersion of 10% at a temperature of 300 K. (a) Magnetization curves of media with various saturation magnetizations. (b) Remanence curves of media with and without interaction.
The gradient of the magnetization curve accordingly increases with Aex. Fig. 2(b) shows the remanent curve. Its gradient is reduced by the effects of demagnetization. The gradient of the remanent curve does, however, approach that of the curve without interaction when Aex is 0.2 106 erg/cm. It seems that the exchange field makes the effective switching field distribution narrower. Fig. 3 shows the dependence of the saturation field on the normalized maximum exchange field Hnex, where the maximum exchange field is normalized to the maximum demagnetization field, 4pMs. In the case of large Ms, Hs is large for small Hnex but decreases rapidly as Hnex increases. All curves intersect around Hnex of 1.0, where the maximum exchange field is same as the maximum demagnetization field. The demagnetization field and the exchange field take the maximum values near the saturation field. All saturation fields of the medium with differing Ms approach the same value as that of the medium without interaction, because the exchange and demagnetization fields
2 4 Normalized exchange field HAmax/Hdmax
6
Fig. 3. Saturation field dependence on a normalized maximum exchange field for anisotropy field dispersion of 10%.
cancel each other out, and the medium behaves, therefore, as if there is no interaction field. However, the nucleation field does not agree with the values found for the medium without interaction. Near the nucleation field, the demagnetization field reaches maximum value, but the exchange field is very small. 3.3. Influence of magneto-static interaction on recording characteristics Fig. 4 shows medium SNR dependence of saturation magnetization at a linear recording density of 1000 kFCI, when the intergranular exchange stiffness is very small. Medium SNR is calculated by the signal output and integration of noise in the expression 0 , 1 sffiffiffiffiffiffiffiffiffiffiffiffiffi X SNR ¼ 20 log @pi p2 A k
kai
ARTICLE IN PRESS E. Miyashita et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2921–2924
2923
with small intergranular exchange stiffness, a reduction not only of sHk but also that of Ms improves the medium SNR.
0 σHk = 1%
SNR [dB]
-5
3.4. Influence of intergranular exchange interaction on recording characteristics
-10 σHk = 10%
-15
-20 200
400
600
Saturation magnetization
800
[emu /cm3]
Fig. 4. Depencence of SNR on saturation magnetization at a linear recording density of 1000 kFCI for small exchange stiffness. (a) SNR at a linear recording density of 1000 kFCI with an anisotropy field dispersion of 1%. (b) SNR at a linear recording density of 1000 kFCI with an anisotropy field dispersion of 10%.
0 Ms [emu/cm3] 300 500
-5 SNR [dB]
800
-10 -15 -20 -25 0
2 4 Normalized exchange field HAmax/Hdmax
6
0 3
Ms [emu/cm ]
SNR [dB]
-5
300 500 800
-10
Fig. 5 shows the dependence of medium SNR on a normalized maximum exchange field. The anisotropy field dispersion is 1% in Fig. 5(a) and 10% in Fig. 5(b). In both cases, the SNR increases with Aex for small Aex. The SNR reaches its maximum value at a moderate Aex and then falls as Aex increases for large Aex. All SNR curves reach their maximum value near the normalized exchange field of 1.0. The maximum values of SNR are almost equal, and none depends on Ms. The decrease of SNR for large Aex is caused by the increase of transition noise. In addition, magnetic cluster size increases with Aex and this impairs recording resolution. Fig. 5 also reveals the tendency of the most suitable SNR range with Aex to become narrower as Ms increases. The SNR decreases rapidly as Aex deviates from the suitable point. A medium with high Ms is better for obtaining low thermal fluctuation than one with low Ms if the SNR is the same. However, it is difficult to optimize the SNR of a medium with high Ms, because the optimal range of the SNR becomes much narrower. For larger anisotropic field dispersion, the peak SNR drops and the peak shifts to a larger Aex. This is because the gradient of the magnetization curve decreases with the increase of sHk in addition to the effect of the demagnetization field. The location of the most suitable exchange field is shifted upwards, but all media take the maximum SNR in the same normalized exchange field. The maximum SNR value is also almost the same for media with various values for Ms. SNR loss due to the demagnetization field can be compensated by adjusting the intergranular exchange field, but SNR loss due to the large sHk cannot be compensated by adjusting the intergranular exchange field. Fig. 6 shows the recorded pattern for a medium with anisotropy dispersion of 1% at a linear recording density of 1000 kFCI. The uppermost pattern represents the medium without intergranular interaction. The pattern near the normalized exchange field of 1.0 is clear, and resembles that without
Normalized exchange field HAmax/Hdmax
-15
no interaction
-20 -25
0.005
-30 0
2 4 Normalized exchange field HAmax/Hdmax
6
Fig. 5. SNR dependence on a normalized maximum exchange field for various saturation magnetizations. (a) SNR at a linear recording density of 1000 kFCI with an anisotropy field dispersion of 1%. (b) SNR at a linear recording density of 1000 kFCI with an anisotropy field dispersion of 10%.
1.02
2.04
3.06 where pk and pi are, respectively, the Fourier component of the read signal and the signal component. The curves for anisotropy dispersions of 1% and 10% reveal a monotonous decrease of SNR as Ms increases. The reduction of SNR for large Ms is due to the demagnetization field. The transition broadening effect due to the demagnetization field occurs because the demagnetization field reduces the gradient of the magnetization curve. For a medium
4.07
Fig. 6. Recorded magnetization patterns of media with saturation magnetization of 500 emu/cm3 and anisotropy field dispersion of 1%.
ARTICLE IN PRESS 2924
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interaction. The recorded pattern is disordered for a small normalized exchange field. For a large normalized exchange field, deformation of the bit shape is observed.
4. Conclusion The effect of intergranular interaction of a medium on the magnetization curve and recording characteristic was investigated by micromagnetic simulation. It was found that demagnetization field reduces the gradient of the magnetization curve, and that it reduces the SNR at high linear recording densities. The intergranular exchange field, on the other hand, makes the gradient of
the magnetization curve steeper. The medium SNR is maximized at the normalized exchange field of 1.0, where the magnitude of the maximum exchange field is same as that of the maximum demagnetization field. References [1] [2] [3] [4] [5] [6] [7]
E. Miyashita, et al., JMMM 235 (2001) 413. E. Miyashita, et al., IEEE Trans. Magn. 38 (5) (2002) 2075. Y. Nakamura, JMMM 200 (1999) 634. M. Mallary, IEEE Trans. Magn. 38 (4) (2002) 1719. R.H. Victra, IEEE. Trans. Magn. 39 (2) (2003) 710. E. Miyashita, et al., JMMM 287 (2005) 96. Y. Nakatani, Y. Uesaka, N. Hayashi, Jpn. J. Appl. Phys. 28 (12) (1989) 2485.