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Particle size effect on recording performance and thermal stability in high-density particulate tapes
Journal of Magnetism and Magnetic Materials 193 (1999) 374—377
Particle size effect on recording performance and thermal stability in high-density particulate tapes Toshiyuki Suzuki* Kyushu Institute of Design, Minami-ku, Fukuoka 815-8540, Japan
Abstract An experimental and theoretical study of high-density digital recording performances and thermal stability of magnetization were performed for several tapes with known physical and magnetic properties of the particles used. Also discussed were the relationships between recording performances and thermal stability of magnetization. 1999 Elsevier Science B.V. All rights reserved. Keywords: Particulate tape; Particle size; Particle size distribution; High-density recording; Magnetization time decay; Magnetic viscosity
1. Introduction
2. Recording density response
Recently magnetic particles used for particulate tapes have been reduced significantly in size, to attain very high recording density and low noise [1]. For such small particles, thermal stability of magnetization becomes one of the important issues [2—4]. The author has recently reported the temperature effect on magnetization thermal stability of particulate tapes [5]. However, the analysis on activation volume, for example, was limited, due to the lack of data on the size and magnetic properties of particles used in the tested tapes. In this paper, high-density digital recording performances and thermal stability of magnetization were studied for several tapes with known physical and magnetic properties of the particles used. Special emphasis was placed on analyzing the effect of particle size and size distribution on recording performances and thermal stability.
The samples used were three metal particulate tapes. Their properties are listed in Table 1 [6]. Fig. 1 shows the recording density curves, experimentally and theoretically simulated, for the tapes. In the experiment, all one’s recorded signals were reproduced to measure fundamental frequency components with a spectrum-analyzer. An MIG head with g "0.19 lm was used. The bit lengths at the second peaks (310 kFRPI, bit length"83 nm), and at the third peak for Sample A (620 kFRPI, bit length"41 nm) are comparative to or shorter than the mean particle length of the tapes. At densities higher than the second peaks, particle length and tape surface roughness should have more significant effect on the output level than the conventional demagnetization parameters, such as H , or B d. To analyze these effects, it was assumed that the signal output loss is proportional to the product of gap loss GL, spacing loss SL, and particle length loss PL. GL was calculated by assuming Fan’s head-field function [7]. For SL, head-to-medium spacing d, was set equal to nR [8]. PL was calculated by assuming that particles have a normal distribution f (¸), in their length ¸, with standard deviation p, and mean length ¸ , and that particles are
* Corresponding author. Fax: #81-92-553-4548; e-mail: [email protected].
0304-8853/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 4 5 8 - 2
T. Suzuki / Journal of Magnetism and Magnetic Materials 193 (1999) 374—377 Table 1 Magnetic and physical properties of particles and tapes Sample no
A
B
C
Particle Mean length (nm) Lenght dev. (nm) Aspect ratio Vol.(;10\ cm) H (Oe) H (Oe) p (emu/g) k (;10erg/cm)
71 21 4.63 1.32 2130 5780 140 2.43
102 38 5.90 2.39 1780 5830 131 2.28
148 79 7.75 4.21 1520 5820 121 2.03
2250 327 0.762 2.0 3.3
1870 314 0.853 1.7 3.4
1610 252 0.873 2.7 5.3
¹ape H (Oe) M (emu/cm) SQ Thickness (lm) R (nm)
375
of mean length and length deviation of the particles and R of each tape listed in Table 1. The adjustable parameter was only n in d"nR . The best fit was obtained when n"11. If the length deviation was not correctly evaluated, that is, if Samples B and C were assumed to have the same length distribution as Sample A, the simulated curves for Samples B and C exhibit more dips and the experimental result cannot be explained. Using the above established simulation equation, the effects of particle mean length, length deviation, and spacing were evaluated regarding D recording density. Fig. 2 shows the effect of mean length, in which length deviation"30% of the mean length, spacing"15 nm and gap length"70 nm (physical). It is seen that D of around 400 kFRPI is attainable for the mean length of 50 or 35 nm. Thus, recording performance improves when particles become smaller in size with a sharper size distribution curve. Although little difference was observed in density response at around 400 kFRPI for 50 and 35 nm mean length particles, a large difference in thermal stability was observed, as will be shown in the following. The effect of spacing was also evaluated for the case of mean length"50 nm, length deviation"20 nm, and gap length"70 nm. Naturally, spacing is one of the most influential parameters, and it must be kept as small as possible.
3. Thermal stability
Fig. 1. Recording density curves. Marks are for experiment in which the fundamental frequency component of output signal was measured. Lines are for simulation with the sample parameters. Matching point is at 50 kFRPI for Sample A.
longitudinally oriented [9].
Sin(p¸/j) f (¸) d¸ f (¸) d¸, p¸/j 1 (¸!¸ )
. f (¸)" Exp ! 2p (2pp
PL"
(1)
(2)
The simulated results for the three tapes are drawn by solid curves, to compare with their experimental data indicated by symbols in Fig. 1. The simulation used data
Fig. 3 shows activation volume » , as a function of physical volume » , obtained by the measurement of magnetization time decay. In the figure, the circles are for the present tape samples listed in Table 1 and for a fourth tape sample, which is very similar to Sample A but its physical volume is 1.82;10\ cm. The heavy triangles are for other MP tape data, which were referred to from a literature [10]. All data are consistent and on a single line. The ratio of » /» for the present Sample A is already smaller than 2, approaching to unity. Starting from the Arrhenius equation, magnetization of particle with volume », at time t, M(t), in the presence of a constant opposing field, can be expressed as follows. Here, M "M(t"0): K» M(t) "2 Exp !At Exp ! !1, (3) k¹ M where A is the frequency term, k is Boltzmann’s constant, and ¹ is the absolute temperature. Consider a particle assembly, which has a volume distribution of h(») and a normalized magnetization of m(t) at time t. Then m(t) is given by
m(t)"
M(t) h(»)» d» M
h(»)» d».
(4)
376
T. Suzuki / Journal of Magnetism and Magnetic Materials 193 (1999) 374—377
Fig. 4. Magnetization reversal threshold after t"10 s (+3 years) as a function of particle length ¸. Parameters are those for Sample A, except K . (a) K "2.43;10, (b) 2.43;10 and (c) 2.43;10 erg/cm. Also shown are the accumulated densities of particle length and volume for Sample A. Fig. 2. Simulated density curve with mean length as parameter. Length deviation"30% of mean length, spacing"15 nm, and gap length"70 nm.
Fig. 5. Magnetization time decay, with particle mean length and deviation as parameters. K "2.43;10 erg/cm, ¹"300°K.
Fig. 3. Activation volume » versus physical volume » , for MP tapes. Heavy triangles are after Nishio [10].
The volume distribution h(») can be expressed in terms of the length distribution given by Eq. (2), assuming that all particles have the same cylindrical shape with a long-axis length, ¸, a short-axis length, S, and a constant aspect ratio, a"¸/S. Fig. 4 shows magnetization reversal threshold for different length particles after t"10 s (3.2 years), with K as a parameter. For (a) K "2.43;10 erg/cm (Sample A), magnetization reversal takes place in very few particles, resulting in a very small amount of magnetization decay. This fact does not agree with the experimental result, in which an appreciable amount of magnetization decay is observed. This discrepancy may be
due to the fact that the applied opposing field would reduce an effective K value. For (b) K " 2.43;10 erg/cm, magnetization reversal takes place in 24% of the total particles, but volume contribution is still negligible. For (c) K "2.43;10 erg/cm, most par ticles reverse their magnetization, and magnetization decay is very large. This analysis explains magnetization time decay mechanism for the case where particles have distribution in their volume. Fig. 5 shows the case where particle length was changed as a parameter. In this case, the length deviation per mean length was kept 30%. Naturally, the shorter the length, the greater the magnetization decay becomes. Increasing K value would diminish the magnetization decay.
4. Conclusion In this paper, the size effects of magnetic particles on high-density recording performance and thermal decay
T. Suzuki / Journal of Magnetism and Magnetic Materials 193 (1999) 374—377
were discussed, experimentally and theoretically. To attain 400 kFRPI in recording density response curves, particle length must be less than 50 nm and length distribution less than 20 nm. However, the analysis showed that such particles suffer severe thermal instability in their magnetization, if K is less than 10 erg/cm, and that particle length deviation, as well as length itself, plays a very important role in magnetization time decay.
Acknowledgements The author would like to acknowledge Fuji Photo Film Co. for providing tape samples. This work was partly supported by a grant from the Storage Research Consortium in Japan.
377
References [1] S. Saitoh et al., IEEE Trans. Magn. MAG-31 (1995) 2859. [2] R.M. Kloepper et al., IEEE Trans. Magn. MAG-20 (1984) 757. [3] P.J. Flanders, M.P. Sharrock, J. Appl. Phys. 62 (1987) 2918. [4] R.W. Chantrell, J. Magn. Magn. Mater. 95 (1991) 365. [5] T. Suzuki, T. Mitsugi, IEICE Trans. Electron. E80-C (1997) 1168. [6] K. Masaki, T. Miura, J. Japan Soc. Powder and Powder Metall. 43 (1996) 961. [7] G.J. Fan, IBM J. Res. Dev. 5 (1961) 321. [8] K. Kamijo, T. Matsui, IEICE Tech. Report, MR94-9, 1994. [9] L. Thurings, Thesis, Techn. Univ., Eindhoven, The Netherlands, 1982. [10] H. Nishio, J. Magn. Soc. Japan 15 (1991) 697.
Particle size effect on recording performance and thermal stability in high-density particulate tapes Toshiyuki Suzuki* Kyushu Institute of Design, Minami-ku, Fukuoka 815-8540, Japan
Abstract An experimental and theoretical study of high-density digital recording performances and thermal stability of magnetization were performed for several tapes with known physical and magnetic properties of the particles used. Also discussed were the relationships between recording performances and thermal stability of magnetization. 1999 Elsevier Science B.V. All rights reserved. Keywords: Particulate tape; Particle size; Particle size distribution; High-density recording; Magnetization time decay; Magnetic viscosity
1. Introduction
2. Recording density response
Recently magnetic particles used for particulate tapes have been reduced significantly in size, to attain very high recording density and low noise [1]. For such small particles, thermal stability of magnetization becomes one of the important issues [2—4]. The author has recently reported the temperature effect on magnetization thermal stability of particulate tapes [5]. However, the analysis on activation volume, for example, was limited, due to the lack of data on the size and magnetic properties of particles used in the tested tapes. In this paper, high-density digital recording performances and thermal stability of magnetization were studied for several tapes with known physical and magnetic properties of the particles used. Special emphasis was placed on analyzing the effect of particle size and size distribution on recording performances and thermal stability.
The samples used were three metal particulate tapes. Their properties are listed in Table 1 [6]. Fig. 1 shows the recording density curves, experimentally and theoretically simulated, for the tapes. In the experiment, all one’s recorded signals were reproduced to measure fundamental frequency components with a spectrum-analyzer. An MIG head with g "0.19 lm was used. The bit lengths at the second peaks (310 kFRPI, bit length"83 nm), and at the third peak for Sample A (620 kFRPI, bit length"41 nm) are comparative to or shorter than the mean particle length of the tapes. At densities higher than the second peaks, particle length and tape surface roughness should have more significant effect on the output level than the conventional demagnetization parameters, such as H , or B d. To analyze these effects, it was assumed that the signal output loss is proportional to the product of gap loss GL, spacing loss SL, and particle length loss PL. GL was calculated by assuming Fan’s head-field function [7]. For SL, head-to-medium spacing d, was set equal to nR [8]. PL was calculated by assuming that particles have a normal distribution f (¸), in their length ¸, with standard deviation p, and mean length ¸ , and that particles are
* Corresponding author. Fax: #81-92-553-4548; e-mail: [email protected].
0304-8853/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 4 5 8 - 2
T. Suzuki / Journal of Magnetism and Magnetic Materials 193 (1999) 374—377 Table 1 Magnetic and physical properties of particles and tapes Sample no
A
B
C
Particle Mean length (nm) Lenght dev. (nm) Aspect ratio Vol.(;10\ cm) H (Oe) H (Oe) p (emu/g) k (;10erg/cm)
71 21 4.63 1.32 2130 5780 140 2.43
102 38 5.90 2.39 1780 5830 131 2.28
148 79 7.75 4.21 1520 5820 121 2.03
2250 327 0.762 2.0 3.3
1870 314 0.853 1.7 3.4
1610 252 0.873 2.7 5.3
¹ape H (Oe) M (emu/cm) SQ Thickness (lm) R (nm)
375
of mean length and length deviation of the particles and R of each tape listed in Table 1. The adjustable parameter was only n in d"nR . The best fit was obtained when n"11. If the length deviation was not correctly evaluated, that is, if Samples B and C were assumed to have the same length distribution as Sample A, the simulated curves for Samples B and C exhibit more dips and the experimental result cannot be explained. Using the above established simulation equation, the effects of particle mean length, length deviation, and spacing were evaluated regarding D recording density. Fig. 2 shows the effect of mean length, in which length deviation"30% of the mean length, spacing"15 nm and gap length"70 nm (physical). It is seen that D of around 400 kFRPI is attainable for the mean length of 50 or 35 nm. Thus, recording performance improves when particles become smaller in size with a sharper size distribution curve. Although little difference was observed in density response at around 400 kFRPI for 50 and 35 nm mean length particles, a large difference in thermal stability was observed, as will be shown in the following. The effect of spacing was also evaluated for the case of mean length"50 nm, length deviation"20 nm, and gap length"70 nm. Naturally, spacing is one of the most influential parameters, and it must be kept as small as possible.
3. Thermal stability
Fig. 1. Recording density curves. Marks are for experiment in which the fundamental frequency component of output signal was measured. Lines are for simulation with the sample parameters. Matching point is at 50 kFRPI for Sample A.
longitudinally oriented [9].
Sin(p¸/j) f (¸) d¸ f (¸) d¸, p¸/j 1 (¸!¸ )
. f (¸)" Exp ! 2p (2pp
PL"
(1)
(2)
The simulated results for the three tapes are drawn by solid curves, to compare with their experimental data indicated by symbols in Fig. 1. The simulation used data
Fig. 3 shows activation volume » , as a function of physical volume » , obtained by the measurement of magnetization time decay. In the figure, the circles are for the present tape samples listed in Table 1 and for a fourth tape sample, which is very similar to Sample A but its physical volume is 1.82;10\ cm. The heavy triangles are for other MP tape data, which were referred to from a literature [10]. All data are consistent and on a single line. The ratio of » /» for the present Sample A is already smaller than 2, approaching to unity. Starting from the Arrhenius equation, magnetization of particle with volume », at time t, M(t), in the presence of a constant opposing field, can be expressed as follows. Here, M "M(t"0): K» M(t) "2 Exp !At Exp ! !1, (3) k¹ M where A is the frequency term, k is Boltzmann’s constant, and ¹ is the absolute temperature. Consider a particle assembly, which has a volume distribution of h(») and a normalized magnetization of m(t) at time t. Then m(t) is given by
m(t)"
M(t) h(»)» d» M
h(»)» d».
(4)
376
T. Suzuki / Journal of Magnetism and Magnetic Materials 193 (1999) 374—377
Fig. 4. Magnetization reversal threshold after t"10 s (+3 years) as a function of particle length ¸. Parameters are those for Sample A, except K . (a) K "2.43;10, (b) 2.43;10 and (c) 2.43;10 erg/cm. Also shown are the accumulated densities of particle length and volume for Sample A. Fig. 2. Simulated density curve with mean length as parameter. Length deviation"30% of mean length, spacing"15 nm, and gap length"70 nm.
Fig. 5. Magnetization time decay, with particle mean length and deviation as parameters. K "2.43;10 erg/cm, ¹"300°K.
Fig. 3. Activation volume » versus physical volume » , for MP tapes. Heavy triangles are after Nishio [10].
The volume distribution h(») can be expressed in terms of the length distribution given by Eq. (2), assuming that all particles have the same cylindrical shape with a long-axis length, ¸, a short-axis length, S, and a constant aspect ratio, a"¸/S. Fig. 4 shows magnetization reversal threshold for different length particles after t"10 s (3.2 years), with K as a parameter. For (a) K "2.43;10 erg/cm (Sample A), magnetization reversal takes place in very few particles, resulting in a very small amount of magnetization decay. This fact does not agree with the experimental result, in which an appreciable amount of magnetization decay is observed. This discrepancy may be
due to the fact that the applied opposing field would reduce an effective K value. For (b) K " 2.43;10 erg/cm, magnetization reversal takes place in 24% of the total particles, but volume contribution is still negligible. For (c) K "2.43;10 erg/cm, most par ticles reverse their magnetization, and magnetization decay is very large. This analysis explains magnetization time decay mechanism for the case where particles have distribution in their volume. Fig. 5 shows the case where particle length was changed as a parameter. In this case, the length deviation per mean length was kept 30%. Naturally, the shorter the length, the greater the magnetization decay becomes. Increasing K value would diminish the magnetization decay.
4. Conclusion In this paper, the size effects of magnetic particles on high-density recording performance and thermal decay
T. Suzuki / Journal of Magnetism and Magnetic Materials 193 (1999) 374—377
were discussed, experimentally and theoretically. To attain 400 kFRPI in recording density response curves, particle length must be less than 50 nm and length distribution less than 20 nm. However, the analysis showed that such particles suffer severe thermal instability in their magnetization, if K is less than 10 erg/cm, and that particle length deviation, as well as length itself, plays a very important role in magnetization time decay.
Acknowledgements The author would like to acknowledge Fuji Photo Film Co. for providing tape samples. This work was partly supported by a grant from the Storage Research Consortium in Japan.
377
References [1] S. Saitoh et al., IEEE Trans. Magn. MAG-31 (1995) 2859. [2] R.M. Kloepper et al., IEEE Trans. Magn. MAG-20 (1984) 757. [3] P.J. Flanders, M.P. Sharrock, J. Appl. Phys. 62 (1987) 2918. [4] R.W. Chantrell, J. Magn. Magn. Mater. 95 (1991) 365. [5] T. Suzuki, T. Mitsugi, IEICE Trans. Electron. E80-C (1997) 1168. [6] K. Masaki, T. Miura, J. Japan Soc. Powder and Powder Metall. 43 (1996) 961. [7] G.J. Fan, IBM J. Res. Dev. 5 (1961) 321. [8] K. Kamijo, T. Matsui, IEICE Tech. Report, MR94-9, 1994. [9] L. Thurings, Thesis, Techn. Univ., Eindhoven, The Netherlands, 1982. [10] H. Nishio, J. Magn. Soc. Japan 15 (1991) 697.