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Noise in magnetic recording media
Journal of Magnetism and Magnetic Materials 177-181 (1998) 905-906
J~
ELSEVIER
Journalof magnetism and magnetic materials
Noise in magnetic recording media Jing Ju Lu, Huei Li Huang* Department of Physics, National Yaiwan University, Taipei, Taiwan, ROC
Abstract
Fluctuation in the magnetization transition for a given distribution of the physical parameters of the particle and orientation of the easy axis of a system of thermally activated noninteracting single-domain particles under a pulsed recording-head field has been analyzed. Our analysis takes into account the vector nature of the head field as observed by the particle in the media. Under the same head, the layer of the media closer to the head gap exhibits much lower noise than the layer farther from the head gap. ~ 1998 Elsevier Science B.V. All rights reserved. Ke)~vords: Transition noise; Media optimization
1. Introduction
Any fluctuation in the distribution of the relevant physical parameters such as the particle volume V, anisotropy constant K, the in-plane and out-of-plane misorientation of the easy axis, and so on, are liable to result in transition variance. Smaller particle size may be considered favorable for the purpose of attaining a higher recording density. However, an increasingly small particle size or small K V value is liable to make the particles more easily susceptible to thermal activation which destabilizes the system, causing a serious thermally induced magnetization reversal [-11, producing undesirable transition noise and a loss of memory [2]. The proper trade-off point between enhancing the recording density and at the same time reducing thermal noise for small particles is a matter of great concern yet to be more carefully optimized. In this paper, the thermally activated medium writing transition noise for a given distribution of position, size, anisotropy constant and misorientation of the easy axis, among others, will be elaborated based on the coherent rotation model [-3,4] using the recording-head field which varies in magnitude and orientation as seen by the particle in the media. 2. The model A Monte Carlo method of simulation has been employed to carry out the calculation. Consider a thin * Corresponding author. Tel.: + 886 2 352 0635; fax: + 886 2 363 9984; e-mail: [email protected].
particulate medium consisting of a system of uniaxial noninteracting single-domain particles with a log-normal distribution of the particle's volume V, the anisotropy constant K, with fz(V) oc exp[ - log(V/Vo)2/2~2], f2(K) ocexp[-- Iog(K/Ko)2/2cr2], and a Gaussian inplane and out-of-plane misorientation (the latter being the tilted angle) distribution of the easy axis of the polar and azimuthal angle (0, 0) relative to the track direction x with f(0, q~) oc exp[-- ((0 - ~z/2)2/2~02 + q52/2a~)] (0 = 0 is along the z-axis). The system of particles are under the action of the Karlqvist recording-head field. For a bi-stable system where a fraction of nl particles are in the first well and n2 = 1 - nl particles in the second well, the rate of change of n~ from the first well is simply dn~/dt = - Kt2nl + ~ca~n2, where ~q2 is the thermal decay rate out of the first well into the second one, given by Kz2 =fo exp[ - (QiffkBT)] where Qij is the barrier height from the well i ~ j , K21 is the thermal decay rate in the reverse direction [3, 4]. In the absence of external magnetic fields Q~j = K V , the mean half-life of the n~ magnetization state is simply z = ½ ~12. Thus, by taking f0 = e 2s Hz, we find that r ~ i s if K V = 25kBT, and r ~ 1 y i f K V = 43kBT, which is a clear indication of the sensitivity of the magnetization state of a 'small' particle, or K V-value due to the thermal relaxation effect. The calculation procedures for thermomagnetic switching from the first-well state to the second-well state for a well-oriented medium has been reported elsewhere [-3, 4]. We can express M as a function of the ni(t), which in turn is a function of the history of applied head fields H we are then capable of tracing out the hysteresis loops.
0304-8853/98/$19.00 ,~ 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 8 4 3 - 3
906
J.J. Lu, H.L. Huang / Journal of Magnedsm amt ~'~MgneticMaterials ] 77-18J (1998) 905- 906
So far the medium has been assumed to be well oriented along the track direction. Since the orientation angle (0, ~b), as the particle in the medium 'sees' it, between the head field H and the easy axis of the particle varies as the medium moves past underneath the head, consequently, only for the particles located in a certain limited region from the gap center where the write field versus its orientation angle fits in well with the specific switching field versus orientation relationship does the particle switch. In the case where the particle is misoriented from the track direction by a certain angle, in-plane (in the media plane) or out-of-plane (perpendicular to the media plane), the nucleation (switching) field variation versus the orientation angle of the particles should be modified accordingly.
0,8
y/g=1/4
&"" 0.8
g vo,4
{a)
O.OE+O
1.0E-6
x (m)
0.8 3
3. Simulation results
The read-out voltage from the ith particle under the action of the head field at X may be written in Monte Carlo approximation as [5, 6] Vi(X) ~-. Ami(x;, y}) H'(X + x;, 3@
~"
y/g=3/s
0.6
"4"
(1)
It follows that the variance in the read-out voltage can be expressed as
02
N
o-2 cC Z H'2( x + xi, .'it" ((Ami (x', 3/))25,
(2)
i
where H ' is the derivative of the head field and A is an appropriate constant. Thus, a fluctuation in the distribution of the particle's volume and its misorientation, etc., will result in various magnetization transition patterns, (m,(x',3")) and its fluctuation leading to what is known as the medium writing transition noise, (Am~(x', y,)2) [6]. Media with a strong coercivity have been known to lead to a sharper switching field distribution. Our simulation shows, however, that a strong head field relative to the medium coercivity causes less fluctuation in the magnetization transition, hence less transition noise. Thus, under the same head, the layer of medium closer to the head gap switches much more readily and exhibits a sharper magnetization transition and contributes less to the medium noise than the layer of medium farther from the head gap. From the magnetization transition patterns at a given flying height, we are able to obtain the corresponding fluctuation in the magnetization transition or the noise, as shown in Fig. 1. In the figure we set fro = 30 °, % = 5% G~: = 0.1, Gv = 0.1, KoVo/kBT = 45, H,j = HI<, and y/g = ¼ (upper curve) and -~(lower curve). A total of 3000 particles (300 points, 10 particles per point) were involved in the present calculations and the medium appears noisier than it should. This is due to the fact that the noise level at each point is inversely proportional to the square root of the n u m b e r of particles involved in the calculation. What is significant, however,
(b)
O,OE+O
2,0E-7
4.0E-7
S,Og-7
x (m)
B.OE-7
1.0E-6
Fig. 1. The magnetization transition pattern for a random medium at a given flying height at (a) y/g = i, and (b) y/g = ~ when it is subjected to a pulsed Karlqvist head field. The physical parameters used are given in the text.
is that the medium transition noise increases steadily with the ratio of the head field to the coercivity. In other words, a thinner medium is favored to a thicker one from the medium noise point of view. There are indications also that the media particles with a specific tilted orientation may exhibit a lower noise. This research is supported by a contract from NSC; # 86-2216-E-005-037 of the Republic of China, References
[1"1 J.J. Lu, H.L Huang, IEEE Trans. Magn. 31 (6) (1995) 3764. I-2"1 P.-L. Lu, S.H. Charap, IEEE Trans. Magn. 30 (6) (1994) 4230. ]-3"1 H i . Huang, J.J. Lu, J, Appl. Phys. 77 (7) (I995) 3323. [4I J.J. Lu, H.L. Huang, J. Appk Phys. 76 (3) (I994) 1726. 1-5] B.L. Chen, H.L. Huang, J. Magn. Magn. Mater. 17t (1997) 218. [61 H.N. Bertram, Theory of Magnetic Recording, Cambridge University Press, Cambridge, MA, 1994.
J~
ELSEVIER
Journalof magnetism and magnetic materials
Noise in magnetic recording media Jing Ju Lu, Huei Li Huang* Department of Physics, National Yaiwan University, Taipei, Taiwan, ROC
Abstract
Fluctuation in the magnetization transition for a given distribution of the physical parameters of the particle and orientation of the easy axis of a system of thermally activated noninteracting single-domain particles under a pulsed recording-head field has been analyzed. Our analysis takes into account the vector nature of the head field as observed by the particle in the media. Under the same head, the layer of the media closer to the head gap exhibits much lower noise than the layer farther from the head gap. ~ 1998 Elsevier Science B.V. All rights reserved. Ke)~vords: Transition noise; Media optimization
1. Introduction
Any fluctuation in the distribution of the relevant physical parameters such as the particle volume V, anisotropy constant K, the in-plane and out-of-plane misorientation of the easy axis, and so on, are liable to result in transition variance. Smaller particle size may be considered favorable for the purpose of attaining a higher recording density. However, an increasingly small particle size or small K V value is liable to make the particles more easily susceptible to thermal activation which destabilizes the system, causing a serious thermally induced magnetization reversal [-11, producing undesirable transition noise and a loss of memory [2]. The proper trade-off point between enhancing the recording density and at the same time reducing thermal noise for small particles is a matter of great concern yet to be more carefully optimized. In this paper, the thermally activated medium writing transition noise for a given distribution of position, size, anisotropy constant and misorientation of the easy axis, among others, will be elaborated based on the coherent rotation model [-3,4] using the recording-head field which varies in magnitude and orientation as seen by the particle in the media. 2. The model A Monte Carlo method of simulation has been employed to carry out the calculation. Consider a thin * Corresponding author. Tel.: + 886 2 352 0635; fax: + 886 2 363 9984; e-mail: [email protected].
particulate medium consisting of a system of uniaxial noninteracting single-domain particles with a log-normal distribution of the particle's volume V, the anisotropy constant K, with fz(V) oc exp[ - log(V/Vo)2/2~2], f2(K) ocexp[-- Iog(K/Ko)2/2cr2], and a Gaussian inplane and out-of-plane misorientation (the latter being the tilted angle) distribution of the easy axis of the polar and azimuthal angle (0, 0) relative to the track direction x with f(0, q~) oc exp[-- ((0 - ~z/2)2/2~02 + q52/2a~)] (0 = 0 is along the z-axis). The system of particles are under the action of the Karlqvist recording-head field. For a bi-stable system where a fraction of nl particles are in the first well and n2 = 1 - nl particles in the second well, the rate of change of n~ from the first well is simply dn~/dt = - Kt2nl + ~ca~n2, where ~q2 is the thermal decay rate out of the first well into the second one, given by Kz2 =fo exp[ - (QiffkBT)] where Qij is the barrier height from the well i ~ j , K21 is the thermal decay rate in the reverse direction [3, 4]. In the absence of external magnetic fields Q~j = K V , the mean half-life of the n~ magnetization state is simply z = ½ ~12. Thus, by taking f0 = e 2s Hz, we find that r ~ i s if K V = 25kBT, and r ~ 1 y i f K V = 43kBT, which is a clear indication of the sensitivity of the magnetization state of a 'small' particle, or K V-value due to the thermal relaxation effect. The calculation procedures for thermomagnetic switching from the first-well state to the second-well state for a well-oriented medium has been reported elsewhere [-3, 4]. We can express M as a function of the ni(t), which in turn is a function of the history of applied head fields H we are then capable of tracing out the hysteresis loops.
0304-8853/98/$19.00 ,~ 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 8 4 3 - 3
906
J.J. Lu, H.L. Huang / Journal of Magnedsm amt ~'~MgneticMaterials ] 77-18J (1998) 905- 906
So far the medium has been assumed to be well oriented along the track direction. Since the orientation angle (0, ~b), as the particle in the medium 'sees' it, between the head field H and the easy axis of the particle varies as the medium moves past underneath the head, consequently, only for the particles located in a certain limited region from the gap center where the write field versus its orientation angle fits in well with the specific switching field versus orientation relationship does the particle switch. In the case where the particle is misoriented from the track direction by a certain angle, in-plane (in the media plane) or out-of-plane (perpendicular to the media plane), the nucleation (switching) field variation versus the orientation angle of the particles should be modified accordingly.
0,8
y/g=1/4
&"" 0.8
g vo,4
{a)
O.OE+O
1.0E-6
x (m)
0.8 3
3. Simulation results
The read-out voltage from the ith particle under the action of the head field at X may be written in Monte Carlo approximation as [5, 6] Vi(X) ~-. Ami(x;, y}) H'(X + x;, 3@
~"
y/g=3/s
0.6
"4"
(1)
It follows that the variance in the read-out voltage can be expressed as
02
N
o-2 cC Z H'2( x + xi, .'it" ((Ami (x', 3/))25,
(2)
i
where H ' is the derivative of the head field and A is an appropriate constant. Thus, a fluctuation in the distribution of the particle's volume and its misorientation, etc., will result in various magnetization transition patterns, (m,(x',3")) and its fluctuation leading to what is known as the medium writing transition noise, (Am~(x', y,)2) [6]. Media with a strong coercivity have been known to lead to a sharper switching field distribution. Our simulation shows, however, that a strong head field relative to the medium coercivity causes less fluctuation in the magnetization transition, hence less transition noise. Thus, under the same head, the layer of medium closer to the head gap switches much more readily and exhibits a sharper magnetization transition and contributes less to the medium noise than the layer of medium farther from the head gap. From the magnetization transition patterns at a given flying height, we are able to obtain the corresponding fluctuation in the magnetization transition or the noise, as shown in Fig. 1. In the figure we set fro = 30 °, % = 5% G~: = 0.1, Gv = 0.1, KoVo/kBT = 45, H,j = HI<, and y/g = ¼ (upper curve) and -~(lower curve). A total of 3000 particles (300 points, 10 particles per point) were involved in the present calculations and the medium appears noisier than it should. This is due to the fact that the noise level at each point is inversely proportional to the square root of the n u m b e r of particles involved in the calculation. What is significant, however,
(b)
O,OE+O
2,0E-7
4.0E-7
S,Og-7
x (m)
B.OE-7
1.0E-6
Fig. 1. The magnetization transition pattern for a random medium at a given flying height at (a) y/g = i, and (b) y/g = ~ when it is subjected to a pulsed Karlqvist head field. The physical parameters used are given in the text.
is that the medium transition noise increases steadily with the ratio of the head field to the coercivity. In other words, a thinner medium is favored to a thicker one from the medium noise point of view. There are indications also that the media particles with a specific tilted orientation may exhibit a lower noise. This research is supported by a contract from NSC; # 86-2216-E-005-037 of the Republic of China, References
[1"1 J.J. Lu, H.L Huang, IEEE Trans. Magn. 31 (6) (1995) 3764. I-2"1 P.-L. Lu, S.H. Charap, IEEE Trans. Magn. 30 (6) (1994) 4230. ]-3"1 H i . Huang, J.J. Lu, J, Appl. Phys. 77 (7) (I995) 3323. [4I J.J. Lu, H.L. Huang, J. Appk Phys. 76 (3) (I994) 1726. 1-5] B.L. Chen, H.L. Huang, J. Magn. Magn. Mater. 17t (1997) 218. [61 H.N. Bertram, Theory of Magnetic Recording, Cambridge University Press, Cambridge, MA, 1994.