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Noise time series simulation for a thin film recording medium
Journal of Magnetism and Magnetic Materials 155 (1996) 19-21
~
~
ELSEVIER
Jeurnalof magnetism and magnetic materials
Noise time series simulation for a thin film recording medium A.P. Warren a.,, C. Dean a, P.R. Bissell a, R.W. Chantrell
b, J.A.
Gotaas
a Department of Physics and Astronomy, Unicersity of Central Lancashire. Preston PRI 2HE. UK b Department of Physics. UnirersiO' ofKeele, Keele ST5 5BG. UK Abstract A previously developed simulation of a thin film recording medium has been extended to include evaluation of noise characteristics. The recording medium has been taken through the dc demagnetisation curve and noise characteristics at various remanent states computed for three degrees of inter-granular exchange coupling. The IRM curves were also computed, to allow the computation of the 6 M ( H ) curves. The remanence curves and noise curves were in good agreement with experiment. It was found that the peak in the noise curves for all three degrees of exchange coupling occurred at approximately the same field as the maximum slope in the 6 M ( H ) curves.
1. Introduction As recording densities in magnetic media continue to increase, bit cell areas approach the size of the microstrucrural features. Static magnetic measurements quantify bulk interaction effects, but can give only limited information about recording properties. Local interactions can provide such information, and several experimental studies have been undertaken to relate noise characteristics to local interaction effects and, hence, to microstructure [ 1]. In this work, a previously described simulation [2] has been utilised to generate dc demagnetisation curves and the moment configurations (hereafter referred to as 'microstates') at several remanent states. These microstates were then utilised for the computation of noise characteristics to obtain the total noise power as a function of applied field.
2. Noise voltage calculation An adequate description of the thin film model has been given elsewhere [2]. The number of grains in the simulation was increased to 28 × 340 = 9520, which corresponded to track widths of 1.3 and 13.0 I~m along the recording direction, to give an adequate track length for the time series calculation. The coordinate convention utilised specifies x as the recording direction, z is in-plane transverse to the track
* Corresponding author. Present address: Anacomp Magnetics, Intermediate road, Brynmawr, Gwent NP3 4YA, UK. Fax: +441495-313305.
and y is the normal to the plane. ( x ' , y ' , z ' ) specifies a coordinate in the plane of the film. An inductive read head was moved along the length of the recording medium in the x direction. The noise voltage was defined as the time derivative of the fringing flux, but since the h e a d - m e d i u m velocity ( c ) was constant, we could make the transformation: t ~ x. Thus d
e( x ) = - Nt,s-; '~tot( x ),
( l)
where (/)tot(X) is the total flux at the head from all the moments in the microstate and N is the number of turns. The flux contribution from the ith grain detected by the head, ~ , was computed using the reciprocity theorem [3] and the stray field from the recording medium was approximated by the Karlqvist field [4]. For a head of infinite width, there would be no z component of the Karlqvist field. Furthermore, there would be no out-of-plane component of M i. Thus, the noise voltage at a position x is given by N e(x)=-Nt'M~
E
d
V~-~xai(x',Y',z')H,i(x'- x),
(2)
i=1
where ( x ' , y ' , z ' ) is the coordinate of the ith grain, c~i is the cosine of the angle between the ith moment and the applied field, and H ~ i ( x ' - x ) is the x component of the Karlqvist field, ( x ' - x) being the separation in the recording direction from the gap centre. In order to compute the noise voltage, the microstates along the dc demagnetisation curve were stored and used for the noise voltage computations.
0304-8853/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSD/ 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 6 5 4 - 0
20
A.P. Warren et al. / Journal of Magnetism and Magnetic Materials 155 (1996) 19-21 1.00-
3. Results and discussion
o~,
The dc demagnetisation curves were obtained for three degrees of intergranular exchange coupling chosen to be zero, an intermediate degree of coupling, and strong coupling represented by the letting the exchange parameter, C*, be 0.00, 0.15 and 0.30, respectively. As in previous work [2], H i / H k - which controls the magnitude of the magnetostatic interaction - was set to 0.78. With these settings, there was a significant amount of cooperative reversal which produced large changes in M r ( H ) along the dc demagnetisation curves. In order to produce smoothing, each curve shown in Figs. 2 - 4 was produced by averaging four computations computed with the same parameters but a different set of easy axes. A field of 0.50H~ was sufficient to saturate the sample, and remanence states and noise curves were computed in steps of 0.02 H~. The saturation magnetisation of the recording medium was M, = 1500 e m u / c m 3, and the anisotropy constant K = 2.25 X 106 e r g / c m 3 gives rise to an anisotropy field, H~ = 3 kOe. The grains were 40 nm in diameter by 50 nm thick, for consistency with previous work [2]. The coercivity for each film for C * = 0.00, 0.15 and 0.30 was approximately 600, 400 and 350 Oe, respectively. The head gap length was 300 nm and flying height of 75 nm for consistency with transition noise simulations in thin film media by Zhu et al. [5]. Fig. 1 shows a time series (noise voltage versus x) for the remanent coercive state (the applied field was He~t = 0.22H~) obtained for C * = 0.00. Fig. 2 shows the (averaged) dc demagnetisation curves for the three degrees of exchange coupling. As expected, the increase in C * caused an increase in the saturation remanence, a decrease in the remanent coercivity, and an increase in the gradient around H r . The saturation remanence increased because the coupling tends to keep the moments aligned. The decrease in H r and increased slope close to H~ occurred as a consequence of increased cooperative reversal which produced an avalanche effect. This is also evident in Fig. 3, which shows the 3 M ( H ) curves for the three degrees of cou-
0,6ff
"'A
~\
o.~
030
0.40 0.20 0.00 -02.0 -0.40 -0.60
E rr
-0.80 -1.0~.00
[~
15
o~ o~ o.~o o.~. Field (H/Hk)
o.~
o.'4s o.so
0 . 0 0 --~ - 5.15 - m - 0.30 ]
Fig. 2. dc demagnetisation curves for three degrees of exchange coupling.
piing. As obtained theoretically [6] and experimentally [7], a predominantly positive 8 M ( H ) curve indicates strong exchange coupling and a negative curve is indicative of a dipolar (zero exchange) coupled film. The results presented here are in good agreement with these observations. The avalanche effect also gives rise to the slight negative overshoot in Fig. 3 for C * = 0.30. The noise curves were calculated as follows. The square of the noise voltage is integrated over x, averaged over the four easy axes and plotted against the field. It can be seen from Fig. 4 that the noise power is the same for all C* values at positive and negative saturation which suggests that noise power at saturation is independent of the degree of exchange coupling. This suggests that the grains themselves are major noise sources. The noise power peak is seen to increase considerably with C *, an effect that also occurs with transition noise [5]. Furthermore, it can be seen from Fig. 4 that the peaks for C* = 0.15 and 0.30 occur at fields of 0.20 and 0.14 H k, respectively. From the 6 M ( H ) curves in Fig. 3 it
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0.05
0.10
0,15
-15
0.20
0.25
0.30
0.35
0.40
0.4-5
Field (H/Hk) 0
2
4
6 8 x (microns)
10
12
14
Fig. 1. Time series for the remanent coercive state and C * = 0.00.
[---
o.15- - o., }
Fig. 3. 6M(H) curves for C* = 0.00, 0.15 and 0.30.
0.S0
A.P. Warren et al. / Journal of Magnetism and Magnetic Materials 155 (1996) 19-21 ~o c-
D
60
/T 50 t I I
~..o 40
~
3o I
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5 z
10 0 0
0.1
0.2 0.3 Field (H/Hk)
0.4
0.5
Fig. 4. Noise curves for C* = 0.00, 0.15 and 0.30.
appears that these fields correspond to the largest rate of change in 6 M ( H ) . Unfortunately, this cannot be confirmed quantitatively by the current work because of the small sample size and large statistical errors. However, this may be regarded as a tentative confirmation of the relationship between noise and maximum slope in the 6 M ( H ) curve.
4. Conclusions
The reciprocity principle has been used in conjunction with the Karlqvist approximation to generate noise voltage time series from microstates computed during the dc demagnetisation process in a thin film micromagnetic model. The following observations were made: (1) An increase in exchange coupling increased the
21
squareness, reduced the remanent coercivity and increased the amount of cooperative reversal. (2) The 6 M ( H ) curve was negative for a dipolar coupled thin film and predominantly positive for a strongly exchange coupled film, as predicted experimentally [7]. (3) Increased exchange coupling shifted the noise power peak to lower field and considerably increased the height of the peak. (4) There was good agreement between the field at which the noise peak occurred and the maximum slope in the ~ M ( H ) curve. Acknowledgements
The financial support of the UK EPSRC is gratefully acknowledged. The work was carried out within the framework of the EU CAMST project. References
[1] M.D. Clarke, P.R. Bissell, R.W. Chantrell and R.G. Gilson, J. Magn. Magn. Mater. 95 (1991) 17. [2] C. Dean, R.W. Chantrell, A. Hart, D.A. Parker and J.J. Miles, IEEE Trans. Magn. 27 (1991) 4769. [3] W.K. Westmijze, Philips Res. Rep. 8 (1953) 148. [4] O. Karlqvist, Trans. R. Inst. Tech. No. 86 (1954). [5] J.G. Zhu and H.N. Bertram, IEEE Trans. Magn. 27 (1988) 2706. [6] I.A. Beardsley and J.G. Zhu, IEEE Trans. Magn. 27 (1991) 5037. [7] P.I. Mayo, K. O'Grady, P.E. Kelly, J. Cambridge, I.L. Sanders, T. Yogi and R.W. Chantrell, J. Appl. Phys. 69 (1991) 4733.
~
~
ELSEVIER
Jeurnalof magnetism and magnetic materials
Noise time series simulation for a thin film recording medium A.P. Warren a.,, C. Dean a, P.R. Bissell a, R.W. Chantrell
b, J.A.
Gotaas
a Department of Physics and Astronomy, Unicersity of Central Lancashire. Preston PRI 2HE. UK b Department of Physics. UnirersiO' ofKeele, Keele ST5 5BG. UK Abstract A previously developed simulation of a thin film recording medium has been extended to include evaluation of noise characteristics. The recording medium has been taken through the dc demagnetisation curve and noise characteristics at various remanent states computed for three degrees of inter-granular exchange coupling. The IRM curves were also computed, to allow the computation of the 6 M ( H ) curves. The remanence curves and noise curves were in good agreement with experiment. It was found that the peak in the noise curves for all three degrees of exchange coupling occurred at approximately the same field as the maximum slope in the 6 M ( H ) curves.
1. Introduction As recording densities in magnetic media continue to increase, bit cell areas approach the size of the microstrucrural features. Static magnetic measurements quantify bulk interaction effects, but can give only limited information about recording properties. Local interactions can provide such information, and several experimental studies have been undertaken to relate noise characteristics to local interaction effects and, hence, to microstructure [ 1]. In this work, a previously described simulation [2] has been utilised to generate dc demagnetisation curves and the moment configurations (hereafter referred to as 'microstates') at several remanent states. These microstates were then utilised for the computation of noise characteristics to obtain the total noise power as a function of applied field.
2. Noise voltage calculation An adequate description of the thin film model has been given elsewhere [2]. The number of grains in the simulation was increased to 28 × 340 = 9520, which corresponded to track widths of 1.3 and 13.0 I~m along the recording direction, to give an adequate track length for the time series calculation. The coordinate convention utilised specifies x as the recording direction, z is in-plane transverse to the track
* Corresponding author. Present address: Anacomp Magnetics, Intermediate road, Brynmawr, Gwent NP3 4YA, UK. Fax: +441495-313305.
and y is the normal to the plane. ( x ' , y ' , z ' ) specifies a coordinate in the plane of the film. An inductive read head was moved along the length of the recording medium in the x direction. The noise voltage was defined as the time derivative of the fringing flux, but since the h e a d - m e d i u m velocity ( c ) was constant, we could make the transformation: t ~ x. Thus d
e( x ) = - Nt,s-; '~tot( x ),
( l)
where (/)tot(X) is the total flux at the head from all the moments in the microstate and N is the number of turns. The flux contribution from the ith grain detected by the head, ~ , was computed using the reciprocity theorem [3] and the stray field from the recording medium was approximated by the Karlqvist field [4]. For a head of infinite width, there would be no z component of the Karlqvist field. Furthermore, there would be no out-of-plane component of M i. Thus, the noise voltage at a position x is given by N e(x)=-Nt'M~
E
d
V~-~xai(x',Y',z')H,i(x'- x),
(2)
i=1
where ( x ' , y ' , z ' ) is the coordinate of the ith grain, c~i is the cosine of the angle between the ith moment and the applied field, and H ~ i ( x ' - x ) is the x component of the Karlqvist field, ( x ' - x) being the separation in the recording direction from the gap centre. In order to compute the noise voltage, the microstates along the dc demagnetisation curve were stored and used for the noise voltage computations.
0304-8853/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSD/ 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 6 5 4 - 0
20
A.P. Warren et al. / Journal of Magnetism and Magnetic Materials 155 (1996) 19-21 1.00-
3. Results and discussion
o~,
The dc demagnetisation curves were obtained for three degrees of intergranular exchange coupling chosen to be zero, an intermediate degree of coupling, and strong coupling represented by the letting the exchange parameter, C*, be 0.00, 0.15 and 0.30, respectively. As in previous work [2], H i / H k - which controls the magnitude of the magnetostatic interaction - was set to 0.78. With these settings, there was a significant amount of cooperative reversal which produced large changes in M r ( H ) along the dc demagnetisation curves. In order to produce smoothing, each curve shown in Figs. 2 - 4 was produced by averaging four computations computed with the same parameters but a different set of easy axes. A field of 0.50H~ was sufficient to saturate the sample, and remanence states and noise curves were computed in steps of 0.02 H~. The saturation magnetisation of the recording medium was M, = 1500 e m u / c m 3, and the anisotropy constant K = 2.25 X 106 e r g / c m 3 gives rise to an anisotropy field, H~ = 3 kOe. The grains were 40 nm in diameter by 50 nm thick, for consistency with previous work [2]. The coercivity for each film for C * = 0.00, 0.15 and 0.30 was approximately 600, 400 and 350 Oe, respectively. The head gap length was 300 nm and flying height of 75 nm for consistency with transition noise simulations in thin film media by Zhu et al. [5]. Fig. 1 shows a time series (noise voltage versus x) for the remanent coercive state (the applied field was He~t = 0.22H~) obtained for C * = 0.00. Fig. 2 shows the (averaged) dc demagnetisation curves for the three degrees of exchange coupling. As expected, the increase in C * caused an increase in the saturation remanence, a decrease in the remanent coercivity, and an increase in the gradient around H r . The saturation remanence increased because the coupling tends to keep the moments aligned. The decrease in H r and increased slope close to H~ occurred as a consequence of increased cooperative reversal which produced an avalanche effect. This is also evident in Fig. 3, which shows the 3 M ( H ) curves for the three degrees of cou-
0,6ff
"'A
~\
o.~
030
0.40 0.20 0.00 -02.0 -0.40 -0.60
E rr
-0.80 -1.0~.00
[~
15
o~ o~ o.~o o.~. Field (H/Hk)
o.~
o.'4s o.so
0 . 0 0 --~ - 5.15 - m - 0.30 ]
Fig. 2. dc demagnetisation curves for three degrees of exchange coupling.
piing. As obtained theoretically [6] and experimentally [7], a predominantly positive 8 M ( H ) curve indicates strong exchange coupling and a negative curve is indicative of a dipolar (zero exchange) coupled film. The results presented here are in good agreement with these observations. The avalanche effect also gives rise to the slight negative overshoot in Fig. 3 for C * = 0.30. The noise curves were calculated as follows. The square of the noise voltage is integrated over x, averaged over the four easy axes and plotted against the field. It can be seen from Fig. 4 that the noise power is the same for all C* values at positive and negative saturation which suggests that noise power at saturation is independent of the degree of exchange coupling. This suggests that the grains themselves are major noise sources. The noise power peak is seen to increase considerably with C *, an effect that also occurs with transition noise [5]. Furthermore, it can be seen from Fig. 4 that the peaks for C* = 0.15 and 0.30 occur at fields of 0.20 and 0.14 H k, respectively. From the 6 M ( H ) curves in Fig. 3 it
IE;CJR
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035
i
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~
Noise Peak
i
10
Q.
i
I
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',
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o
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-0.4-
~
; i
,o •
•
',//
Q >
~ z
40 ~'o.lxl
0.05
0.10
0,15
-15
0.20
0.25
0.30
0.35
0.40
0.4-5
Field (H/Hk) 0
2
4
6 8 x (microns)
10
12
14
Fig. 1. Time series for the remanent coercive state and C * = 0.00.
[---
o.15- - o., }
Fig. 3. 6M(H) curves for C* = 0.00, 0.15 and 0.30.
0.S0
A.P. Warren et al. / Journal of Magnetism and Magnetic Materials 155 (1996) 19-21 ~o c-
D
60
/T 50 t I I
~..o 40
~
3o I
•
5 z
10 0 0
0.1
0.2 0.3 Field (H/Hk)
0.4
0.5
Fig. 4. Noise curves for C* = 0.00, 0.15 and 0.30.
appears that these fields correspond to the largest rate of change in 6 M ( H ) . Unfortunately, this cannot be confirmed quantitatively by the current work because of the small sample size and large statistical errors. However, this may be regarded as a tentative confirmation of the relationship between noise and maximum slope in the 6 M ( H ) curve.
4. Conclusions
The reciprocity principle has been used in conjunction with the Karlqvist approximation to generate noise voltage time series from microstates computed during the dc demagnetisation process in a thin film micromagnetic model. The following observations were made: (1) An increase in exchange coupling increased the
21
squareness, reduced the remanent coercivity and increased the amount of cooperative reversal. (2) The 6 M ( H ) curve was negative for a dipolar coupled thin film and predominantly positive for a strongly exchange coupled film, as predicted experimentally [7]. (3) Increased exchange coupling shifted the noise power peak to lower field and considerably increased the height of the peak. (4) There was good agreement between the field at which the noise peak occurred and the maximum slope in the ~ M ( H ) curve. Acknowledgements
The financial support of the UK EPSRC is gratefully acknowledged. The work was carried out within the framework of the EU CAMST project. References
[1] M.D. Clarke, P.R. Bissell, R.W. Chantrell and R.G. Gilson, J. Magn. Magn. Mater. 95 (1991) 17. [2] C. Dean, R.W. Chantrell, A. Hart, D.A. Parker and J.J. Miles, IEEE Trans. Magn. 27 (1991) 4769. [3] W.K. Westmijze, Philips Res. Rep. 8 (1953) 148. [4] O. Karlqvist, Trans. R. Inst. Tech. No. 86 (1954). [5] J.G. Zhu and H.N. Bertram, IEEE Trans. Magn. 27 (1988) 2706. [6] I.A. Beardsley and J.G. Zhu, IEEE Trans. Magn. 27 (1991) 5037. [7] P.I. Mayo, K. O'Grady, P.E. Kelly, J. Cambridge, I.L. Sanders, T. Yogi and R.W. Chantrell, J. Appl. Phys. 69 (1991) 4733.