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Influence of anisotropy dispersion on permeability of CoNbZr thin films
Journal of Magnetism and Magnetic Materials 148 (1995) 129-131
~
ELSEVIER
|ournal of amn~gneUsm magnetic mateflals
Influence of anisotropy dispersion on permeability of CoNbZr thin films M. Rivas a, J.F.-Calleja a, I. Iglesias a, M.C. Contreras a,*, M. Guyot b, M. Porte b, V. Cagan b R. Krishnan b a DebPartamento de Fisica de la Universidad de Oviedo. Cairo Sotelo s / n . 33007 Ooiedo, Spain CNRS, Laboratoire de Magn&isme et Mat3riaux Magn3tiques. 92195 Meudon, France
Abstract The initial permeability ~-gi and quantitative analysis of anisotropy effective field were exanainated for CoNbZr amorphous films. The magnitude of ~i was found to be dependent on the anisotropy dispersion.
Amorphous CoNbZr alloys with negligible magnetostriction are well known for their relatively high thermal and chemical stabilities with respect to metallic glasses and their magnetically soft properties which make them good candidates for application in video heads [1,2]. The purpose of this work is to discuss the magnitude of the initial permeability in this alloy in terms of short and long-range magnetization fluctuation in connection with the microstrueture of the films, To clarify the relations between the initial permeability and local anisotropy fluctuation in amorphous CoNbZr, the local anisotropy is evaluated by the differential susceptibility method proposed by H. Hoffmaml [3]. Amorphous Coa0Nbt0Zrl0 films were prepared from an alloy target by rf diode sputtering. For some samples an in-plane de field of 300 Oe was applied during deposition. Other information on deposition conditions is given in Ref.
[41. The film thickness was measured using a long scan profiler. The saturation magnetization was measured with a vibrating-sample magnetometer (Table 1). The initial magnetic permeability was measured from 1 kHz to 500 MHz using a previously described inductive system, adapted to the ease of thin films [4]. Transverse-biased initial susceptibility measurements (TBIS) were made using a magneto-optical transverse Kerr effect system (MOKE). The inverse of the transverse
* Corresponding author. Fax: +34-8-5103324; e-mail: [email protected].
susceptibility obtained experimentally may be expressed as
[3]: Xt--'(/3 ) ----~ {(h + 1) + b ( h +. 1)-3/4 + c ( h + 1)-1}, Ms
(1) where the plus sign corresponds to /$ = 0 (de bias field applied along the easy axis) and the minus sign corresponds to fl----~r/2 (de bias field applied along the hard axis), M s is the saturation magnetization, H k = 2 K u / M s is the uniaxial macroscopic anisotropy field and h = H d c / H k , where HUe is the applied field. The first term in Eq. (1) corresponds to the coherent rotation process (Stoner-Wohlfarth model). The second one is the contribution of the ripple. Let us recall that the ripple structure of a fdm is composed of tiny regions which act like ideal monodomains and are at the origin of the short-range fluctuations of the magnetization. In an amorphous film this structure is determined by intrinsic parameters which are the random local anisotropy Kioc Table 1 Deposition conditions and magnetic parameters of amorphous CoNbZr films Sample
Applied field (300 Oe)
Thickness (nm) + 5%
Ms (emu/em 3) + 10%
1 2 3 4 5 6
no yes yes no no no
207 420 210 210 86 240
709 688 697 698 700 626
0304-8853/95/$~J9.50 © 1995 Elsevier Science B.V. All rights reserved $SDI 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 1 7 7 - 8
M. Rivas et al. ~Journal of Magnetism and Magnetic Materials 148 (1995) 129-131
130
Table 2 Anisotropy field, dispersion parameters and initial permeability of amorphous CoNbZr films Sample
Hk (Oe) + 1%
b
e
/zlaa
1 2 3 4 5 6
12.6 10.5 11.8 11.8 19,3 13.2
0.1 0.2 0.1 0.1 0.1 0.1
0.02 0.1 -
660 650 630 620 450 585
-4 -4,5
_
-6 -6,5
-7,5
and the structural correlation length d. The ripple parameter b is given by:
1 b--- 4 ~ - ~
s2Mj; (AKu) 5/4'
b=0.1
-5
(2)
where S is the structure constant o f the film. T h e third term in Eq. (1) corresponds to the skew. It is related to the long-range fluetuatio.ns o f the magnetization and generally due to the dispersion o f the anisotropy field H k. c is given by c - - 3 ( 0 2) where ( 0 2} is the mean square value o f the skew angle. To get the value o f the anisotropy field H k f r o m the experimental data we used the procedure proposed by Feldtkeller [5]. To obtain b and c we operated as follows: values o f b can usually be obtained b y linear extrapolation of Xt--l( f l X h -I- 1) 1/4 versus ( h -6 1) 5/4 for high enough values o f ( h 4- 1) 5/a when c is negligible. W h e n this is not the case a careful numerical analysis must be carried out to find the values o f b and c that provide the best fit to the experimental points, Experimental values of b and c obtained for these films are shown in Table 2. In the ease o f films with
-I
-0,5
0
0.5
I
1,5
2
Fig. 2. Graphical representation of In( .,ytl("rc/2)--(Hk/MsXh --1)) versus ln(h--1) for sample 4 with b - - 0.1 and appreciable skew, c = 0.1. Squares represent experimental data and solid line represents the linear extrapolation, far away from the - - 1 / 4 power law, due to long range dispersion. negligible skew we m a y test the validity of the - - 1 / 4 p o w e r law (characteristic o f approximating c--~ 0 in Eq. (1)) by representing I n ( x t l ( ' r r / 2 ) - ( H k / M s ) ( h - 1)) versus l n ( h - 1) as ha_q been done in Fig. 1 for sample 3. For comparison w e m a y see this grap.Mcal representation (Fig. 2) for sample 4 with appreciable s k e w where no - - 1 / 4 power law is observed. A s is k n o w n [6], the rotational permeability in a monodomain with saturation magnetization M s and uniaxial anisotropy constant K , is related to the initial susceptibility as follows: /.ti ---- 1 +
4'11",,3(i "
4q'r,Vi
(3)
SO the initial permeability o f the S t o n e r - W o h l f a r t h m o d e l after saturation along the easy axis at easy axis de field h = 0 with tickle field along the hard axis is given by: 4'trMs /.ts- w ~ ~
(4)
//k
•T:•
L .
800 z~ Calculated as 4~Ms
/
-l/41aw
2,5
In(h- 1)
"
,,'/
H~
• Calculated as
"
4~Ms Hk(l+b+c) T
,.-'"'" "'"' • -"/ I,,"
-I
.0,5
0
0,5
1
1,5
2
|~J
2,5 rS
In(h- 1)
. .~! I
Fig. 1. Graphical representation of l n ( x t l ( ~ r / 2 ) - - ( H k / M s X h --1)) versus l n ( h - 1 ) for sample 3 with b = 0.1 and negligible skew. Squares represent experimental data and solid lir,e represents the prediction for a - 1 / 4 power law for the transverse susceptibility.
~400
500
I
I
6OO 7OO Iq (calculated)
I
8OO
Fig. 3, Experimentally obtained /~i along the hard axis as a function of: calculated 4~rMs / H k ( , a ) and calculated 4~rMs / Hk(1 + b + c) (11).
M. Rivas et aL /Journal of Magnetism and Magnetic Materials 148 (1995) 129-131
According to Eqs. (1) and (3) the correction of the Stoner-Wohlfarth expression due to the ripple and skew is given by: --
4 w Ms + b+
(5)
In Fig. 3 the initial permeability value measured using an inductive permeameter is plotted versus the calculated value assuming the Stoner-Wohlfarth model (these points are represented by triangles in the graph) and also versus the calculated value using the above-mentioned correction (these corrected points are represented by solid squares). The dashed line represents the ideal line where the measured values would be equal to the calculated ones. The number on the right of each marker in the graph is the number of the sample as given in Tables 1 and 2. Fig. 3 In Fig. 3 we may see that for some samples (5 and 6) the value of the measured initial permeability agrees well with that predicted by the Stoner-Wohlfarth model but for the rest of the samples the predicted value is significantly higher than the measured one, especially in those films with higher dispersion (2 and 4). The fact is that in real films the local demagnetizing field must be taken into account as part of the effective in-plane uniaxial anisotropy. The magnitude of local demagnetizing fields may be evaluated in terms o f parameters b and c, as mentioned above, which allows us to assume the effective field as Hk(1 "Jr b
+ c) in Eq. (5).
131
In all the films the experimental values are equal to the calculated ones, within the experimental error, which indicates that the effective field is well evaluated by Hk(1 + b + c) taking into account the short and long-range demagnetizing fields. It also indicates that permeability along the hard axis is mainly determined by coherent rotation of magnetization. In conclusion, we find that with increasing dispersion, the magnitude of ~ n a was determined not only by H k but also by b and c. These results on amorphous films are similar to some previously published works on policrystalline films [7]. Acknowledgement: This work is partially supported by the Comisi6n Interministerial de Cieneia y Tecnologia (CICYT) MAT92-0778 and MAT93-1431.
Refereaces [1] Y. Shimada and H. Kojima, J. Appl. Phys. 53 (1982) 3156. [2] R. Krishnan, M. Tarhouni, M. Tessier and A. Gangulee, J. Appl. Phys. 53 (1982) 2243. [3] H. Hoffmann, IEEE Trans. Magn. 4 (1968) 32. [4] V. Cagan and M. Guyot, IEEE Trans. Magn. 20 (1984) 2157. [5] E. Feldtkeller, Z. Phys. 176 (1963) 510. [6] S. Chikazumi, Physics of Magnetism (Wiley, New York, 1964) p. 290. [7] T. Shimatsu, M. Takahashi and T. Wakiyama, J. Magn. Soe. Jpn., 13 [Sl] (1989) 577.
~
ELSEVIER
|ournal of amn~gneUsm magnetic mateflals
Influence of anisotropy dispersion on permeability of CoNbZr thin films M. Rivas a, J.F.-Calleja a, I. Iglesias a, M.C. Contreras a,*, M. Guyot b, M. Porte b, V. Cagan b R. Krishnan b a DebPartamento de Fisica de la Universidad de Oviedo. Cairo Sotelo s / n . 33007 Ooiedo, Spain CNRS, Laboratoire de Magn&isme et Mat3riaux Magn3tiques. 92195 Meudon, France
Abstract The initial permeability ~-gi and quantitative analysis of anisotropy effective field were exanainated for CoNbZr amorphous films. The magnitude of ~i was found to be dependent on the anisotropy dispersion.
Amorphous CoNbZr alloys with negligible magnetostriction are well known for their relatively high thermal and chemical stabilities with respect to metallic glasses and their magnetically soft properties which make them good candidates for application in video heads [1,2]. The purpose of this work is to discuss the magnitude of the initial permeability in this alloy in terms of short and long-range magnetization fluctuation in connection with the microstrueture of the films, To clarify the relations between the initial permeability and local anisotropy fluctuation in amorphous CoNbZr, the local anisotropy is evaluated by the differential susceptibility method proposed by H. Hoffmaml [3]. Amorphous Coa0Nbt0Zrl0 films were prepared from an alloy target by rf diode sputtering. For some samples an in-plane de field of 300 Oe was applied during deposition. Other information on deposition conditions is given in Ref.
[41. The film thickness was measured using a long scan profiler. The saturation magnetization was measured with a vibrating-sample magnetometer (Table 1). The initial magnetic permeability was measured from 1 kHz to 500 MHz using a previously described inductive system, adapted to the ease of thin films [4]. Transverse-biased initial susceptibility measurements (TBIS) were made using a magneto-optical transverse Kerr effect system (MOKE). The inverse of the transverse
* Corresponding author. Fax: +34-8-5103324; e-mail: [email protected].
susceptibility obtained experimentally may be expressed as
[3]: Xt--'(/3 ) ----~ {(h + 1) + b ( h +. 1)-3/4 + c ( h + 1)-1}, Ms
(1) where the plus sign corresponds to /$ = 0 (de bias field applied along the easy axis) and the minus sign corresponds to fl----~r/2 (de bias field applied along the hard axis), M s is the saturation magnetization, H k = 2 K u / M s is the uniaxial macroscopic anisotropy field and h = H d c / H k , where HUe is the applied field. The first term in Eq. (1) corresponds to the coherent rotation process (Stoner-Wohlfarth model). The second one is the contribution of the ripple. Let us recall that the ripple structure of a fdm is composed of tiny regions which act like ideal monodomains and are at the origin of the short-range fluctuations of the magnetization. In an amorphous film this structure is determined by intrinsic parameters which are the random local anisotropy Kioc Table 1 Deposition conditions and magnetic parameters of amorphous CoNbZr films Sample
Applied field (300 Oe)
Thickness (nm) + 5%
Ms (emu/em 3) + 10%
1 2 3 4 5 6
no yes yes no no no
207 420 210 210 86 240
709 688 697 698 700 626
0304-8853/95/$~J9.50 © 1995 Elsevier Science B.V. All rights reserved $SDI 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 1 7 7 - 8
M. Rivas et al. ~Journal of Magnetism and Magnetic Materials 148 (1995) 129-131
130
Table 2 Anisotropy field, dispersion parameters and initial permeability of amorphous CoNbZr films Sample
Hk (Oe) + 1%
b
e
/zlaa
1 2 3 4 5 6
12.6 10.5 11.8 11.8 19,3 13.2
0.1 0.2 0.1 0.1 0.1 0.1
0.02 0.1 -
660 650 630 620 450 585
-4 -4,5
_
-6 -6,5
-7,5
and the structural correlation length d. The ripple parameter b is given by:
1 b--- 4 ~ - ~
s2Mj; (AKu) 5/4'
b=0.1
-5
(2)
where S is the structure constant o f the film. T h e third term in Eq. (1) corresponds to the skew. It is related to the long-range fluetuatio.ns o f the magnetization and generally due to the dispersion o f the anisotropy field H k. c is given by c - - 3 ( 0 2) where ( 0 2} is the mean square value o f the skew angle. To get the value o f the anisotropy field H k f r o m the experimental data we used the procedure proposed by Feldtkeller [5]. To obtain b and c we operated as follows: values o f b can usually be obtained b y linear extrapolation of Xt--l( f l X h -I- 1) 1/4 versus ( h -6 1) 5/4 for high enough values o f ( h 4- 1) 5/a when c is negligible. W h e n this is not the case a careful numerical analysis must be carried out to find the values o f b and c that provide the best fit to the experimental points, Experimental values of b and c obtained for these films are shown in Table 2. In the ease o f films with
-I
-0,5
0
0.5
I
1,5
2
Fig. 2. Graphical representation of In( .,ytl("rc/2)--(Hk/MsXh --1)) versus ln(h--1) for sample 4 with b - - 0.1 and appreciable skew, c = 0.1. Squares represent experimental data and solid line represents the linear extrapolation, far away from the - - 1 / 4 power law, due to long range dispersion. negligible skew we m a y test the validity of the - - 1 / 4 p o w e r law (characteristic o f approximating c--~ 0 in Eq. (1)) by representing I n ( x t l ( ' r r / 2 ) - ( H k / M s ) ( h - 1)) versus l n ( h - 1) as ha_q been done in Fig. 1 for sample 3. For comparison w e m a y see this grap.Mcal representation (Fig. 2) for sample 4 with appreciable s k e w where no - - 1 / 4 power law is observed. A s is k n o w n [6], the rotational permeability in a monodomain with saturation magnetization M s and uniaxial anisotropy constant K , is related to the initial susceptibility as follows: /.ti ---- 1 +
4'11",,3(i "
4q'r,Vi
(3)
SO the initial permeability o f the S t o n e r - W o h l f a r t h m o d e l after saturation along the easy axis at easy axis de field h = 0 with tickle field along the hard axis is given by: 4'trMs /.ts- w ~ ~
(4)
//k
•T:•
L .
800 z~ Calculated as 4~Ms
/
-l/41aw
2,5
In(h- 1)
"
,,'/
H~
• Calculated as
"
4~Ms Hk(l+b+c) T
,.-'"'" "'"' • -"/ I,,"
-I
.0,5
0
0,5
1
1,5
2
|~J
2,5 rS
In(h- 1)
. .~! I
Fig. 1. Graphical representation of l n ( x t l ( ~ r / 2 ) - - ( H k / M s X h --1)) versus l n ( h - 1 ) for sample 3 with b = 0.1 and negligible skew. Squares represent experimental data and solid lir,e represents the prediction for a - 1 / 4 power law for the transverse susceptibility.
~400
500
I
I
6OO 7OO Iq (calculated)
I
8OO
Fig. 3, Experimentally obtained /~i along the hard axis as a function of: calculated 4~rMs / H k ( , a ) and calculated 4~rMs / Hk(1 + b + c) (11).
M. Rivas et aL /Journal of Magnetism and Magnetic Materials 148 (1995) 129-131
According to Eqs. (1) and (3) the correction of the Stoner-Wohlfarth expression due to the ripple and skew is given by: --
4 w Ms + b+
(5)
In Fig. 3 the initial permeability value measured using an inductive permeameter is plotted versus the calculated value assuming the Stoner-Wohlfarth model (these points are represented by triangles in the graph) and also versus the calculated value using the above-mentioned correction (these corrected points are represented by solid squares). The dashed line represents the ideal line where the measured values would be equal to the calculated ones. The number on the right of each marker in the graph is the number of the sample as given in Tables 1 and 2. Fig. 3 In Fig. 3 we may see that for some samples (5 and 6) the value of the measured initial permeability agrees well with that predicted by the Stoner-Wohlfarth model but for the rest of the samples the predicted value is significantly higher than the measured one, especially in those films with higher dispersion (2 and 4). The fact is that in real films the local demagnetizing field must be taken into account as part of the effective in-plane uniaxial anisotropy. The magnitude of local demagnetizing fields may be evaluated in terms o f parameters b and c, as mentioned above, which allows us to assume the effective field as Hk(1 "Jr b
+ c) in Eq. (5).
131
In all the films the experimental values are equal to the calculated ones, within the experimental error, which indicates that the effective field is well evaluated by Hk(1 + b + c) taking into account the short and long-range demagnetizing fields. It also indicates that permeability along the hard axis is mainly determined by coherent rotation of magnetization. In conclusion, we find that with increasing dispersion, the magnitude of ~ n a was determined not only by H k but also by b and c. These results on amorphous films are similar to some previously published works on policrystalline films [7]. Acknowledgement: This work is partially supported by the Comisi6n Interministerial de Cieneia y Tecnologia (CICYT) MAT92-0778 and MAT93-1431.
Refereaces [1] Y. Shimada and H. Kojima, J. Appl. Phys. 53 (1982) 3156. [2] R. Krishnan, M. Tarhouni, M. Tessier and A. Gangulee, J. Appl. Phys. 53 (1982) 2243. [3] H. Hoffmann, IEEE Trans. Magn. 4 (1968) 32. [4] V. Cagan and M. Guyot, IEEE Trans. Magn. 20 (1984) 2157. [5] E. Feldtkeller, Z. Phys. 176 (1963) 510. [6] S. Chikazumi, Physics of Magnetism (Wiley, New York, 1964) p. 290. [7] T. Shimatsu, M. Takahashi and T. Wakiyama, J. Magn. Soe. Jpn., 13 [Sl] (1989) 577.