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Magnetic anisotropy distribution in transverse and obliquely field annealed amorphous ribbons
4~i journalof magnetism and magnetic
N ELSEVIER
Journal of Magnetism and Magnetic Materials 133 (1994) 46-48
.~
materials
Magnetic anisotropy distribution in transverse and obliquely field annealed amorphous ribbons J.M.
Barandiarfin *, A. Garcla-Arribas, J. Guti6rrez
Dpto. Electricidad y Electr6nica and ISEM, Universidad del Pals Vasco, Apartado 644, 48080-Bilbao, Spain
Abstract
Anisotropies with different angles with respect to the perpendicular direction have been induced in amorphous ferromagnetic ribbons by magnetic annealing. The direction of the anisotropy and its dispersion have been tested with the experimental techniques that are sensitive to it: the resonance-antiresonance method of measuring the AE effect, and the second harmonic method of obtaining the anisotropy distribution. The results obtained in these samples are analyzed with standard models that assume easy axes perpendicular to the direction of the magnetic field, as well as more elaborate ones. It is concluded that the large angular dispersion of the anisotropy mask any accurate evaluation of the anisotropy angle in the basis of these methods and models.
1. I n t r o d u c t i o n
The mechanisms of anisotropy in amorphous metallic ribbons are still not well understood, but it is clear that the anisotropy energy density K has to be regarded as a distributed quantity. The simple rotational model describes the magnetic and magnetoelastic properties of the samples in terms of the perpendicular 1 k , where H k is the anisotropy value ( K = ~lzoMsH anisotropy field and M s is the saturation magnetization) and applied field strength H, predicting that the Young's modulus at zero field E 0 equals the saturation modulus E s. Experimental determination of the E ( H ) curve (AE effect) usually gives E o / E ~ < 1 and provides a criterion in the analysis of the deviation of the anisotropy from the perpendicular direction [1]. On the other hand, a new direct method to determine the anisotropy distribution has been recently developed [2]. It consists of the detection of the second harmonic response of the sample to an alternating magnetic excitation. The high resolution of this technique makes it possible to reveal fine features of the
;~ Corresponding author. Fax: +34(4) 464 8500; e-mail: [email protected].
distribution arising from both magnitude and angle spread of K. In this paper we use these methods to check the distribution of magnetic anisotropies in the samples annealed at different angles with the perpendicular direction of the ribbon.
2. E x p e r i m e n t a l
Samples of composition Fe61COl6Sil2Bll were magnetically annealed for 10 min at 480°C under a static magnetic field H = 1.7 kOe applied in the plane of the ribbon and perpendicular to its longitudinal axis (sample A) as well as with 7° (sample B) and 12° (sample C) deviation from this perpendicular direction. The AE effect was measured by the resonance-antiresonance method with an experimental setup described elsewhere [3]. The anisotropy distribution was measured by the second harmonic method described in Ref. [2] at a frequency of 5 kHz, well below the resonance frequencies to avoid spurious features in the distribution. All the samples were measured with the field applied along the axis of the ribbon, while for sample B (7° deviation) measurements were also performed with a deviation of 7° and - 7 ° from the perpendicular
0304-8853/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0304-8853(94)00037-R
47
J.M. Barandiardn et al. /Journal of Magnetism and Magnetic Materials 133 (1994) 46-48
1.8 1.3 f easy_axis...s_
_
_
(A)
__
0.91
Position 1
Position2
0.4i
Position 3
Fig. 1. Experimental disposition for the measurements performed in sample B. Positions 2 and 3 cancel and double, respectively, the mean angle of the anisotropy with respect to the bias field.
direction, first, in order to compensate the deviation induced in the annealing, and second, to increase this deviation with the perpendicular direction (see Fig. 1) without any geometry changes relative to the field.
2.0
1.5
°I
~
1.o
~
o.5
(B)
1.6 (C)
3. Results and discussion
The AE data yield a modulus ratio E o / E s close to one, which is typical of samples with transverse anisotropy. For the case of small dispersion 6 of the perpendicular anisotropy, Squire [4] has developed the following expression: 2
1
9 AsEs ]
0.8 0.4
-1
0.0
2
2.5
3
3.5
4
4.5
5
5.5
6
H (Oe) Table 1 shows measured values of E o / E s and a mean deviation of the easy axis ( 6 ) derived from Eq. (1). The latter reproduces rather well the annealing angle S2. Fig. 2 shows the measured anisotropy distributions for the three samples, all of which present a broad distribution with sharp peaks superimposed on it. These peaks are related to the presence of well-defined values of the magnitude of the anisotropies perpendicular to the magnetic field (and therefore to the axis of the samples). The broad distribution is related to the angular dispersion of the easy axes in the sample, and it becomes wider and more asymmetric as the angle of annealing increases. This behaviour is predicted by the
Table 1 Comparison of annealing angles g2 and experimentally determined angles (6) for the anisotropy Sample
A
B
C
g2 (deg)
0 0.972(10) 4.6_+ 1
7 0.949(15) 6.9_+ 1
12 0.855(20) 11.6_+ 1
Eo/E s
(8) (deg)
Fig. 2. Anisotropy field distributions obtained from the second harmonic response for samples A, B and C.
simple rotational model, but the broadening observed is not as severe as expected [5]. In order to establish a correlation between the differences in the distribution of the samples and the deviation and spread of the anisotropy, we have measured sample B in different positions corresponding to Fig. 1. The results are displayed in Fig. 3. Curve (a) corresponds to the anisotropy perpendicular to the field, curve (b) to the sample aligned with the field, and curve (c) to a deviation of the anisotropy twice the original value. Very few differences can be observed in the distributions. Some differences can be observed in the fine structure of the peaks, increasing the intensity of region I and decreasing in region II as the angle is changed. They also show a slight displacement of the position due to the effect of the demagnetizing factor. However, the broad part corresponding to the non-perpendicular anisotropies is very similar in all the curves, in accordance with the results obtained in measure-
48
J.M. Barandiardn et al. / Journal of Magnetism and Magnetic Materials 133 (1994) 46-48 2
ments of the E ( H ) curves, which show no difference at all between positions 2 and 3. The main results obtained in this sample can be explained with a wide square distribution of angle probability which, however, does not appear so wide in the measurements due to the effect of the magnetostatic interactions between different domains [6]. The width of this distribution must be greater than the maximum deviation measured, that is, 14 ° . Thus, whatever the angle selected with respect to the field, the anisotropies are nearly in the same disposition. In conclusion, the two techniques used do not distinguish clear changes in the orientation of the anisotropy when changing the orientation of the sample. To account for these results we must invoke a very wide angular dispersion narrowed by the magnetostatic interaction during the magnetization process.
1.6 1.2 0.8 0.4 2
~', ~i(i ,
, i ....
i ....
i ' ,
1.6 1.2 2"
0.8
=
0.4 Acknowledgements. This work has been supported by the Spanish CICyT under grant No. MAT90-0877. O n e of the authors (AG) wish to thank to the Basque government for financial support.
(c)
1.6 1.2
II x/
0.8
References
0.4 0
2
2.5
3
3.5 H
4
4.5
5
5.5
6
(Oe)
Fig. 3. Anisotropy field distributions obtained from the second harmonic response for sample B. Curve (a) corresponds to position 2 in Fig. 1, (b) to position 1 and (c) to position 3.
[1] P.T. Squire, J. Magn. Magn. Mater. 87 (1990) 299. [2] A. Garcia-Arribas, J.M. Barandiar(m and G. Herzer, J. Appl. Phys. 71 (1992) 3047. [3] J. Guti6rrez, J.M. Barandiar~n and O.V. Nielsen, Phys. Stat. Solidi (a) 111 (1989)279. [4] P.T. Squire, M.R.J. Gibbs, J.M. Barandiar~n, J. Gutigrrez and A. Garcla-Arribas, J. Magn. Magn. Mater. 104-107 (1992) 107. [5] A. Garcla-Arribas, Graduate Degree Report (1992). [6] J.M. Barandiar~n and A. Hernando. J. Magn. Magn. Mater. 104-107 (1992) 73.
N ELSEVIER
Journal of Magnetism and Magnetic Materials 133 (1994) 46-48
.~
materials
Magnetic anisotropy distribution in transverse and obliquely field annealed amorphous ribbons J.M.
Barandiarfin *, A. Garcla-Arribas, J. Guti6rrez
Dpto. Electricidad y Electr6nica and ISEM, Universidad del Pals Vasco, Apartado 644, 48080-Bilbao, Spain
Abstract
Anisotropies with different angles with respect to the perpendicular direction have been induced in amorphous ferromagnetic ribbons by magnetic annealing. The direction of the anisotropy and its dispersion have been tested with the experimental techniques that are sensitive to it: the resonance-antiresonance method of measuring the AE effect, and the second harmonic method of obtaining the anisotropy distribution. The results obtained in these samples are analyzed with standard models that assume easy axes perpendicular to the direction of the magnetic field, as well as more elaborate ones. It is concluded that the large angular dispersion of the anisotropy mask any accurate evaluation of the anisotropy angle in the basis of these methods and models.
1. I n t r o d u c t i o n
The mechanisms of anisotropy in amorphous metallic ribbons are still not well understood, but it is clear that the anisotropy energy density K has to be regarded as a distributed quantity. The simple rotational model describes the magnetic and magnetoelastic properties of the samples in terms of the perpendicular 1 k , where H k is the anisotropy value ( K = ~lzoMsH anisotropy field and M s is the saturation magnetization) and applied field strength H, predicting that the Young's modulus at zero field E 0 equals the saturation modulus E s. Experimental determination of the E ( H ) curve (AE effect) usually gives E o / E ~ < 1 and provides a criterion in the analysis of the deviation of the anisotropy from the perpendicular direction [1]. On the other hand, a new direct method to determine the anisotropy distribution has been recently developed [2]. It consists of the detection of the second harmonic response of the sample to an alternating magnetic excitation. The high resolution of this technique makes it possible to reveal fine features of the
;~ Corresponding author. Fax: +34(4) 464 8500; e-mail: [email protected].
distribution arising from both magnitude and angle spread of K. In this paper we use these methods to check the distribution of magnetic anisotropies in the samples annealed at different angles with the perpendicular direction of the ribbon.
2. E x p e r i m e n t a l
Samples of composition Fe61COl6Sil2Bll were magnetically annealed for 10 min at 480°C under a static magnetic field H = 1.7 kOe applied in the plane of the ribbon and perpendicular to its longitudinal axis (sample A) as well as with 7° (sample B) and 12° (sample C) deviation from this perpendicular direction. The AE effect was measured by the resonance-antiresonance method with an experimental setup described elsewhere [3]. The anisotropy distribution was measured by the second harmonic method described in Ref. [2] at a frequency of 5 kHz, well below the resonance frequencies to avoid spurious features in the distribution. All the samples were measured with the field applied along the axis of the ribbon, while for sample B (7° deviation) measurements were also performed with a deviation of 7° and - 7 ° from the perpendicular
0304-8853/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0304-8853(94)00037-R
47
J.M. Barandiardn et al. /Journal of Magnetism and Magnetic Materials 133 (1994) 46-48
1.8 1.3 f easy_axis...s_
_
_
(A)
__
0.91
Position 1
Position2
0.4i
Position 3
Fig. 1. Experimental disposition for the measurements performed in sample B. Positions 2 and 3 cancel and double, respectively, the mean angle of the anisotropy with respect to the bias field.
direction, first, in order to compensate the deviation induced in the annealing, and second, to increase this deviation with the perpendicular direction (see Fig. 1) without any geometry changes relative to the field.
2.0
1.5
°I
~
1.o
~
o.5
(B)
1.6 (C)
3. Results and discussion
The AE data yield a modulus ratio E o / E s close to one, which is typical of samples with transverse anisotropy. For the case of small dispersion 6 of the perpendicular anisotropy, Squire [4] has developed the following expression: 2
1
9 AsEs ]
0.8 0.4
-1
0.0
2
2.5
3
3.5
4
4.5
5
5.5
6
H (Oe) Table 1 shows measured values of E o / E s and a mean deviation of the easy axis ( 6 ) derived from Eq. (1). The latter reproduces rather well the annealing angle S2. Fig. 2 shows the measured anisotropy distributions for the three samples, all of which present a broad distribution with sharp peaks superimposed on it. These peaks are related to the presence of well-defined values of the magnitude of the anisotropies perpendicular to the magnetic field (and therefore to the axis of the samples). The broad distribution is related to the angular dispersion of the easy axes in the sample, and it becomes wider and more asymmetric as the angle of annealing increases. This behaviour is predicted by the
Table 1 Comparison of annealing angles g2 and experimentally determined angles (6) for the anisotropy Sample
A
B
C
g2 (deg)
0 0.972(10) 4.6_+ 1
7 0.949(15) 6.9_+ 1
12 0.855(20) 11.6_+ 1
Eo/E s
(8) (deg)
Fig. 2. Anisotropy field distributions obtained from the second harmonic response for samples A, B and C.
simple rotational model, but the broadening observed is not as severe as expected [5]. In order to establish a correlation between the differences in the distribution of the samples and the deviation and spread of the anisotropy, we have measured sample B in different positions corresponding to Fig. 1. The results are displayed in Fig. 3. Curve (a) corresponds to the anisotropy perpendicular to the field, curve (b) to the sample aligned with the field, and curve (c) to a deviation of the anisotropy twice the original value. Very few differences can be observed in the distributions. Some differences can be observed in the fine structure of the peaks, increasing the intensity of region I and decreasing in region II as the angle is changed. They also show a slight displacement of the position due to the effect of the demagnetizing factor. However, the broad part corresponding to the non-perpendicular anisotropies is very similar in all the curves, in accordance with the results obtained in measure-
48
J.M. Barandiardn et al. / Journal of Magnetism and Magnetic Materials 133 (1994) 46-48 2
ments of the E ( H ) curves, which show no difference at all between positions 2 and 3. The main results obtained in this sample can be explained with a wide square distribution of angle probability which, however, does not appear so wide in the measurements due to the effect of the magnetostatic interactions between different domains [6]. The width of this distribution must be greater than the maximum deviation measured, that is, 14 ° . Thus, whatever the angle selected with respect to the field, the anisotropies are nearly in the same disposition. In conclusion, the two techniques used do not distinguish clear changes in the orientation of the anisotropy when changing the orientation of the sample. To account for these results we must invoke a very wide angular dispersion narrowed by the magnetostatic interaction during the magnetization process.
1.6 1.2 0.8 0.4 2
~', ~i(i ,
, i ....
i ....
i ' ,
1.6 1.2 2"
0.8
=
0.4 Acknowledgements. This work has been supported by the Spanish CICyT under grant No. MAT90-0877. O n e of the authors (AG) wish to thank to the Basque government for financial support.
(c)
1.6 1.2
II x/
0.8
References
0.4 0
2
2.5
3
3.5 H
4
4.5
5
5.5
6
(Oe)
Fig. 3. Anisotropy field distributions obtained from the second harmonic response for sample B. Curve (a) corresponds to position 2 in Fig. 1, (b) to position 1 and (c) to position 3.
[1] P.T. Squire, J. Magn. Magn. Mater. 87 (1990) 299. [2] A. Garcia-Arribas, J.M. Barandiar(m and G. Herzer, J. Appl. Phys. 71 (1992) 3047. [3] J. Guti6rrez, J.M. Barandiar~n and O.V. Nielsen, Phys. Stat. Solidi (a) 111 (1989)279. [4] P.T. Squire, M.R.J. Gibbs, J.M. Barandiar~n, J. Gutigrrez and A. Garcla-Arribas, J. Magn. Magn. Mater. 104-107 (1992) 107. [5] A. Garcla-Arribas, Graduate Degree Report (1992). [6] J.M. Barandiar~n and A. Hernando. J. Magn. Magn. Mater. 104-107 (1992) 73.