- Email: [email protected]
The influence of pinning centres on magnetization and loss in Fe-Ni-B-Si amorphous alloys
Journal of Magnetism and Magnetic Materials 82 (1989) 5-11 North-Holland, Amsterdam
5
THE INFLUENCE OF PINNING CENTRES ON MAGNETIZATION AND LOSS IN F e - N i - B - S i AMORPHOUS ALLOYS J. H O R V A T
1, ~.
MAROHNI(~ and E. BABI(~ 2
Institute of Physics of the University, P.O. Box 304, 41000 Zagreb, Yugoslavia Received 5 May 1989; in revised form 13 July 1989
The magnetic hysteresis of as-received Fe60Ni20BlsSi 2 and Fe~Ni40BlsSi 2 amorphous ribbons has been measured by the induction method, at different values of the maximum magnetization (Mm) and in a broad frequency range (0.1-105 Hz). The variations of the remanent magnetization, coercive field and hysteresis loss with M m at different frequencies are analysed in parallel, in order to explain the nature of processes occurring during the magnetization of the samples. All observed variations can be qualitatively explained by assuming the existence of two types of domain wall pinning centres with different pinning energies. The frequency dependence of the loss at selected M m values also supports this picture. The relevance of these results for the improvement of the soft magnetic properties of amorphous alloys is briefly discussed.
1. Introduction
Soft magnetic materials dominate in the industrial applications of ferromagnetism. The discovery of the soft magnetism in amorphous alloys associated with their availability in the form of thin ribbons and sheets of practically unlimited length, gave a strong impetus to further improvement of amorphous and conventional (polycrystalline) soft ferromagnets. In order to gain information which will help the development of advanced soft magnetic materials, a detailed study of the processes associated with the magnetization in such materials is required. Particular attention should be paid to the factors affecting the domain wall movement and to the mechanisms of the influence of these factors on the magnetization of the samples. In this paper we present the results of an attempt to explain the above mechanisms in amorphous Fe-Ni base alloys. For that purpose, i Department of Materials, Electrotechnical Institute, Rade Kon~ar, Zagreb, Yugoslavia. 2 Department of Physics, Faculty of Science, P.O. Box 162, Zagreb, Yugoslavia.
systematic measurements of the dependence of the total loss (E), coercive field (He) and remanent magnetization (MT) on maximum magnetization (M m) which extended up to the saturation magnetization (Ms), have been performed for two amorphous FeNiBSi samples at different frequencies. In addition to these measurements, the variation of the eddy current loss with frequency at selected values of M m has also been investigated. Simultaneous analysis of the frequency and M m dependences of the above mentioned parameters yielded rather detailed insight into the magnetization processes in these alloys. In particular, such analysis enabled us to single out two regimes in the magnetization process associated with different domain wall pinning mechanisms, and to explain a rapid increase in the loss with M m, when M m is approaching the saturation magnetization [1]. The proposed explanation is necessarily a qualitative one, since many factors affect the process of magnetization in a given ferromagnetic sample. For a quantitative description of the resuits a complete domain structure and the actual types and distribution of the domain wall pinning centres should be known.
0304-8853/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
6
J. Horvat et al. / Pinning centres and magnetization in FeNiBSi alloys
2. Experimental
The samples were glued onto straight fiberglass plates and then introduced into the pick-up coil. All the measurements were performed at room temperature which is well below their respective Curie temperatures (table 1).
All the parameters (E, M r, M s, He) studied in this paper were obtained from the measurements of the hysteresis loops. The measurements were performed by the use of an induction method on the samples in a form of long straight ribbon (150 × 2 × 0.023 mm3). The as-obtained samples of Fe60Ni2oB18Si 2 and Fe40Ni4oB18Si2 amorphous alloys were investigated. The samples were produced by melt spinning [2] in an inert atmosphere (He) and had smooth surfaces. Practically the same quenching conditions and cross-sections probably ensured the same degree of disorder in both samples. Some basic parameters relevant to our alloys are given in table 1. The set-up for the measurement of the hysteresis curve consisted of two mutually perpendicular primary coils of length 180 mm and diameter 18 ram. The pick-up coil with the diameter of 5.2 mm was placed in the middle of the primary one. For the frequencies below 1 kHz a pick-up coil with 3000 turns and 12 nun length was employed, whereas for higher frequencies 8 turn pick-up coil was used. An additional secondary connected in opposition to the pick-up coil was placed in other primary in order to compensate the signal from the pick-up coil when no sample was introduced into this coil. Through the primary coils connected in series, a sinusoidal current from the signal generator was passed. The current (and thus the magnetic field) was measured via a potential difference developed across a 10 fl standard resistor. The maximum magnetic field was about 4000 A / m . For the frequencies below 1 kHz, the voltage signal from the pick-up coil was first fed to an integrator and then stored in a computer. At higher frequencies ( < 100 kHz) the numerical integration was performed.
3. Results and discussion The dependence of the coercive field and the remanent magnetization on the normalized maximum magnetization (Mm/Ms) for the sample F%0Ni20B18Si 2 is shown in fig. 1. The results obtained at four different frequencies (1, 15, 220 and 8000 Hz, respectively) of the magnetizing magnetic field are displayed. We note that both H e and M r exhibit distinctly different dependences on M m in two regions. The first region extends up to M m = 0.5M s and is characterised by a nearly linear increase of M r with M m (the lines drawn in fig. 1 correspond to M r_ 0.5Ms) M r tends to saturation, whereas H e exhibits faster variation with M m. At lower frequencies the rate of increase of H c with M m (He ~ M m) depends rather strongly on frequency. In this range the exponent takes on the values m = 0.56, 1.10, 1.14 and 2.25 at 1, 10, 15 and 220 Hz, respectively. At higher frequencies the exponent m increases more slowly (m = 2.35 at 8 kHz) and probably saturates. It is interesting to compare the observed variations of H~ and M r with the corresponding hys-
Table 1 Data relevant to our samples: H c and E are the static coercive field and loss, respectively. The other symbols have their usual meaning Sample
Ms (T)
Tc (K)
E ( J / m 3 cyc)
P3oo (tim) × 108
Hc (A/m)
Fe4oNi4oBlsS2 FesoNi2oBlsS2
0.96 1.31
665 730
15 35
121 122
7.3 11
J. Horvat et al. / Pinning centres and magnetization in FeNiBSi alloys
I
' ' '~ Hc 'Mr . . . . . . . i f: IHz • o ~gv 15Hz • o /~.~% 220Hz • & /~ 8kHz • v //~
A
./" :o~
,;
|
l,
,I/ ,/.7S,>
,,I
.
0.1
.
.
.
.
==u
20
.
.
, .zo
10
0.1
I
0.2
1
teresis curves. In fig. 2 we show the hysteresis curves for the Fe60Ni20B18Si2 alloy at f = 10 Hz with M m / M s as an parameter. In addition to the already noted faster increase of H c and saturating M r the hysteresis loops for M m / g s > 0.5 are also qualitatively different from those for M m / M ~ < 0.5. The group of hysteresis curves at M m > 0.5Ms shows pronounced "tails" protruding to higher f i d d values. This occurs because of approach to saturation and is reflected in their average suscept-
f:lOHz Mrn/ M 1.00 0.84
,r~ ,~ /
P
Fig. 1. Variation of remanent magnetization and coercive field with normalized maximum magnetization for the F%oNi20BlsSi2 alloy.
I
_:
f= 8 kHz n 220Hz ~
Io
Mm/M s
Ms
100
.
.
.
"~
s
//~t_.~L
~
0.22 0.28
-I
-Msl Fig. 2. Hysteresis loops for the Fe~oNi20BzsSi 2 alloy in two regions of maximum magnetization.
02
Mm/M s
Fig. 3. Loss per unit volume per cycle for the F%oNi2oBlsSi2 alloy vs. normalized maximum magnetization at different
frequencies.
ibility ( A M m / A H m ) which is an order of magnitude lower than that derived for M m < 0.5M s. Qualitatively the same variations of M r and H c with Mm have also been observed in the sample Fe4oNi4oB18Si 2. We note that for both samples the regions of approximately linear increase of M r can be described by an empirical relation (Mr~Ms) oc ( Mm/Ms) 1-1. This probably indicates that the nature of the magnetization processes in this range of M m is the same for both samples. Two different types of variation are also observed in the dependence of the loss per unit volume per cycle ( E ) on M m (fig. 3). In the first region ( M m < 0.5Ms) the loss varies almost independently of frequency a s M 1"6 (Steinmetz's exponent), whereas at higher M m values there appears a frequency dependent enhancement of E vs. M m variation. In particular, at 1 Hz Steinmetz's exponent describes rather well the variation of E vs. M m for all values of M m, whereas at higher frequencies for M m >__0.5Ms, E 0c Mmk with k = 2 and 3 for f = 15 and 220 Hz, respectively. Similarly to the exponent m (He oc Mm~), k becomes constant (-- 3) at higher frequencies (fig. 3). The enhanced increase of E with M m at higher M m values is also observed in other amorphous and crystalline soft ferromagnets at power frequencies [1,3,4].
J. Horvat et al, / Pinning centres and magnetization in FeNiBSi alloys
become
pinned
at
stronger
pinning
centres
(C'-N-O).
"0
xl
l V lI
Fig. 4. Schematic drawing of the derivative of the domain wall surface energy vs. domain wall displacement. Broken line indicates the crossover to the strong pinning regime.
The observed variations of M r, H c and E can be qualitatively explained by assuming the existence of two types of domain wall pinning centres. For the sake of clarity we briefly evoke a qualitative picture of the process of magnetization in the ferromagnetic sample [5]. When an external magnetic field ( H ) acts on the ferromagnet its effect on the domain wall is equivalent to a pressure p = 21 s • H , where l~ is the spontaneous magnetization of the domain. As a consequence, the domain wall with the surface energy E w will be shifted from the previous position (A) of the minimum energy to a position in which the restoring force is balanced by the pressure of the magnetic field: (dew/ds)
= 21 s • H.
(1)
This process is illustrated by the shift from point A to B in fig. 4. Further increase of the applied field causes the Barkhausen jumps of the domain wall ( B - B ' ; C - C ' in fig. 4) at certain field values. These values of the magnetic field correspond to the pinning energies of given pinning centres. If the magnetic field is now reduced, the domain wall moves back in a different way ( C ' - D - E - F ) . However, if the magnetic field is increased beyond the point C', the domain wall will jump over the weaker pinning centres and
In the amrophous samples the actual domain wall motion depends, in general, on the magnetic anisotropy, surface irregularities, chemical dusters (if present), local concentration fluctuations and especially on the local strains and defects in the magnetostrictive samples [3]. The magnitudes of the static coercive fields for our samples (table 1) confirm that the stresses associated with defects in magnetostrictive materials are the main source of the domain wall pinning in our alloys [3]. Within the framework of a simple model depicted above (fig. 4) one may conclude that during the magnetization of our samples up to M m < 0.5 M s the domain walls move over the regions occupied with weak pinning centres (path A - B - B ' C - C ' - D - E - F in fig. 4). (Note that the magnetization corresponds to the shift of the domain wall and H corresponds to d E w / d s ). T h e contribution of a small part of the domain wall to magnetization depends on the number of Barkhausen jumps and on their length. In the same way the remanent magnetization (point D in fig. 4), depends on essentially the same parameters. Therefore, in the region of weak pinning centres one would expect an approximate proportionality between M r and Mm, as was observed (fig. 1). In the region Mrn > 0.5Ms, some parts of the domain wall may become pinned on stronger pinning centres and the remaining parts are bending [5,6]. On increasing H this part of the domain wall gets more and more expanded and its E w monotonically increases ( d E w / d s ) does not become zero during this process). On decreasing H the remanent magnetization remains practically the same as upon magnetizing up to 0.53,/, (path O - P - O - M r in fig. 4). This process is accompanied by a much reduced average susceptibility. All these features are indeed observed in our experiments (figs. 1 and 2). Apparently, for a real sample, the hysteresis curve is obtained by suitable averaging over all domain walls. One would expect, however, the overal behavior which is qualitatively similar to that described above. We also observed the frequency dependent increase of H c (fig. 1) for M m > 0.5M,, which can also be explained by the domain wall bending.
J. Horvat et al. / Pinning centres and magnetization in FeNiBSi alloys
During the bending of the domain walls the change of their length with respect to the change of the magnetization increases, hence the volume fraction in which the excess eddy currents occur, increases as well. These currents tend to slow down the motion of the domain walls, hence increase Hc and E, in agreement with the results (figs. 1 and 3). In particular, the enhanced increase of Hc for M m > 0 . S M s at higher frequencies (fig. 1) causes an enhanced increase of loss (fig. 3) although Mr remains practically constant in this range of M m. We note here that the observed variations of H~ with M m w a s qualitatively explained in terms of the interplay between the weak and strong pinning centers (fig. 4). Thus, the variation of E with M m c a n also be explained in the same terms. Moreover, a similar variation of E with M m observed in some other amorphous and crystalline ferromagnets [1,3,4] also seem consistent with our model. The above explanations are based on the existence of two types of domain wall pinning centres with very different energies. In crystalline ferromagnets the energy of domain wall pinning at dislocations is several orders of magnitude larger than that at the point defects [5]. The existence of the point defects and some extended defects in amorphous solids seems obvious, but the knowledge of these defects is less detailed than in the crystalline solids. Therefore, we can only assume that the point defects and the local concentration (or density) fluctuations can act as weak pinning centres. Strong pinning centres can arise as specific extended defects (quasidislocations) and local strain created during the preparation (quenching) procedure. (Note that as-obtained samples of magnetostrictive alloys were studied.) In discussing the variation of H c and E with M m , w e used the frequency as parameter. In order to obtain an insight into the nature of the eddy current loss of our samples, we also measured the frequency dependence (0.1-10 s Hz) of the loss per unit volume per cycle for our samples at three values of g m (0.4, 0.7 and 0.gMs, respectively). In general, the hysteresis loss can be divided into frequency dependent and frequency independent contributions. Since the eddy currents occurring in the vicinity of the domain wall are stronger (ex-
9
cess) than elsewhere, the frequency dependent loss exhibits, in general, two regimes. In the first one, the classical eddy currents (associated with the regions with homogeneous magnetization) dominate, whereas in the other one, the excess eddy currents prevail [8]. The crossover from one to the other regime is expected to depend on the ratio of the sample thickness to the distance between the domain walls [9]. (There is also a transitional region between two regimes.) Since the distance betweeen the domain walls and their shape may change with frequency and M m [10,11], the change of these parameters will lead to a change of the loss regime. The dominant type of eddy current loss shows up in the frequency dependence of E: for classical eddy currents E ~ f is expected, whereas for the excess ones a slower increase with frequency is usually observed [3,8,12]. (We note that for our samples the field penetration depth is several times larger than their thickness over the entire interval of explored frequencies.) The variation of the eddy current loss with frequency for our samples is shown in fig. 5. For the F%0Ni2oB18Si2 alloy loss was measured at M m --- 0 . 4 , 0.7 and 0.gMs, respectively. The loss for M m > 0 . S M s is dominated by the excess eddy currents (E txf 0"45)already above 5 Hz. However, at
I000
Dj~ c~°
iO0
~m° ~ ' : ~ j
//o ° oi
;
f
,b
16o
I
,;3
,o4
io5
f(Hz) Fig. 5. Variation of the eddy current loss with frequency for Fe4oNi4oBlsSi 2 (full symbol) and FetoNiT,oBlsSi 2 (empty symbols) alloys at different maximtun magnetization ( M m / M s = 0.4 (A), 0.7 (O) and 0.9 (r7, m)).
10
J. Horoat et al. / Pinning centres and magnetization in FeNiBSi alloys
M m -- 0.4Ms a considerably higher frequency ('~ 50
Hz) is required in order to obtain the excess eddy currents dominant. This, probably, indicates that for M m > 0.5M~, the volume fraction of the sample occupied by excess eddy currents is larger than that below 0.5Ms. Therefore, the enhanced increase of the loss above 0.5M~ probably arises due to an increase in the volume fraction with the excess eddy currents with respect to the increase of the magnetization during the bending of the domain walls. For the Fe40Ni40BlsSi2 sample (fig. 5), the excess eddy currents prevail at even lower frequencies. This possibly means that the volume fraction under excess eddy currents in this sample is larger than in Fet0Ni20BlsSi 2. This view is also supported by the result of Hc vs. M m measurements for this sample. For the Fe40Ni40BlsSi 2 alloy, the increase of He with M m (M m > 0.6Ms) was faster than that for Fet0Ni20B18Si2. We note that nearly the same crossover value of M m for both samples indicates the possibility of approximately the same fractions of different pinning centres in both samples. We also note (fig. 5) that at the same value of M m / M s (0.9), the coefficient of t h e f0.45 term in the eddy current loss for the sample Fe60Ni20B18Si 2 is about 1.4 times larger than that for Fe40Ni40BlsSi 2. Thus, the ratio of these coefficients is close to the ratio of their respective M~ values (table 1). However, in accordance with our previous findings (fig. 3) at the same value of Mm (--0.9 T) and the same frequency, the eddy current loss for FetoNi20B~sSi 2 alloy is several times smaller than that for Fe40Ni40BlsSi 2. The proposed explanation of E, Hc and M r in FeNiBSi alloys in terms of two types of domain wall pinning centres suggests some further experiments. A suitable annealing (relaxation) treatment should decrease the internal strains in the samples. This should affect some domain wall pinning centres and hence the variations of M r, H~ and E with M m and frequency. Therefore, careful investigations of the annealed specimens can be used in order to check the above hypothesis and may also provide a better insight into the magnetization processes in magnetostrictive Fe-Ni base amorphous alloys in general.
4. Conclusion The results of our systematic investigation of the remanent magnetization and the coercive field variation with the maximum magnetization in amorphous FeNiBSi samples indicate the existence of two types of the domain wall pinning centres with considerably different pinning energies. In the region of larger M m (_> 0.5M~) the influence of stronger pinning centres results in the dominant role of the domain wall bending processes which is reflected through the saturation of the remanent magnetization and a more rapid increase of the coercive field and the hysteresis loss with M m. The excess eddy currents play a dominant role in the frequency dependent loss already at frequencies of a few Hz if the samples are magnetized to the magnetization values at which domain wall bending becomes important (M m >i 0.5M~). In the region of lower M m (weaker pinning) the crossover to the regime of excess eddy currents occurs at higher frequencies about one order of magnitude. Apparently, further improvement of the soft magnetic properties of the amorphous ferromagnets is associated with the ability to reduce the excess eddy currents in these materials. According to our results, this is, among other factors, related also to the achievement of suitably treated alloys in which the bending of domain walls becomes important at as high as possible maximum magnetization (M m ~ M s).
Acknowledgements We thank Dr. H.H. Liebermann for skillful preparation of amorphous ribbons. This work was partially supported by N.B.S.
References [1] K. Foster, F.E. Werner and R.M. Del Vechio, J. Appl. Phys. 53(1982) 8308. [2] H.H. Liebermann and C.D. Graham, IEEE Trans. Magn. MAG-12 (1976) 921. [3] F.E. Luborsky, in: Amorphous Metallic Alloys, ed. F.E. Luborsky (Butterworths, London, 1983) p. 360.
J. Horvat et al. / Pinning centres and magnetization in FeNiBSi alloys
[4] H. Warlimont, in: Rapidly Quenched Metals, eds. S. Steeb and H. Warlimont (North-HoUand, Amsterdam, 1985) p. 1599. [5] S. Chikazumi, The Physics of Ferromagnetism. Magnetic Properties and Practical Applications (Mir, Moscow, 1986) p. 248 (in Russian). [6] D.C. Jiles and D.L. Atherton, J. Magn. Magn. Mat. 61 (1986) 48.
11
[7] M. Kersten, Z. Angew. Phys. 7 (1956) 313. [8] G. Lyudkovsky, P.K. Rastogi and M. Bala, J. Met. (1986) 18. [9] R.H. Pry and C.P. Bean, J. Appl. Phys. 29 (1958) 532. [10] T.R. Hailer and J.J. Kramer, J. Appl. Phys. 41 (1970) 1034. [11] C.D. Graham Jr., J. Appl. Phys. 53 (1982) 8276. [12] G. Bertotti, J. Magn. Magn. Mat. 41 (1984) 253.
5
THE INFLUENCE OF PINNING CENTRES ON MAGNETIZATION AND LOSS IN F e - N i - B - S i AMORPHOUS ALLOYS J. H O R V A T
1, ~.
MAROHNI(~ and E. BABI(~ 2
Institute of Physics of the University, P.O. Box 304, 41000 Zagreb, Yugoslavia Received 5 May 1989; in revised form 13 July 1989
The magnetic hysteresis of as-received Fe60Ni20BlsSi 2 and Fe~Ni40BlsSi 2 amorphous ribbons has been measured by the induction method, at different values of the maximum magnetization (Mm) and in a broad frequency range (0.1-105 Hz). The variations of the remanent magnetization, coercive field and hysteresis loss with M m at different frequencies are analysed in parallel, in order to explain the nature of processes occurring during the magnetization of the samples. All observed variations can be qualitatively explained by assuming the existence of two types of domain wall pinning centres with different pinning energies. The frequency dependence of the loss at selected M m values also supports this picture. The relevance of these results for the improvement of the soft magnetic properties of amorphous alloys is briefly discussed.
1. Introduction
Soft magnetic materials dominate in the industrial applications of ferromagnetism. The discovery of the soft magnetism in amorphous alloys associated with their availability in the form of thin ribbons and sheets of practically unlimited length, gave a strong impetus to further improvement of amorphous and conventional (polycrystalline) soft ferromagnets. In order to gain information which will help the development of advanced soft magnetic materials, a detailed study of the processes associated with the magnetization in such materials is required. Particular attention should be paid to the factors affecting the domain wall movement and to the mechanisms of the influence of these factors on the magnetization of the samples. In this paper we present the results of an attempt to explain the above mechanisms in amorphous Fe-Ni base alloys. For that purpose, i Department of Materials, Electrotechnical Institute, Rade Kon~ar, Zagreb, Yugoslavia. 2 Department of Physics, Faculty of Science, P.O. Box 162, Zagreb, Yugoslavia.
systematic measurements of the dependence of the total loss (E), coercive field (He) and remanent magnetization (MT) on maximum magnetization (M m) which extended up to the saturation magnetization (Ms), have been performed for two amorphous FeNiBSi samples at different frequencies. In addition to these measurements, the variation of the eddy current loss with frequency at selected values of M m has also been investigated. Simultaneous analysis of the frequency and M m dependences of the above mentioned parameters yielded rather detailed insight into the magnetization processes in these alloys. In particular, such analysis enabled us to single out two regimes in the magnetization process associated with different domain wall pinning mechanisms, and to explain a rapid increase in the loss with M m, when M m is approaching the saturation magnetization [1]. The proposed explanation is necessarily a qualitative one, since many factors affect the process of magnetization in a given ferromagnetic sample. For a quantitative description of the resuits a complete domain structure and the actual types and distribution of the domain wall pinning centres should be known.
0304-8853/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
6
J. Horvat et al. / Pinning centres and magnetization in FeNiBSi alloys
2. Experimental
The samples were glued onto straight fiberglass plates and then introduced into the pick-up coil. All the measurements were performed at room temperature which is well below their respective Curie temperatures (table 1).
All the parameters (E, M r, M s, He) studied in this paper were obtained from the measurements of the hysteresis loops. The measurements were performed by the use of an induction method on the samples in a form of long straight ribbon (150 × 2 × 0.023 mm3). The as-obtained samples of Fe60Ni2oB18Si 2 and Fe40Ni4oB18Si2 amorphous alloys were investigated. The samples were produced by melt spinning [2] in an inert atmosphere (He) and had smooth surfaces. Practically the same quenching conditions and cross-sections probably ensured the same degree of disorder in both samples. Some basic parameters relevant to our alloys are given in table 1. The set-up for the measurement of the hysteresis curve consisted of two mutually perpendicular primary coils of length 180 mm and diameter 18 ram. The pick-up coil with the diameter of 5.2 mm was placed in the middle of the primary one. For the frequencies below 1 kHz a pick-up coil with 3000 turns and 12 nun length was employed, whereas for higher frequencies 8 turn pick-up coil was used. An additional secondary connected in opposition to the pick-up coil was placed in other primary in order to compensate the signal from the pick-up coil when no sample was introduced into this coil. Through the primary coils connected in series, a sinusoidal current from the signal generator was passed. The current (and thus the magnetic field) was measured via a potential difference developed across a 10 fl standard resistor. The maximum magnetic field was about 4000 A / m . For the frequencies below 1 kHz, the voltage signal from the pick-up coil was first fed to an integrator and then stored in a computer. At higher frequencies ( < 100 kHz) the numerical integration was performed.
3. Results and discussion The dependence of the coercive field and the remanent magnetization on the normalized maximum magnetization (Mm/Ms) for the sample F%0Ni20B18Si 2 is shown in fig. 1. The results obtained at four different frequencies (1, 15, 220 and 8000 Hz, respectively) of the magnetizing magnetic field are displayed. We note that both H e and M r exhibit distinctly different dependences on M m in two regions. The first region extends up to M m = 0.5M s and is characterised by a nearly linear increase of M r with M m (the lines drawn in fig. 1 correspond to M r
Table 1 Data relevant to our samples: H c and E are the static coercive field and loss, respectively. The other symbols have their usual meaning Sample
Ms (T)
Tc (K)
E ( J / m 3 cyc)
P3oo (tim) × 108
Hc (A/m)
Fe4oNi4oBlsS2 FesoNi2oBlsS2
0.96 1.31
665 730
15 35
121 122
7.3 11
J. Horvat et al. / Pinning centres and magnetization in FeNiBSi alloys
I
' ' '~ Hc 'Mr . . . . . . . i f: IHz • o ~gv 15Hz • o /~.~% 220Hz • & /~ 8kHz • v //~
A
./" :o~
,;
|
l,
,I/ ,/.7S,>
,,I
.
0.1
.
.
.
.
==u
20
.
.
, .zo
10
0.1
I
0.2
1
teresis curves. In fig. 2 we show the hysteresis curves for the Fe60Ni20B18Si2 alloy at f = 10 Hz with M m / M s as an parameter. In addition to the already noted faster increase of H c and saturating M r the hysteresis loops for M m / g s > 0.5 are also qualitatively different from those for M m / M ~ < 0.5. The group of hysteresis curves at M m > 0.5Ms shows pronounced "tails" protruding to higher f i d d values. This occurs because of approach to saturation and is reflected in their average suscept-
f:lOHz Mrn/ M 1.00 0.84
,r~ ,~ /
P
Fig. 1. Variation of remanent magnetization and coercive field with normalized maximum magnetization for the F%oNi20BlsSi2 alloy.
I
_:
f= 8 kHz n 220Hz ~
Io
Mm/M s
Ms
100
.
.
.
"~
s
//~t_.~L
~
0.22 0.28
-I
-Msl Fig. 2. Hysteresis loops for the Fe~oNi20BzsSi 2 alloy in two regions of maximum magnetization.
02
Mm/M s
Fig. 3. Loss per unit volume per cycle for the F%oNi2oBlsSi2 alloy vs. normalized maximum magnetization at different
frequencies.
ibility ( A M m / A H m ) which is an order of magnitude lower than that derived for M m < 0.5M s. Qualitatively the same variations of M r and H c with Mm have also been observed in the sample Fe4oNi4oB18Si 2. We note that for both samples the regions of approximately linear increase of M r can be described by an empirical relation (Mr~Ms) oc ( Mm/Ms) 1-1. This probably indicates that the nature of the magnetization processes in this range of M m is the same for both samples. Two different types of variation are also observed in the dependence of the loss per unit volume per cycle ( E ) on M m (fig. 3). In the first region ( M m < 0.5Ms) the loss varies almost independently of frequency a s M 1"6 (Steinmetz's exponent), whereas at higher M m values there appears a frequency dependent enhancement of E vs. M m variation. In particular, at 1 Hz Steinmetz's exponent describes rather well the variation of E vs. M m for all values of M m, whereas at higher frequencies for M m >__0.5Ms, E 0c Mmk with k = 2 and 3 for f = 15 and 220 Hz, respectively. Similarly to the exponent m (He oc Mm~), k becomes constant (-- 3) at higher frequencies (fig. 3). The enhanced increase of E with M m at higher M m values is also observed in other amorphous and crystalline soft ferromagnets at power frequencies [1,3,4].
J. Horvat et al, / Pinning centres and magnetization in FeNiBSi alloys
become
pinned
at
stronger
pinning
centres
(C'-N-O).
"0
xl
l V lI
Fig. 4. Schematic drawing of the derivative of the domain wall surface energy vs. domain wall displacement. Broken line indicates the crossover to the strong pinning regime.
The observed variations of M r, H c and E can be qualitatively explained by assuming the existence of two types of domain wall pinning centres. For the sake of clarity we briefly evoke a qualitative picture of the process of magnetization in the ferromagnetic sample [5]. When an external magnetic field ( H ) acts on the ferromagnet its effect on the domain wall is equivalent to a pressure p = 21 s • H , where l~ is the spontaneous magnetization of the domain. As a consequence, the domain wall with the surface energy E w will be shifted from the previous position (A) of the minimum energy to a position in which the restoring force is balanced by the pressure of the magnetic field: (dew/ds)
= 21 s • H.
(1)
This process is illustrated by the shift from point A to B in fig. 4. Further increase of the applied field causes the Barkhausen jumps of the domain wall ( B - B ' ; C - C ' in fig. 4) at certain field values. These values of the magnetic field correspond to the pinning energies of given pinning centres. If the magnetic field is now reduced, the domain wall moves back in a different way ( C ' - D - E - F ) . However, if the magnetic field is increased beyond the point C', the domain wall will jump over the weaker pinning centres and
In the amrophous samples the actual domain wall motion depends, in general, on the magnetic anisotropy, surface irregularities, chemical dusters (if present), local concentration fluctuations and especially on the local strains and defects in the magnetostrictive samples [3]. The magnitudes of the static coercive fields for our samples (table 1) confirm that the stresses associated with defects in magnetostrictive materials are the main source of the domain wall pinning in our alloys [3]. Within the framework of a simple model depicted above (fig. 4) one may conclude that during the magnetization of our samples up to M m < 0.5 M s the domain walls move over the regions occupied with weak pinning centres (path A - B - B ' C - C ' - D - E - F in fig. 4). (Note that the magnetization corresponds to the shift of the domain wall and H corresponds to d E w / d s ). T h e contribution of a small part of the domain wall to magnetization depends on the number of Barkhausen jumps and on their length. In the same way the remanent magnetization (point D in fig. 4), depends on essentially the same parameters. Therefore, in the region of weak pinning centres one would expect an approximate proportionality between M r and Mm, as was observed (fig. 1). In the region Mrn > 0.5Ms, some parts of the domain wall may become pinned on stronger pinning centres and the remaining parts are bending [5,6]. On increasing H this part of the domain wall gets more and more expanded and its E w monotonically increases ( d E w / d s ) does not become zero during this process). On decreasing H the remanent magnetization remains practically the same as upon magnetizing up to 0.53,/, (path O - P - O - M r in fig. 4). This process is accompanied by a much reduced average susceptibility. All these features are indeed observed in our experiments (figs. 1 and 2). Apparently, for a real sample, the hysteresis curve is obtained by suitable averaging over all domain walls. One would expect, however, the overal behavior which is qualitatively similar to that described above. We also observed the frequency dependent increase of H c (fig. 1) for M m > 0.5M,, which can also be explained by the domain wall bending.
J. Horvat et al. / Pinning centres and magnetization in FeNiBSi alloys
During the bending of the domain walls the change of their length with respect to the change of the magnetization increases, hence the volume fraction in which the excess eddy currents occur, increases as well. These currents tend to slow down the motion of the domain walls, hence increase Hc and E, in agreement with the results (figs. 1 and 3). In particular, the enhanced increase of Hc for M m > 0 . S M s at higher frequencies (fig. 1) causes an enhanced increase of loss (fig. 3) although Mr remains practically constant in this range of M m. We note here that the observed variations of H~ with M m w a s qualitatively explained in terms of the interplay between the weak and strong pinning centers (fig. 4). Thus, the variation of E with M m c a n also be explained in the same terms. Moreover, a similar variation of E with M m observed in some other amorphous and crystalline ferromagnets [1,3,4] also seem consistent with our model. The above explanations are based on the existence of two types of domain wall pinning centres with very different energies. In crystalline ferromagnets the energy of domain wall pinning at dislocations is several orders of magnitude larger than that at the point defects [5]. The existence of the point defects and some extended defects in amorphous solids seems obvious, but the knowledge of these defects is less detailed than in the crystalline solids. Therefore, we can only assume that the point defects and the local concentration (or density) fluctuations can act as weak pinning centres. Strong pinning centres can arise as specific extended defects (quasidislocations) and local strain created during the preparation (quenching) procedure. (Note that as-obtained samples of magnetostrictive alloys were studied.) In discussing the variation of H c and E with M m , w e used the frequency as parameter. In order to obtain an insight into the nature of the eddy current loss of our samples, we also measured the frequency dependence (0.1-10 s Hz) of the loss per unit volume per cycle for our samples at three values of g m (0.4, 0.7 and 0.gMs, respectively). In general, the hysteresis loss can be divided into frequency dependent and frequency independent contributions. Since the eddy currents occurring in the vicinity of the domain wall are stronger (ex-
9
cess) than elsewhere, the frequency dependent loss exhibits, in general, two regimes. In the first one, the classical eddy currents (associated with the regions with homogeneous magnetization) dominate, whereas in the other one, the excess eddy currents prevail [8]. The crossover from one to the other regime is expected to depend on the ratio of the sample thickness to the distance between the domain walls [9]. (There is also a transitional region between two regimes.) Since the distance betweeen the domain walls and their shape may change with frequency and M m [10,11], the change of these parameters will lead to a change of the loss regime. The dominant type of eddy current loss shows up in the frequency dependence of E: for classical eddy currents E ~ f is expected, whereas for the excess ones a slower increase with frequency is usually observed [3,8,12]. (We note that for our samples the field penetration depth is several times larger than their thickness over the entire interval of explored frequencies.) The variation of the eddy current loss with frequency for our samples is shown in fig. 5. For the F%0Ni2oB18Si2 alloy loss was measured at M m --- 0 . 4 , 0.7 and 0.gMs, respectively. The loss for M m > 0 . S M s is dominated by the excess eddy currents (E txf 0"45)already above 5 Hz. However, at
I000
Dj~ c~°
iO0
~m° ~ ' : ~ j
//o ° oi
;
f
,b
16o
I
,;3
,o4
io5
f(Hz) Fig. 5. Variation of the eddy current loss with frequency for Fe4oNi4oBlsSi 2 (full symbol) and FetoNiT,oBlsSi 2 (empty symbols) alloys at different maximtun magnetization ( M m / M s = 0.4 (A), 0.7 (O) and 0.9 (r7, m)).
10
J. Horoat et al. / Pinning centres and magnetization in FeNiBSi alloys
M m -- 0.4Ms a considerably higher frequency ('~ 50
Hz) is required in order to obtain the excess eddy currents dominant. This, probably, indicates that for M m > 0.5M~, the volume fraction of the sample occupied by excess eddy currents is larger than that below 0.5Ms. Therefore, the enhanced increase of the loss above 0.5M~ probably arises due to an increase in the volume fraction with the excess eddy currents with respect to the increase of the magnetization during the bending of the domain walls. For the Fe40Ni40BlsSi2 sample (fig. 5), the excess eddy currents prevail at even lower frequencies. This possibly means that the volume fraction under excess eddy currents in this sample is larger than in Fet0Ni20BlsSi 2. This view is also supported by the result of Hc vs. M m measurements for this sample. For the Fe40Ni40BlsSi 2 alloy, the increase of He with M m (M m > 0.6Ms) was faster than that for Fet0Ni20B18Si2. We note that nearly the same crossover value of M m for both samples indicates the possibility of approximately the same fractions of different pinning centres in both samples. We also note (fig. 5) that at the same value of M m / M s (0.9), the coefficient of t h e f0.45 term in the eddy current loss for the sample Fe60Ni20B18Si 2 is about 1.4 times larger than that for Fe40Ni40BlsSi 2. Thus, the ratio of these coefficients is close to the ratio of their respective M~ values (table 1). However, in accordance with our previous findings (fig. 3) at the same value of Mm (--0.9 T) and the same frequency, the eddy current loss for FetoNi20B~sSi 2 alloy is several times smaller than that for Fe40Ni40BlsSi 2. The proposed explanation of E, Hc and M r in FeNiBSi alloys in terms of two types of domain wall pinning centres suggests some further experiments. A suitable annealing (relaxation) treatment should decrease the internal strains in the samples. This should affect some domain wall pinning centres and hence the variations of M r, H~ and E with M m and frequency. Therefore, careful investigations of the annealed specimens can be used in order to check the above hypothesis and may also provide a better insight into the magnetization processes in magnetostrictive Fe-Ni base amorphous alloys in general.
4. Conclusion The results of our systematic investigation of the remanent magnetization and the coercive field variation with the maximum magnetization in amorphous FeNiBSi samples indicate the existence of two types of the domain wall pinning centres with considerably different pinning energies. In the region of larger M m (_> 0.5M~) the influence of stronger pinning centres results in the dominant role of the domain wall bending processes which is reflected through the saturation of the remanent magnetization and a more rapid increase of the coercive field and the hysteresis loss with M m. The excess eddy currents play a dominant role in the frequency dependent loss already at frequencies of a few Hz if the samples are magnetized to the magnetization values at which domain wall bending becomes important (M m >i 0.5M~). In the region of lower M m (weaker pinning) the crossover to the regime of excess eddy currents occurs at higher frequencies about one order of magnitude. Apparently, further improvement of the soft magnetic properties of the amorphous ferromagnets is associated with the ability to reduce the excess eddy currents in these materials. According to our results, this is, among other factors, related also to the achievement of suitably treated alloys in which the bending of domain walls becomes important at as high as possible maximum magnetization (M m ~ M s).
Acknowledgements We thank Dr. H.H. Liebermann for skillful preparation of amorphous ribbons. This work was partially supported by N.B.S.
References [1] K. Foster, F.E. Werner and R.M. Del Vechio, J. Appl. Phys. 53(1982) 8308. [2] H.H. Liebermann and C.D. Graham, IEEE Trans. Magn. MAG-12 (1976) 921. [3] F.E. Luborsky, in: Amorphous Metallic Alloys, ed. F.E. Luborsky (Butterworths, London, 1983) p. 360.
J. Horvat et al. / Pinning centres and magnetization in FeNiBSi alloys
[4] H. Warlimont, in: Rapidly Quenched Metals, eds. S. Steeb and H. Warlimont (North-HoUand, Amsterdam, 1985) p. 1599. [5] S. Chikazumi, The Physics of Ferromagnetism. Magnetic Properties and Practical Applications (Mir, Moscow, 1986) p. 248 (in Russian). [6] D.C. Jiles and D.L. Atherton, J. Magn. Magn. Mat. 61 (1986) 48.
11
[7] M. Kersten, Z. Angew. Phys. 7 (1956) 313. [8] G. Lyudkovsky, P.K. Rastogi and M. Bala, J. Met. (1986) 18. [9] R.H. Pry and C.P. Bean, J. Appl. Phys. 29 (1958) 532. [10] T.R. Hailer and J.J. Kramer, J. Appl. Phys. 41 (1970) 1034. [11] C.D. Graham Jr., J. Appl. Phys. 53 (1982) 8276. [12] G. Bertotti, J. Magn. Magn. Mat. 41 (1984) 253.