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The influence of pinning centres on the magnetization of a Co70.3Fe4.7Si15B10 amorphous alloy
Journal of Magnetism and Magnetic Materials 87 (1990) 339-344 North-Holland
339
THE INFLUENCE OF PINNING CENTRES ON THE MAGNETIZATION O F A C070.3Fe4.7SilsBto A M O R P H O U S ALLOY J. HORVAT 1, E. BABI(~ 2, ~. M A R O H N I ( ~ and H.H. L I E B E R M A N N 3 Institute of Physics of the University, P.O. Box 304, 41000 Zagreb, (Croatia), Yugoslavia
Received 25 October 1989; in revised form 15 January 1990
Accurate measurements of ferromagnetic hysteresis curves of non-magnetostrictiveamorphous Co-Fe-Si-B alloys have been performed. The 0"omparisonof present results with those of magnetostrictive Fe-Ni-B-Si alloys supports the recent suggestion that processes occurring upon magnetizing Fe-Ni-B-Si alloys to the highest maximum magnetizations are associated with magnetostriction. In Co-Fe-Si-B alloys three .types of variation of the remanent magnetization (Mr) and coercive field (He) with maximum magnetization(Mm) can be distinguished at different ranges of Mm. Each of these regions is associatedwith the dominant effect of one type of the domain wall pinning centres only. The magnitude of Hc indicates that the strongest pinning centres in Co-Fe-Si-B alloys are associated with surface irregularities and relaxation effects. The possibility of investigation of the effects of various sample treatments via variations of He and Mr with Mm is briefly discussed.
1. Introduction Soft ferromagnets are the most widely employed magnetic materials in present-day technology. Therefore further improvement of their soft magnetic properties is of particular importance. However, in order to achieve this goal detailed investigation of the processes which occur during the magnetization of materials of potential interest is required. Namely, although the process of magnetization of ferromagnetic materials has been extensively studied (and its general features are rather well understood), some details of this process which are of technological relevance are still not well explained. In our previous reports [1,2] we have presented the results of a systematic investigat:,on of the magnetization process in F e - N i - B - S i amorphous alloys. The dependence of the coercive field, He, I Department of Materials, Electrotechnical Institute, Rade Kon~ar, Ba~tijanovabb, Zagreb, Yugoslavia. 2 Department of Physics, Faculty of Science, P.O. Box 162, Zagreb, Yugoslavia. 3 Metglas Products, AUied-SignalInc., Parsippany, NJ 07054, USA.
remanent magnetization, M r, and loss, E, on the maximum magnetization, Mm, at a fixed frequency were investigated. The v,'u'iation of the eddy current loss, E e, vAth frequency, f , at selected M m was also studied. A parallel analysis of the variation of the above parameters with Mm and f has shown that the process of magnetization in these alloys is essentially determined by at least two types of domain wall pinning centres. There was also an indication that the strongest pinning centres (those corresponding to the largest pinning force) are associated with the localized magnetostrictive strains. In order to verify this conjecture we have performed a similar investigation of H c, M r, E and E e for the non-magnetostrictive amorphous C070.3Fe4.7SilsBlo alloy. The measurements were made using an induction method for as-quenched samples in the form of a long straight ribbon with the dimensions 150 x 2 x 0.025 m m 3 [3]. The experimental set-up and the measurement technique were reported earlier [1,2]. A comparison of the results reported here for a C o - F e - S i - B alloy with the earlier ones for F e - N i - B - S i alloys lends further support to the model employed to understand
0304-8853/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
340
J. Horvat et al. / Pinning centres and magnetization in CoFeSiB alloy
Table 1 Data relevant to our samples: H c and E are dc coercive field and loss respectively. The other symbols have their usual meaning. M r / M s ratio was measured at power frequencies Sample
Ms (T)
Tc (K)
E ( J / m 3 eye.)
P3oo (tim) × 10 s
He (A/m)
Mr/M s
F~0Ni~BlsS2 Fe40Ni40BlsS2 FeroNi 20BiaS/2 FeToNil0BlsSi 2 Fe40Ni40B20 COT0.3Fe4.TSilsBlo
0.48 0.96 1.31 1.47 1.05 0.84
400 665 730 710 669 658
6 15 35 49 22 7
110 121 122 123 120 -
6.5 7.3 11.0 14.8 9.3 2.0
0.4 0.6 0.5 0.6 0.6 0.7
the correlations of M r, He and E with M m and 'also supports the earlier suggestion associating the strong pinning centres with magnetostriction in F e - N i - B - S i alloys. In table 1 the most important parameters for C o - F e - S i - B alloy are compared with those previously reported for F e - N i - B - S i alloys [1,21.
increasing frequency the variation of Mr with M m tends to become the same as that observed at lower M m values ( M m / M s < 0.5), i.e. one obtains a unique variation of M r with M m for 0.1 < M m / M s < 0.75. In the region of the highest maxim u m magnetization ( M m > 0.8Ms) , a tendency to saturation of M r with M m appears at lower fre-
2. Results f :500Hz
The dependence of the remanent magnetization and coercive field on maximum magnetization normalized to the saturation magnetization (Mm/Ms) for the CoT0.3Fe4.TSilsB10 amorphous alloy at four different frequencies (1, 4, 100 and 500 Hz respectively) is shown in fig. 1. At all frequencies one can notice three different types of variation of H c within the explored range of M m ( > 0.1Ms). In the range M m < 0.5M s we find that Hc ~ (Mm/Ms) m with m = 0 . 1 , 0.13 and 0.5 at frequencies 1, 4 and 100 Hz respectively. For 0.5 < Mm/M s < 0.75, He increases faster with/Vim. In this range the exponent m takes on the values m = 0.8, 1.0, 1.3 and 1.7 at f = 1, 4, 100 and 500 Hz respectively. The highest values of m are obtained for M= > 0.75Ms. There m = !.4, 3.0, 3.6 and 3.6 for f = 1, 4, 100 and 500 Hz respectively. Similarly one can identify three types of variation of M r with Mm, in approximately the same ranges of M m described above. For M~ < 0.5Ms, M r increases with Mm as Mr ~ (Mm/Ms)" with n = 0.5, 0.6, 0.9 and 0.9 at f = 1, 4, 100 and 500 Hz respectively. At somewhat higher values of M m ( 0 . 5 < M m / M ~<0.75), n = 1 . 1 at 1 Hz, but on
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J. Horvat et al.
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frequencies and M m the exc,',ss eddy currents dominate the loss [4,1,2]. (We note that the magnetic field penetration depth in the sample is larger than the thickness of the sample at all frequencies used in this study.)
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quencies; however this vanishes at higher frequencies (fig. 1). For the sake of comparison the dependences of Mr and Hc on Mm at a frequency of 1 Hz for the magnetostrictive Fe60Ni20B18Si2 alloy is also shown in fig. 1. Fig. 2 shows the dependence of total loss ( E ) on the maximum magnetization at frequencies 5, 100 and 500 Hz respectively. Here one can distinguish two different regions. For M m _< 0.7Ms, it ;e f~,,~A , h ~ t ~ or l" M
341
/ ~ " '~1.6 ( t h o ~t~inmet7 laW)
at all frequencies. At higher maximum magnetizations a frequency-dependent increase of F with M m occurs. There E increases as E oc ( M m / M s ) p with p = 3.0, 3.9 and 3.9 at f = 5, 100 and 500 Hz. In the ~nset to fig. 2 the frequency dependence of eddy current loss (E~) at Mm = Ms is shown in the frequency range 5-500 Hz. It can be seen that E~ ~fO.41, which implies that in this range of
Comparing the results of the measurements on the non-magnetostrictive C o - F e - S i - B sample with those for magnetostdctive F e - N i - B - S i alloys [1,2] we note a considerable difference in the variation of Mr with M m. In magnetost.-ictive a l l o y s M m increases almost linearly with M m for 0.1 < M m / M s < 0.6 and saturates at higher M m (fig. 1). In the non-magnetostrictive sample for M m > 0.1Ms there are in general three regions with different variation of M r with M m. In contrast to what is observed in magnetostrictive samples a saturation of Mr occurs only at the lowest frequencies and for M m > 0.8)k/s (fig. 1). T h i s s u p ports our earlier claim that a saturation of Mr occurring for M m > 0.6Ms (or even somewhat below that value) at all frequencies in F e - N i - B - S i alloys reflects the relation between the strongest pinning centres and magnetostriction in these alloys. (Note that in the C o - F e - S i - B alloy the tendency of Mr to saturate disappears at higher frequencies.) Further support to this claim is obtained from the comparison of the coercive fields in two cases (table 1): Hc in magnetostdctive alloys is about one order of magnitude larger than that for the non-magnetostrictive sample [5]. Judging by the magnitude of the coercive fie,~d, one may conclude that in the C o - F e - S i - B alloy the strongest pinning centres could be associated vAth the surface irregularities and with relaxation effects (which OCCL,r because of the local structural rearrangements) [5]. All the phenomena described above can be explained within the framework of the same model employed in our previous papers [1,2] assure'rag that there are more than two types of pinning centres (two types of pinning centres were sufficient in order to explain the results for F e - N i - B Si alloys) with differing pm~±ug forces. According
342
J. Horvat et al. / Pinning centres and magnetization in CoFeSiB alloy
to that model [1,2], during the process of magnetization in very small applied fields, the domain walls will move over regions with the weakest pinning centres [6]. If, however, in the course of this process the domain wall encounters a stronger pinning center, it will not move any further (in such small fields) and hence would not contribute to a change of magnetization. In higher magnetic fields (when the sample is magnetized to higher Mm) parts of the domain walls become pinned at stronger pinning centres. Thereafter two types of processes (depending on the ratio between the surface energy of the domain wall (Ew) and the pinning energy, the distribution of the pinning centres and on the ratio of the distance between the neighbouring pinning centres with respect to the distance between the domain walls [7]) may OCCur.
If Ew is much smaller than the pinning energy of the stronger pinning centres, free parts of the domain wall (those which are not anchored at the stronger pinning centres) will bulge under the influence of the applied field. Because of this the remanent magnetization will tend to saturate with respect to M m, whereas H c will exhibit an enhanced increase with M m as explained earlier [1,2]. If, in the course of that process, the applied field achieves an intensity which is sufficient to release the pinned parts of the domain wall, a Barkhausen jump will occur and the remanent magnetization will consequently change. In the same way, if the distance between the neighbouring strong pinning centres (at which the domain wall is simultaneously anchored) is small compared with the size of the region in which the movement of a domain wall is dominated by this particular type of pinning centres, the influence of bulging of the domain walls on M r and H c curve will be rather unimportant. (The domain wall will free itself from the strong pinning centres when the radius of curvature of the expanded part of the domain wall reaches half of that distance [6].) If, however, E w is much larger than the pinning energy of the stronger pinning centres, the domain wall will perform a Barkhausen jump when the applied field reaches the value sufficient to release the anchored part of the wall. Before that, the bulging of the remaining part of the domain wall
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will not occur, hence the whole domain wall will not be active in the process of magnetization until it gets released from the strong pinning center. In the course of such release (Barkhausen jump) Mr will change with M m. The rate of increase of Mr with M m will depend on the ratio of the average distance between two neighbouring pinning centres between which the Barkhausen jump occurs (on which the domain wall was not simultaneously pinned) in respect to the average size of the region in which the movement of this domain wall is dominated by given type of pinning centres. Adapting the model introduced earlier [6,1,2] to the present case, the above ratio rouglfly corresponds to the ratio of lengths O M r and OM~' in fig. 3. The number of zero-points of the curve of the derivative of the domain wall surface energy (Ew) in respect to a position of the domain wall (s) should be equal to twice the number of pinning centres over which some part of the domain wall moves during the process of magnetization. Thereafter we denote the number of strongest pinning centres in the studied range of n m in the volume of sample by r/, and the ratio between the average volume of the region within which the movement of the domain walls occurs (for a specified M~) and total volume of the sample by 8. We first consider the case when ,1/8 is such that the number of zero-points of the curve dEw/ds versus s for the region in which the change of magnetization is dominated by the investigated pinning centres is small (rl/8--~'). In the course of the process of magnetization the magnitude of M r will depend on the number
J. Horvat et al. / Pinning centres and magnetization in CoFeSiB alloy
of Barkhausen jumps and their length (for example point M r during j u m p A - B in fig. 3). The value of M m will depend, in addition, on the number and lengths of the same Barkhausen jumps, also on the part B - E of the curve dEw/ds versus s in fig. 3. Thus the same value of Mr can be obtained for different (larger) values of M m (i.e. for different values of s). This is reflected as a saturation of M r versus M m, for M m larger than M r but smaller than the value of M m corresponding to point E in fig. 3. However, since many domain walls participate in the process of magnetization of the sample, and the maxima in their corresponding dEw/ds versus s curves, although similar, will have somewhat different magnitudes, some of them will perform Barkhausen jumps ( E - F in fig. 3) which results in a change of M r ( M " in fig. 3). This will manifest itself in the total magnetization of the sample as an slow increase of M r versus M m. The above model accounts well for the results on the C o - F e - S i - B sample (fig. 1) for M m < 0.5M~. The observed shape of the hysteresis curves (F-types) in the same range of M m also supports the above explanation. Indeed, because of the simultaneous influence of stronger and weaker pinning centres, sm',dler maxima may be superposed on the large ones as in fig. 3, hence smaller Barkhausen jumps ( C - D in fig. 3) can occur. An average over all domain walls then results in an inclined hysteresis curve as was observed in our measurements. The essential difference between the process described above and the process of bulging of the domain walls [1,2] is reflected in the enhanced effects of the excess eddy currents on the change of magnetization with time in the latter case. (This occurs because of the increase of the surface area of the domain wall and because of enhanced increase of dEw/ds with increase of M m during clc~rrtnlrt tvnll h n l o i n o $ l ~ l a r t h e r m o r e ~ Jr! the process described above, M r of the sample will not saturate completely on increasing M m because the heights of the peaks in d Ew/ds in disordered material are not exactly the same even for the same type of pinning centres. A roughly linear variation of M r with M m will result for rl/6 >> ~'. In that case the interval B - E in fig. 3 is negligible with respect to the average
343
distance to which the domain wall has to be removed during the process of magnetization in certain region of Mm, hence these effects will bardly affect the variation of Mr with M m. Because of this both M r and M m depend in the same way on the (same) Barkhausen jumps and their lengths, thus an approximately linear variation of M.. with M m is expected [1,2]. This description agrees well with the observed variation of Mr with M m for M m < 0 . 6 M s i n magnetostrictive F e - N i B-Si samples (fig. 1). When a magnetic field of sufficiently high frequency and amplitude is applied to the sample, the domain wall movement will lag behind the applied field. Because of this the domain wall will not move over the "quasi-static" d Ew/ds versus s curve in fig. 3. Instead, its movement may correspond for example to a curve E - G in fig. 3. This will cause an increase of M r (Mr" rather than M r) at fixed Mm, and an enhanced increase of Mr with M m at elevated frequencies. The observed enhancement of the rate of increase of M r with M m for M m < 0.5 M s as well as the general increase of Mr for all values of M m a t elevated frequencies (fig. 1) can be explained in the above manner. The behaviour of the coercive field (fig. 1) and loss (fig. 2) with M m for the C o - F e - S i - B sample are qualitatively the same as those observed in F e - N i - B - S i samples, hence their explanations in terms of our model have been given in previous papers [1,2]. We note that similar variations of the parameters discussed above with Mm have been observed earlier both for amorphous and crystalline ferromagnets [8-10] but no parallel analysis of the dependences of M r, He and E on Mm/M s has been performed. There were also experiments in which bulging of the domain walls was observed [11-13]. We also note that the hysteresis curves for Y I G samples [14] were explained in terms of the model concerning the domain wall displacement and bulging mechanisms [15]. This probably indicates that in all ferromagnetic materiMs the influence of different pinning centres on the process of magnetization [2] can be studied by analyzing the variations of Mr and H c with M m. In that manner one may obtain information as to which type of pinning centre dominates in a specified
344
J. Horvat et al. / Pinning centres and magnetization in CoFeSiB alloy
range of M m, what influence it has on the process of magnetization (E, Mr, He) and how different treatments of the sample affect particular types of pinning centre. This would probably be useful for further improvement of the properties of soft magnetic materials. Simultaneous experiments which enable one to identify which type(s) of pinning centres cause given variations of Mr and Hc with M m are required. Some of such possible experiments are now in progress in our laboratory.
4. Conclusion Parallel analysis of the variations of M r, H c and E with Mm, as well as the dependence of E e on frequency for a non-magnetostrictive C o - F e Si-B sample lend further support to our earlier claim [1,2] that pinning centres associated with magnetostrietion are responsible for the saturation of Mr and the enhanced increase of/arc and E at elevated M m in Fe--Ni-B-Si aUoys. It also appeared that the model introduced earlier for magnetostrictive alloys [1,2] can be used for the explanation of the variations observed in a non-magnetostrictive alloy. Comparing our experimental results with those for crystalline ferromagnets [8,10,11] it seems that the same model can also be applied to these materials. This indicates a possible use of the method for investigation of particular pinning centres, of the range of M m in which they are effective, of their influence on the process of magnetization and of the effects of various treatments of the samples on particular pinning centres. Also, there is a possibility of quantitative determination of the effects of particular type of pinning centres on the increase of loss, At r and H c which may indicate what type of sample treatment is required in order to improve its soft magnetic properties. For instance if in a given material some type of pinning centres is absent (for example those associated with magnetostriction) then the effect of weaker types of pinning centres will
show up in the range of higher maximum magnetization. However, in order to obtain a more complete picture of the processes occurring during the magnetization of a sample, the study of the effects of averaging of the processes proposed by our model over all domain walls on the variation of the investigated parameters would be desirable.
Acknowledgement This work was supported by N.B.S. via funds made available through Yugoslavia-USA Scientific Cooperation.
References [11 J. Horvat, Z. Marohni6 and E. Babir, J. Magn. Magn. Mat. 82 (1989) 5.
[21 J. Horvat, E. Babid, ~. Marohni6 and H.H. Liebermann, IEEE Trans. Magn. (submitted).
[31 H.H. Liebermann, Mater. Sci. Eng. 43 (1980) 203. [4] G. Bertotti, J. Magn. Magn. Mat. 41 (1984) 253. [51 H. KronmiiUer, J. Magn. Magn. Mat. 24 (1981) 159. [61 S. Chikazumi, The Physics of Ferromagnetism. Magnetic Properties and Practical Applications (Mir, Moscow, 1987) p. 248 [in Russian]. [71 D.C. Jiles and D.L. Atherton, J. Magn. Magn. Mat. 61 (1986) 48. [81 K. Fostec, F.E. Werner and R.M. Del Vechio, J. Appl. Phys. 53 (1982) 8308. [91 F.E. Luborsky, in: Amorphous Metallic Alloys, ed. F.E. Luborsky (Butterworths, London, 1983) p. 366. [101 R.M. Bozorth, Ferromagnetism (Van Nostrand, Toronto, New York, London, 1953) p. 500. [111 T. Nozawa, T. Yamamoto, Y. Matsuo and Y. Ohya, IEEE Trans. Magn. MAG-14 (1978) 252. [121 D.J. Buttle, J.P. Jakubovics, G.A.D. Briggs and C.B. Scruby, Phil. Mag. A 55 (1987) 735. [131 D.J. Craik and R.S. Tebble, Ferromagnetism and Ferromagnetic Domains (North-Holland, Amsterdam, and John Wiley, New York, 1965) p. !!2. [14] A. Globus and M. Guyot, Phys. Stat. Sol. (b) 52 (1972) 427. [151 A. Globus, P. Duplex and M. Guyot, IEEE Trans. Magn. MAG-7 (1971) 017.
339
THE INFLUENCE OF PINNING CENTRES ON THE MAGNETIZATION O F A C070.3Fe4.7SilsBto A M O R P H O U S ALLOY J. HORVAT 1, E. BABI(~ 2, ~. M A R O H N I ( ~ and H.H. L I E B E R M A N N 3 Institute of Physics of the University, P.O. Box 304, 41000 Zagreb, (Croatia), Yugoslavia
Received 25 October 1989; in revised form 15 January 1990
Accurate measurements of ferromagnetic hysteresis curves of non-magnetostrictiveamorphous Co-Fe-Si-B alloys have been performed. The 0"omparisonof present results with those of magnetostrictive Fe-Ni-B-Si alloys supports the recent suggestion that processes occurring upon magnetizing Fe-Ni-B-Si alloys to the highest maximum magnetizations are associated with magnetostriction. In Co-Fe-Si-B alloys three .types of variation of the remanent magnetization (Mr) and coercive field (He) with maximum magnetization(Mm) can be distinguished at different ranges of Mm. Each of these regions is associatedwith the dominant effect of one type of the domain wall pinning centres only. The magnitude of Hc indicates that the strongest pinning centres in Co-Fe-Si-B alloys are associated with surface irregularities and relaxation effects. The possibility of investigation of the effects of various sample treatments via variations of He and Mr with Mm is briefly discussed.
1. Introduction Soft ferromagnets are the most widely employed magnetic materials in present-day technology. Therefore further improvement of their soft magnetic properties is of particular importance. However, in order to achieve this goal detailed investigation of the processes which occur during the magnetization of materials of potential interest is required. Namely, although the process of magnetization of ferromagnetic materials has been extensively studied (and its general features are rather well understood), some details of this process which are of technological relevance are still not well explained. In our previous reports [1,2] we have presented the results of a systematic investigat:,on of the magnetization process in F e - N i - B - S i amorphous alloys. The dependence of the coercive field, He, I Department of Materials, Electrotechnical Institute, Rade Kon~ar, Ba~tijanovabb, Zagreb, Yugoslavia. 2 Department of Physics, Faculty of Science, P.O. Box 162, Zagreb, Yugoslavia. 3 Metglas Products, AUied-SignalInc., Parsippany, NJ 07054, USA.
remanent magnetization, M r, and loss, E, on the maximum magnetization, Mm, at a fixed frequency were investigated. The v,'u'iation of the eddy current loss, E e, vAth frequency, f , at selected M m was also studied. A parallel analysis of the variation of the above parameters with Mm and f has shown that the process of magnetization in these alloys is essentially determined by at least two types of domain wall pinning centres. There was also an indication that the strongest pinning centres (those corresponding to the largest pinning force) are associated with the localized magnetostrictive strains. In order to verify this conjecture we have performed a similar investigation of H c, M r, E and E e for the non-magnetostrictive amorphous C070.3Fe4.7SilsBlo alloy. The measurements were made using an induction method for as-quenched samples in the form of a long straight ribbon with the dimensions 150 x 2 x 0.025 m m 3 [3]. The experimental set-up and the measurement technique were reported earlier [1,2]. A comparison of the results reported here for a C o - F e - S i - B alloy with the earlier ones for F e - N i - B - S i alloys lends further support to the model employed to understand
0304-8853/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
340
J. Horvat et al. / Pinning centres and magnetization in CoFeSiB alloy
Table 1 Data relevant to our samples: H c and E are dc coercive field and loss respectively. The other symbols have their usual meaning. M r / M s ratio was measured at power frequencies Sample
Ms (T)
Tc (K)
E ( J / m 3 eye.)
P3oo (tim) × 10 s
He (A/m)
Mr/M s
F~0Ni~BlsS2 Fe40Ni40BlsS2 FeroNi 20BiaS/2 FeToNil0BlsSi 2 Fe40Ni40B20 COT0.3Fe4.TSilsBlo
0.48 0.96 1.31 1.47 1.05 0.84
400 665 730 710 669 658
6 15 35 49 22 7
110 121 122 123 120 -
6.5 7.3 11.0 14.8 9.3 2.0
0.4 0.6 0.5 0.6 0.6 0.7
the correlations of M r, He and E with M m and 'also supports the earlier suggestion associating the strong pinning centres with magnetostriction in F e - N i - B - S i alloys. In table 1 the most important parameters for C o - F e - S i - B alloy are compared with those previously reported for F e - N i - B - S i alloys [1,21.
increasing frequency the variation of Mr with M m tends to become the same as that observed at lower M m values ( M m / M s < 0.5), i.e. one obtains a unique variation of M r with M m for 0.1 < M m / M s < 0.75. In the region of the highest maxim u m magnetization ( M m > 0.8Ms) , a tendency to saturation of M r with M m appears at lower fre-
2. Results f :500Hz
The dependence of the remanent magnetization and coercive field on maximum magnetization normalized to the saturation magnetization (Mm/Ms) for the CoT0.3Fe4.TSilsB10 amorphous alloy at four different frequencies (1, 4, 100 and 500 Hz respectively) is shown in fig. 1. At all frequencies one can notice three different types of variation of H c within the explored range of M m ( > 0.1Ms). In the range M m < 0.5M s we find that Hc ~ (Mm/Ms) m with m = 0 . 1 , 0.13 and 0.5 at frequencies 1, 4 and 100 Hz respectively. For 0.5 < Mm/M s < 0.75, He increases faster with/Vim. In this range the exponent m takes on the values m = 0.8, 1.0, 1.3 and 1.7 at f = 1, 4, 100 and 500 Hz respectively. The highest values of m are obtained for M= > 0.75Ms. There m = !.4, 3.0, 3.6 and 3.6 for f = 1, 4, 100 and 500 Hz respectively. Similarly one can identify three types of variation of M r with Mm, in approximately the same ranges of M m described above. For M~ < 0.5Ms, M r increases with Mm as Mr ~ (Mm/Ms)" with n = 0.5, 0.6, 0.9 and 0.9 at f = 1, 4, 100 and 500 Hz respectively. At somewhat higher values of M m ( 0 . 5 < M m / M ~<0.75), n = 1 . 1 at 1 Hz, but on
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J. Horvat et al.
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Pinning centres and magnetization in CoFeSiB alloy
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frequencies and M m the exc,',ss eddy currents dominate the loss [4,1,2]. (We note that the magnetic field penetration depth in the sample is larger than the thickness of the sample at all frequencies used in this study.)
100 200 / I
m
//
•
/
IOOHz A
/
10
/
"
;
/
-
o~
SA~ /
"' 2
Q
1
I
0.1
i
0.2
I
i
i
I
t
I
Mm/Ms
Fig. 2. Loss per unit volume per cycle for the CoT0.3Fe4.vSilsB10 alloy vs. normalized maximum magnetization at different frequencies. Inset: Eddy current loss vs. frequency at M m = M s for the same sample.
quencies; however this vanishes at higher frequencies (fig. 1). For the sake of comparison the dependences of Mr and Hc on Mm at a frequency of 1 Hz for the magnetostrictive Fe60Ni20B18Si2 alloy is also shown in fig. 1. Fig. 2 shows the dependence of total loss ( E ) on the maximum magnetization at frequencies 5, 100 and 500 Hz respectively. Here one can distinguish two different regions. For M m _< 0.7Ms, it ;e f~,,~A , h ~ t ~ or l" M
341
/ ~ " '~1.6 ( t h o ~t~inmet7 laW)
at all frequencies. At higher maximum magnetizations a frequency-dependent increase of F with M m occurs. There E increases as E oc ( M m / M s ) p with p = 3.0, 3.9 and 3.9 at f = 5, 100 and 500 Hz. In the ~nset to fig. 2 the frequency dependence of eddy current loss (E~) at Mm = Ms is shown in the frequency range 5-500 Hz. It can be seen that E~ ~fO.41, which implies that in this range of
Comparing the results of the measurements on the non-magnetostrictive C o - F e - S i - B sample with those for magnetostdctive F e - N i - B - S i alloys [1,2] we note a considerable difference in the variation of Mr with M m. In magnetost.-ictive a l l o y s M m increases almost linearly with M m for 0.1 < M m / M s < 0.6 and saturates at higher M m (fig. 1). In the non-magnetostrictive sample for M m > 0.1Ms there are in general three regions with different variation of M r with M m. In contrast to what is observed in magnetostrictive samples a saturation of Mr occurs only at the lowest frequencies and for M m > 0.8)k/s (fig. 1). T h i s s u p ports our earlier claim that a saturation of Mr occurring for M m > 0.6Ms (or even somewhat below that value) at all frequencies in F e - N i - B - S i alloys reflects the relation between the strongest pinning centres and magnetostriction in these alloys. (Note that in the C o - F e - S i - B alloy the tendency of Mr to saturate disappears at higher frequencies.) Further support to this claim is obtained from the comparison of the coercive fields in two cases (table 1): Hc in magnetostdctive alloys is about one order of magnitude larger than that for the non-magnetostrictive sample [5]. Judging by the magnitude of the coercive fie,~d, one may conclude that in the C o - F e - S i - B alloy the strongest pinning centres could be associated vAth the surface irregularities and with relaxation effects (which OCCL,r because of the local structural rearrangements) [5]. All the phenomena described above can be explained within the framework of the same model employed in our previous papers [1,2] assure'rag that there are more than two types of pinning centres (two types of pinning centres were sufficient in order to explain the results for F e - N i - B Si alloys) with differing pm~±ug forces. According
342
J. Horvat et al. / Pinning centres and magnetization in CoFeSiB alloy
to that model [1,2], during the process of magnetization in very small applied fields, the domain walls will move over regions with the weakest pinning centres [6]. If, however, in the course of this process the domain wall encounters a stronger pinning center, it will not move any further (in such small fields) and hence would not contribute to a change of magnetization. In higher magnetic fields (when the sample is magnetized to higher Mm) parts of the domain walls become pinned at stronger pinning centres. Thereafter two types of processes (depending on the ratio between the surface energy of the domain wall (Ew) and the pinning energy, the distribution of the pinning centres and on the ratio of the distance between the neighbouring pinning centres with respect to the distance between the domain walls [7]) may OCCur.
If Ew is much smaller than the pinning energy of the stronger pinning centres, free parts of the domain wall (those which are not anchored at the stronger pinning centres) will bulge under the influence of the applied field. Because of this the remanent magnetization will tend to saturate with respect to M m, whereas H c will exhibit an enhanced increase with M m as explained earlier [1,2]. If, in the course of that process, the applied field achieves an intensity which is sufficient to release the pinned parts of the domain wall, a Barkhausen jump will occur and the remanent magnetization will consequently change. In the same way, if the distance between the neighbouring strong pinning centres (at which the domain wall is simultaneously anchored) is small compared with the size of the region in which the movement of a domain wall is dominated by this particular type of pinning centres, the influence of bulging of the domain walls on M r and H c curve will be rather unimportant. (The domain wall will free itself from the strong pinning centres when the radius of curvature of the expanded part of the domain wall reaches half of that distance [6].) If, however, E w is much larger than the pinning energy of the stronger pinning centres, the domain wall will perform a Barkhausen jump when the applied field reaches the value sufficient to release the anchored part of the wall. Before that, the bulging of the remaining part of the domain wall
~'
.A
_
BC 0
.E
_-_
F/
oI Fig. 3. Schematic drawing of variation of the derivative of the domain wall surface energy with domain wall displacement.
will not occur, hence the whole domain wall will not be active in the process of magnetization until it gets released from the strong pinning center. In the course of such release (Barkhausen jump) Mr will change with M m. The rate of increase of Mr with M m will depend on the ratio of the average distance between two neighbouring pinning centres between which the Barkhausen jump occurs (on which the domain wall was not simultaneously pinned) in respect to the average size of the region in which the movement of this domain wall is dominated by given type of pinning centres. Adapting the model introduced earlier [6,1,2] to the present case, the above ratio rouglfly corresponds to the ratio of lengths O M r and OM~' in fig. 3. The number of zero-points of the curve of the derivative of the domain wall surface energy (Ew) in respect to a position of the domain wall (s) should be equal to twice the number of pinning centres over which some part of the domain wall moves during the process of magnetization. Thereafter we denote the number of strongest pinning centres in the studied range of n m in the volume of sample by r/, and the ratio between the average volume of the region within which the movement of the domain walls occurs (for a specified M~) and total volume of the sample by 8. We first consider the case when ,1/8 is such that the number of zero-points of the curve dEw/ds versus s for the region in which the change of magnetization is dominated by the investigated pinning centres is small (rl/8--~'). In the course of the process of magnetization the magnitude of M r will depend on the number
J. Horvat et al. / Pinning centres and magnetization in CoFeSiB alloy
of Barkhausen jumps and their length (for example point M r during j u m p A - B in fig. 3). The value of M m will depend, in addition, on the number and lengths of the same Barkhausen jumps, also on the part B - E of the curve dEw/ds versus s in fig. 3. Thus the same value of Mr can be obtained for different (larger) values of M m (i.e. for different values of s). This is reflected as a saturation of M r versus M m, for M m larger than M r but smaller than the value of M m corresponding to point E in fig. 3. However, since many domain walls participate in the process of magnetization of the sample, and the maxima in their corresponding dEw/ds versus s curves, although similar, will have somewhat different magnitudes, some of them will perform Barkhausen jumps ( E - F in fig. 3) which results in a change of M r ( M " in fig. 3). This will manifest itself in the total magnetization of the sample as an slow increase of M r versus M m. The above model accounts well for the results on the C o - F e - S i - B sample (fig. 1) for M m < 0.5M~. The observed shape of the hysteresis curves (F-types) in the same range of M m also supports the above explanation. Indeed, because of the simultaneous influence of stronger and weaker pinning centres, sm',dler maxima may be superposed on the large ones as in fig. 3, hence smaller Barkhausen jumps ( C - D in fig. 3) can occur. An average over all domain walls then results in an inclined hysteresis curve as was observed in our measurements. The essential difference between the process described above and the process of bulging of the domain walls [1,2] is reflected in the enhanced effects of the excess eddy currents on the change of magnetization with time in the latter case. (This occurs because of the increase of the surface area of the domain wall and because of enhanced increase of dEw/ds with increase of M m during clc~rrtnlrt tvnll h n l o i n o $ l ~ l a r t h e r m o r e ~ Jr! the process described above, M r of the sample will not saturate completely on increasing M m because the heights of the peaks in d Ew/ds in disordered material are not exactly the same even for the same type of pinning centres. A roughly linear variation of M r with M m will result for rl/6 >> ~'. In that case the interval B - E in fig. 3 is negligible with respect to the average
343
distance to which the domain wall has to be removed during the process of magnetization in certain region of Mm, hence these effects will bardly affect the variation of Mr with M m. Because of this both M r and M m depend in the same way on the (same) Barkhausen jumps and their lengths, thus an approximately linear variation of M.. with M m is expected [1,2]. This description agrees well with the observed variation of Mr with M m for M m < 0 . 6 M s i n magnetostrictive F e - N i B-Si samples (fig. 1). When a magnetic field of sufficiently high frequency and amplitude is applied to the sample, the domain wall movement will lag behind the applied field. Because of this the domain wall will not move over the "quasi-static" d Ew/ds versus s curve in fig. 3. Instead, its movement may correspond for example to a curve E - G in fig. 3. This will cause an increase of M r (Mr" rather than M r) at fixed Mm, and an enhanced increase of Mr with M m at elevated frequencies. The observed enhancement of the rate of increase of M r with M m for M m < 0.5 M s as well as the general increase of Mr for all values of M m a t elevated frequencies (fig. 1) can be explained in the above manner. The behaviour of the coercive field (fig. 1) and loss (fig. 2) with M m for the C o - F e - S i - B sample are qualitatively the same as those observed in F e - N i - B - S i samples, hence their explanations in terms of our model have been given in previous papers [1,2]. We note that similar variations of the parameters discussed above with Mm have been observed earlier both for amorphous and crystalline ferromagnets [8-10] but no parallel analysis of the dependences of M r, He and E on Mm/M s has been performed. There were also experiments in which bulging of the domain walls was observed [11-13]. We also note that the hysteresis curves for Y I G samples [14] were explained in terms of the model concerning the domain wall displacement and bulging mechanisms [15]. This probably indicates that in all ferromagnetic materiMs the influence of different pinning centres on the process of magnetization [2] can be studied by analyzing the variations of Mr and H c with M m. In that manner one may obtain information as to which type of pinning centre dominates in a specified
344
J. Horvat et al. / Pinning centres and magnetization in CoFeSiB alloy
range of M m, what influence it has on the process of magnetization (E, Mr, He) and how different treatments of the sample affect particular types of pinning centre. This would probably be useful for further improvement of the properties of soft magnetic materials. Simultaneous experiments which enable one to identify which type(s) of pinning centres cause given variations of Mr and Hc with M m are required. Some of such possible experiments are now in progress in our laboratory.
4. Conclusion Parallel analysis of the variations of M r, H c and E with Mm, as well as the dependence of E e on frequency for a non-magnetostrictive C o - F e Si-B sample lend further support to our earlier claim [1,2] that pinning centres associated with magnetostrietion are responsible for the saturation of Mr and the enhanced increase of/arc and E at elevated M m in Fe--Ni-B-Si aUoys. It also appeared that the model introduced earlier for magnetostrictive alloys [1,2] can be used for the explanation of the variations observed in a non-magnetostrictive alloy. Comparing our experimental results with those for crystalline ferromagnets [8,10,11] it seems that the same model can also be applied to these materials. This indicates a possible use of the method for investigation of particular pinning centres, of the range of M m in which they are effective, of their influence on the process of magnetization and of the effects of various treatments of the samples on particular pinning centres. Also, there is a possibility of quantitative determination of the effects of particular type of pinning centres on the increase of loss, At r and H c which may indicate what type of sample treatment is required in order to improve its soft magnetic properties. For instance if in a given material some type of pinning centres is absent (for example those associated with magnetostriction) then the effect of weaker types of pinning centres will
show up in the range of higher maximum magnetization. However, in order to obtain a more complete picture of the processes occurring during the magnetization of a sample, the study of the effects of averaging of the processes proposed by our model over all domain walls on the variation of the investigated parameters would be desirable.
Acknowledgement This work was supported by N.B.S. via funds made available through Yugoslavia-USA Scientific Cooperation.
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