The magnetic hysteresis of Fe77.5B22.5 amorphous ribbon has been studied by the induction method. The results for coercive field (Hc), maximum magnetization (Mm) and remanent magnetization (Mr) are explained by the twofold domain structure of amorphous alloys in form of ribbons. The analysis of the measurements shows that the inner domains are responsible for the magnetization up to about 65% saturation magnetization (Ms) and that the interaction between two domain structures plays an important role in enhanced increase of Hc on Mm > 0.5 Ms. The frequency dependence of parameters of the hysteresis curve is briefly discussed.Indukcijskom metodom mjerene su krivulje magnetizacije amorfne vrpce Fe77.5B22.5. Ovisnosti koercitivnog polja (Hc ), maksimalne magnetizacije (Mm ) i remanentne magnetizacije (Mr) mogu se objasniti dvostrukom domenskom strukturom karakterističnom za ovakve uzorke. Analiza mjerenja pokazuje da su unutrašnje domene odgovorne za magnetizaciju do 65% magnetizacije zasićenja (Ms) te da interakcija između dviju domenskih struktura igra važnu ulogu pri ubrzanom rastu Hc pri Mm > 0.5 Ms. Razmatrana je i ovisnost parametara krivulje histereze o frekvenciji

Kolanović, Marko

Pajić, Damir

English

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ISSN1330–0008CODENFIZAE4THE INFLUENCE OF DOMAIN STRUCTURE ON THE VARIATION OFCOERCIVE FIELD AND MAXIMUM MAGNETIZATION OFFe77.5B22.5AMORPHOUS ALLOYMARKO KOLANOVIĆ and DAMIR PAJIĆDepartment of Physics, Faculty of Science, P.O.Box 162, University of Zagreb,10001 Zagreb, CroatiaReceived 15 July 1996UDC 539.213PACS 75.50.Kj, 75.60.-d, 75.60.ChThe magnetic hysteresis of Fe77.5B22.5 amorphous ribbon has been studied by the in-duction method. The results for coercive field (Hc), maximum magnetization (Mm)and remanent magnetization (Mr) are explained by the twofold domain structure ofamorphous alloys in form of ribbons. The analysis of the measurements shows thatthe inner domains are responsible for the magnetization up to about 65% saturationmagnetization (Ms) and that the interaction between two domain structures playsan important role in enhanced increase of Hc on Mm > 0.5 Ms. The frequencydependence of parameters of the hysteresis curve is briefly discussed.1. IntroductionThe discovery of the soft magnetism in amorphous alloys allowed considerableimprovement of some devices that use soft magnetic materials. Since in present-daytechnology the most widely employed magnetic materials are soft ferromagnets, fur-ther improvement of their properties is of particular importance. In order to obtaininformation that will help the development of soft magnetic materials, a detailedstudy of the processes associated with the magnetization in such materials is re-quired. Although these processes have been extensively studied and their generalfeatures are rather well understood, some details are still not well explained.FIZIKA A 5 (1996) 3, 133–140 133kolanović and pajić: the influence of domain structure . . .In order to analyse and explain the variation of parameters of magnetic hys-teresis curve during the process of magnetization of Fe77.5B22.5 amorphous mag-netostrictive alloy, systematic measurements of the hysteresis curves have beenperformed at different frequencies and driving field amplitudes.It is known [1] that amorphous alloys in the form of long straight ribbon exhibittwo different domain structures: a narrow one in spaced surface domain structureswith irregular maze domain patterns, partly similar to fingerprints (hereafter do-mains A), and several orders of magnitude wider, long inner domains which areresponsible for magnetization up to 0.7 Ms and which are parallel at a small angleto the ribbon axis. This kind of domain structure was directly observed by use ofthe magnetotactic bacteria method [2] (domains A) and Kerr–effect laser–scanningtechnique [3]. All measurements of the hysteresis loops (which yielded parametersHc, Mr, Mm) have been performed on a sample of amorphous alloy Fe77.5B22.5. Thesample was produced by melt-spinning [4] in an inert atmosphere and was in formof a long straight ribbon. According to the results of Refs. 1 and 2, for dimensionsof our sample, width of domain B is of the order of a few tenths of a millimetreand width of domain A of order of a micrometer.The aim of this work is to explain the variation of parameters of hysteresiscurves, in particular ofMm andHc, assuming the existence of two domain structuresand their interaction.2. ExperimentalMeasurements of the hysteresis curves were made by an induction method [5].The experimental set–up consisted of two mutually perpendicular coils, 180 mmlong and 18 mm in diameter, connected in series. Triangular current from thesignal generator was passed through the coils. The pick-up coil with 3000 turns, 12mm long and 5.2 mm in diameter, was placed in the middle of the primary coil. Anadditional secondary coil, connected in opposition to the pick–up coil, was placedin the second primary coil in order to compensate the signal from the pick–up coilwhen no sample was placed in it.The induced voltage across a standard resistor is proportional to the time deriva-tive of magnetization of our sample, and the strength of the magnetic field is pro-portional to the current passing through the primary coils. Experiment yieldedthe dM(H)/dt dependence that was stored in a computer for further analysis.Some of measurements (at large drive field amplitudes) have been performed witha vibrating–sample magnetometer (VSM).3. Results and discussionThe variation of maximum magnetization with driving field amplitude at thefrequency of 6 Hz is shown in Fig. 1.Driving field H is a parameter whose influence on the system is determined bythe amplitude H0 and frequency f , while Mm is a parameter that represents finaldomain configuration, as the system’s response to the driving field. After rapid134 FIZIKA A 5 (1996) 3, 133–140kolanović and pajić: the influence of domain structure . . .increase up to a driving field amplitude of 70 A/m, increase of Mm slows down andtends to saturate to a value of approximately 1 T. Measurements of magnetizationat saturation with VSM at driving field amplitude of 0.1 T yielded Ms = 1.45 T.Experimental results show the existence of two regimes in the process of magneti-zation. At small driving fields, magnetization is caused by the change of volume ofdomains B. Relatively small driving fields are needed to set in motion the walls ofthe domains B, and maximum magnetization achieved by changing volume domainstructure of the bulk is about 65% Ms. This is in agreement with the estimationof Ref. 3 about the contribution of domains B in volume of the sample. It shouldbe noted that regions of influence of domains A and B on sample magnetizationare not clearly separated. In the transition region between two regimes, increase ofmagnetization is slowed down by bulging of domain B region to the surface, anni-hilation of domain walls in region of domains B and rotations of magnetization ofdomains B in the direction of the driving field (parallel to the ribbon axis). On thebasis of a model for magnetization of amorphous ribbons carrying DC current [6],we find that magnetization of domains B is at an angle δ ≈ 6o to the ribbon axis.Fig. 1. Variation of maximum magnetization with driving field amplitude at thefrequency of 6 Hz.The dependence of the coercive field Hc on maximum magnetization Mm upto 1 T at six frequencies is shown in Fig. 2. The region of 0.8 T < Mm < 1 T istransitional region in which changes of the domain structure of the bulk (domainsB) end, and pronounced changes in surface domain structure (domains A) begin.One can notice three qualitatively different types of variation of Hc within theexplored range of Mm. In the range Mm < 0.2 T, the increase is fast. It is caused bythe Barkhausen jumps of domain walls at weaker pinning centres. Sudden depinningof domain walls is followed by an increase of the volume of domains favourablyoriented with respect to the driving field and in the generation of eddy currents.Fast increase of losses in this region results in fast increase of Hc. This enhancedincrease is plausible because hysteresis curves develop from almost reversible lines tobroad hysteresis curves of the well–known shape. In the region of 0.2 T < Mm < 0.8FIZIKA A 5 (1996) 3, 133–140 135kolanović and pajić: the influence of domain structure . . .T, the increase of Hc is slower. In this region, as in the preceding one, processesof magnetization are determined by movement of walls of domains B. This regionshows the best soft–magnetic properties, what is important for their industrialapplication. In the region Mm > 0.8 T, the increase of Hc is enhanced.Fig. 2. Dependence of coercive field on the maximum magnetization at different fre-quencies. Points for which the driving field had the same amplitude, are connectedby lines.Points in Fig. 2, corresponding to the same amplitudes of the driving field,are connected by lines. With the help of these lines, we can simply explain theinfluence of frequency of driving field on the sample magnetization and determinethe boundary (i.e. transition region) between domination of domains A and domainsB in the process of magnetization. For small Mm, the lines are nearly parallel tothe Mm (horizontal) axis, which means that Hc had the same values for the sameamplitudes of the driving field. An increase of the frequency decreased Mm for thesame driving field amplitude. That is the consequence of a ”viscous” influence ofeddy currents on the domain walls dynamics that increases at higher frequencies.At high frequencies, smaller Mm was obtained and more energy was dissipated ongeneration of eddy currents during the Barkhausen jumps. At lower frequencies,larger Mm was achieved (the domain walls moved farther) and during Barkhausenjumps smaller amounts of energy were dissipated. Of course, total energy lossesincreased because they are mainly determined by Mm. That can be seen from therelationE = 45.1 · M1.643m· f̃0.05 (1)where E = E/(1J), Mm = M/(1T) and f̃ = f/(1Hz), derived for results of mea-surements at frequencies from 1 to 550 Hz and maximum magnetization up to 1 T.1.6 is well-known Steinmetz’s exponent. The dominant type of eddy–current loss(classical eddy currents) is proportional to frequency (E ∝ f) , while the loss due136 FIZIKA A 5 (1996) 3, 133–140kolanović and pajić: the influence of domain structure . . .to the excess eddy currents in the vicinity of the domain walls is proportional tof0.45 [5]. At larger Mm, the lines for the same amplitude H0 become vertical, whatmeans that frequency does not determine the final domain structure. Increase ofHc with frequency is only a consequence of eddy current losses before the domainwalls reach the same locations in the sample. From this fact we can conclude that at0.8 T < Mm < 1 T, domains B with the direction of magnetization nearly parallelto the driving field occupy almost all volume under the surface domain structure.This is another proof that domains B are responsible for magnetization up to 65%Ms. Figure 3 shows the dependence of Hc on Mm (logarithmic scale) with powerlaw fit in the considered regions.Fig. 3. Variation of the coercive field with maximum magnetization at frequencies50.5, 206 and 550 Hz. Note three different regions of variations.At frequencies of 550, 206 and 50.5 Hz, we find that Hc ∝ (Mm)n, with n =0.87, 0.82 and 0.75 in the first region, 0.56, 0.56 and 0.47 in the second region and1.16, 1.16 and 0.88 in the third region, respectively. Almost the same division inthree regions and the same exponents were found by Horvat et al. [7] for similaramorphous magnetostrictive alloys. Enhanced increase of Hc in the third region wasexplained by pinning of domain walls on stronger pinning centres what is followedby the domain wall–bending [6,8]. During the bending of the domain walls, volumefraction in which the excess eddy currents occur increases, increasing also E andHc.Observed saturation of Mr at Mm > 0.7 Ms was also explained by the domain–wallbending.The assumption of twofold domain structure allowed an explaination of thesephenomena more precisely. Enhanced increase of Hc in the third region can beexplained by the penetration of boundaries of the domains B into the region ofdomains A. This leads to a more intensive interaction between the two domainstructures. In this region begin the changes in surface domain structure that are”locking-up” domain structure of the bulk and manifests itself as an increase ofFIZIKA A 5 (1996) 3, 133–140 137kolanović and pajić: the influence of domain structure . . .the field needed for returning the structure to the initial state, i.e. as an increaseof Hc. As a supporting evidence for this phenomenon, we can consider hysteresiscurve measured with VSM at driving field amplitude H0 = 0.1 T shown in Fig. 4.Fig. 4. Hysteresis loop at driving field amplitude of 0.1 T.The coercive field Hc = 370 A/m is about 30 times larger than the typical valuesof the driving fields that were changing the bulk domain structure. We also findthat Mm = 0.7 T at the driving field amplitude H0 = 2000 A/m (dashed lines inFig. 4). This is about 0.5 Ms (that value of Mm was achieved at fields of about 40A/m, before the changes in surface domain structure appeared), and is an evidencethat the changes of domains B are strongly influenced by changes in the surfacedomain structure.It is important to mention that the period of driving field was 2 min., so thecoercive field is almost unaffected by the frequency dependence, and its major partdescribes strength of “locking–up” changes in surface domain structure. Slow andoval transition to a ”tail” of the hysteresis curve at large driving field amplitudeis an evidence for the existence of paraprocesses, which are in our case rotation ofdomains, and changes and destruction of surface domain structure.The appearance of hysteresis curves of this shape (with slower rate of change ofMm(H0) ) results in slower increase of Mr with respect to the Mm, i.e. saturationof Mr(Mm). The dependence of the remanent magnetization on maximum magne-tization is shown in Fig. 5. At Mm > 0.7 T, we find a mild tendency to saturation,which indicates slow changes in surface domain structure at these fields.In the region Mm < 0.7 T and for lower frequencies, the dependence of Mron Mm is approximately linear and frequency independent. The best fit (for lowerfrequencies) isMr = 0.82 · M1.03m, (2)138 FIZIKA A 5 (1996) 3, 133–140kolanović and pajić: the influence of domain structure . . .where Mr = Mr/(1T) and Mm = Mm/(1T). The inset to Fig. 5 shows the depen-dence of Mr on Mm at higher frequencies for which the increase of Mr is enhancedin the region 0.1 T < Mm < 0.7 T. The remanent magnetization cannot be literallyinterpreted as the magnetization of the system after the driving field is turned off,but must be considered in terms of the process of dynamical change of magneti-zation. Otherwise, at different frequencies, different values of Mr would not havebeen obtained.Fig. 5. Variation of remanent magnetization with maximum magnetization for givenfrequencies. Inset: The same dependence at higher frequencies.4. ConclusionOn the basis of systematic detailed measurements of parameters of hysteresiscurves (Hc, Mm, Mr) for an Fe77.5B22.5 amorphous alloy, and the existence of thetwofold domain structure of amorphous alloys in form of long straight ribbons, wecan conclude:a) Inner domain structure (domains B), which contributes to the magnetizationof the sample up to about 65% Ms, can be completely changed with rather smalldriving field amplitudes (up to 100 A/m).b) Analysis of the variation of Hc with Mm and f for the same driving fieldamplitude has shown a ”viscous” effect of eddy currents on the domain wall move-ment, and hence on the final domain configuration, i.e. on Mm. The existence of thetwo contributions to magnetization, which are caused by domains A and domainsB, was indicated by achieving the same Mm at all frequencies.c) Changes in the surface domain structure at large driving field amplitudes,which have the character of a paraprocess, are locking-up the inner domain config-FIZIKA A 5 (1996) 3, 133–140 139kolanović and pajić: the influence of domain structure . . .uration of the bulk. All our results show the influence of interaction between theregion of domains A and region of domains B, which allows the assumption thatin addition to classical pinning centres that are, e.g. impurities, density fluctua-tions, quasidislocation, etc., the domain wall pinning of domains B probably canbe caused by the interaction with surface domain structure (domains A). In agree-ment with this assumption are also the results of Ref. 9 in which it is shown thatthe strongest pinning centres are situated near the surface of the sample, while thepinning centres in the bulk are much weaker.AcknowledgementAuthors are grateful to Prof. Dr. E. Babić for his discussion and comments onthe manuscript. All measurements were performed at the Department of Physics,Faculty of Science, University of Zagreb.References1) H. Kronmüller, J. Magn. Magn. Mater. 24 (1981) 159;2) P. Schönhuber, H. Pfützner, G. Harasko, T. Klinger and K. Futschik, J. Magn. Magn.Mater. 112 (1992) 349;3) P. Schönhuber, H. Pfützner, Y. Simpson and G. S. Radley, J. Magn. Magn. Mater.112 (1992) 125;4) H. H. Liebermann and C. D. Graham, IEEE Trans. Magn. MAG-12 (1976) 921;5) J. Horvat, Ž. Marohnić and E. Babić, J. Magn. Magn. Mater. 82 (1989) 5;6) S. Sabolek, Fizika A 2 (1993) 101;7) J. Horvat, E. Babić, Ž. Marohnić and H. H. Liebermann, Mater. Sci. Eng. A133 (1991)192;8) J. Horvat, Phys. Stat. Sol. (a) 129 (1992) 519;9) S. Sabolek and S. Zrnčić, Fizika A 4 (1995) 501.UTJECAJ DOMENSKE STRUKTURE NA OVISNOST KOERCITIVNOGPOLJA I MAKSIMALNE MAGNETIZACIJE AMORFNE SLITINE Fe77.5B22.5Indukcijskom metodommjerene su krivulje magnetizacije amorfne vrpce Fe77.5B22.5.Ovisnosti koercitivnog polja (Hc ), maksimalne magnetizacije (Mm ) i remanentnemagnetizacije (Mr) mogu se objasniti dvostrukom domenskom strukturom karak-terističnom za ovakve uzorke. Analiza mjerenja pokazuje da su unutrašnje domeneodgovorne za magnetizaciju do 65% magnetizacije zasićenja (Ms) te da interak-cija izmedu dviju domenskih struktura igra važnu ulogu pri ubrzanom rastu Hc priMm > 0.5 Ms. Razmatrana je i ovisnost parametara krivulje histereze o frekvenciji.140 FIZIKA A 5 (1996) 3, 133–140

Utjecaj domenske strukture na ovisnost koercitivnog polja i maksimalne magnetizacije amorfne slitine Fe77.5B22.5

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