ࡱ> 5@ ےbjbj22 @XXQ4(>(>(>8`>4?\Yo?(?:??@`O`O`Onnnnnnn$SqRs^>nQNNNNQQ>n?@ oXXXQ??fXQnX.XXndJe?? 0b (>Ue @fT)o0Yoe t[Xt@etep`OvOTX*PDnP=`O`O`O>n>n$ (>[X4(>The influence of surface domains on magnetization of very soft magnetic ribbons S. Sabolek, E. Babi, D. Posedel, and M. `uaak Department of Physics, Faculty of Science, University of Zagreb, Bijeni ka 32, 10000 Zagreb, Croatia Received zzz, revised zzz, accepted zzz Published online zzz PACS 75.50.Kj; 75.60.-d; 81.07.Bc The influence of surface fields Hp (generated by core currents) on the parameters of M-H loops (the coercive field Hc, the maximum magnetization Mm, etc.) of amorphous and nanocrystalline Fe73.5Cu1Nb3Si15.5B7 ribbon and amorphous VITROVAC 6025Z ribbon has been investigated. In amorphous Fe73.5Cu1Nb3Si15.5B7 ribbon Hc decreases with Hp with unchanged Mm, whereas in nanocrystalline Fe73.5Cu1Nb3Si15.5B7 and VITROVAC 6025Z ribbons Hc increases with Hp and Mm decreases with Hp. This unusual increase of Hc with Hp is ascribed to the influence of Hp on the surface domain structure (SDS) and strong interaction between SDS and inner (main) domain structure (MDS) in these materials. 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction The motion of domain walls (DW) of the main domain structure (MDS) usually dominates the magnetization along the axis of very soft magnetic ribbons in moderate magnetizing fields H [1]. This magnetization mechanism prevails due to a small average angle ((( between the magnetizations of MDS domains and ribbon axis (also, direction of H) [2]. In these samples the strongest DW pinning centres are usually located near the surfaces of the ribbon. They originate from the surface inhomogeneities, stresses and irregularities (intrinsic pinning [3]) but also from some domains of SDS with magnetizations forming large angles with ribbon axis (SDS pinning, [4]). Since these materials provide numerous opportunities for applications [5], the investigation of the surface pinning of DWs is of considerable interest. The influence of surface pinning on magnetization processes shows up best upon the application of an oblique surface field Hp [6]. Detailed investigation of the influence of Hp, generated by core currents, on the M-H loops of soft amorphous ferromagnetic ribbons showes that Hp usually reduces Hc, shifts the M-H loop, and may change the maximum (Mm) and remanent (Mr) magnetization [7]. These effects have been explained in terms of a simple model which takes into account the intrinsic pinning of DWs only and predicts a linear decrease of Hc with Hp [8]. However, recent measurements on optimally annealed (nanocrystalline) Fe73.5Cu1Nb3Si15.5B7 ribbon (thereafter FeCuNbSiB) and amorphous VITROVAC 6025Z ribbon have shown that Hc in these very soft magnetic materials increases with Hp [9].Here we show that the variations of Hc with Hp in these materials can be quantitatively explained with an improved model for the influence of Hp on the magnetization processes in soft magnetic ribbons. 2 Experimental procedure The dimensions of the samples were 200(2(0.025 mm3 and 200(2(0.020 mm3 for the optimally annealed FeCuNbSiB and VITROVAC 6025Z ribbon, respectively. The M-H loops were measured with an  Fig.  SEQ Fig. \* ARABIC 1 Variations of the coercive field Hc ((), maximum magnetization Mm (() and the position of the center of the M-H loop C ((), for the nanocrystalline Fe73.5Cu1Nb3Si15.5B7 sample, with the static surface field Hp. The inset: M-H loops for the same sample in the amorphous (dashed) and nanocrystalline (solid) state. The measurements were performed with a triangular drive field with amplitude H0 = 100 A/m and the frequency f = 5.5 Hz. induction technique at room temperature [10]. A triangular magnetizing field H with the amplitude H0 = 100 A/m and frequency f = 5.5 Hz was used. During the magnetization process, direct (JD) core current (static Hp) was passed along the ribbon. For FeCuNbSiB sample M-H loops and the corresponding dM/dt vs. H curves were measured both in the amorphous state and after anneal at 540(C for one hour in pure Ar gas atmosphere. 3 Results and discussion The amorphous FeCuNbSiB samples show poor soft magnetic properties consistent with a strong local magnetic anisotropy which develops during the their fabrication [11]. Therefore (inset to Fig. 1), for H0 = 100 A/m, the coercive field is large (Hc0 = 13.5 A/m) and Mm quite low. Static Hp causes a weak linear decrease of Hc and does not change Mm and the position of the center (C) of the M-H loop [9]. These effects are consistent with strong volume pinning of DWs [11], hence the surface pinning and Hp have slight influence on the magnetization processes. The optimally annealed FeCuNbSiB sample shows excellent soft magnetic properties (Fig. 1) [12]. Accordingly, for H0 = 100 A/m and Hp = 0 Hc is low (Hc0 = 1.3 A/m) and Mm large (Mm ( Ms with Ms the saturation magnetization). However, its Hc increases rapidly with static Hp ((Hc/(Hp ( 0.067) for (Hp(( 5 A/m, but the rate of the increase of Hc with Hp slows down ((Hc/(Hp ( 0.023) for (Hp(( 5 A/m (Fig. 1). Simultaneously, Mm decreases a little with Hp, whereas center C of the M-H loop shifts linearly with Hp for (Hp(( 5 A/m and shows little change for (Hp(( 5 A/m. The nonmagnetostrictive VITROVAC 6025Z ribbon (Fig. 2) shows a similar deterioration of soft magnetic properties due to Hp. Here, Hc initially increases with static Hp ((Hc/(Hp ( 0.05) for (Hp(( 6 A/m whereas for (Hp(( 6 A/m Hc remains constant. These results can be explained by means of a model for the influence of Hp on magnetization of soft magnetic ribbons which takes into account the influence of Hp on intrinsic pinning of DWs and the novel effect: the Hp-enhanced SDS pinning of DWs [13]. This model is obtained by a simple modification of the previous model [7, 8] for the influence of Hp on parameters of the M-H loops of amorphous ferromagnetic ribbons. It is known that the strengths of DW pinning at the opposite surfaces of the ribbon are usually not the same [13]. Therefore, we denote the magnitudes of H necessary for depinning of DWs from the upper and lower surface of the sample in the absence of Hp with Hsu0 and Hsl0 respectively, and  Fig.  SEQ Fig. \* ARABIC 2 Variations of the coercive field Hc ((), maximum magnetization Mm (() and the position of the center of the M-H loop C ((), for the amorphous VITROVAC 6025Z sample with the static surface field Hp. The inset: M-H loop for the same sample in the absence of Hp. The amplitude and the frequency of the magnetizing field were the same as in Fig. 1. assume Hsu0 ( Hsl0 [8]. According to the previous model (which takes into account only intrinsic pinning of DWs of MDS) the projection of Hp on the magnetization I of MDS domain (P = Hpsin((() may influence the intrinsic pinning by either increasing or decreasing the pressure on the DW (depending on the direction of Hp). In particular, due to the difference between Hsu0 and Hsl0 the effects of static Hp on Hc show two regimes. For lower magnitudes of Hp (Hp ( (Hsl0 - Hsu0)/2tan((() the model predicts a constant Hc and linear shift of the center C of the M-H loop [8]: Hc = Hsu0 (1) C = ( Hp tan((( . (2) For larger Hp (Hp ( (Hsl0 - Hsu0)/2tan((() Hc decrease with Hp, whereas C remains constant [8]: Hc = (Hsu0 + Hsl0)/2 Hp tan((( (3) C = ( (Hsl0 - Hsu0)/2 = const. (4) Since this model cannot explain the observed increase of Hc with Hp, it could be improved by taking into account that Hp simultaneously tends to fix the directions of I of the SDS domains forming large angles with the ribbon axis which enhances the DW pinning (SDS pinning) [4]. For simplicity, we assume that SDS pinning increases linearly with Hp i.e. that this enhancement is kHp, where k is the coefficient which shows the rate of the increase of SDS pinning due to Hp (for simplicity we assumed that k is the same for both surfaces of the ribbon). The addition of this enhancement of SDS pinning in the calculation of Hc and C converts the equations (1) and (3) into: Hc = Hsu0 + kHp (5) Hc = (Hsu0 + Hsl0)/2 + kHp Hp tan((( . (6) Simultaneously, C remains independent of SDS pinning, hence his variation with Hp is still described with equations (2) and (4). Accordingly, for Hp ( (Hsl0 - Hsu0)/2tan((( Hc increases with Hp if SDS pinning is present i.e. if k ( 0 (eq. (5)). For larger Hp (Hp ( (Hsl0 - Hsu0)/2tan((() Hc may increase or decrease with Hp depending on whether the influence of Hp on intrinsic pinning of DWs is larger or smaller than that on SDS pinning (eq. (6)). Now, we apply this model to the results for Hc shown in Figs. 1 and 2. The annealing of FeCuNbSiB sample at 540 (C leads to the formation of fine Fe3Si nanocrystalls, the local anisotropy vanishes and the sample becomes nonmagnetostrictive [12]. The excellent soft magnetic properties of the annealed sample (Fig. 1) show the absence of strong volume pinning of DWs and practically all domains (Mm ( Ms) participate in the magnetization processes. Therefore, the motion of MDS DWs is determined by the surface pinning centres and Fig. 1 shows the pronounced influence of SDS pinning. In particular, Hc increases linearly with Hp for (Hp(( 5 A/m according to eq. (5) due to enhancement of SDS pinning by Hp which tends to fix and/or rotate the magnetizations of the SDS domains perpendicular to the ribbon axis, i.e. parallel to Hp [2]. This explanation is supported by simultaneous weak decrease of Mm with Hp (Fig. 1). According to eq. (5) we find k ( 0.067. For (Hp(( 5 A/m Hc increases less rapidly with Hp due to the influence of Hp on intrinsic pinning of DWs (eq. (6)). However, the enhancement of SDS pinning with Hp overcomes that of Hp (i.e. P = Hpsin((() on depinning of DWs due to the smallness of angle(((. Indeed from the slopes of Hc vs Hp for (Hp((/( 5 A/m by the use of eqs. (5) and (6) we find a rather small angle ((( = 2.4(. This result confirms that the main mechanism of the magnetization is the movement of 180(-DWs of MDS [2]. The nonmagnetostrictive VITROVAC 6025Z ribbon has also very good soft magnetic properties (Hc = 1.4 A/m and Mm ( Ms at H0 = 100 A/m) but Hp causes deteriorate them Hc (Fig. 2). The increase of Hc with Hp for Hp ( 6 A/m, shows a strong influence of SDS pinning on the dynamics of DWs. By using eq. (5) we can estimate k ( 0.05 for this sample. However, for Hp ( 6 A/m Hc is practically independent of Hp, which means that the enhancement of SDS pinning with Hp is approximately the same as the influence of Hp (P) on the depinning of DWs of MDS. According to eq. (6) Hc is constant if k = tan((( which yields ((( ( 2.8(. 4 Conclusion Due to small angles ((( between the magnetizations Of MDS domains and ribbon axis (((( ( 3( for both samples) the dominant magnetization mechanism in nanocrystalline FeCuNbSiB and amorphous VITROVAC 6025Z ribbons is the motion of 180(-DWs of MDS. However, a static surface field Hp enhances the SDS pinning of DWs [4] in these samples. This effect may ruin their soft magnetic properties when exposed to oblique external fields [6]. On the basis of an extended model for the influence of Hp on the parameters of the M-H loops, we find that the negative effects of oblique fields on Hc can be attenuated for instance by the introduction of an uniaxial anisotropy, which would increase somewhat the angle ((( and hence enhance the direct influence of Hp (or similar oblique field) on the intrinsic pinning of DWs. Alternatively, one can use some surface treatment [14] in order to modify the surface domain structure of very soft magnetic ribbons. Acknowledgements We wish to thank Dr. G. Herzer for giving us FeCuNbSiB samples. References [1] P. Schnhuber, H. Pftzner, G. Harasko, T. Klinger, and K. Futschik, J. Magn. Magn. Mater. 112, 349 (1992). [2] P. T. Squire, J. Magn. Magn. Mater. 87, 299 (1990). [3] T. Sato, and T. Yamada, IEEE Trans. Magnetic 28, 2775 (1992). [4] K. H. Stewart, Ferromagnetic Domains (Cambridge University Press, Cambridge, 1954) p. 165. [5] A. Hernando, M. Vazquez, and J. Barandiaran, Journal of Physics E 21, 1129 (1998). [6] P. Tiberto, F. Vinai, O Rampado, H. 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