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Magnetoresistance and magnetic properties in amorphous Fe-based wires
Journal of Magnetism and Magnetic Materials 231 (2001) 179–184
Magnetoresistance and magnetic properties in amorphous Fe-based wires G. Bordin, G. Buttino, A. Cecchetti, M. Poppi* Department of Physics. (INFM) Istituto Nazionale Fisica della Materia University of Ferrara, Via Paradiso 12, I-44100, Ferrara Italy Received 14 September 2000; received in revised form 8 February 2001
Abstract The longitudinal and transverse magnetoresistances in amorphous Fe77.5Si7.5B15 wires are studied at different values of the DC-bias currents in order to clarify the mechanism of the magnetization according to a ‘core-shell’ domain model. The role of closure domain structures in the magnetization process of the wires is analysed. Moreover, the effects of the Joule heating on the internal stresses, introduced during the rapid quenching in the sample preparation, are examined. # 2001 Published by Elsevier Science B.V. PACS: 72.15.Gd; 75.50.Kj Keywords: Fe-rich amorphous wires; Magnetoresistance
1. Introduction The magnetic properties of the amorphous ferromagnetic alloys, in form of wire, produced by in-rotating-water quenching technique are very interesting for their practical applications. The transition metal (Fe,Co,Ni) contents are in the range 70–80% in the compositions of these alloys and determine their magnetostrictive properties. In fact, Fe-based wires have large positive saturation magnetostriction ls , Co-based wires have small negative or nearly zero magnetostriction depending on the content of Fe in the alloy. These features are very important in determining magnetic domain structures and magnetomechanical *Corresponding author. Tel.: +39-0532-291811; fax: +390532-29810. E-mail address: [email protected] (M. Poppi).
behaviour of the wires because of the residual stresses introduced during the sample preparation [1]. The as-cast amorphous wires with positive and negative magnetostriction coefficients are considered on the basis of different models of ‘core-shell’ domain structures that consist of an inner core and an outer shell produced during the rapid quenching process. In the inner core the easy magnetization directions are roughly parallel to the wire axis. In the outer shell the stress fields give rise to magnetic anisotropies that are either radial or circumferential, depending on whether the sign of ls is positive or negative [2,3]. In the present work we study the longitudinal and transverse magnetoresistances, MR, of amorphous Fe77.5Si7.5B15 wires by different DC-bias currents along their axis and the MR dependence on thermal treatment obtained by Joule heating.
0304-8853/01/$ - see front matter # 2001 Published by Elsevier Science B.V. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 1 8 3 - 4
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G. Bordin et al. / Journal of Magnetism and Magnetic Materials 231 (2001) 179–184
the wires of 1, 3 and 5 mA, respectively. In the Figs. 2–7 the MR results are presented in terms of Dr ½rðH Þ r0 ¼ ; r0 r0
ð1Þ
where ro is the resistivity at zero magnetic field.
Fig. 1. ‘Core-shell’ domain structure for the amorphous wires, as proposed by Makino et al. [4]: (A) inner core, (B) outer shell.
The results are interpreted by assuming the domain structure of the ‘core-shell’ model represented in Fig. 1 and by considering the magnetization processes for the amorphous wires proposed by Makino et al. [4]. The effect of different DC-bias currents on MR was proposed by Ziman et al. in order to study the magnetic anisotropy in amorphous Co-based ribbons [5] and in surface crystallised FeSiB wires [6]. Moreover, annealing effects on the domain structure of FeSiB amorphous wires were related in previous works, in particular by Atkinson et al. [1,7]. In that context annealing was performed in the range of temperatures from the Curie temperature to the crystallization temperature where eventually surface crystallization occurs.
Fig. 2. Longitudinal MR for as-cast samples with DC-bias currents of 1, 3 and 5 mA, respectively.
2. Experimental results The examined Fe77.5Si7.5B15 amorphous wires (supplied by Goodfellow Cambridge Ltd.) have diameter of 125 mm and large positive magnetostriction with ls =35 10–6. In the longitudinal magnetoresistance the directions of magnetizing field and DC-bias current in the sample are parallel, while in the transverse magnetoresistance the magnetizing field direction is perpendicular to DC-bias current. The experimental MR data were obtained at room temperature using the conventional four terminal technique. In our measurements we have employed DC-bias currents along
Fig. 3. Transverse MR for as-cast samples; DC-bias currents as in Fig. 2.
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 231 (2001) 179–184
181
Fig. 4. Longitudinal MR after Joule heating of the sample at 450 mA for 1 min.
Fig. 6. Longitudinal MR after Joule heating of a sample at 450 mA for 15 min.
Fig. 5. Longitudinal MR after Joule heating of a sample at 450 mA for 5 min.
Fig. 7. Transverse MR after Joule heating of a sample at 450 mA for 5 min.
The Figs. 2 and 3 represent the longitudinal and transverse MR curves for an as-cast sample at the different values of the DC-bias current. The curves of the Figs. 4–6, relative to longitudinal MR, have been obtained after a Joule heating of the samples at 450 mA for 1, 5 and 15 min, respectively. Fig. 7
shows transverse MR in samples annealed for 5 min: in this context the annealing time does not influence significantly transverse MR. The average annealing temperature stabilizes in about 10 s around 3708C [8]. This temperature is well below the crystallization temperature of
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G. Bordin et al. / Journal of Magnetism and Magnetic Materials 231 (2001) 179–184
the alloy. The Curie temperature of the material is 4228C, the crystallization temperature is 5538C.
3. Discussion 3.1. As-cast samples The curves of Fig. 2 show a negative minimum at low magnetizing fields, then they assume positive values with a trend to saturation. The shape of the curves detected by different values of the DC-bias current along the wire is quite similar to that obtained by Makino et al. [4] with an ACbias current having the conventional value of 1 mA. The above behaviour may be explained by assuming the ‘core-shell’ model with the domain structure sketched in Fig. 1 and by considering, as it is known, that in the ferromagnetic materials the MR is generally negative when the applied magnetic field is perpendicular to the bias current in the sample and positive when magnetic field and current are parallel to each other. Therefore, to explain the negative minimum in the curves of Fig. 2, we assume that low axial magnetic fields may give rise to an increase in the volume fraction of the domains whose magnetization is perpendicular to the DC-bias current. It being understood that MR is associated with magnetization rotation, the latter process would occur at the expense of the closure domains having their magnetization opposite to the magnetizing field [4]. In this context it is possible to explain: (i) the reduction in the negative minimum and the rise of the positive values, in longitudinal MR, with increasing the driving axial current, (ii) the shift towards lower values of the axial magnetic field at which longitudinal MR changes its sign when the current increases. In fact, the circular magnetic field due to the axial current favours the magnetization orientation in its direction and reduces the action of the longitudinal field on the magnetic volumes that give negative longitudinal MR. The MR dependence on the circular magnetic self-field, Hy , due to the current flow is significant to test the validity of the model and allows us to get insight into the distribution of the magnetic
anisotropies. To this purpose one can take into account that the saturation magnetization Is in this sample is 1.6 T and that the circular magnetic field is given by Ref. [9] Hy ¼ ir=2pR20
ðr4R0 Þ
ð2Þ
In particular, the field at the surface of the wire (i.e. for r ¼ R0 ¼ 62:5 mm), varies from 0.031 to 0.155 Oe when the current i ranges from 1 to 5 mA. It is interesting to observe that a circular field varying from 0.031 to 0.155 Oe is sufficient to cause a large shift, of at least 20 Oe, of the crossing point of the Dr=r curves with the H-axis (Fig. 2). This is due to the different mechanisms involved in the process and may be explained as follows. The circular field assumes its highest values in outer shell, where the magnetization is radially oriented and the zigzag closure domains are directed in both the circular and longitudinal directions of the wire. Now, for bias current intensities higher than about 1 mA the circular field enhances the circular magnetization to expense of closure domains of the shell. The subsequent application of the longitudinal field H produces at first the rotation of the circular magnetization towards the longitudinal axis. This, in turn, gives rise to positive magnetoresistance variations which mask partially the initial negative minimum described according to Makino [4] and force the crossing point of the Dr=r curves towards longitudinal fields lower than that obtained by a bias current of 1 mA. As regards the radial magnetic anisotropy it maintains high values and the rotational processes of the radial magnetization towards the longitudinal direction continue gradually up to high values of H. Thus, the crossing points result from the counterbalance of the different effects above described and the effectiveness of the circular field is due to the absence of demagnetizing effects in that direction. By considering the mean value of Hy across the section of the sample, ðHy Þm ¼ ðHy Þs =2, as the critical field for magnetic rotational processes with anisotropy constant K having the order of magnitude of Is ðHy Þm , values of K are found which increase from about 2 to 10 J/m3 when i varies from 1 to 5 mA. Fig. 3 represents the transverse MR of an ascast sample obtained when the magnetizing field is
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 231 (2001) 179–184
perpendicular to the DC-bias current along the wire. In this situation the influence of the circular magnetic fields is negligible in comparison to that of the applied magnetic field. Accordingly to the previous domain model, the MR values are always negative because the external field favours a magnetization rotation in the direction perpendicular to the wire axis. Moreover, the transverse MR saturation is several times higher than the longitudinal one as it is to be expected by deducing the volume fraction of the inner core, with respect to that of the outer shell [10], from magnetic measurements of the hysteresis loops. 3.2. Annealed samples The effects of the thermal heating on MR are considered here. In this connection, the Figs. 4–6 represent the longitudinal MR in samples subjected to Joule heating obtained with a DC current of 450 mA for 1, 5 and 15 min, respectively. The transverse MR shows the behaviour represented in Fig. 7 that refers to the heating time of 5 min. By comparing the Figs. 4–6 with Fig. 2, one can observe a smaller negative contribution with a shift to lower values of the magnetic field at which MR changes its sign. The higher the annealing time and the DC-bias current intensity, the more significant the effect. This effect of heating on MR results somehow similar to the effect obtained by Makino et al. [4] through an axial tensile stress. Actually, both tensile stress and Joule heating can diminish the magnetic anisotropy induced, by compressive and radial stresses, in the directions perpendicular to the wire axis during the preparation process. However, heating relieves also longitudinal stresses so that the domain structure can be significantly modified [10]. Once the residual internal stresses are removed, a counterbalance occurs between circular anisotropy due to the heating current and longitudinal shape anisotropy. This seems to lead to quasirandom local anisotropy over the entire sample. In fact, in annealed wires the MR reaches saturation values about five times higher than in as-quenched samples where only the outer-shell contributes to the longitudinal MR. Furthermore, longitudinal
183
and transverse MR show saturation values closer each other than in the as-quenched state. On the other hand, the strong dependence of longitudinal MR on the measuring current, at least in specimens annealed for 1 min, emphasises a particular weakness in the local anisotropies of some regions in the wire. In fact, by varying the measuring current from 1 to 3 mA, as results from Fig. 4, the MR saturation value increases of about 30%. By changing the current from 3 to 5 mA the differences in the MR curves are no so important. It is noteworthy to consider that the removal of the outer-shell regions magnetized in radial directions occurs progressively with increasing heating time. Indeed, only a trace of the initial outer-shell domain structure should remains in samples heated for 15 min because in these specimens the negative minimum in MR curves is only just evident. Moreover, the negative minimum in annealed samples is obtained only in the curves relative to i ¼ 1 mA and thus for circular field low enough. This well agrees with the fact that the disappearance of the outer-shell structures responsible for the negative minimum makes the MR curves almost independent of the measuring current intensity. On the other hand, the above heating effect is consistent with the observed reduction in intensity of the longitudinal MR saturation value and with the correspondent lowering of the axial magnetic field that leads to MR saturation when heating time increases. In fact, the removal of the outer shell reduces the volume fraction of the domains whose magnetization is radially oriented and the progressive elimination of the residual internal stresses produces a continuous reduction of the local magnetoelastic anisotropies in any direction. As regards the transverse MR, it presents unexpected characteristics. In fact, as results from Fig. 7, the curves show a positive maximum at low applied fields and they present negative values only when the applied field becomes high enough. This anomalous behaviour at low field seems to be due to a mechanism quite similar to that invoked to explain the negative minimum in the longitudinal MR of as-cast samples. In this case, we assume that closure domains at the ends of the wire [10] play the main role and that structure
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G. Bordin et al. / Journal of Magnetism and Magnetic Materials 231 (2001) 179–184
rearrangement of these domains increase initially the volume fraction of the longitudinal magnetization. This mechanism is made possible in annealed samples because of the weakness of the local anisotropies. In this connection, the strong demagnetizing effects in the transverse direction can justify the high magnetic fields needed to obtain negative MR.
4. Concluding remarks The magnetoresistance of amorphous wires with different DC-bias currents along the wire axis has been examined and the experimental data have been explained on he basis of a ‘core-shell’ domain model. A Joule heating of the samples favours a great change in magnetic anisotropies introduced during the preparation process of the wire. As a consequence, the original domain structure of the wire is destroyed or deformed and this reflects on MR. In particular, annealing produces a very important reduction in the local anisotropies. Besides, even low electrical currents, like those generally used for this kind of measure, produce circular magnetic fields which may contribute to modify the magnetic structure of the system. Finally, MR has been here described by considering the relative changes in resistivity rðHÞ with respect to the resistivity r0 at zero field. This procedure allowed us to emphasize well some characteristics of the phenomenon; however, in many cases MR changes are referred to the saturation resistivity. The Fig. 8 reports, for our samples, some longitudinal MR behaviours expressed as in Eq. (1) where r0 is now the saturation resistivity at a field of about 650 Oe. The longitudinal field is changed here from positive to negative values. The principal feature of these curves is that they show negative values of MR. This characteristic can be attributed to the sign of the saturation magnetostriction of the sample. In fact, the result is opposite to that obtained in Cobased amorphous wires where the magnetostriction coefficient is negative [11].
Fig. 8. Longitudinal MR, relative to the saturation resistivity, for as-cast samples (the inset refers to the lowest value of H).
References [1] D. Atkinson, P.T. Squire, M.R.J. Gibbs, S.N. Hogsdon, J. Phys. D 27 (1994) 1354. [2] P.T. Squire, D. Atkinson, M.R.J. Gibbs, S. Atalay, J. Magn. Magn. Mater. 132 (1994) 10. [3] K. Mohri, F.B. Humphrey, K. Kawashima, K. Kimura, M. Mizutani, IEEE Trans. Magn. 26 (1990) 1789. [4] Y. Makino, J.L. Costa, V. Madurga, K.V. Rao, IEEE Trans. Magn. 25 (1989) 3620. [5] J. Ziman, M. Hrab"eak, B. Zagyi, M. Kon"e, IEEE Trans. Magn. 30 (1994) 884. [6] J. Ziman, B. Zagyi, J. Magn. Magn. Mater. 169 (1997) 98. [7] D. Atkinson, R.S. Beach, P.T. Squire, C.L. Platt, S.N. Hogsdon, IEEE Trans. Magn. 31 (1995) 3892. ! [8] C. Gomez-Polo, M. V!azquez, J. Magn. Magn. Mater. 118 (1993) 86. [9] J.L. Costa, Y. Makino, K.V. Rao, IEEE Trans. Magn. 26 (1990) 1792. [10] M. V!azquez, A. Hernando, J. Phys. D 29 (1996) 939. [11] K. Mandal, S.K. Ghatak, Phys. Rev. B 47 (1993) 14233.
Magnetoresistance and magnetic properties in amorphous Fe-based wires G. Bordin, G. Buttino, A. Cecchetti, M. Poppi* Department of Physics. (INFM) Istituto Nazionale Fisica della Materia University of Ferrara, Via Paradiso 12, I-44100, Ferrara Italy Received 14 September 2000; received in revised form 8 February 2001
Abstract The longitudinal and transverse magnetoresistances in amorphous Fe77.5Si7.5B15 wires are studied at different values of the DC-bias currents in order to clarify the mechanism of the magnetization according to a ‘core-shell’ domain model. The role of closure domain structures in the magnetization process of the wires is analysed. Moreover, the effects of the Joule heating on the internal stresses, introduced during the rapid quenching in the sample preparation, are examined. # 2001 Published by Elsevier Science B.V. PACS: 72.15.Gd; 75.50.Kj Keywords: Fe-rich amorphous wires; Magnetoresistance
1. Introduction The magnetic properties of the amorphous ferromagnetic alloys, in form of wire, produced by in-rotating-water quenching technique are very interesting for their practical applications. The transition metal (Fe,Co,Ni) contents are in the range 70–80% in the compositions of these alloys and determine their magnetostrictive properties. In fact, Fe-based wires have large positive saturation magnetostriction ls , Co-based wires have small negative or nearly zero magnetostriction depending on the content of Fe in the alloy. These features are very important in determining magnetic domain structures and magnetomechanical *Corresponding author. Tel.: +39-0532-291811; fax: +390532-29810. E-mail address: [email protected] (M. Poppi).
behaviour of the wires because of the residual stresses introduced during the sample preparation [1]. The as-cast amorphous wires with positive and negative magnetostriction coefficients are considered on the basis of different models of ‘core-shell’ domain structures that consist of an inner core and an outer shell produced during the rapid quenching process. In the inner core the easy magnetization directions are roughly parallel to the wire axis. In the outer shell the stress fields give rise to magnetic anisotropies that are either radial or circumferential, depending on whether the sign of ls is positive or negative [2,3]. In the present work we study the longitudinal and transverse magnetoresistances, MR, of amorphous Fe77.5Si7.5B15 wires by different DC-bias currents along their axis and the MR dependence on thermal treatment obtained by Joule heating.
0304-8853/01/$ - see front matter # 2001 Published by Elsevier Science B.V. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 1 8 3 - 4
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G. Bordin et al. / Journal of Magnetism and Magnetic Materials 231 (2001) 179–184
the wires of 1, 3 and 5 mA, respectively. In the Figs. 2–7 the MR results are presented in terms of Dr ½rðH Þ r0 ¼ ; r0 r0
ð1Þ
where ro is the resistivity at zero magnetic field.
Fig. 1. ‘Core-shell’ domain structure for the amorphous wires, as proposed by Makino et al. [4]: (A) inner core, (B) outer shell.
The results are interpreted by assuming the domain structure of the ‘core-shell’ model represented in Fig. 1 and by considering the magnetization processes for the amorphous wires proposed by Makino et al. [4]. The effect of different DC-bias currents on MR was proposed by Ziman et al. in order to study the magnetic anisotropy in amorphous Co-based ribbons [5] and in surface crystallised FeSiB wires [6]. Moreover, annealing effects on the domain structure of FeSiB amorphous wires were related in previous works, in particular by Atkinson et al. [1,7]. In that context annealing was performed in the range of temperatures from the Curie temperature to the crystallization temperature where eventually surface crystallization occurs.
Fig. 2. Longitudinal MR for as-cast samples with DC-bias currents of 1, 3 and 5 mA, respectively.
2. Experimental results The examined Fe77.5Si7.5B15 amorphous wires (supplied by Goodfellow Cambridge Ltd.) have diameter of 125 mm and large positive magnetostriction with ls =35 10–6. In the longitudinal magnetoresistance the directions of magnetizing field and DC-bias current in the sample are parallel, while in the transverse magnetoresistance the magnetizing field direction is perpendicular to DC-bias current. The experimental MR data were obtained at room temperature using the conventional four terminal technique. In our measurements we have employed DC-bias currents along
Fig. 3. Transverse MR for as-cast samples; DC-bias currents as in Fig. 2.
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 231 (2001) 179–184
181
Fig. 4. Longitudinal MR after Joule heating of the sample at 450 mA for 1 min.
Fig. 6. Longitudinal MR after Joule heating of a sample at 450 mA for 15 min.
Fig. 5. Longitudinal MR after Joule heating of a sample at 450 mA for 5 min.
Fig. 7. Transverse MR after Joule heating of a sample at 450 mA for 5 min.
The Figs. 2 and 3 represent the longitudinal and transverse MR curves for an as-cast sample at the different values of the DC-bias current. The curves of the Figs. 4–6, relative to longitudinal MR, have been obtained after a Joule heating of the samples at 450 mA for 1, 5 and 15 min, respectively. Fig. 7
shows transverse MR in samples annealed for 5 min: in this context the annealing time does not influence significantly transverse MR. The average annealing temperature stabilizes in about 10 s around 3708C [8]. This temperature is well below the crystallization temperature of
182
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 231 (2001) 179–184
the alloy. The Curie temperature of the material is 4228C, the crystallization temperature is 5538C.
3. Discussion 3.1. As-cast samples The curves of Fig. 2 show a negative minimum at low magnetizing fields, then they assume positive values with a trend to saturation. The shape of the curves detected by different values of the DC-bias current along the wire is quite similar to that obtained by Makino et al. [4] with an ACbias current having the conventional value of 1 mA. The above behaviour may be explained by assuming the ‘core-shell’ model with the domain structure sketched in Fig. 1 and by considering, as it is known, that in the ferromagnetic materials the MR is generally negative when the applied magnetic field is perpendicular to the bias current in the sample and positive when magnetic field and current are parallel to each other. Therefore, to explain the negative minimum in the curves of Fig. 2, we assume that low axial magnetic fields may give rise to an increase in the volume fraction of the domains whose magnetization is perpendicular to the DC-bias current. It being understood that MR is associated with magnetization rotation, the latter process would occur at the expense of the closure domains having their magnetization opposite to the magnetizing field [4]. In this context it is possible to explain: (i) the reduction in the negative minimum and the rise of the positive values, in longitudinal MR, with increasing the driving axial current, (ii) the shift towards lower values of the axial magnetic field at which longitudinal MR changes its sign when the current increases. In fact, the circular magnetic field due to the axial current favours the magnetization orientation in its direction and reduces the action of the longitudinal field on the magnetic volumes that give negative longitudinal MR. The MR dependence on the circular magnetic self-field, Hy , due to the current flow is significant to test the validity of the model and allows us to get insight into the distribution of the magnetic
anisotropies. To this purpose one can take into account that the saturation magnetization Is in this sample is 1.6 T and that the circular magnetic field is given by Ref. [9] Hy ¼ ir=2pR20
ðr4R0 Þ
ð2Þ
In particular, the field at the surface of the wire (i.e. for r ¼ R0 ¼ 62:5 mm), varies from 0.031 to 0.155 Oe when the current i ranges from 1 to 5 mA. It is interesting to observe that a circular field varying from 0.031 to 0.155 Oe is sufficient to cause a large shift, of at least 20 Oe, of the crossing point of the Dr=r curves with the H-axis (Fig. 2). This is due to the different mechanisms involved in the process and may be explained as follows. The circular field assumes its highest values in outer shell, where the magnetization is radially oriented and the zigzag closure domains are directed in both the circular and longitudinal directions of the wire. Now, for bias current intensities higher than about 1 mA the circular field enhances the circular magnetization to expense of closure domains of the shell. The subsequent application of the longitudinal field H produces at first the rotation of the circular magnetization towards the longitudinal axis. This, in turn, gives rise to positive magnetoresistance variations which mask partially the initial negative minimum described according to Makino [4] and force the crossing point of the Dr=r curves towards longitudinal fields lower than that obtained by a bias current of 1 mA. As regards the radial magnetic anisotropy it maintains high values and the rotational processes of the radial magnetization towards the longitudinal direction continue gradually up to high values of H. Thus, the crossing points result from the counterbalance of the different effects above described and the effectiveness of the circular field is due to the absence of demagnetizing effects in that direction. By considering the mean value of Hy across the section of the sample, ðHy Þm ¼ ðHy Þs =2, as the critical field for magnetic rotational processes with anisotropy constant K having the order of magnitude of Is ðHy Þm , values of K are found which increase from about 2 to 10 J/m3 when i varies from 1 to 5 mA. Fig. 3 represents the transverse MR of an ascast sample obtained when the magnetizing field is
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 231 (2001) 179–184
perpendicular to the DC-bias current along the wire. In this situation the influence of the circular magnetic fields is negligible in comparison to that of the applied magnetic field. Accordingly to the previous domain model, the MR values are always negative because the external field favours a magnetization rotation in the direction perpendicular to the wire axis. Moreover, the transverse MR saturation is several times higher than the longitudinal one as it is to be expected by deducing the volume fraction of the inner core, with respect to that of the outer shell [10], from magnetic measurements of the hysteresis loops. 3.2. Annealed samples The effects of the thermal heating on MR are considered here. In this connection, the Figs. 4–6 represent the longitudinal MR in samples subjected to Joule heating obtained with a DC current of 450 mA for 1, 5 and 15 min, respectively. The transverse MR shows the behaviour represented in Fig. 7 that refers to the heating time of 5 min. By comparing the Figs. 4–6 with Fig. 2, one can observe a smaller negative contribution with a shift to lower values of the magnetic field at which MR changes its sign. The higher the annealing time and the DC-bias current intensity, the more significant the effect. This effect of heating on MR results somehow similar to the effect obtained by Makino et al. [4] through an axial tensile stress. Actually, both tensile stress and Joule heating can diminish the magnetic anisotropy induced, by compressive and radial stresses, in the directions perpendicular to the wire axis during the preparation process. However, heating relieves also longitudinal stresses so that the domain structure can be significantly modified [10]. Once the residual internal stresses are removed, a counterbalance occurs between circular anisotropy due to the heating current and longitudinal shape anisotropy. This seems to lead to quasirandom local anisotropy over the entire sample. In fact, in annealed wires the MR reaches saturation values about five times higher than in as-quenched samples where only the outer-shell contributes to the longitudinal MR. Furthermore, longitudinal
183
and transverse MR show saturation values closer each other than in the as-quenched state. On the other hand, the strong dependence of longitudinal MR on the measuring current, at least in specimens annealed for 1 min, emphasises a particular weakness in the local anisotropies of some regions in the wire. In fact, by varying the measuring current from 1 to 3 mA, as results from Fig. 4, the MR saturation value increases of about 30%. By changing the current from 3 to 5 mA the differences in the MR curves are no so important. It is noteworthy to consider that the removal of the outer-shell regions magnetized in radial directions occurs progressively with increasing heating time. Indeed, only a trace of the initial outer-shell domain structure should remains in samples heated for 15 min because in these specimens the negative minimum in MR curves is only just evident. Moreover, the negative minimum in annealed samples is obtained only in the curves relative to i ¼ 1 mA and thus for circular field low enough. This well agrees with the fact that the disappearance of the outer-shell structures responsible for the negative minimum makes the MR curves almost independent of the measuring current intensity. On the other hand, the above heating effect is consistent with the observed reduction in intensity of the longitudinal MR saturation value and with the correspondent lowering of the axial magnetic field that leads to MR saturation when heating time increases. In fact, the removal of the outer shell reduces the volume fraction of the domains whose magnetization is radially oriented and the progressive elimination of the residual internal stresses produces a continuous reduction of the local magnetoelastic anisotropies in any direction. As regards the transverse MR, it presents unexpected characteristics. In fact, as results from Fig. 7, the curves show a positive maximum at low applied fields and they present negative values only when the applied field becomes high enough. This anomalous behaviour at low field seems to be due to a mechanism quite similar to that invoked to explain the negative minimum in the longitudinal MR of as-cast samples. In this case, we assume that closure domains at the ends of the wire [10] play the main role and that structure
184
G. Bordin et al. / Journal of Magnetism and Magnetic Materials 231 (2001) 179–184
rearrangement of these domains increase initially the volume fraction of the longitudinal magnetization. This mechanism is made possible in annealed samples because of the weakness of the local anisotropies. In this connection, the strong demagnetizing effects in the transverse direction can justify the high magnetic fields needed to obtain negative MR.
4. Concluding remarks The magnetoresistance of amorphous wires with different DC-bias currents along the wire axis has been examined and the experimental data have been explained on he basis of a ‘core-shell’ domain model. A Joule heating of the samples favours a great change in magnetic anisotropies introduced during the preparation process of the wire. As a consequence, the original domain structure of the wire is destroyed or deformed and this reflects on MR. In particular, annealing produces a very important reduction in the local anisotropies. Besides, even low electrical currents, like those generally used for this kind of measure, produce circular magnetic fields which may contribute to modify the magnetic structure of the system. Finally, MR has been here described by considering the relative changes in resistivity rðHÞ with respect to the resistivity r0 at zero field. This procedure allowed us to emphasize well some characteristics of the phenomenon; however, in many cases MR changes are referred to the saturation resistivity. The Fig. 8 reports, for our samples, some longitudinal MR behaviours expressed as in Eq. (1) where r0 is now the saturation resistivity at a field of about 650 Oe. The longitudinal field is changed here from positive to negative values. The principal feature of these curves is that they show negative values of MR. This characteristic can be attributed to the sign of the saturation magnetostriction of the sample. In fact, the result is opposite to that obtained in Cobased amorphous wires where the magnetostriction coefficient is negative [11].
Fig. 8. Longitudinal MR, relative to the saturation resistivity, for as-cast samples (the inset refers to the lowest value of H).
References [1] D. Atkinson, P.T. Squire, M.R.J. Gibbs, S.N. Hogsdon, J. Phys. D 27 (1994) 1354. [2] P.T. Squire, D. Atkinson, M.R.J. Gibbs, S. Atalay, J. Magn. Magn. Mater. 132 (1994) 10. [3] K. Mohri, F.B. Humphrey, K. Kawashima, K. Kimura, M. Mizutani, IEEE Trans. Magn. 26 (1990) 1789. [4] Y. Makino, J.L. Costa, V. Madurga, K.V. Rao, IEEE Trans. Magn. 25 (1989) 3620. [5] J. Ziman, M. Hrab"eak, B. Zagyi, M. Kon"e, IEEE Trans. Magn. 30 (1994) 884. [6] J. Ziman, B. Zagyi, J. Magn. Magn. Mater. 169 (1997) 98. [7] D. Atkinson, R.S. Beach, P.T. Squire, C.L. Platt, S.N. Hogsdon, IEEE Trans. Magn. 31 (1995) 3892. ! [8] C. Gomez-Polo, M. V!azquez, J. Magn. Magn. Mater. 118 (1993) 86. [9] J.L. Costa, Y. Makino, K.V. Rao, IEEE Trans. Magn. 26 (1990) 1792. [10] M. V!azquez, A. Hernando, J. Phys. D 29 (1996) 939. [11] K. Mandal, S.K. Ghatak, Phys. Rev. B 47 (1993) 14233.