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Giant magnetoimpedance strip and coil sensors
Sensors and Actuators A 91 (2001) 116±119
Giant magnetoimpedance strip and coil sensors G.V. Kurlyandskayaa,1, A. GarcõÂa-Arribasa,*, J.M. BarandiaraÂna, E. Kiskerb b
a Departamento de Electricidad y ElectroÂnica, Universidad del PaõÂs Vasco, Apartado 644, 48080 Bilbao, Spain Institut fuÈr Angewandte Physik, Heinrich-Heine-UniversitaÈt DuÈsseldorf, UniversitaÈtsstraûe 1, 40225 DuÈsseldorf, Germany
Abstract We present noticeable values of giant magnetoimpedance on a cobalt-rich amorphous alloy, together with a new approach to giant magnetoimpedance devices of reduced size. Values as high as 260% of impedance variation as a function of the applied magnetic ®eld are obtained with the samples in the usual form of long ribbons. The bene®ts of speci®c thermal treatments in reaching these high values are studied through the magnetic domain structure. In order to reduce the size of the system and therefore extending the practical use of giant magnetoimpedance devices, we present the results obtained in wound ribbons in the form of coils. Though the magnetoimpedance is considerably reduced, it is still large enough to be applicable in sensor devices. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Giant magnetoimpedance; Magnetic domains; GMI sensors
1. Introduction Giant magnetoimpedance (GMI) is the phenomenon that exhibits certain magnetic materials consisting of a huge variation of the electrical impedance as a function of the applied magnetic ®eld. The origin of this phenomenon is completely classical [1] and is based on the dependence of the depth of penetration of the alternating current on the magnetic permeability, which in turn is coupled with the applied magnetic ®eld. Great interest has been paid to this phenomenon in the last years in a great variety of materials, mainly amorphous wires and ribbons, due to its potential application as sensors of the different magnitudes that can affect the magnetic permeability and therefore the impedance: magnetic ®eld, current, torsion, stress, etc. The magnitude of the GMI effect depends strongly on sample characteristics and serious efforts have been made from both theoretical and experimental points of view to determine the in¯uence of anisotropy, stress, and other magnetic and structural parameters that can be controlled on the sample [2]. The aim of this work is two-fold. First, we present our GMI results in a Co-rich nearly zero magnetostriction
* Corresponding author. Tel.: 34-946015307; fax: 34-946013071. E-mail address: [email protected] (A. GarcõÂa-Arribas). 1 Present address: Institut fuÈr Angewandte Physik, Heinrich-HeineUniversitaÈt DuÈsseldorf, UniversitaÈtsstraûe 1, 40225 DuÈsseldorf, Germany.
amorphous ribbon, thermal treated under stress to homogenize the magnetic anisotropy in the sample. In this case, the GMI experiments have been performed using a conventional disposition of the sample in the form of a long ribbon, and considerably large values of GMI are obtained. A detailed analysis of the magnetic state of the sample that determines this high GMI response is performed from the observation of the magnetic domains. On the other hand, we present a novel con®guration for GMI devices using a sample wound in the form of a coil in order to obtain a system of small size that can take advantage of GMI properties in feasible sensor devices. 2. Experimental Amorphous ribbons of FeCoCrSiB, with nearly zero magnetostriction (ls 10 7 ), have been obtained by melt spinning, having a Curie and crystallization temperatures of 160 and 5708C, respectively. For the usual GMI experiments, two samples, 21 mm thick and 1.1 mm wide, were cut into ribbons 100 mm long. Both samples were pre-annealed in vacuum at T 3508C for 1 h. We shall denote as `preannealed' (PA) the sample that was only submitted to this treatment. The other sample was afterwards annealed at T 3508C under uniaxial stress, applied parallel to the sample axis (s 210 MPa) for 1 h. We shall call this sample `stress-annealed' (SA). This second heat treatment induced a transverse magnetic anisotropy of magnitude K u 51 J/m3, as estimated from the longitudinal quasi-static magnetization
0924-4247/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 ( 0 1 ) 0 0 4 6 3 - 0
G.V. Kurlyandskaya et al. / Sensors and Actuators A 91 (2001) 116±119
117
Fig. 1. Hysteresis loops for pre-annealed (PA) and stress-annealed (SA) samples.
curves, measured using a conventional ¯uxmetric technique (Fig. 1). Domain structure observation at room temperature was performed with a ThermoMicroscope Explorer Atomic Force Microscope working in magnetic imaging regime in remanent state. For the measure of the magnetoimpedance, we used a conventional experimental set-up, though great care was paid to reduce noise and external interferences that can appear at elevated frequencies. In this sense, the sample holder has been designed very carefully. The feeding and sensing connections are done very close to the sample and guided to the appropriate instruments by shielded wires. A signal generator capable of producing a sinusoidal signal up to 60 MHz, was used to feed the sample. To match the output impedance of the signal generator a low inductance resistor was connected in series with the sample. The voltage drop across the sample was recorded in a digitizing oscilloscope, while the variable magnetic ®eld was applied by a pair of Helmholtz coils. The full experiment is completely computer controlled. The magnetic ®eld is swept along the full magnetic loop (from a positive saturating ®eld to a negative one and back). At each step, the exciting current amplitude was measured using a high frequency current transformer (that provides electrical isolation from the rest of the circuit, avoiding undesirable ground loops) and the output of the signal generator changed accordingly, in order to maintain a constant current amplitude regardless of the impedance variations. Prior to the measurement of the GMI curve, a quick survey of the frequency at which the maximum effect is achieved is performed, and the measurement made at that optimum frequency. For the samples in the form of coils, we used the same SA ribbon 10 mm long wound on a cylindrical support. To prevent electrical contact between consecutive turns, the sample is painted with a non-conductive varnish. We constructed two coils with different radii, 2.5 and 3.5 mm. Coil axis was placed perpendicular to the direction of the applied magnetic ®eld.
Fig. 2. GMI results for ribbon samples. Above: pre-annealed (PA) sample. The inset on the left shows the GMI dependence on excitation frequency. The maximum at 10 MHz is selected for the measurement. The inset on the right display the central part of the curve, where the sensitivity is maximum. Bottom: stress-annealed (SA) sample.
3. Results and discussion Fig. 2 shows the GMI curves obtained for the PA and SA samples obtained at 10 MHz, where the larger GMI is obtained (see inset). GMI is de®ned in the usual way as GMI % Z Z H max =Z H max 100. Values as high as 260% are obtained for both samples and sensitivities of more than 200% per Oe are obtained at low ®elds for the PA sample. The differences observed in both samples are caused by the stress annealing that, as it is well known, modi®es the magnetic anisotropy and the domain structure. Heat treatments of Co-rich amorphous ribbons with near zero magnetostriction under tensile stress induce a magnetic anisotropy with an easy plane perpendicular to the direction of the applied stress [3]. While the conditions of the heat treatments determine rather well the anisotropy in these samples, the domain structure of such stress-annealed ribbons can be rather complex. In short, it consists on wide stripe domains (tens of mm) with 1808 zigzag domain walls, formed during the stress annealing. Zigzag domain walls have neither a uniform thickness nor a plane form. They are
118
G.V. Kurlyandskaya et al. / Sensors and Actuators A 91 (2001) 116±119
Fig. 3. Left: Image of surface topography (with depth scale) for FeCoCrSiB amorphous ribbon without stress annealing. Right: Surface magnetic domain structure taken in magnetic mode. Observation was done by ThermoMicroscope Explorer Atomic Force Microscope in remanent state at room temperature for the sample of about 1 cm length.
tilted with respect to the magnetization direction, at least near the surface, and contain Bloch lines that minimize the local and demagnetization energies [4,5]. Previous experimental results and theoretical calculations [6,7] let us conclude that the best condition to obtain a great GMI effect is the existence of a narrow anisotropy distribution. This condition is even more preferable than a high value of the induced anisotropy but with a large angular spread. We pretend to create a uniform anisotropy in the sample by annealing under very small applied stress, in such a way that the new, induced anisotropy, is very little distributed, while the remaining anisotropy from the preparation process is relaxed out. The magnetic domain observation shows the peculiarities of the surface domain structure (Fig. 3). In the initial state (AP), the domain structure is not perfectly oriented along the ribbon axis as expected [6]. It consists of quite regular antiparallel domains, very homogeneous over the sample. The angle between the axis of the sample and the domain walls show variations between 45 and 608 over the sample. This domain structure suggests a magnetization process by pure magnetization rotation. The large GMI values obtained with this sample makes it a good candidate for its use as a GMI sensor. However, if used in the form of ribbon, a minimum length of 3 cm is required to minimize the effect of the demagnetized ®eld. This fact greatly reduces its application in a practical device. Thus, we suggest in this work a coil con®guration that avoids the demagnetizing ®eld problem and considerably reduces the size problem. The results obtained with two coils having different radii is shown in the Fig. 4. It is clear that the GMI properties are greatly reduced in this con®guration (between 10 and 20% instead of 260% in the original sample), but the obtained values are still large enough to be used in a device. It is to be noted that the curves are not saturated, that is, the impedance can be further reduced by increasing the magnetic ®eld. Using ®elds up to 150 Oe, a maximum variation of 40% is achieved. Besides, the maximum GMI is obtained now at lower frequencies (7 MHz) due to a resonance that
Fig. 4. GMI in coil shaped samples. The inset on the left shows the GMI dependence on excitation frequency. The inset on the right shows the existence of a resonance at 16 MHz (see text).
takes place at about 16 MHz (see inset), that can be caused by the autoinductance of the coil. The reduction of the GMI effect can be caused by both the inhomogeneity of the effective magnetic ®eld acting on the sample and the competing compression and traction stresses produced by the winding. Besides, coil radius seems to have a decisive role in the results. The coil with greater radius displays half of the GMI than the other one. More work must to be done to clarify the cause for this. For instance, taking into account that the autoinductance of the coil depends on its radius, the differences may be caused by the different position of resonance that is seen in the inset of the Fig. 4. In any case, the winding of amorphous samples in order to reduce the size is a promising one for magnetoimpedance sensor devices. 4. Conclusions Large magnetoimpedance effect is measured in a Co-rich, nearly zero magnetostriction, amorphous alloy. Values of
G.V. Kurlyandskaya et al. / Sensors and Actuators A 91 (2001) 116±119
260% variation in the impedance are obtained and sensibilities of 200% per Oe at low ®elds. Magnetic domain observation shows the existence of considerable anisotropy spread. A considerable reduction of size, desirable for applicable sensor devices is obtained by winding the sample in a cylindrical support to obtain a coil shaped sample. The GMI effect is reduced but it is still largely usable. Coil radius has an important role in the value of the effect obtained. Acknowledgements G.K. would like to thank The Basque Government for the ®nancial support in the form of Visiting Scientist Grant. We thank Dr. A. Potapov for his help with preparation of the samples and Dr. Bernd MuÈller-ZuÈlow of ATOS GmbH, Pfungstadt for his assistance with domain structure observation by ThermoMicroscope Explorer Atomic Force Microscope. This work has been partially ®nanced by the Spanish Government under project MAT99-0667.
119
References [1] L.D. Landau, E.M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, Oxford, 1975, p. 211. [2] R.L. Sommer, C.L. Chien, Role of magnetic anisotropy in the magneto-impedance effect in amorphous alloys, Appl. Phys. Lett. 67 (1995) 3346. [3] H.R. Hilzinger, Stress-induced magnetic anisotropy in non-magnetostrictive amorphous alloy, in: Proceedings of the 4th International Conference on Rapidly Quenched Metals, Sendai, 1981, pp. 791±794. [4] G.V. Kurlyandskaya, M. VaÂzquez, J.L. MunÄoz, D. GarcõÂa, J. McCord, Effect of induced magnetic anisotropy and domain structure features on magnetoimpedance in stress-annealed Co-rich amorphous ribbons, J. Magn. Magn. Mater. 196/197 (1999) 259±261. [5] A. Hubert, R. SchaÈfer, Magnetic Domains, Springer, Berlin, 1998, p. 439. [6] G.V. Kurlyandskaya, M. VaÂzquez, J. McCord, J.L. MunÄoz, D. Garcia, A.P. Potapov, Domain structure and magnetoimpedance effect in stress-annealed Co-rich amorphous ribbons with different stress induced magnetic anisotropy, Fiz. Met. Metalloved 90 (2000) 549± 556. [7] J.L. MunÄoz, G.V. Kurlyandskaya, J.M. Barandiaran, A.P. Potapov, V.A. Lukshina M. VaÂzquez, Non-uniform anisotropy and magneto impedance in stress annealed amorphous ribbons, Fiz. Met. Metalloved., in print
Giant magnetoimpedance strip and coil sensors G.V. Kurlyandskayaa,1, A. GarcõÂa-Arribasa,*, J.M. BarandiaraÂna, E. Kiskerb b
a Departamento de Electricidad y ElectroÂnica, Universidad del PaõÂs Vasco, Apartado 644, 48080 Bilbao, Spain Institut fuÈr Angewandte Physik, Heinrich-Heine-UniversitaÈt DuÈsseldorf, UniversitaÈtsstraûe 1, 40225 DuÈsseldorf, Germany
Abstract We present noticeable values of giant magnetoimpedance on a cobalt-rich amorphous alloy, together with a new approach to giant magnetoimpedance devices of reduced size. Values as high as 260% of impedance variation as a function of the applied magnetic ®eld are obtained with the samples in the usual form of long ribbons. The bene®ts of speci®c thermal treatments in reaching these high values are studied through the magnetic domain structure. In order to reduce the size of the system and therefore extending the practical use of giant magnetoimpedance devices, we present the results obtained in wound ribbons in the form of coils. Though the magnetoimpedance is considerably reduced, it is still large enough to be applicable in sensor devices. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Giant magnetoimpedance; Magnetic domains; GMI sensors
1. Introduction Giant magnetoimpedance (GMI) is the phenomenon that exhibits certain magnetic materials consisting of a huge variation of the electrical impedance as a function of the applied magnetic ®eld. The origin of this phenomenon is completely classical [1] and is based on the dependence of the depth of penetration of the alternating current on the magnetic permeability, which in turn is coupled with the applied magnetic ®eld. Great interest has been paid to this phenomenon in the last years in a great variety of materials, mainly amorphous wires and ribbons, due to its potential application as sensors of the different magnitudes that can affect the magnetic permeability and therefore the impedance: magnetic ®eld, current, torsion, stress, etc. The magnitude of the GMI effect depends strongly on sample characteristics and serious efforts have been made from both theoretical and experimental points of view to determine the in¯uence of anisotropy, stress, and other magnetic and structural parameters that can be controlled on the sample [2]. The aim of this work is two-fold. First, we present our GMI results in a Co-rich nearly zero magnetostriction
* Corresponding author. Tel.: 34-946015307; fax: 34-946013071. E-mail address: [email protected] (A. GarcõÂa-Arribas). 1 Present address: Institut fuÈr Angewandte Physik, Heinrich-HeineUniversitaÈt DuÈsseldorf, UniversitaÈtsstraûe 1, 40225 DuÈsseldorf, Germany.
amorphous ribbon, thermal treated under stress to homogenize the magnetic anisotropy in the sample. In this case, the GMI experiments have been performed using a conventional disposition of the sample in the form of a long ribbon, and considerably large values of GMI are obtained. A detailed analysis of the magnetic state of the sample that determines this high GMI response is performed from the observation of the magnetic domains. On the other hand, we present a novel con®guration for GMI devices using a sample wound in the form of a coil in order to obtain a system of small size that can take advantage of GMI properties in feasible sensor devices. 2. Experimental Amorphous ribbons of FeCoCrSiB, with nearly zero magnetostriction (ls 10 7 ), have been obtained by melt spinning, having a Curie and crystallization temperatures of 160 and 5708C, respectively. For the usual GMI experiments, two samples, 21 mm thick and 1.1 mm wide, were cut into ribbons 100 mm long. Both samples were pre-annealed in vacuum at T 3508C for 1 h. We shall denote as `preannealed' (PA) the sample that was only submitted to this treatment. The other sample was afterwards annealed at T 3508C under uniaxial stress, applied parallel to the sample axis (s 210 MPa) for 1 h. We shall call this sample `stress-annealed' (SA). This second heat treatment induced a transverse magnetic anisotropy of magnitude K u 51 J/m3, as estimated from the longitudinal quasi-static magnetization
0924-4247/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 ( 0 1 ) 0 0 4 6 3 - 0
G.V. Kurlyandskaya et al. / Sensors and Actuators A 91 (2001) 116±119
117
Fig. 1. Hysteresis loops for pre-annealed (PA) and stress-annealed (SA) samples.
curves, measured using a conventional ¯uxmetric technique (Fig. 1). Domain structure observation at room temperature was performed with a ThermoMicroscope Explorer Atomic Force Microscope working in magnetic imaging regime in remanent state. For the measure of the magnetoimpedance, we used a conventional experimental set-up, though great care was paid to reduce noise and external interferences that can appear at elevated frequencies. In this sense, the sample holder has been designed very carefully. The feeding and sensing connections are done very close to the sample and guided to the appropriate instruments by shielded wires. A signal generator capable of producing a sinusoidal signal up to 60 MHz, was used to feed the sample. To match the output impedance of the signal generator a low inductance resistor was connected in series with the sample. The voltage drop across the sample was recorded in a digitizing oscilloscope, while the variable magnetic ®eld was applied by a pair of Helmholtz coils. The full experiment is completely computer controlled. The magnetic ®eld is swept along the full magnetic loop (from a positive saturating ®eld to a negative one and back). At each step, the exciting current amplitude was measured using a high frequency current transformer (that provides electrical isolation from the rest of the circuit, avoiding undesirable ground loops) and the output of the signal generator changed accordingly, in order to maintain a constant current amplitude regardless of the impedance variations. Prior to the measurement of the GMI curve, a quick survey of the frequency at which the maximum effect is achieved is performed, and the measurement made at that optimum frequency. For the samples in the form of coils, we used the same SA ribbon 10 mm long wound on a cylindrical support. To prevent electrical contact between consecutive turns, the sample is painted with a non-conductive varnish. We constructed two coils with different radii, 2.5 and 3.5 mm. Coil axis was placed perpendicular to the direction of the applied magnetic ®eld.
Fig. 2. GMI results for ribbon samples. Above: pre-annealed (PA) sample. The inset on the left shows the GMI dependence on excitation frequency. The maximum at 10 MHz is selected for the measurement. The inset on the right display the central part of the curve, where the sensitivity is maximum. Bottom: stress-annealed (SA) sample.
3. Results and discussion Fig. 2 shows the GMI curves obtained for the PA and SA samples obtained at 10 MHz, where the larger GMI is obtained (see inset). GMI is de®ned in the usual way as GMI % Z Z H max =Z H max 100. Values as high as 260% are obtained for both samples and sensitivities of more than 200% per Oe are obtained at low ®elds for the PA sample. The differences observed in both samples are caused by the stress annealing that, as it is well known, modi®es the magnetic anisotropy and the domain structure. Heat treatments of Co-rich amorphous ribbons with near zero magnetostriction under tensile stress induce a magnetic anisotropy with an easy plane perpendicular to the direction of the applied stress [3]. While the conditions of the heat treatments determine rather well the anisotropy in these samples, the domain structure of such stress-annealed ribbons can be rather complex. In short, it consists on wide stripe domains (tens of mm) with 1808 zigzag domain walls, formed during the stress annealing. Zigzag domain walls have neither a uniform thickness nor a plane form. They are
118
G.V. Kurlyandskaya et al. / Sensors and Actuators A 91 (2001) 116±119
Fig. 3. Left: Image of surface topography (with depth scale) for FeCoCrSiB amorphous ribbon without stress annealing. Right: Surface magnetic domain structure taken in magnetic mode. Observation was done by ThermoMicroscope Explorer Atomic Force Microscope in remanent state at room temperature for the sample of about 1 cm length.
tilted with respect to the magnetization direction, at least near the surface, and contain Bloch lines that minimize the local and demagnetization energies [4,5]. Previous experimental results and theoretical calculations [6,7] let us conclude that the best condition to obtain a great GMI effect is the existence of a narrow anisotropy distribution. This condition is even more preferable than a high value of the induced anisotropy but with a large angular spread. We pretend to create a uniform anisotropy in the sample by annealing under very small applied stress, in such a way that the new, induced anisotropy, is very little distributed, while the remaining anisotropy from the preparation process is relaxed out. The magnetic domain observation shows the peculiarities of the surface domain structure (Fig. 3). In the initial state (AP), the domain structure is not perfectly oriented along the ribbon axis as expected [6]. It consists of quite regular antiparallel domains, very homogeneous over the sample. The angle between the axis of the sample and the domain walls show variations between 45 and 608 over the sample. This domain structure suggests a magnetization process by pure magnetization rotation. The large GMI values obtained with this sample makes it a good candidate for its use as a GMI sensor. However, if used in the form of ribbon, a minimum length of 3 cm is required to minimize the effect of the demagnetized ®eld. This fact greatly reduces its application in a practical device. Thus, we suggest in this work a coil con®guration that avoids the demagnetizing ®eld problem and considerably reduces the size problem. The results obtained with two coils having different radii is shown in the Fig. 4. It is clear that the GMI properties are greatly reduced in this con®guration (between 10 and 20% instead of 260% in the original sample), but the obtained values are still large enough to be used in a device. It is to be noted that the curves are not saturated, that is, the impedance can be further reduced by increasing the magnetic ®eld. Using ®elds up to 150 Oe, a maximum variation of 40% is achieved. Besides, the maximum GMI is obtained now at lower frequencies (7 MHz) due to a resonance that
Fig. 4. GMI in coil shaped samples. The inset on the left shows the GMI dependence on excitation frequency. The inset on the right shows the existence of a resonance at 16 MHz (see text).
takes place at about 16 MHz (see inset), that can be caused by the autoinductance of the coil. The reduction of the GMI effect can be caused by both the inhomogeneity of the effective magnetic ®eld acting on the sample and the competing compression and traction stresses produced by the winding. Besides, coil radius seems to have a decisive role in the results. The coil with greater radius displays half of the GMI than the other one. More work must to be done to clarify the cause for this. For instance, taking into account that the autoinductance of the coil depends on its radius, the differences may be caused by the different position of resonance that is seen in the inset of the Fig. 4. In any case, the winding of amorphous samples in order to reduce the size is a promising one for magnetoimpedance sensor devices. 4. Conclusions Large magnetoimpedance effect is measured in a Co-rich, nearly zero magnetostriction, amorphous alloy. Values of
G.V. Kurlyandskaya et al. / Sensors and Actuators A 91 (2001) 116±119
260% variation in the impedance are obtained and sensibilities of 200% per Oe at low ®elds. Magnetic domain observation shows the existence of considerable anisotropy spread. A considerable reduction of size, desirable for applicable sensor devices is obtained by winding the sample in a cylindrical support to obtain a coil shaped sample. The GMI effect is reduced but it is still largely usable. Coil radius has an important role in the value of the effect obtained. Acknowledgements G.K. would like to thank The Basque Government for the ®nancial support in the form of Visiting Scientist Grant. We thank Dr. A. Potapov for his help with preparation of the samples and Dr. Bernd MuÈller-ZuÈlow of ATOS GmbH, Pfungstadt for his assistance with domain structure observation by ThermoMicroscope Explorer Atomic Force Microscope. This work has been partially ®nanced by the Spanish Government under project MAT99-0667.
119
References [1] L.D. Landau, E.M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, Oxford, 1975, p. 211. [2] R.L. Sommer, C.L. Chien, Role of magnetic anisotropy in the magneto-impedance effect in amorphous alloys, Appl. Phys. Lett. 67 (1995) 3346. [3] H.R. Hilzinger, Stress-induced magnetic anisotropy in non-magnetostrictive amorphous alloy, in: Proceedings of the 4th International Conference on Rapidly Quenched Metals, Sendai, 1981, pp. 791±794. [4] G.V. Kurlyandskaya, M. VaÂzquez, J.L. MunÄoz, D. GarcõÂa, J. McCord, Effect of induced magnetic anisotropy and domain structure features on magnetoimpedance in stress-annealed Co-rich amorphous ribbons, J. Magn. Magn. Mater. 196/197 (1999) 259±261. [5] A. Hubert, R. SchaÈfer, Magnetic Domains, Springer, Berlin, 1998, p. 439. [6] G.V. Kurlyandskaya, M. VaÂzquez, J. McCord, J.L. MunÄoz, D. Garcia, A.P. Potapov, Domain structure and magnetoimpedance effect in stress-annealed Co-rich amorphous ribbons with different stress induced magnetic anisotropy, Fiz. Met. Metalloved 90 (2000) 549± 556. [7] J.L. MunÄoz, G.V. Kurlyandskaya, J.M. Barandiaran, A.P. Potapov, V.A. Lukshina M. VaÂzquez, Non-uniform anisotropy and magneto impedance in stress annealed amorphous ribbons, Fiz. Met. Metalloved., in print