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Bulk and surface magnetization of nearly zero magnetostrictive Co-based amorphous glass-coated microwires
Sensors and Actuators A 129 (2006) 37–40
Bulk and surface magnetization of nearly zero magnetostrictive Co-based amorphous glass-coated microwires ´ ari, F. Borza ∗ , T. Meydan T.A. Ov´ Wolfson Centre for Magnetics Technology, School of Engineering, Cardiff University, UK Received 5 July 2004; received in revised form 23 August 2005; accepted 19 September 2005 Available online 27 December 2005
Abstract A method for the calculation of magnetoelastic anisotropy distribution and coercivity values in nearly zero magnetostrictive Co-based amorphous glass-coated microwires is presented. Bulk coercivity and surface anisotropy distribution are analyzed as a function of microwire dimensions (metallic core diameter and glass coating thickness). Calculated results are in good agreement with experimental ones. The results allow us to explain which type of internal stresses (rapid solidification or glass coating induced ones) mainly contribute to the formation of anisotropy axes in each region of the microwire (inner core and outer shell) as well as to discuss the major characteristics of the magnetization process in these materials. © 2005 Elsevier B.V. All rights reserved. Keywords: Amorphous glass-coated microwires; Coercivity; Magnetoelastic anisotropy; Nearly zero magnetostriction; Surface anisotropy
1. Introduction Glass-coated ferromagnetic amorphous microwires display remarkable soft magnetic properties that are suitable for various sensor applications [1]. Their magnetic properties and behaviour are strongly dependent on the sign and magnitude of their magnetostriction constant. Co-based amorphous microwires with low negative magnetostriction or the so called nearly zero magnetostrictive microwires (e.g. (Co1−x Fex )72.5 Si12.5 B15 with λS ≈ −1 × 10−7 for x = 0.06) are extremely attractive both for applications as high permeability materials as well as in sensors based on the giant magneto-impedance (GMI) effect [2]. The first type of applications is based on the bulk or volume magnetization process of microwires while the second one depends entirely on the surface magnetization process. The high quenching rates involved in the preparation of amorphous microwires (105 –106 K s−1 ) along with the presence of the glass coating are responsible for huge internal stresses (of the order of 1 GPa) induced during preparation [3]. Due to the amorphous structure and magnetostrictive character of the alloys, the magnetic properties and behaviour of microwires are determined
∗
Corresponding author. E-mail address: [email protected] (F. Borza).
0924-4247/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2005.09.041
by the magnetoelastic anisotropy that originates in the coupling between the large internal stresses and magnetostriction, coupling that gives rise to a significant magnetoelastic energy term even in the case of nearly zero magnetostrictive microwires. The aim of this paper is to calculate the volume and surface distribution of the magnetoelastic anisotropy and subsequently to estimate the coercivity of Co-based amorphous microwires with nearly zero magnetostriction. Coercivity is calculated considering the magnetization process as nucleation at coercivity. We also discuss the changes in coercivity with the microwires’ dimensions (metallic core diameter and glass coating thickness). We have also investigated the surface anisotropy distribution and its dependence on the microwire dimensions. 2. Anisotropy distribution The calculation of magnetoelastic anisotropy distribution requires first the calculation of internal stress distribution. Taking into account the rather complicated mechanism by which internal stresses are induced in microwires, several simplifying assumptions were done. Calculation of internal stress distributions for microwires with different dimensions were performed by considering stresses induced due to the rapid solidification of metal and those induced due to the difference between thermal expansion coefficients of metal and glass. For simplicity, only
´ ari et al. / Sensors and Actuators A 129 (2006) 37–40 T.A. Ov´
38
Calculated results show that radial (transverse) magnetoelastic anisotropy dominates on about 92% of the microwire radius starting from its centre towards the surface. We called this region of the microwire the inner core (IC). On the remaining region at the sample surface, called the outer shell (OS), the magnetoelastic anisotropy has a circumferential direction and its value increases abruptly towards the surface. The radial direction of anisotropy in the IC originates in the coupling between large axial tensile stresses and the negative magnetostriction (−1 × 10−7 ), while the circumferential direction of anisotropy in the OS results from the magnetomechanical coupling between large circumferential compressive stresses and the negative magnetostriction. Due to the existence of anisotropy axes which are perpendicular to the axially applied magnetic field, the axial magnetization process of such microwires will always be almost anhysteretic, displaying at the same time small coercivities as a result of the rather small values of the anisotropy constants. Fig. 1. Radial distribution of magnetoelastic anisotropy in the metallic part of a (Co0.94 Fe0.06 )72.5 Si12.5 B15 amorphous microwire with the metallic core diameter of 15.6 m and the glass coating thickness of 5 m. IC refers to the ‘inner core’ dominated by transverse anisotropy, and OS to the ‘outer shell’ dominated by circumferential anisotropy.
the diagonal components of the stress tensor were calculated. The fully developed mathematical formulation of the physical processes involved in the microwire preparation is presented in a previous work [3]. Thus, it is possible to calculate the radial distribution of the stress tensor components expressed in cylindrical coordinates. Knowing the stress distribution, the next step is to see which component is the dominant one (i.e. the radial, axial, or circumferential component) at each point on the microwire’s radius. This procedure must be followed due to the tensor character of stresses, which leads to the formation of an easy axis of anisotropy as a result of the coupling between magnetostriction and the largest component of the stress tensor. It is also important to know the distribution of the other stress components, besides the dominant one, since they play an important role in establishing the anisotropy axis when the dominant component and the magnetostriction constant have opposite signs. The next step is the calculation of the radial distribution of magnetoelastic anisotropy. The magnetoelastic anisotropy constant on the direction of the dominant component of the stress tensor is given by: K=
3 λS σii 2
(1)
where σ ii is the dominant component of the stress tensor and λS the saturation magnetostriction constant. Consequently, from the radial distribution of the diagonal components of the internal stress tensor, one can quickly obtain the radial distribution of anisotropy. Fig. 1 shows the radial distribution of magnetoelastic anisotropy in a (Co0.94 Fe0.06 )72.5 Si12.5 B15 microwire with the metallic core diameter of 15.6 m and the glass coating thickness of 5 m.
3. Coercivity calculation. Dependence on microwire dimensions We analyze the magnetization reversal in Co-based amorphous glass-coated microwires with nearly zero magnetostriction considering it as a nucleation at coercivity process. Nucleation implies the formation of a domain wall. The reversal is in this way controlled by the balance of three energy terms: wall energy, magnetostatic energy variation, and Zeeman energy, since the whole process is caused by an axially applied field. This energy balance results in the following expression of coercivity: γW HC ∼ (2) =α µ0 MS V 1/3 in which γ W is the wall surface tension, µ0 the magnetic permeability of vacuum, MS the saturation magnetization, V the volume of the reversed nucleus driving the reversal process, and α is a phenomenological parameter which reflects the existence of an anisotropy distribution. We neglected the demagnetization effects due to the high length to diameter ratio of the considered cylindrical samples. The wall surface tension is given by: γW = β AKIC (3) where β is a coefficient that depends on the wall shape, A is the exchange constant, and KIC is the weighted mean of the magnetoelastic anisotropy constants associated to the cylindrical shells of thickness dr from within the IC, since the magnetization of this region drives the reversal process and it is reasonable to assume that the reversed nucleus appears in the IC. We will use β = 2, a reasonable value that has been also employed for ‘conventional’ in-rotating-water quenched amorphous wires [4]. For A we employed the value of the exchange constant for Co, i.e. A = 3.3 × 10−11 J m−1 . As concerns the volume of the reversed nucleus, V, it is plausible to consider an axial dimension of the order of the wall thickness, δW , and transverse dimensions comparable to the cross-section area of the microwire’s metallic core, πR2m , where
´ ari et al. / Sensors and Actuators A 129 (2006) 37–40 T.A. Ov´
Fig. 2. Coercivity dependence on glass coating thickness with the metallic core diameter as a parameter for a (Co0.94 Fe0.06 )72.5 Si12.5 B15 amorphous glasscoated microwire.
Rm is the metallic core radius. The transverse dimensions of the reversed nucleus should also depend on the anisotropy distribution. The most important parameter related to the anisotropy distribution is the ratio between the metallic core radius, Rm , and the glass coating thickness, tg . Thus, the radial dimension of the nucleus is R2m /tg , and its cross-section area becomes: πR4m /tg2 . Considering α = (tg /Rm )2/3 (α √ reflects the contribution of the anisotropy distribution), δW = π A/KIC , and by taking into account (3) and the expression for V, expression (2) for the coercivity becomes: 2A1/3 HC = µ0 M S
39
Fig. 3. Coercivity dependence on metallic core diameter with the glass coating thickness as a parameter for a (Co0.94 Fe0.06 )72.5 Si12.5 B15 amorphous glasscoated microwire.
4. Dependence of surface anisotropy on microwire dimensions Next we refer to the magnetoelastic anisotropy from the microwire’s surface region, i.e. within the outer shell (OS). Surface anisotropy KOS was calculated as the weighted mean of the magnetoelastic anisotropy constants that correspond to the cylindrical shells of thickness dr from the OS. Figs. 4 and 5 show the dependence of surface magnetoelastic anisotropy on metallic core diameter and glass coating thickness, respectively.
2/3
tg KIC π · R2m
(4)
Thus, we achieved a method for the calculation of magnetoelastic anisotropy distribution and coercivity values for microwires with nearly zero magnetostriction having different dimensions. Figs. 2 and 3 illustrate the dependence of calculated and measured coercivity values on glass thickness and metallic core diameter, respectively. Experimental coercivity values were determined from hysteresis loops measured using an inductive method. One observes that calculated results are in good agreement with measured ones and expression (4) predicts with high accuracy the dependence of HC on microwire dimensions. Coercivity increases as expected with glass coating thickness for constant values of the metallic core diameter due to the reinforcement of transverse anisotropy within the IC as a result of larger axial tensile stresses determined by the thicker glass coating. On the other hand, at constant glass coating thickness coercivity decreases with the increase of the metallic core diameter due to lower transverse anisotropy in the IC as a result of smaller axial tensile stresses induced by the rapid solidification process.
Fig. 4. Dependence of surface anisotropy on metallic core diameter with the glass coating thickness as a parameter for a (Co0.94 Fe0.06 )72.5 Si12.5 B15 amorphous glass-coated microwire.
40
´ ari et al. / Sensors and Actuators A 129 (2006) 37–40 T.A. Ov´
5. Conclusion The weak dependence of surface anisotropy on glass coating thickness and its non-linear dependence on the diameter of the metallic nucleus indicate that surface magnetoelastic anisotropy mainly originates in the coupling between magnetostriction and stresses induced by rapid solidification rather than stresses induced by the presence of the glass coating. Bulk magnetization behaviour (anisotropy, coercivity) is affected by both glass coating thickness and diameter of the actual metallic wire. The obtained results allow a better understanding of previous experimental results and they are essential for tailoring the magnetic properties of nearly zero magnetostrictive Cobased amorphous glass-coated microwires for sensor applications. Fig. 5. Dependence of surface anisotropy on glass coating thickness with the metallic core diameter as a parameter for a (Co0.94 Fe0.06 )72.5 Si12.5 B15 amorphous glass-coated microwire.
The large values of the circumferential anisotropy constant in the surface region of the microwires lead to circumferential magnetization processes taking place mainly by domain wall displacements, as it has been reported by most of the authors who performed GMI measurements at frequencies below the 1 MHz domain wall relaxation frequency [5]. Both the weak dependence of surface anisotropy on glass coating thickness and the non-linear dependence of surface anisotropy on metallic core diameter have been emphasized by means of ferromagnetic resonance experiments [6], although a systematic experimental study of the latter has not been performed yet.
References [1] M. V´azquez, Soft magnetic wires, Physica B 299 (2001) 302–313. [2] T. Uchiyama, T. Meydan, Impedance strain gauge characteristics of glasscovered amorphous magnetic wires, J. Optoelectron. Adv. M. 4 (2002) 277–280. ´ ari, Gh. Pop, Internal stress distribution in [3] H. Chiriac, T.A. Ov´ glass-covered amorphous magnetic wires, Phys. Rev. B 52 (1995) 10104–10113. [4] A.M. Severino, C. G´omez-Polo, P. Mar´ın, M. V´azquez, Influence of the sample length on the switching process of magnetostrictive amorphous wire, J. Magn. Magn. Mater. 103 (1992) 117–125. [5] L.V. Panina, K. Mohri, T. Uchiyama, Giant magneto-impedance (GMI) in amorphous wire, single layer film and sandwich film, Physica A 241 (1997) 429–438. ´ ari, F.J. Casta˜no, Ferromagnetic [6] H. Chiriac, C.N. Colesniuc, T.A. Ov´ resonance investigation of surface anisotropy distribution in amorphous glass-covered wires, J. Appl. Phys. 87 (2000) 4816–4818.
Bulk and surface magnetization of nearly zero magnetostrictive Co-based amorphous glass-coated microwires ´ ari, F. Borza ∗ , T. Meydan T.A. Ov´ Wolfson Centre for Magnetics Technology, School of Engineering, Cardiff University, UK Received 5 July 2004; received in revised form 23 August 2005; accepted 19 September 2005 Available online 27 December 2005
Abstract A method for the calculation of magnetoelastic anisotropy distribution and coercivity values in nearly zero magnetostrictive Co-based amorphous glass-coated microwires is presented. Bulk coercivity and surface anisotropy distribution are analyzed as a function of microwire dimensions (metallic core diameter and glass coating thickness). Calculated results are in good agreement with experimental ones. The results allow us to explain which type of internal stresses (rapid solidification or glass coating induced ones) mainly contribute to the formation of anisotropy axes in each region of the microwire (inner core and outer shell) as well as to discuss the major characteristics of the magnetization process in these materials. © 2005 Elsevier B.V. All rights reserved. Keywords: Amorphous glass-coated microwires; Coercivity; Magnetoelastic anisotropy; Nearly zero magnetostriction; Surface anisotropy
1. Introduction Glass-coated ferromagnetic amorphous microwires display remarkable soft magnetic properties that are suitable for various sensor applications [1]. Their magnetic properties and behaviour are strongly dependent on the sign and magnitude of their magnetostriction constant. Co-based amorphous microwires with low negative magnetostriction or the so called nearly zero magnetostrictive microwires (e.g. (Co1−x Fex )72.5 Si12.5 B15 with λS ≈ −1 × 10−7 for x = 0.06) are extremely attractive both for applications as high permeability materials as well as in sensors based on the giant magneto-impedance (GMI) effect [2]. The first type of applications is based on the bulk or volume magnetization process of microwires while the second one depends entirely on the surface magnetization process. The high quenching rates involved in the preparation of amorphous microwires (105 –106 K s−1 ) along with the presence of the glass coating are responsible for huge internal stresses (of the order of 1 GPa) induced during preparation [3]. Due to the amorphous structure and magnetostrictive character of the alloys, the magnetic properties and behaviour of microwires are determined
∗
Corresponding author. E-mail address: [email protected] (F. Borza).
0924-4247/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2005.09.041
by the magnetoelastic anisotropy that originates in the coupling between the large internal stresses and magnetostriction, coupling that gives rise to a significant magnetoelastic energy term even in the case of nearly zero magnetostrictive microwires. The aim of this paper is to calculate the volume and surface distribution of the magnetoelastic anisotropy and subsequently to estimate the coercivity of Co-based amorphous microwires with nearly zero magnetostriction. Coercivity is calculated considering the magnetization process as nucleation at coercivity. We also discuss the changes in coercivity with the microwires’ dimensions (metallic core diameter and glass coating thickness). We have also investigated the surface anisotropy distribution and its dependence on the microwire dimensions. 2. Anisotropy distribution The calculation of magnetoelastic anisotropy distribution requires first the calculation of internal stress distribution. Taking into account the rather complicated mechanism by which internal stresses are induced in microwires, several simplifying assumptions were done. Calculation of internal stress distributions for microwires with different dimensions were performed by considering stresses induced due to the rapid solidification of metal and those induced due to the difference between thermal expansion coefficients of metal and glass. For simplicity, only
´ ari et al. / Sensors and Actuators A 129 (2006) 37–40 T.A. Ov´
38
Calculated results show that radial (transverse) magnetoelastic anisotropy dominates on about 92% of the microwire radius starting from its centre towards the surface. We called this region of the microwire the inner core (IC). On the remaining region at the sample surface, called the outer shell (OS), the magnetoelastic anisotropy has a circumferential direction and its value increases abruptly towards the surface. The radial direction of anisotropy in the IC originates in the coupling between large axial tensile stresses and the negative magnetostriction (−1 × 10−7 ), while the circumferential direction of anisotropy in the OS results from the magnetomechanical coupling between large circumferential compressive stresses and the negative magnetostriction. Due to the existence of anisotropy axes which are perpendicular to the axially applied magnetic field, the axial magnetization process of such microwires will always be almost anhysteretic, displaying at the same time small coercivities as a result of the rather small values of the anisotropy constants. Fig. 1. Radial distribution of magnetoelastic anisotropy in the metallic part of a (Co0.94 Fe0.06 )72.5 Si12.5 B15 amorphous microwire with the metallic core diameter of 15.6 m and the glass coating thickness of 5 m. IC refers to the ‘inner core’ dominated by transverse anisotropy, and OS to the ‘outer shell’ dominated by circumferential anisotropy.
the diagonal components of the stress tensor were calculated. The fully developed mathematical formulation of the physical processes involved in the microwire preparation is presented in a previous work [3]. Thus, it is possible to calculate the radial distribution of the stress tensor components expressed in cylindrical coordinates. Knowing the stress distribution, the next step is to see which component is the dominant one (i.e. the radial, axial, or circumferential component) at each point on the microwire’s radius. This procedure must be followed due to the tensor character of stresses, which leads to the formation of an easy axis of anisotropy as a result of the coupling between magnetostriction and the largest component of the stress tensor. It is also important to know the distribution of the other stress components, besides the dominant one, since they play an important role in establishing the anisotropy axis when the dominant component and the magnetostriction constant have opposite signs. The next step is the calculation of the radial distribution of magnetoelastic anisotropy. The magnetoelastic anisotropy constant on the direction of the dominant component of the stress tensor is given by: K=
3 λS σii 2
(1)
where σ ii is the dominant component of the stress tensor and λS the saturation magnetostriction constant. Consequently, from the radial distribution of the diagonal components of the internal stress tensor, one can quickly obtain the radial distribution of anisotropy. Fig. 1 shows the radial distribution of magnetoelastic anisotropy in a (Co0.94 Fe0.06 )72.5 Si12.5 B15 microwire with the metallic core diameter of 15.6 m and the glass coating thickness of 5 m.
3. Coercivity calculation. Dependence on microwire dimensions We analyze the magnetization reversal in Co-based amorphous glass-coated microwires with nearly zero magnetostriction considering it as a nucleation at coercivity process. Nucleation implies the formation of a domain wall. The reversal is in this way controlled by the balance of three energy terms: wall energy, magnetostatic energy variation, and Zeeman energy, since the whole process is caused by an axially applied field. This energy balance results in the following expression of coercivity: γW HC ∼ (2) =α µ0 MS V 1/3 in which γ W is the wall surface tension, µ0 the magnetic permeability of vacuum, MS the saturation magnetization, V the volume of the reversed nucleus driving the reversal process, and α is a phenomenological parameter which reflects the existence of an anisotropy distribution. We neglected the demagnetization effects due to the high length to diameter ratio of the considered cylindrical samples. The wall surface tension is given by: γW = β AKIC (3) where β is a coefficient that depends on the wall shape, A is the exchange constant, and KIC is the weighted mean of the magnetoelastic anisotropy constants associated to the cylindrical shells of thickness dr from within the IC, since the magnetization of this region drives the reversal process and it is reasonable to assume that the reversed nucleus appears in the IC. We will use β = 2, a reasonable value that has been also employed for ‘conventional’ in-rotating-water quenched amorphous wires [4]. For A we employed the value of the exchange constant for Co, i.e. A = 3.3 × 10−11 J m−1 . As concerns the volume of the reversed nucleus, V, it is plausible to consider an axial dimension of the order of the wall thickness, δW , and transverse dimensions comparable to the cross-section area of the microwire’s metallic core, πR2m , where
´ ari et al. / Sensors and Actuators A 129 (2006) 37–40 T.A. Ov´
Fig. 2. Coercivity dependence on glass coating thickness with the metallic core diameter as a parameter for a (Co0.94 Fe0.06 )72.5 Si12.5 B15 amorphous glasscoated microwire.
Rm is the metallic core radius. The transverse dimensions of the reversed nucleus should also depend on the anisotropy distribution. The most important parameter related to the anisotropy distribution is the ratio between the metallic core radius, Rm , and the glass coating thickness, tg . Thus, the radial dimension of the nucleus is R2m /tg , and its cross-section area becomes: πR4m /tg2 . Considering α = (tg /Rm )2/3 (α √ reflects the contribution of the anisotropy distribution), δW = π A/KIC , and by taking into account (3) and the expression for V, expression (2) for the coercivity becomes: 2A1/3 HC = µ0 M S
39
Fig. 3. Coercivity dependence on metallic core diameter with the glass coating thickness as a parameter for a (Co0.94 Fe0.06 )72.5 Si12.5 B15 amorphous glasscoated microwire.
4. Dependence of surface anisotropy on microwire dimensions Next we refer to the magnetoelastic anisotropy from the microwire’s surface region, i.e. within the outer shell (OS). Surface anisotropy KOS was calculated as the weighted mean of the magnetoelastic anisotropy constants that correspond to the cylindrical shells of thickness dr from the OS. Figs. 4 and 5 show the dependence of surface magnetoelastic anisotropy on metallic core diameter and glass coating thickness, respectively.
2/3
tg KIC π · R2m
(4)
Thus, we achieved a method for the calculation of magnetoelastic anisotropy distribution and coercivity values for microwires with nearly zero magnetostriction having different dimensions. Figs. 2 and 3 illustrate the dependence of calculated and measured coercivity values on glass thickness and metallic core diameter, respectively. Experimental coercivity values were determined from hysteresis loops measured using an inductive method. One observes that calculated results are in good agreement with measured ones and expression (4) predicts with high accuracy the dependence of HC on microwire dimensions. Coercivity increases as expected with glass coating thickness for constant values of the metallic core diameter due to the reinforcement of transverse anisotropy within the IC as a result of larger axial tensile stresses determined by the thicker glass coating. On the other hand, at constant glass coating thickness coercivity decreases with the increase of the metallic core diameter due to lower transverse anisotropy in the IC as a result of smaller axial tensile stresses induced by the rapid solidification process.
Fig. 4. Dependence of surface anisotropy on metallic core diameter with the glass coating thickness as a parameter for a (Co0.94 Fe0.06 )72.5 Si12.5 B15 amorphous glass-coated microwire.
40
´ ari et al. / Sensors and Actuators A 129 (2006) 37–40 T.A. Ov´
5. Conclusion The weak dependence of surface anisotropy on glass coating thickness and its non-linear dependence on the diameter of the metallic nucleus indicate that surface magnetoelastic anisotropy mainly originates in the coupling between magnetostriction and stresses induced by rapid solidification rather than stresses induced by the presence of the glass coating. Bulk magnetization behaviour (anisotropy, coercivity) is affected by both glass coating thickness and diameter of the actual metallic wire. The obtained results allow a better understanding of previous experimental results and they are essential for tailoring the magnetic properties of nearly zero magnetostrictive Cobased amorphous glass-coated microwires for sensor applications. Fig. 5. Dependence of surface anisotropy on glass coating thickness with the metallic core diameter as a parameter for a (Co0.94 Fe0.06 )72.5 Si12.5 B15 amorphous glass-coated microwire.
The large values of the circumferential anisotropy constant in the surface region of the microwires lead to circumferential magnetization processes taking place mainly by domain wall displacements, as it has been reported by most of the authors who performed GMI measurements at frequencies below the 1 MHz domain wall relaxation frequency [5]. Both the weak dependence of surface anisotropy on glass coating thickness and the non-linear dependence of surface anisotropy on metallic core diameter have been emphasized by means of ferromagnetic resonance experiments [6], although a systematic experimental study of the latter has not been performed yet.
References [1] M. V´azquez, Soft magnetic wires, Physica B 299 (2001) 302–313. [2] T. Uchiyama, T. Meydan, Impedance strain gauge characteristics of glasscovered amorphous magnetic wires, J. Optoelectron. Adv. M. 4 (2002) 277–280. ´ ari, Gh. Pop, Internal stress distribution in [3] H. Chiriac, T.A. Ov´ glass-covered amorphous magnetic wires, Phys. Rev. B 52 (1995) 10104–10113. [4] A.M. Severino, C. G´omez-Polo, P. Mar´ın, M. V´azquez, Influence of the sample length on the switching process of magnetostrictive amorphous wire, J. Magn. Magn. Mater. 103 (1992) 117–125. [5] L.V. Panina, K. Mohri, T. Uchiyama, Giant magneto-impedance (GMI) in amorphous wire, single layer film and sandwich film, Physica A 241 (1997) 429–438. ´ ari, F.J. Casta˜no, Ferromagnetic [6] H. Chiriac, C.N. Colesniuc, T.A. Ov´ resonance investigation of surface anisotropy distribution in amorphous glass-covered wires, J. Appl. Phys. 87 (2000) 4816–4818.