- Email: [email protected]
Evaluation of the linear magnetostriction in amorphous wires using the giant magneto-impedance effect
Journal of Magnetism and Magnetic Materials 160 (1996) 243-244
Journal of magnetism and magnetic materials
ELSEVIER
Evaluation of the linear magnetostriction in amorphous wires using the giant magneto-impedance effect M. Knobel a.*, C. G6mez-Polo b,c, M. Vfizquez b Instituto de Ffsica 'Gleb Wataghin ', Unit:ersidade Estadual de Campinas (UNICAMP), C.P. 6165, Campinas 13.083-970 S.P., Brazil lnstituto de Magnetismo Aplicado ( UCM) and lnstituto de Ciencia de Materiales (CSIC). P.O. Box 155, 28230 Las Rozas, Madrid, Spain Depto. de Fisica de Materiales. Fac. Fisica, Unit'ersidad Complutense de Madrid. Madrid, Spain
Abstract The stress dependence of the magneto-impedance effect is explored to estimate the magnetostriction constant and its stress derivative on a nearly non-magnetostrictive Co68nFe4.4Sit2.sB]5 amorphous wire. Comparing the results with those obtained with the small-angle magnetization rotation method, good accuracy is obtained. Keywords: Magneto-impedance: Amorphous wires; Magnetostriction
A new and fascinating phenomenon has recently been discovered in soft magnetic materials, the so-called giant magneto-impedance (GMI) effect [1-3]. Large changes in the high-frequency impedance Z have been observed in nearly non-magnetostrictive Co-rich amorphous wires (room temperature GMI ratios up to 360% [4]) and ribbons (up to 130% [1]) under the application of a dc magnetic field. Furthermore, very low magnetic fields are necessary to obtain large changes in Z, accompanied by huge field sensitivities (up to 1700%/Oe [5]). In the case of amorphous wires, the main characteristics of the field dependence of high-frequency impedance can be explained within the framework of the classical Maxwell equations of electrodynamics. Basically, the GMI effect reflects the field dependence of the circular magnetic permeability when the wire is magnetized by the flow of an ac electrical current. These field-induced changes give rise to modifications in the corresponding magnetic penetration depth, and consequently to strong changes in the complex impedance, whose behaviour with field and frequency depends on the anisotropies and overall domain configuration of the specific samples [6,7]. In this work, the stress dependence of the GMI effect has been used to estimate the saturation magnetostriction constant, A~, of a Co-rich amorphous wire. In order to test the proposed method of measurement, a well known composition was chosen to perform our
* Corresponding author. Email: [email protected]: fax: +55-192-39-3137.
experiment. The amorphous wire of composition Co68.1Fe4.4Silz.sB15 (diameter 2a = 124 p,m) was kindly supplied by Unitika Ltd. The magnetostriction constant of this wire was previously measured by the well known small-angle magnetization rotation (SAMR) technique [8], leading to a stress (o-) dependent behaviour usually written as A~ = A~.o + ko-, with A~,0 = - 0 . 3 8 × 10 -v and k = - 1 × 10-J° (MPa) i [9]. To measure the room-temperature field dependence of the impedance, the ends of a 45 cm long wire were clamped to allow the application of both a tensile stress, o-, and a sinusoidal ac current, Irm~. The voltage across a resistor connected in series to the wire was continuously monitored in order to keep the current amplitude constant (lrm ~ = 10 mA). The real and imaginary components of the impedance were measured using a lock-in amplifier (for a fixed frequency f = 100 kHz). The dc magnetic field (Hdc _< 8 kA m ]) was generated by a long solenoid with axis perpendicular to the Earth's magnetic field. Special attention was paid to reducing the circuit dimensions as far as possible, and to use coaxial wires, in order to reduce the non-magnetic contribution at high frequencies. In the unstressed state, the impedance drops continuously with the applied field Hac, reaching a relative variation of 248%. This behaviour is a direct consequence of the decrease in the circular permeability, which consists mainly of magnetic moment rotations. However, due to the negative magnetostriction of the wire, the tensile stresses o- cause an opposite effect, i.e. they strengthen the circular magnetoelastic anisotropy field, giving rise to the occurrence of a maximum in the impedance that shifts towards
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0304-885 3(96)00 178-3
M. Knobel et al. / Journal of Magnetism and Magnetic Materials 160 (1996) 243-244
244 80 70 ~60
g
~4o 1'o .~ 20 10 0
1
1 O0
10
1000
10000
Hdc ( A / m ) Fig. 1. Field dependence of the quadrature component of the impedance, the reactance X, for several applied tensile stresses (values given in the inset).
higher Hdc values as cr increases. This is clearly visible in the field and stress dependence of the imaginary component of the impedance, the reactance X, which is directly related to the circular permeability p,+. As can be seen in Fig. 1, the X versus Hdc curves always present a maximum, even in the unstressed state. Moreover, the decrease with ~y in the zero applied field reactance reflects the parallel decrease in the circular permeability of the domain wall magnetization process. The occurrence of such a maximum can be interpreted as the result of the competition in the rotational magnetization process between the axial field Hdc and the circular anisotropy field H k induced by the stress. Therefore, as previously pointed out by Panina et al. [6], the position of the maximum is determined by Hjc = H k, a condition that allows us to determine the magnetostriction of the sample. We have found that H k estimated from the above condition does not vary linearly with stress (see Fig. 2), but instead its stress dependence can be well fitted by a second-order polynomial of the form H k = act 2 + bo- + c, where a, b and c are constants. Considering the relationship between the linear magnetostriction and the anisotropy field, AS = ( t z o M J 3 ) ( d H k / d ~ y ) , one can easily verify that the saturation magnetostriction is a linear function of
i
v
i
i
i
-100
-150
~.
o
-200
-300
i
o
,
i 200
,
I
400
,
i 600
, 800
applied stress c,(MPa)
Fig. 2. Stress dependence of the anisotropy field H k. The solid line is the best fit curve using a second-order polynomial.
stress, A~ = A~.0 + ko-, where As,0 = (1/3)tzoM, b is the unstressed value of the saturation magnetostriction, and k = dA~/dcr = (2/3)txoM~a is the measured slope [10]. Using this procedure, we have found the following values: A~.0 = - 0 . 3 7 × 10 7 (less than 3% of the difference with the SAMR method) and k = - 0 . 8 5 x 10 -~° (15% of the difference with the SAMR method). Notice also that the value of the constant c is not negligible (c = - 3 7 A / m ) , indicating a strong effect of the quenched-in stresses present in the amorphous wire, whose magnitude is estimated to be approximately 270 MPa. This value of the average internal stress is also in agreement with previous data obtained using different magnetic methods [9]. Although the method has been demonstrated to be reasonably accurate, some specific problems should be pointed out. As can be seen in Fig. 1, the maxima in the X versus Hac curves are quite broad and are not symmetric. This makes it difficult to estimate correctly the position of the peak, and therefore induces some errors in the proper estimation of the magnetostriction constant. Furthermore, in the way shown, the method works only for negative magnetostriction samples, in which the effects of the external stress and applied field are competing. In the case of positive magnetostriction wires, no maxima appear, because both the stress and the field act to promote the axial domain configuration. In conclusion, we have used the stress dependence of the magneto-impedance effect to estimate the linear negative magnetostriction of a Co-based amorphous wire. The field dependences of both impedance components present clear maxima, related to the anisotropy field of the wire. In this way, it is possible to obtain, with good precision, not only the value of the saturation magnetostriction constant, but also its stress dependence.
References [1] F.L.A. Machado, C.S. Martins and S.M. Rezende, Phys. Rev. B 51 (1995) 3926. [2] R.S. Beach and A.E. Berkowitz, Appl. Phys. Len. 64 (1994) 3652. [3] L.V. Panina and K. Mohri, Appl. Phys. Lett. 65 (1994) 1189. [4] M.L. Sfinchez, M. Knobel and D.-X. Chert, in: Nanostructured and Non-Crystalline Materials, Eds. M. Vfizquez and A. Hernando (World Scientific, Singapore 1995) p. 592. [5] J.L. Costa-Kr~imer and K.V. Rao, IEEE Trans. MaSh. 31 (1995) 1261. [6] L.V. Panina, K. Mohri, T. Uchiyama, M. Noda and K. Bushida, IEEE Trans. Magn. 31 (1995) 1249. [7] M. Knobel, M.L. Sfinchez, J. Velfizquez and M. Vfizquez, J. Phys.: Condens. Matter 7 (1995) L115. [8] K. Narita, J. Yamasaki and H. Fukunaga, IEEE Trans. Magn. 16 (1980) 435. [9] C. G6mez-Polo and M. Vfizquez, J. Magn. Magn. Mater. 118 (1993) 86. [10] A. Siemko and H.K. Lachowicz, J. Magn. Magn. Mater. 66 (1987) 31.
Journal of magnetism and magnetic materials
ELSEVIER
Evaluation of the linear magnetostriction in amorphous wires using the giant magneto-impedance effect M. Knobel a.*, C. G6mez-Polo b,c, M. Vfizquez b Instituto de Ffsica 'Gleb Wataghin ', Unit:ersidade Estadual de Campinas (UNICAMP), C.P. 6165, Campinas 13.083-970 S.P., Brazil lnstituto de Magnetismo Aplicado ( UCM) and lnstituto de Ciencia de Materiales (CSIC). P.O. Box 155, 28230 Las Rozas, Madrid, Spain Depto. de Fisica de Materiales. Fac. Fisica, Unit'ersidad Complutense de Madrid. Madrid, Spain
Abstract The stress dependence of the magneto-impedance effect is explored to estimate the magnetostriction constant and its stress derivative on a nearly non-magnetostrictive Co68nFe4.4Sit2.sB]5 amorphous wire. Comparing the results with those obtained with the small-angle magnetization rotation method, good accuracy is obtained. Keywords: Magneto-impedance: Amorphous wires; Magnetostriction
A new and fascinating phenomenon has recently been discovered in soft magnetic materials, the so-called giant magneto-impedance (GMI) effect [1-3]. Large changes in the high-frequency impedance Z have been observed in nearly non-magnetostrictive Co-rich amorphous wires (room temperature GMI ratios up to 360% [4]) and ribbons (up to 130% [1]) under the application of a dc magnetic field. Furthermore, very low magnetic fields are necessary to obtain large changes in Z, accompanied by huge field sensitivities (up to 1700%/Oe [5]). In the case of amorphous wires, the main characteristics of the field dependence of high-frequency impedance can be explained within the framework of the classical Maxwell equations of electrodynamics. Basically, the GMI effect reflects the field dependence of the circular magnetic permeability when the wire is magnetized by the flow of an ac electrical current. These field-induced changes give rise to modifications in the corresponding magnetic penetration depth, and consequently to strong changes in the complex impedance, whose behaviour with field and frequency depends on the anisotropies and overall domain configuration of the specific samples [6,7]. In this work, the stress dependence of the GMI effect has been used to estimate the saturation magnetostriction constant, A~, of a Co-rich amorphous wire. In order to test the proposed method of measurement, a well known composition was chosen to perform our
* Corresponding author. Email: [email protected]: fax: +55-192-39-3137.
experiment. The amorphous wire of composition Co68.1Fe4.4Silz.sB15 (diameter 2a = 124 p,m) was kindly supplied by Unitika Ltd. The magnetostriction constant of this wire was previously measured by the well known small-angle magnetization rotation (SAMR) technique [8], leading to a stress (o-) dependent behaviour usually written as A~ = A~.o + ko-, with A~,0 = - 0 . 3 8 × 10 -v and k = - 1 × 10-J° (MPa) i [9]. To measure the room-temperature field dependence of the impedance, the ends of a 45 cm long wire were clamped to allow the application of both a tensile stress, o-, and a sinusoidal ac current, Irm~. The voltage across a resistor connected in series to the wire was continuously monitored in order to keep the current amplitude constant (lrm ~ = 10 mA). The real and imaginary components of the impedance were measured using a lock-in amplifier (for a fixed frequency f = 100 kHz). The dc magnetic field (Hdc _< 8 kA m ]) was generated by a long solenoid with axis perpendicular to the Earth's magnetic field. Special attention was paid to reducing the circuit dimensions as far as possible, and to use coaxial wires, in order to reduce the non-magnetic contribution at high frequencies. In the unstressed state, the impedance drops continuously with the applied field Hac, reaching a relative variation of 248%. This behaviour is a direct consequence of the decrease in the circular permeability, which consists mainly of magnetic moment rotations. However, due to the negative magnetostriction of the wire, the tensile stresses o- cause an opposite effect, i.e. they strengthen the circular magnetoelastic anisotropy field, giving rise to the occurrence of a maximum in the impedance that shifts towards
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0304-885 3(96)00 178-3
M. Knobel et al. / Journal of Magnetism and Magnetic Materials 160 (1996) 243-244
244 80 70 ~60
g
~4o 1'o .~ 20 10 0
1
1 O0
10
1000
10000
Hdc ( A / m ) Fig. 1. Field dependence of the quadrature component of the impedance, the reactance X, for several applied tensile stresses (values given in the inset).
higher Hdc values as cr increases. This is clearly visible in the field and stress dependence of the imaginary component of the impedance, the reactance X, which is directly related to the circular permeability p,+. As can be seen in Fig. 1, the X versus Hdc curves always present a maximum, even in the unstressed state. Moreover, the decrease with ~y in the zero applied field reactance reflects the parallel decrease in the circular permeability of the domain wall magnetization process. The occurrence of such a maximum can be interpreted as the result of the competition in the rotational magnetization process between the axial field Hdc and the circular anisotropy field H k induced by the stress. Therefore, as previously pointed out by Panina et al. [6], the position of the maximum is determined by Hjc = H k, a condition that allows us to determine the magnetostriction of the sample. We have found that H k estimated from the above condition does not vary linearly with stress (see Fig. 2), but instead its stress dependence can be well fitted by a second-order polynomial of the form H k = act 2 + bo- + c, where a, b and c are constants. Considering the relationship between the linear magnetostriction and the anisotropy field, AS = ( t z o M J 3 ) ( d H k / d ~ y ) , one can easily verify that the saturation magnetostriction is a linear function of
i
v
i
i
i
-100
-150
~.
o
-200
-300
i
o
,
i 200
,
I
400
,
i 600
, 800
applied stress c,(MPa)
Fig. 2. Stress dependence of the anisotropy field H k. The solid line is the best fit curve using a second-order polynomial.
stress, A~ = A~.0 + ko-, where As,0 = (1/3)tzoM, b is the unstressed value of the saturation magnetostriction, and k = dA~/dcr = (2/3)txoM~a is the measured slope [10]. Using this procedure, we have found the following values: A~.0 = - 0 . 3 7 × 10 7 (less than 3% of the difference with the SAMR method) and k = - 0 . 8 5 x 10 -~° (15% of the difference with the SAMR method). Notice also that the value of the constant c is not negligible (c = - 3 7 A / m ) , indicating a strong effect of the quenched-in stresses present in the amorphous wire, whose magnitude is estimated to be approximately 270 MPa. This value of the average internal stress is also in agreement with previous data obtained using different magnetic methods [9]. Although the method has been demonstrated to be reasonably accurate, some specific problems should be pointed out. As can be seen in Fig. 1, the maxima in the X versus Hac curves are quite broad and are not symmetric. This makes it difficult to estimate correctly the position of the peak, and therefore induces some errors in the proper estimation of the magnetostriction constant. Furthermore, in the way shown, the method works only for negative magnetostriction samples, in which the effects of the external stress and applied field are competing. In the case of positive magnetostriction wires, no maxima appear, because both the stress and the field act to promote the axial domain configuration. In conclusion, we have used the stress dependence of the magneto-impedance effect to estimate the linear negative magnetostriction of a Co-based amorphous wire. The field dependences of both impedance components present clear maxima, related to the anisotropy field of the wire. In this way, it is possible to obtain, with good precision, not only the value of the saturation magnetostriction constant, but also its stress dependence.
References [1] F.L.A. Machado, C.S. Martins and S.M. Rezende, Phys. Rev. B 51 (1995) 3926. [2] R.S. Beach and A.E. Berkowitz, Appl. Phys. Len. 64 (1994) 3652. [3] L.V. Panina and K. Mohri, Appl. Phys. Lett. 65 (1994) 1189. [4] M.L. Sfinchez, M. Knobel and D.-X. Chert, in: Nanostructured and Non-Crystalline Materials, Eds. M. Vfizquez and A. Hernando (World Scientific, Singapore 1995) p. 592. [5] J.L. Costa-Kr~imer and K.V. Rao, IEEE Trans. MaSh. 31 (1995) 1261. [6] L.V. Panina, K. Mohri, T. Uchiyama, M. Noda and K. Bushida, IEEE Trans. Magn. 31 (1995) 1249. [7] M. Knobel, M.L. Sfinchez, J. Velfizquez and M. Vfizquez, J. Phys.: Condens. Matter 7 (1995) L115. [8] K. Narita, J. Yamasaki and H. Fukunaga, IEEE Trans. Magn. 16 (1980) 435. [9] C. G6mez-Polo and M. Vfizquez, J. Magn. Magn. Mater. 118 (1993) 86. [10] A. Siemko and H.K. Lachowicz, J. Magn. Magn. Mater. 66 (1987) 31.