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Field dependence of second-harmonic amplitude of magnetoimpedance in FeCoSiB joule heated wires
Journal of Magnetism and Magnetic Materials 226}230 (2001) 712}714
Field dependence of second-harmonic amplitude of magnetoimpedance in FeCoSiB joule heated wires C. GoH mez-Polo *, M. VaH zquez, M. Knobel Departamento. de Fisica, Universidad Pu& blica de Navarra, Campus de Arrosadia s/n, 31006 Pamplona, Spain Inst. de Magnetismo Aplicado, UCM-RENFE-CSIC. P.O. Box 155, 28230 Las Rozas, Spain Inst. de Fn& sica **Gleb Wataghin++, Universidade Estadual de Campinas (UNICAMP), Caixa Postal 6165, 13.083-970 Campinas, Sao Paulo, Brazil
Abstract The existence of a second-harmonic component of the giant magnetoimpedance (GMI) voltage in an amorphous FeCoSiB Joule heated wire is analysed. The evolution of the "rst-harmonic component of the GMI voltage with the axial DC applied magnetic "eld can be suitably described in terms of the evolution of the circumferential magnetic permeability. With regard to the second-harmonic component, its amplitude sensitively evolves with the axial DC magnetic "eld and its appearance is associated to an asymmetry in the circular magnetization process. A simple rotational magnetization model is presented where the harmonic components of the GMI voltage are estimated through Fourier analysis. 2001 Elsevier Science B.V. All rights reserved. Keywords: Amorphous systems*wires; Anisotropy*induced; Magnetization*circular; Magnetoimpedance
The giant magnetoimpedance (GMI) e!ect, in which the high-frequency impedance, Z, of a high-permeability material, sensitively changes upon the application of an external DC "eld, has been extensively studied during the last few years [1]. From a technological point of view, its main interest lies in the design of new sensitive and quick response micromagnetic sensors [2]. While its origin can be well understood within the framework of classical electrodynamics [3], there are still several aspects, related to the micromagnetic characteristics, that must be studied further in detail. Among them, the contribution of high-order harmonics in the GMI response. In this work, the sample, an amorphous wire with nominal composition (Fe Co ) Si B was obtained by the so-called in-rotating-water quenching technique. In order to induce a circumferential anisotropy, a piece 8 cm in length was subjected to a current annealing at a current density, j"24.3 A/mm for 5 min.
* Corresponding author. Tel.: #34-948-169576; fax. #34948-169565. E-mail address: [email protected] (C. GoH mez-Polo).
With respect to the GMI measurements, the voltage drops across the wire and in a resistor connected in series were simultaneously recorded through a digital oscilloscope and their real and imaginary components calculated through Fourier analysis. Longitudinal DC magnetic "elds were created by a long solenoid (36.6 Oe/A). Since the Curie point corresponds to a current density of 32.1 A/mm, the induction of a circumferential anisotropy, K , takes place under the performed thermal treat( ment. Fig. 1 shows the axial "eld (H) dependence of resistive, R, and inductive, X, components of Z for rms amplitude of the AC current, I "5 and 15 mA (fre ! quency, f"50 kHz). According to the classical electrodynamic model, a maximum in Z must be observed for maximum values of the circumferential permeability, ,(H+H ). However as Fig. 1 shows, both impedance ( I components do not present their maximum values at the same DC axial "eld. On the other hand, the most noticeable result is the detection of a second-harmonic component, < , of the induced MI voltage (see Fig. 2, where < is plotted as a function of H for I "5 and 15 mA). Moreover, !
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 1 1 4 5 - 8
C. Go& mez-Polo et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 712}714
713
< can be further increased by the application of a DC biased component of the electrical current. In order to understand better the observed behavior, a simple rotational model has been developed, where the equilibrium angle, , of the magnetization M with re spect to the circumferential direction, , can be calculated by minimizing the total energy: E"K sin(! )! M H sin ! M H cos , (1) ( ) 1 1 ( where is the skew angle of the easy magnetization I direction to the circumferential direction. The magnetization M (t)"M cos((t)) response to the "eld H " ( ( H cos(2ft)) is numerically derivated and its Fourier components calculated:
2 2M (t) ( cos(n 2ft) dt, a " L ¹ t 2 2M (t) ( sin(n 2ft) dt, (2) b " L ¹ t where the circumferential permeability can be estimated through " c(!b #ia ), with c a "tting para( meter (c"1/2fH ). Thus, R(H) and X(H) can be evalu ated through the classical electrodynamic model: 1 J (ka) Z"R#iX" R ka , 2 J (ka) where J is the Bessel functions of the "rst kind, G k"(i2 f/, is the electrical resistivity, a the wire ( radius, R "¸/a and L the sample length. Fig. 3 "! displays the calculated R and X components for "135 cm, a"60 m, ¸"6 cm (mean distance between voltage contacts), K "20 J/m, "/10, ( I H , "19 and H , "57 A/m, c "1.9;10\ and c "0.6;10\ s (A/m)\ with 1 and 2 corresponding to 5 and 15 mA, respectively (notice: c /c "H / H +3). With regard to the second-harmonic component, a similar calculation reinforces the nonzero value of . In order to obtain a measurable < voltage, an asym metry in the circular magnetization process must be considered that can be directly obtained when the easy axis of the induced anisotropy makes an angle with the circular direction . The use of second-harmonic signals is a basic detection method in magnetic "eld sensors (#ux-gate sensors) [4]. In this type of sensors, the application of a DC magnetic "eld to a high permeability material introduces an asymmetry in the magnetization process that results in the occurrence of a component of double frequency with respect to the exciting alternating "eld. In our present case, the simulated circular hysteresis loops show maximum asymmetric characteristics for H "eld values where a maximum in < is observed. In this sense, the DC biased current reinforces this asymmetry and would explain the detected increase in < (see
Fig. 1. Axial "eld (H) dependence of impedance components ( f"50 kHz) for I "5 mA (R: (o); X (*)) and I "15 mA ! ! (R: (䊏); X (#)).
Fig. 2. Second harmonic voltage, V , versus the applied axial "eld, H, for I "5 mA (䉫) and I "15 mA: (*), I "0 and ! ! "! (䢇) I "7 mA ( f"50 kHz). "!
Fig. 2). Nevertheless, a similar estimation of the associated impedance values (Z ) using the previous "tting parameters, does not provide a good agreement with the observed experimental values. However, if < is directly related to the second-harmonic component of the time derivative of M (t) (< "A(a #b ; A"0.35 a¸), ( the experimental "eld dependence can be roughly reproduced. Fig. 3 shows the "tted curve (dot line) for I "15 mA with a DC biasing circular "eld of 18 A/m (A"3.9;10\ SI units (Hm)). In conclusion, the axial "eld evolution of the "rst (impedance) and second-harmonic components of the MI voltage in a joule heated amorphous wire is presented and interpreted within a simple rotational model. In particular, the occurrence of a second-harmonic component is associated with the asymmetric characteristics of the circular magnetization process.
714
C. Go& mez-Polo et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 712}714
This work was supported by the Spanish CICYT under project MAT-1999-0422-C02.
References
Fig. 3. Calculated axial "eld (H) dependence of impedance components ( f"50 kHz) for I "5 mA (R: (o); X (*)) and ! I "15 mA (R: (䢇); X (;)). !
[1] F.L.A. Machado, B.L. da Silva, E. Montarroyos, J. Appl. Phys. 73 (1993) 6387. [2] K. Mohri, T. Uchiyama, L.V. Panina, Sens. Actuators A 59 (1997) 1. [3] L.D. Landau, E.M. Lifschitz, L.P. Pitaevskii, Electrodynamics of Continuous Media, ButterworthHeinemann, London, 1995, p. 212. [4] W. BorhoK !t, G. Trenkler, Sensors: A Comprehensive Survey, Vol. 5, VCH, New York, 1989, p. 153.
Field dependence of second-harmonic amplitude of magnetoimpedance in FeCoSiB joule heated wires C. GoH mez-Polo *, M. VaH zquez, M. Knobel Departamento. de Fisica, Universidad Pu& blica de Navarra, Campus de Arrosadia s/n, 31006 Pamplona, Spain Inst. de Magnetismo Aplicado, UCM-RENFE-CSIC. P.O. Box 155, 28230 Las Rozas, Spain Inst. de Fn& sica **Gleb Wataghin++, Universidade Estadual de Campinas (UNICAMP), Caixa Postal 6165, 13.083-970 Campinas, Sao Paulo, Brazil
Abstract The existence of a second-harmonic component of the giant magnetoimpedance (GMI) voltage in an amorphous FeCoSiB Joule heated wire is analysed. The evolution of the "rst-harmonic component of the GMI voltage with the axial DC applied magnetic "eld can be suitably described in terms of the evolution of the circumferential magnetic permeability. With regard to the second-harmonic component, its amplitude sensitively evolves with the axial DC magnetic "eld and its appearance is associated to an asymmetry in the circular magnetization process. A simple rotational magnetization model is presented where the harmonic components of the GMI voltage are estimated through Fourier analysis. 2001 Elsevier Science B.V. All rights reserved. Keywords: Amorphous systems*wires; Anisotropy*induced; Magnetization*circular; Magnetoimpedance
The giant magnetoimpedance (GMI) e!ect, in which the high-frequency impedance, Z, of a high-permeability material, sensitively changes upon the application of an external DC "eld, has been extensively studied during the last few years [1]. From a technological point of view, its main interest lies in the design of new sensitive and quick response micromagnetic sensors [2]. While its origin can be well understood within the framework of classical electrodynamics [3], there are still several aspects, related to the micromagnetic characteristics, that must be studied further in detail. Among them, the contribution of high-order harmonics in the GMI response. In this work, the sample, an amorphous wire with nominal composition (Fe Co ) Si B was obtained by the so-called in-rotating-water quenching technique. In order to induce a circumferential anisotropy, a piece 8 cm in length was subjected to a current annealing at a current density, j"24.3 A/mm for 5 min.
* Corresponding author. Tel.: #34-948-169576; fax. #34948-169565. E-mail address: [email protected] (C. GoH mez-Polo).
With respect to the GMI measurements, the voltage drops across the wire and in a resistor connected in series were simultaneously recorded through a digital oscilloscope and their real and imaginary components calculated through Fourier analysis. Longitudinal DC magnetic "elds were created by a long solenoid (36.6 Oe/A). Since the Curie point corresponds to a current density of 32.1 A/mm, the induction of a circumferential anisotropy, K , takes place under the performed thermal treat( ment. Fig. 1 shows the axial "eld (H) dependence of resistive, R, and inductive, X, components of Z for rms amplitude of the AC current, I "5 and 15 mA (fre ! quency, f"50 kHz). According to the classical electrodynamic model, a maximum in Z must be observed for maximum values of the circumferential permeability, ,(H+H ). However as Fig. 1 shows, both impedance ( I components do not present their maximum values at the same DC axial "eld. On the other hand, the most noticeable result is the detection of a second-harmonic component, < , of the induced MI voltage (see Fig. 2, where < is plotted as a function of H for I "5 and 15 mA). Moreover, !
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 1 1 4 5 - 8
C. Go& mez-Polo et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 712}714
713
< can be further increased by the application of a DC biased component of the electrical current. In order to understand better the observed behavior, a simple rotational model has been developed, where the equilibrium angle, , of the magnetization M with re spect to the circumferential direction, , can be calculated by minimizing the total energy: E"K sin(! )! M H sin ! M H cos , (1) ( ) 1 1 ( where is the skew angle of the easy magnetization I direction to the circumferential direction. The magnetization M (t)"M cos((t)) response to the "eld H " ( ( H cos(2ft)) is numerically derivated and its Fourier components calculated:
2 2M (t) ( cos(n 2ft) dt, a " L ¹ t 2 2M (t) ( sin(n 2ft) dt, (2) b " L ¹ t where the circumferential permeability can be estimated through " c(!b #ia ), with c a "tting para( meter (c"1/2fH ). Thus, R(H) and X(H) can be evalu ated through the classical electrodynamic model: 1 J (ka) Z"R#iX" R ka , 2 J (ka) where J is the Bessel functions of the "rst kind, G k"(i2 f/, is the electrical resistivity, a the wire ( radius, R "¸/a and L the sample length. Fig. 3 "! displays the calculated R and X components for "135 cm, a"60 m, ¸"6 cm (mean distance between voltage contacts), K "20 J/m, "/10, ( I H , "19 and H , "57 A/m, c "1.9;10\ and c "0.6;10\ s (A/m)\ with 1 and 2 corresponding to 5 and 15 mA, respectively (notice: c /c "H / H +3). With regard to the second-harmonic component, a similar calculation reinforces the nonzero value of . In order to obtain a measurable < voltage, an asym metry in the circular magnetization process must be considered that can be directly obtained when the easy axis of the induced anisotropy makes an angle with the circular direction . The use of second-harmonic signals is a basic detection method in magnetic "eld sensors (#ux-gate sensors) [4]. In this type of sensors, the application of a DC magnetic "eld to a high permeability material introduces an asymmetry in the magnetization process that results in the occurrence of a component of double frequency with respect to the exciting alternating "eld. In our present case, the simulated circular hysteresis loops show maximum asymmetric characteristics for H "eld values where a maximum in < is observed. In this sense, the DC biased current reinforces this asymmetry and would explain the detected increase in < (see
Fig. 1. Axial "eld (H) dependence of impedance components ( f"50 kHz) for I "5 mA (R: (o); X (*)) and I "15 mA ! ! (R: (䊏); X (#)).
Fig. 2. Second harmonic voltage, V , versus the applied axial "eld, H, for I "5 mA (䉫) and I "15 mA: (*), I "0 and ! ! "! (䢇) I "7 mA ( f"50 kHz). "!
Fig. 2). Nevertheless, a similar estimation of the associated impedance values (Z ) using the previous "tting parameters, does not provide a good agreement with the observed experimental values. However, if < is directly related to the second-harmonic component of the time derivative of M (t) (< "A(a #b ; A"0.35 a¸), ( the experimental "eld dependence can be roughly reproduced. Fig. 3 shows the "tted curve (dot line) for I "15 mA with a DC biasing circular "eld of 18 A/m (A"3.9;10\ SI units (Hm)). In conclusion, the axial "eld evolution of the "rst (impedance) and second-harmonic components of the MI voltage in a joule heated amorphous wire is presented and interpreted within a simple rotational model. In particular, the occurrence of a second-harmonic component is associated with the asymmetric characteristics of the circular magnetization process.
714
C. Go& mez-Polo et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 712}714
This work was supported by the Spanish CICYT under project MAT-1999-0422-C02.
References
Fig. 3. Calculated axial "eld (H) dependence of impedance components ( f"50 kHz) for I "5 mA (R: (o); X (*)) and ! I "15 mA (R: (䢇); X (;)). !
[1] F.L.A. Machado, B.L. da Silva, E. Montarroyos, J. Appl. Phys. 73 (1993) 6387. [2] K. Mohri, T. Uchiyama, L.V. Panina, Sens. Actuators A 59 (1997) 1. [3] L.D. Landau, E.M. Lifschitz, L.P. Pitaevskii, Electrodynamics of Continuous Media, ButterworthHeinemann, London, 1995, p. 212. [4] W. BorhoK !t, G. Trenkler, Sensors: A Comprehensive Survey, Vol. 5, VCH, New York, 1989, p. 153.