- Email: [email protected]
Parallel permeability of ferromagnetic wires up to GHz frequencies
Journal of Magnetism and Magnetic Materials 249 (2002) 264–268
Parallel permeability of ferromagnetic wires up to GHz frequencies O. Acher*, A.-L. Adenot, S. Deprot CEA Le Ripault, BP 16, F-37260 Monts, France
Abstract The parallel permeability of ferromagnetic wires can be investigated through a variety of measurement set-ups, up to frequencies of 10 GHz or more. Negative magnetostriction wires exhibit significant permeability levels, that can be tailored through the ferromagnetic composition and geometrical characteristics. This makes microwires attractive for a variety of applications. r 2002 Elsevier Science B.V. All rights reserved. PACS: 41.20.Jb; 75.50.Kj; 76.20.+q; 76.50.+g Keywords: Microwave permeability; Permeameter; Amorphous wires
1. Introduction Thin ferromagnetic wires are attractive for a variety of applications as inductive materials over a very wide frequency range. The response of magnetic wires to a large variety of types and orientations of excitations has been reported [1–4]. This presentation focuses on the response of magnetic wires to high-frequency magnetic fields parallel to the wire. It has been established that for a large class of amorphous wires, at least a significant portion of the magnetization is circumferential. This is essentially the case for negative magnetostriction materials. The permeability response of such wires to a magnetic field parallel to the wire is rotational,
*Corresponding author. E-mail address: [email protected] (O. Acher).
and large permeability levels can be observed up to GHz frequencies.
2. Measurement techniques Several techniques allow the determination of the parallel permeability of thin wires at high frequencies. Different types of permeameters have been developed for thin film permeability measurements. Some are based on a two-coil set-up, including an exciting coil and a pickup coil [5]. Other permeameters are based on single coil measurement, that can also be viewed as a shorted microstrip line [6]. The two-coil setups are generally more precise in the lower frequency range, whereas the single-coil devices are more suitable for the high-frequency range, and have been demonstrated up to 6 GHz [7]. All these devices require thin square samples with typical
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 5 4 1 - 3
O. Acher et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 264–268
dimension between 5 and 10 mm, and ferromagnetic volume in the 106–103 mm3 range. Samples made of parallel wires placed parallel on a nonconductive square substrate can be investigated using these devices. However, one should keep in mind that the finite length of the wires may affect their domain structure, and also lead to significant demagnetizing effects that impact the microwave permeability. The flexibility of the wires also offers attractive opportunities for high-frequency wide band characterization [8,9]. Samples suitable for coaxial measurements can be manufactured by winding microwires into torus with 7 mm outer diameter and 3 mm inner diameter. Such samples can be easily manufactured from continuous wire coils, using a conventional winding machine, and providing glue during the torus manufacturing. The torus are measured using a conventional coaxial measurement technique, that yield permeability up to 18 GHz, with a good precision from frequencies as low as 100 MHz. A simple homogenization law then allows the determination of the permeability of the wire from the permeability of the composite and the ferromagnetic volume fraction in the sample. The fundamental mode propagating in the coaxial line can be described analytically, even in the composite material as it has a cylindrical symmetry. As a consequence, the determination of the permeability requires neither extensive calculation, nor any calibration procedure with a reference sample, in contrast with conventional permeameters. This is very valuable, as it is not so easy to have a reference sample with precisely known permeability. Other advantages are related to the very large length of the wire along the circumferential direction, including the absence of end defects and demagnetizing effects. On the other hand, some stress may be generated in the wires due to the bending, and a rather large amount of wire is needed (several hundred meters). Recently, this technique has been improved to allow the characterization of wound wire samples consisting of a limited number of turns [10], which makes it less material-consuming. In addition, the radius of the torus has been increased up to 40 mm, which decreases the stress due to bending. This technique can be operated in reflection mode.
265
Fig. 1. Measurement setups for GHz range permeability measurement on thin magnetic wires; (a) conventional single coil permeameter; (b) wound torus technique in coaxial line (reflection-transmission mode); (c) coaxial perturbation technique in reflection mode.
Comparison between the different techniques suggests that basically all three techniques are suitable, that the stress due to the bending has no significant influence on the permeability, but the demagnetizing effects associated with conventional permeameters may slightly affect the measurements. The precision is definitely better with the coaxial techniques, and they do not require a calibration step requiring a sample with known permeability [10] (Fig. 1).
3. Experimental results The parallel permeability of different types of wires up to GHz frequencies or more has been reported, including positive and negative magnetostriction cold-drawn amorphous wires [11], nonmagnetic metallic wires and nickel wires [8], amorphous glass-covered microwires [12–14]. Glass-covered microwires obtained from the Taylor technique are especially attractive for microwave use. It is possible to control the metallic core diameter over a range that is relevant compared to the skin depth, and to tune the
O. Acher et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 264–268
266
500
500 µ"
100
100 µ'
1
10
Frequency (GHz)
Fig. 2. Real and imaginary permeability measured by the wound torus method for Co70Fe4Ni1.5Mo1.5Si11B12 wires of 17.5 mm total diameter and different core diameters: (a) 5 mm; (b) 7.5 mm; (c) 10.5 mm.
gyromagnetic resonance frequency trough the composition and the thickness of the glass coating [14]. Typical permeability spectra are presented in Figs. 2–4. They are obtained using the coaxial measurement technique. They can be viewed as frequency-resolved ferromagnetic resonance spectra under zero external field. Fig. 2 illustrates the effect of the amorphous ferromagnetic diameter for a constant glass plus ferromagnetic diameter for a slightly negative magnetostrictive ferromagnetic material. For thinner cores, the loss peak is more pronounced, as further illustrated in Fig. 4. As the core diameter increases, the skin effect leads to additional losses below the gyromagnetic resonance frequency, and the loss peak broadens. In addition, the gyromagnetic resonance frequency decreases as a function of the glass shell thickness. This is consistent with a significant contribution of the magnetostrictive effect to the anisotropy of the wires. This effect is further illustrated in Fig. 3. Curve (c) corresponds to a material with vanishing negative magnetostriction, and has a smaller resonance frequency than the material on curve (b) that has a smaller Fe content and therefore a larger negative magnetostriction value. The gyromagnetic resonance frequency can be tuned in the 600 MHz to 2 GHz range by a proper control of the magnetostriction coefficient of the amorphous alloy and of the glass shell thickness. The high-frequency parallel permeability of some positive magnetostriction wires has also been
0.1
1 Frequency (GHz)
-100
10
Fig. 3. Real and imaginary permeability measured by the wound torus method for 7 mm metallic core diameter and 14 mm total diameter wires of (a) CoMnSiB; (b) Co71.8Fe2Ni1.5Mo1.5Si11.2B12; (c) Co67.2Fe4.1Ni1.4Mo1.7Si14.1B11.5.
150 µ'
100 Permeability
0.1
(b) (c)
300
µ'
-100
(a)
µ"
(b) (c)
Permeability
Permeability
(a) 300
µ" 50 0 0.1
1
10
100
-50 -100
Frequency (GHz)
Fig. 4. Measured permeability of a 14 mm total diameter and 4 mm metallic core diameter wire of Co69Fe1Nb10B20.
investigated. The Fe-based UNITIKA wires exhibit significant high-frequency permeability levels [11], indicating that part of the magnetization does not lie along the wire axis. In contrast, most positive magnetostriction amorphous glass-covered microwires exhibit a permeability close to unity, in agreement with the assumption that the magnetization lies along the wire axis.
4. Theoretical approach A fruitful approach to account for the microwave permeability of negative magnetostriction wires is to use the conventional gyromagnetic
O. Acher et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 264–268
equations to compute a so-called ‘‘intrinsic’’ permeability mi ; and then to derive the apparent permeability ma that can be accessed through measurement by taking into account the skin effect [8]. The proper definition of the permeability of inclusions that are small compared to the free space wavelength, but that are not necessarily small compared to the wavelength in the material, has been derived in Ref. [15]. It writes ma ¼ /BS=H0 ;
ð1Þ
where /BS is the average of the induction over the ferromagnetic material for an externally applied microwave field H0 : If one assumes that the ferromagnetic core is circumferentially magnetized, the intrinsic permeability mi can be computed from either Bloch– Bloembergen or Landau–Lifchitz model. The expression for permeability is the same as for an infinite thin film. It can be easily evaluated from the anisotropy field and saturation magnetization that can be accessed through quasi-static measurements. Then the skin effect has to be taken into account. For metallic inclusions such as spheres [16], wires [8] and thin films [15], the relation between the apparent permeability and intrinsic permeability takes the form ma ¼ Aðki aÞmi ;
ð2Þ
where ki is the wavevector in the ferromagnetic material and a is the radius (or half thickness) of the ferromagnetic element. In the case of wires parallel to the excitation, Aðki aÞ ¼
2 J1 ðki aÞ : ki a J0 ðki aÞ
ð3Þ
A good agreement between this theoretical approach and experimental measurements is generally observed [7,11]. However, it has been shown that for wires with low anisotropy, the resonance frequency is somewhat higher than predicted from this model [14]. This may not only be attributed to spatial inhomogeneities of the anisotropy field, but also to exchange effects that are not taken into account in this model. In that case, a more adequate approach should be inspired by Ref. [4]. The emergence of efficient numerical methods to compute the broad band high-frequency perme-
267
ability response of magnetic structures [17] is also expected to be a fruitful approach for the future. The bound of allowed values for microwave permeability have been derived in a rather general case, for magnetic inclusions and composites of any shape [18]. It writes ;
ð4Þ
where is the gyromagnetic ratio over 2p; and 4pMs is the saturation magnetization. This bound applies only to materials with no skin effect. In the case of the material on Fig. 4, it is checked that the integral of the imaginary permeability weighed by the frequency reaches 87% of the bound. This is a useful indication that nearly all the magnetic volume indeed takes part in the gyromagnetic process.
5. Applications There is a large variety of applications for these high-frequency high-permeability wires. Putting aside the giant magneto impedance effects that are not considered here, there are basically two families of applications for these wires. The lowloss applications include wound cores for inductors and chokes [19]. The high-permeability levels up to 10 MHz allow the manufacturing of inductive components and, provided the wires are sufficiently thin, the losses due to skin effect can be pushed to higher frequencies than for conventional amorphous ribbons. The properties of these cores under high magnetic excitation has been proved to be better than that made of conventional ferrites [20], which makes them attractive for radio applications. Another class of application is related to the high-loss properties of the microwires around the gyromagnetic resonance and in the frequency range where strong skin effect is present. The microwires are extremely attractive for coaxial cable shielding [21,22]. They are wound around the inner conductor envelope and interact with the H field created with the AC current flowing through the cable. They allow the suppression of the
268
O. Acher et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 264–268
parasitic signals over the frequency range where the wires exhibit high losses. This frequency range can be tuned by adjusting properly the composition, the diameter of the ferromagnetic core and the thickness of the glass shell. Eq. (2) shows that the expected figure of merit for such application varies as the square of the saturation magnetization. Many other microwave applications in which ferromagnetic thin films are used can also be treated using ferromagnetic wires, such as tuneable filters in microstrip lines [23].
6. Conclusion Negative magnetostriction microwires exhibit significant permeability levels at high frequencies. Several measurement techniques are available to measure the permeability in the GHz range. The techniques developed for thin film measurements on conventional rigid substrates apply, but the flexibility of the wires allows the use of coaxial setups, that yield better precision. The frequency response of the wires can be tailored through their magnetostriction coefficient and their geometrical characteristics, which makes them attractive for a variety of microwave applications.
Acknowledgements We thank P.M. Jacquart, M.J. Malliavin, D. Pain, M. Ledieu and F. Bertin for their contribution to the investigation of the high frequency aspects in magnetic wires presented here.
References [1] K. Mandal, S. Puerta, M. Vazquez, A. Hernando, Phys. Rev. B 62 (2000) 6598 (and references therein). [2] H. Chiriac, G. Pop, T.A. Ovari, F. Barariu, IEEE Trans. Magn. 32 (1996) 4872 (and references therein). [3] L.V. Panina, K. Mohri, Appl. Phys. Lett. 65 (1994) 1189 (and references therein). [4] D. M!enard, Y. Yelon, J. Appl. Phys. 88 (2000) 379. [5] M. Yamaguchi, S. Yabukami, K.I. Arai, IEEE Trans. Magn. 33 (1997) 3619. [6] D. Pain, M. Ledieu, O. Acher, A.-L. Adenot, F. Duverger, J. Appl. Phys. 85 (1999) 5151. [7] M. Yamaguchi, O. Acher, M. Ledieu, Y. Miyazawa, K.I. Arai, to be presented at JEMS, Grenoble, 2001. [8] O. Acher, J.-L. Vermeulen, P.-M. Jacquart, J.-M. Fontaine, Ph. Baclet, J. Magn. Magn. Mater. 136 (1994) 269. [9] P.-M. Jacquart, O. Acher, IEEE Trans. Microwave Theory Tech. 44 (1996) 2116. [10] A.L. Adenot, O. Acher, D. Pain, F. Duverger, M.-J. Malliavin, D. Damiani, T. Taffary, J. Appl. Phys. 87 (2000) 5965. [11] O. Acher, P.-M. Jacquart, C. Boscher, IEEE Trans. Magn. 30 (1994) 4542. [12] M.-J. Malliavin, O. Acher, C. Boscher, F. Bertin, V.S. Larin, J. Magn. Magn. Mater. 196–197 (1999) 420. [13] A.N. Antonenko, E. Sorkine, A. Rubshtein, V.S. Larin, V. Manov, J. Appl. Phys. 83 (1998) 6587. [14] S. Deprot, A.-L. Adenot, F. Bertin, E. Herv!e, O. Acher, IEEE Trans. Magn. 37 (2001) 2404. [15] O. Acher, A.-L. Adenot, F. Duverger, Phys. Rev. B 62 (2000) 13748. [16] D. Rousselle, A. Berthault, O. Acher, J.P. Bouchaud, P.G. Z!erah, J. Appl. Phys. 74 (1993) 475. [17] N. Vukadinovic, O. Vacus, M. Labrune, O. Acher, D. Pain, Phys. Rev. Lett. 85 (2000) 2817. [18] O. Acher, A.-L. Adenot, Phys. Rev. B 62 (2000) 11324. [19] A.N. Antonenko, E. Sorkine, A. Rubshtein, V.S. Larin, V. Manov, J. Magn. Magn. Mater. 196-197 (1999) 397. [20] R. Lebourgeois, J.P. Gannes, G. Peyresoubes, W. Rebernak, O. Acher, A.L. Adenot, to be presented at SMM, Bilbao, 2001. [21] V. Manov, A. Antonenko, A. Alexrod, A. Rubshtein, E. Sorkine, Patent WO 00/31753. [22] N. Yu, B. Giacomini, French Patent 9905981. [23] A.L. Adenot, O. Acher, T. Taffary, P. Qu!eff!elec, G. Tann!e, J. Appl. Phys. 87 (2000) 6914.
Parallel permeability of ferromagnetic wires up to GHz frequencies O. Acher*, A.-L. Adenot, S. Deprot CEA Le Ripault, BP 16, F-37260 Monts, France
Abstract The parallel permeability of ferromagnetic wires can be investigated through a variety of measurement set-ups, up to frequencies of 10 GHz or more. Negative magnetostriction wires exhibit significant permeability levels, that can be tailored through the ferromagnetic composition and geometrical characteristics. This makes microwires attractive for a variety of applications. r 2002 Elsevier Science B.V. All rights reserved. PACS: 41.20.Jb; 75.50.Kj; 76.20.+q; 76.50.+g Keywords: Microwave permeability; Permeameter; Amorphous wires
1. Introduction Thin ferromagnetic wires are attractive for a variety of applications as inductive materials over a very wide frequency range. The response of magnetic wires to a large variety of types and orientations of excitations has been reported [1–4]. This presentation focuses on the response of magnetic wires to high-frequency magnetic fields parallel to the wire. It has been established that for a large class of amorphous wires, at least a significant portion of the magnetization is circumferential. This is essentially the case for negative magnetostriction materials. The permeability response of such wires to a magnetic field parallel to the wire is rotational,
*Corresponding author. E-mail address: [email protected] (O. Acher).
and large permeability levels can be observed up to GHz frequencies.
2. Measurement techniques Several techniques allow the determination of the parallel permeability of thin wires at high frequencies. Different types of permeameters have been developed for thin film permeability measurements. Some are based on a two-coil set-up, including an exciting coil and a pickup coil [5]. Other permeameters are based on single coil measurement, that can also be viewed as a shorted microstrip line [6]. The two-coil setups are generally more precise in the lower frequency range, whereas the single-coil devices are more suitable for the high-frequency range, and have been demonstrated up to 6 GHz [7]. All these devices require thin square samples with typical
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 5 4 1 - 3
O. Acher et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 264–268
dimension between 5 and 10 mm, and ferromagnetic volume in the 106–103 mm3 range. Samples made of parallel wires placed parallel on a nonconductive square substrate can be investigated using these devices. However, one should keep in mind that the finite length of the wires may affect their domain structure, and also lead to significant demagnetizing effects that impact the microwave permeability. The flexibility of the wires also offers attractive opportunities for high-frequency wide band characterization [8,9]. Samples suitable for coaxial measurements can be manufactured by winding microwires into torus with 7 mm outer diameter and 3 mm inner diameter. Such samples can be easily manufactured from continuous wire coils, using a conventional winding machine, and providing glue during the torus manufacturing. The torus are measured using a conventional coaxial measurement technique, that yield permeability up to 18 GHz, with a good precision from frequencies as low as 100 MHz. A simple homogenization law then allows the determination of the permeability of the wire from the permeability of the composite and the ferromagnetic volume fraction in the sample. The fundamental mode propagating in the coaxial line can be described analytically, even in the composite material as it has a cylindrical symmetry. As a consequence, the determination of the permeability requires neither extensive calculation, nor any calibration procedure with a reference sample, in contrast with conventional permeameters. This is very valuable, as it is not so easy to have a reference sample with precisely known permeability. Other advantages are related to the very large length of the wire along the circumferential direction, including the absence of end defects and demagnetizing effects. On the other hand, some stress may be generated in the wires due to the bending, and a rather large amount of wire is needed (several hundred meters). Recently, this technique has been improved to allow the characterization of wound wire samples consisting of a limited number of turns [10], which makes it less material-consuming. In addition, the radius of the torus has been increased up to 40 mm, which decreases the stress due to bending. This technique can be operated in reflection mode.
265
Fig. 1. Measurement setups for GHz range permeability measurement on thin magnetic wires; (a) conventional single coil permeameter; (b) wound torus technique in coaxial line (reflection-transmission mode); (c) coaxial perturbation technique in reflection mode.
Comparison between the different techniques suggests that basically all three techniques are suitable, that the stress due to the bending has no significant influence on the permeability, but the demagnetizing effects associated with conventional permeameters may slightly affect the measurements. The precision is definitely better with the coaxial techniques, and they do not require a calibration step requiring a sample with known permeability [10] (Fig. 1).
3. Experimental results The parallel permeability of different types of wires up to GHz frequencies or more has been reported, including positive and negative magnetostriction cold-drawn amorphous wires [11], nonmagnetic metallic wires and nickel wires [8], amorphous glass-covered microwires [12–14]. Glass-covered microwires obtained from the Taylor technique are especially attractive for microwave use. It is possible to control the metallic core diameter over a range that is relevant compared to the skin depth, and to tune the
O. Acher et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 264–268
266
500
500 µ"
100
100 µ'
1
10
Frequency (GHz)
Fig. 2. Real and imaginary permeability measured by the wound torus method for Co70Fe4Ni1.5Mo1.5Si11B12 wires of 17.5 mm total diameter and different core diameters: (a) 5 mm; (b) 7.5 mm; (c) 10.5 mm.
gyromagnetic resonance frequency trough the composition and the thickness of the glass coating [14]. Typical permeability spectra are presented in Figs. 2–4. They are obtained using the coaxial measurement technique. They can be viewed as frequency-resolved ferromagnetic resonance spectra under zero external field. Fig. 2 illustrates the effect of the amorphous ferromagnetic diameter for a constant glass plus ferromagnetic diameter for a slightly negative magnetostrictive ferromagnetic material. For thinner cores, the loss peak is more pronounced, as further illustrated in Fig. 4. As the core diameter increases, the skin effect leads to additional losses below the gyromagnetic resonance frequency, and the loss peak broadens. In addition, the gyromagnetic resonance frequency decreases as a function of the glass shell thickness. This is consistent with a significant contribution of the magnetostrictive effect to the anisotropy of the wires. This effect is further illustrated in Fig. 3. Curve (c) corresponds to a material with vanishing negative magnetostriction, and has a smaller resonance frequency than the material on curve (b) that has a smaller Fe content and therefore a larger negative magnetostriction value. The gyromagnetic resonance frequency can be tuned in the 600 MHz to 2 GHz range by a proper control of the magnetostriction coefficient of the amorphous alloy and of the glass shell thickness. The high-frequency parallel permeability of some positive magnetostriction wires has also been
0.1
1 Frequency (GHz)
-100
10
Fig. 3. Real and imaginary permeability measured by the wound torus method for 7 mm metallic core diameter and 14 mm total diameter wires of (a) CoMnSiB; (b) Co71.8Fe2Ni1.5Mo1.5Si11.2B12; (c) Co67.2Fe4.1Ni1.4Mo1.7Si14.1B11.5.
150 µ'
100 Permeability
0.1
(b) (c)
300
µ'
-100
(a)
µ"
(b) (c)
Permeability
Permeability
(a) 300
µ" 50 0 0.1
1
10
100
-50 -100
Frequency (GHz)
Fig. 4. Measured permeability of a 14 mm total diameter and 4 mm metallic core diameter wire of Co69Fe1Nb10B20.
investigated. The Fe-based UNITIKA wires exhibit significant high-frequency permeability levels [11], indicating that part of the magnetization does not lie along the wire axis. In contrast, most positive magnetostriction amorphous glass-covered microwires exhibit a permeability close to unity, in agreement with the assumption that the magnetization lies along the wire axis.
4. Theoretical approach A fruitful approach to account for the microwave permeability of negative magnetostriction wires is to use the conventional gyromagnetic
O. Acher et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 264–268
equations to compute a so-called ‘‘intrinsic’’ permeability mi ; and then to derive the apparent permeability ma that can be accessed through measurement by taking into account the skin effect [8]. The proper definition of the permeability of inclusions that are small compared to the free space wavelength, but that are not necessarily small compared to the wavelength in the material, has been derived in Ref. [15]. It writes ma ¼ /BS=H0 ;
ð1Þ
where /BS is the average of the induction over the ferromagnetic material for an externally applied microwave field H0 : If one assumes that the ferromagnetic core is circumferentially magnetized, the intrinsic permeability mi can be computed from either Bloch– Bloembergen or Landau–Lifchitz model. The expression for permeability is the same as for an infinite thin film. It can be easily evaluated from the anisotropy field and saturation magnetization that can be accessed through quasi-static measurements. Then the skin effect has to be taken into account. For metallic inclusions such as spheres [16], wires [8] and thin films [15], the relation between the apparent permeability and intrinsic permeability takes the form ma ¼ Aðki aÞmi ;
ð2Þ
where ki is the wavevector in the ferromagnetic material and a is the radius (or half thickness) of the ferromagnetic element. In the case of wires parallel to the excitation, Aðki aÞ ¼
2 J1 ðki aÞ : ki a J0 ðki aÞ
ð3Þ
A good agreement between this theoretical approach and experimental measurements is generally observed [7,11]. However, it has been shown that for wires with low anisotropy, the resonance frequency is somewhat higher than predicted from this model [14]. This may not only be attributed to spatial inhomogeneities of the anisotropy field, but also to exchange effects that are not taken into account in this model. In that case, a more adequate approach should be inspired by Ref. [4]. The emergence of efficient numerical methods to compute the broad band high-frequency perme-
267
ability response of magnetic structures [17] is also expected to be a fruitful approach for the future. The bound of allowed values for microwave permeability have been derived in a rather general case, for magnetic inclusions and composites of any shape [18]. It writes ;
ð4Þ
where is the gyromagnetic ratio over 2p; and 4pMs is the saturation magnetization. This bound applies only to materials with no skin effect. In the case of the material on Fig. 4, it is checked that the integral of the imaginary permeability weighed by the frequency reaches 87% of the bound. This is a useful indication that nearly all the magnetic volume indeed takes part in the gyromagnetic process.
5. Applications There is a large variety of applications for these high-frequency high-permeability wires. Putting aside the giant magneto impedance effects that are not considered here, there are basically two families of applications for these wires. The lowloss applications include wound cores for inductors and chokes [19]. The high-permeability levels up to 10 MHz allow the manufacturing of inductive components and, provided the wires are sufficiently thin, the losses due to skin effect can be pushed to higher frequencies than for conventional amorphous ribbons. The properties of these cores under high magnetic excitation has been proved to be better than that made of conventional ferrites [20], which makes them attractive for radio applications. Another class of application is related to the high-loss properties of the microwires around the gyromagnetic resonance and in the frequency range where strong skin effect is present. The microwires are extremely attractive for coaxial cable shielding [21,22]. They are wound around the inner conductor envelope and interact with the H field created with the AC current flowing through the cable. They allow the suppression of the
268
O. Acher et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 264–268
parasitic signals over the frequency range where the wires exhibit high losses. This frequency range can be tuned by adjusting properly the composition, the diameter of the ferromagnetic core and the thickness of the glass shell. Eq. (2) shows that the expected figure of merit for such application varies as the square of the saturation magnetization. Many other microwave applications in which ferromagnetic thin films are used can also be treated using ferromagnetic wires, such as tuneable filters in microstrip lines [23].
6. Conclusion Negative magnetostriction microwires exhibit significant permeability levels at high frequencies. Several measurement techniques are available to measure the permeability in the GHz range. The techniques developed for thin film measurements on conventional rigid substrates apply, but the flexibility of the wires allows the use of coaxial setups, that yield better precision. The frequency response of the wires can be tailored through their magnetostriction coefficient and their geometrical characteristics, which makes them attractive for a variety of microwave applications.
Acknowledgements We thank P.M. Jacquart, M.J. Malliavin, D. Pain, M. Ledieu and F. Bertin for their contribution to the investigation of the high frequency aspects in magnetic wires presented here.
References [1] K. Mandal, S. Puerta, M. Vazquez, A. Hernando, Phys. Rev. B 62 (2000) 6598 (and references therein). [2] H. Chiriac, G. Pop, T.A. Ovari, F. Barariu, IEEE Trans. Magn. 32 (1996) 4872 (and references therein). [3] L.V. Panina, K. Mohri, Appl. Phys. Lett. 65 (1994) 1189 (and references therein). [4] D. M!enard, Y. Yelon, J. Appl. Phys. 88 (2000) 379. [5] M. Yamaguchi, S. Yabukami, K.I. Arai, IEEE Trans. Magn. 33 (1997) 3619. [6] D. Pain, M. Ledieu, O. Acher, A.-L. Adenot, F. Duverger, J. Appl. Phys. 85 (1999) 5151. [7] M. Yamaguchi, O. Acher, M. Ledieu, Y. Miyazawa, K.I. Arai, to be presented at JEMS, Grenoble, 2001. [8] O. Acher, J.-L. Vermeulen, P.-M. Jacquart, J.-M. Fontaine, Ph. Baclet, J. Magn. Magn. Mater. 136 (1994) 269. [9] P.-M. Jacquart, O. Acher, IEEE Trans. Microwave Theory Tech. 44 (1996) 2116. [10] A.L. Adenot, O. Acher, D. Pain, F. Duverger, M.-J. Malliavin, D. Damiani, T. Taffary, J. Appl. Phys. 87 (2000) 5965. [11] O. Acher, P.-M. Jacquart, C. Boscher, IEEE Trans. Magn. 30 (1994) 4542. [12] M.-J. Malliavin, O. Acher, C. Boscher, F. Bertin, V.S. Larin, J. Magn. Magn. Mater. 196–197 (1999) 420. [13] A.N. Antonenko, E. Sorkine, A. Rubshtein, V.S. Larin, V. Manov, J. Appl. Phys. 83 (1998) 6587. [14] S. Deprot, A.-L. Adenot, F. Bertin, E. Herv!e, O. Acher, IEEE Trans. Magn. 37 (2001) 2404. [15] O. Acher, A.-L. Adenot, F. Duverger, Phys. Rev. B 62 (2000) 13748. [16] D. Rousselle, A. Berthault, O. Acher, J.P. Bouchaud, P.G. Z!erah, J. Appl. Phys. 74 (1993) 475. [17] N. Vukadinovic, O. Vacus, M. Labrune, O. Acher, D. Pain, Phys. Rev. Lett. 85 (2000) 2817. [18] O. Acher, A.-L. Adenot, Phys. Rev. B 62 (2000) 11324. [19] A.N. Antonenko, E. Sorkine, A. Rubshtein, V.S. Larin, V. Manov, J. Magn. Magn. Mater. 196-197 (1999) 397. [20] R. Lebourgeois, J.P. Gannes, G. Peyresoubes, W. Rebernak, O. Acher, A.L. Adenot, to be presented at SMM, Bilbao, 2001. [21] V. Manov, A. Antonenko, A. Alexrod, A. Rubshtein, E. Sorkine, Patent WO 00/31753. [22] N. Yu, B. Giacomini, French Patent 9905981. [23] A.L. Adenot, O. Acher, T. Taffary, P. Qu!eff!elec, G. Tann!e, J. Appl. Phys. 87 (2000) 6914.