Giant magnetoimpedance in glass-covered amorphous microwires

Transcription

1 Journal of Magnetism and Magnetic Materials (2003) Giant magnetoimpedance in glass-covered amorphous microwires L. Kraus a, *, Z. Frait a, K.R. Pirota b, H. Chiriac c a Institute of Physics, Academy of Sciences Czech Republic, Na Slovance 2, CZ Praha 8, Czech Republic b Instituto de Fisica Gleb Wataghin, Universidade Estadual de Campinas (UNICAMP), P.O. Box 6165, Campinas SP, Brazil c National Institute of R&D for Technical Physics, 47 Mangeron Blvd., 6600 Iasi 3, Romania Abstract GMI was investigated in amorphous Co-rich glass-covered microwires with very low magnetostriction constant. Internal stresses, induced in the metallic core by the glass coating, substantially reduce the magnitude of GMI. To improve GMI properties magnetoelastic coupling was reduced by a careful choice of alloy composition and by subsequent Joule-heat treatment. The maximum magnetoimpedance, DZ=ZE600% measured at frequency 15 MHz, is already close to the theoretical value (1060%) and is one of the highest GMI amplitudes ever reported. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Amorphous systems soft magnetic; Giant magnetoimpedance; Ferromagnetic resonance; Magnetomechanical coupling 1. Introduction The effect of giant magnetoimpedance (GMI) and its possible applications to magnetic field sensing were discovered long time ago [1,2]. The phenomenon, however, did not attract much attention and lately has been forgotten. The rediscovery of GMI in amorphous alloys 9 years ago attracted much attention because of its potential applications in sensors and reading heads. Since then GMI in various soft magnetic metallic materials was investigated. But the magnitudes of GMI effect achieved at MHz frequencies, where the applications are mainly expected, are much lower than the theoretical predictions for ideal soft magnetic metals [3]. Various origins of the large deterioration of GMI effect have been proposed. To improve the GMI behavior of real materials, however, more experimental and theoretical work is needed. Amorphous glass-covered microwires, prepared by the Taylor Ulitovski technique, seem to be particularly suitable for GMI applications. Their advantages are the *Corresponding author. Tel.: ; fax: address: kraus@fzu.cz (L. Kraus). relative simple technology and the glass insulation of the metallic core. The early investigations, however, showed that in as-quenched glass-covered microwires, GMI effect was smaller than in conventional amorphous wires of the same composition [4]. The deterioration of GMI effect in the glass-covered microwires is caused mainly by large internal stresses in the metallic core induced by the glass coat. When the glass coat is removed, GMI can be improved but the advantage of glass insulation is lost. By the careful choice of alloy composition and an appropriate heat treatment, the magnetoelastic coupling with the induced internal stresses can be reduced and the GMI behavior of glass-covered microwires substantially improved. In this paper, an overviewof systematic GMI studies of glass-covered microwires is given and the procedure, which allows to achieve GMI as high as 600%, is described. 2. Theoretical background The GMI is related to the skin effect in ferromagnetic metals. It is well known that AC current propagating through a conductor is not uniformly distributed in the /03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S (02)

2 L. Kraus et al. / Journal of Magnetism and Magnetic Materials (2003) cross-section but p is concentrated in the surface layer of thickness d ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2r=om; which is called the skin depth. In ferromagnetic metals the skin depth can be changed by applied magnetic field because of field dependence of permeability m: The maximum impedance is obtained when d is minimum. The minimum value of skin depth can be theoretically estimated. The theory is based on simultaneous solution of Maxwell equations and the Landau Lifshitz equation of motion M ¼ gm H eff a M M: M ð1þ s At MHz frequencies and higher, the eddy currents effectively damp the domain wall movements and only magnetization rotations are responsible for magnetization process. Then the theory of GMI becomes similar to the theory of ferromagnetic resonance in metals [5]. As is known from the theory the minimum skin depth is reached just at the resonance condition. Generally, four wave modes of magnetization motion are exited by an alternating current in a ferromagnetic conductor. Only two of them, the Larmor electromagnetic wave (LE) and the Larmor spin wave (LS) [6], substantially depend on magnetic field and are responsible for the GMI effect. If the exchange interaction is neglected, only the LE mode is plausible and the minimum skin depth [3] rffiffiffiffiffiffi ar d min ¼ ð2þ gj s is limited mainly by the ferromagnetic relaxation. Here a is the Gilbert damping parameter, r the resistivity and J s ¼ m 0 M s the saturation polarization. Because the exchange interaction hinders the misalignment of spins it acts against the skin effect and increases the actual skin depth. Men!ard and Yelon [7] have shown than belowthe crossover frequency, which in typical amorphous metals is around 200 MHz, the hybridization of LE and LS modes plays an important role and the minimum skin depth is determined mainly by the exchange-conductivity effect. Then, d min E Ar 1=4 ; ð3þ oj 2 s where A is the exchange stiffness constant. For a strong skin effect ðd min 5aÞ the maximum relative resistance is approximately R max =R DC Ea=2d min ; where a is the radius of the wire. The amplitudes of GMI, calculated for amorphous wires from Eqs. (2) and (3), are usually of the order %. Such high amplitudes were experimentally observed only at GHz frequencies [8]. At moderate frequencies ( khz MHz) the experimental values are substantially lower. The reasons, which lead to the decrease and broadening of GMI peaks in real materials, can be divided into two groups. The first are the obstacles, which do not allow satisfy the resonance condition at lowfrequencies. They are, for example, magnetic anisotropy with the hard magnetic axis deviating from the direction of internal magnetic field [9], the Bloch Bloembergen type of ferromagnetic relaxation [2], etc. In the second group are various inhomogeneities, which cause the fluctuation of effective field H eff and consequently, the distribution of resonance fields and the broadening of GMI peaks. For a large GMI effect at moderate frequencies it is necessary to minimize material inhomogeneities and to induce magnetic anisotropy with the easy direction exactly perpendicular to the wire axis. To reduce the surface stray fields, which sustain the two-magnon scattering and consequently the Bloch Bloembergen damping, a high surface quality is required. 3. Experimental Amorphous CoFeSiB glass-covered microwires were prepared by the Taylor Ulitovsky method. Six different nominal compositions, namely Co 72.5 x Fe x Si 12.5 B 15, with x ¼ 4:35; 4:7; 5:2; and Co x Fe x Si B 15, with x ¼ 4:4; 4:45; 4:5; were investigated. The aim was to find the alloy composition with the lowest possible magnetostriction constant l s : To reduce the fluctuations of internal stresses and modify the short-range order of the as-cast wires, some samples were Joule heated for 10 min by a constant current passing through the wire. Annealing with applied tensile stress was used to induce magnetic anisotropy perpendicular to the wire axis. Electrical resistance was measured during the heating to detect possible crystallization of samples. First, a piece of wire was Joule heated with the current increasing at a constant rate of 10 ma/min to find when the crystallization starts. Then the samples were heated with constant currents sufficiently lowto avoid the crystallization. If, however, an irreversible change of resistance was detected the sample was excluded from further investigation. Hysteresis loops at room temperature were measured using a quasistatic PC controlled hysteresis-loop-tracer. The glass coat was mechanically removed from the ends of the sample and electric contacts (one fixed and one free movable) were made by tin soldering. The pick-up coil, 5 cm long, with about 25,000 turns was wound on a ceramic capillary with an outer diameter of 1 mm. Stress could be applied by means of weights hung on the free end of the sample. With this arrangement the heat treatment and the hysteresis loop measurement (also under applied stress) could be done in the same place. One sample could be thus used several times for subsequent annealing with ascending heating current. FMR at two different microwave frequencies (35.7 and 69.9 GHz) were measured in parallel configuration

3 L. Kraus et al. / Journal of Magnetism and Magnetic Materials (2003) on samples about 1 mm long. The sample, inserted into the thin quartz capillary, was placed in the shortended rectangular waveguide at the maximum of microwave electric field. Both the DC magnetic field and the microwave electric field were parallel to the wire axis. In this configuration, the wire is electrically polarized with the microwave frequency and the microwave current passing through the sample induces large circumferential magnetic field around it. The amplitude of microwave current and consequently the power absorbed by the sample strongly depend on the sample length [10]. Though this FMR experiment resembles very much the GMI measurements, the microwave current through the sample cannot be measured and the absolute value of impedance cannot be calculated. For the measurement of complex impedance of wires and its field dependence, two different devices were employed. A self-made computer-controlled equipment based on the lock-in amplifier EG&G 5310 [11] was used for the measurement up to 1 MHz. For the frequency range from 1 to 20 MHz the commercial impedance analyzer, Schloemberger SI 1260, was utilized. 4. Results and discussion Hysteresis loops of as-quenched wires depend, first of all, on the alloy composition. The loops of the alloys with xx4:7 are rectangular with a single Barkhausen jump, while for xp4:45 the loops are sheared with a low remanence-to-saturation ratio m r and lowcoercive field H c : The quenching conditions also influence the shape of hysteresis loop. This is particularly evident for the alloy with x ¼ 4:5; where the loop depends on the diameter f m of metallic core and the class coat thickness t g : For example, for the wire with f m ¼ 9:5 mm and t g ¼ 5 mm a sheared loop with the saturation field about 150 A/m is observed, while the thicker wire of the same composition (f m ¼ 29:3 mm, t g ¼ 16:2 mm) shows nearly rectangular loop with m r E0:8 and saturation field about 30 A/m. The shape of hysteresis loop clearly correlates with the magnetostriction constant of the sample. The sign of l s can be determined from the behavior of hysteresis loop with applied stress. For the rectangular loops the coercive force increases with increasing tensile stress indicating that l s is positive. For the sheared loops l s is negative, because their slopes decrease with applied stress. The thicker wires with x ¼ 4:5 showmore complicated hysteresis behavior when applied stress is changed. It indicates that l s is very small and that it may be stress dependent as well as inhomogeneous in the sample volume. The magnetostriction constants l s o0 were determined from the stress dependence of hysteresis curves according to the formula l s ¼ 2 dw 3 ds ; where W is the magnetizing work (the area above hysteresis loop), and s the applied stress. The results are shown in the lower part of Fig. 1. The values of l s for x > 4:5 are missing in the figure because positive magnetostriction cannot be determined in this way. As can be seen, l s changes sign at xe4:55: The magnetostriction constant, however, is not only the function of alloy composition. For example, different values were found for wires of the same composition ðx ¼ 4:5Þ with different diameters. This can be explained by the variation of the short-range order due to different quenching rate during the wire drawing [12]. Like the hysteresis loops the GMI also strongly depends on the magnetostriction. The maximum relative changes of impedance modulus for some as-quenched wires, measured at 15 MHz, are shown in the upper part of Fig. 1. For negative l s quite large GMI is observed, while for l s > 0 it is rather low. The large difference in GMI of the two samples with x ¼ 4:5 is probably caused by the different radius a rather then by different l s : Large internal stresses in the metallic core are the origin of the extreme sensitivity of magnetic properties to the sign and the magnitude of magnetostriction constant. FMR studies of Fe-rich microwires have shown that tensile stresses from fewmpa to fewhundred MPa can be induced by the glass coat [13]. Because the internal stresses are mainly due to different thermal expansion coefficients of metallic core and the glass coat, they cannot be removed by the stress-relief annealing [14]. Heat treatment, however, can be used to homogenize internal stresses, to tune l s and to induce transverse GMI (%) λ s (ppm) µm 10 µm 30 µm 10 µm Co 85-x-y Fe x Si y B 15 λ s > 0 y = y = x (at.% Fe) Fig. 1. GMI and l s of as-quenched microwires as a function of Fe content in the alloy. ð4þ

4 402 L. Kraus et al. / Journal of Magnetism and Magnetic Materials (2003) magnetic anisotropy. By the proper combination of these effects GMI behavior can be further improved. Let us estimate howlarge GMI can theoretically be achieved in the microwires. The Gilbert damping parameter a; which appears in Eq. (2) can be obtained from the FMR linewidth measured at sufficiently high frequency, where the exchange-conductivity broadening is already ineffective. The resonance curve measured at 35.7 GHz on the as-quenched microwire with x ¼ 4:5 and f m ¼ 29:3 mm is shown in Fig. 2. In the low-field range the ferromagnetic antiresonance is clearly evident. The curve theoretically calculated (open circles in Fig. 2) with the parameters J s ¼ 0:722 T, g ¼ 2:11 and a ¼ 1: ; which best fit the experimental data at both microwave frequencies, is also shown. The agreement between the experimental and the theoretical curves in both the resonance and antiresonance regions is very good. Using the above parameters and the resistivity r ¼ 1:5 mo m the minimum skin depth at resonance according to Eq. (2) is 0.34 mm. For the wire diameter f m ¼ 2a ¼ 29:3 mm the theoretical estimate for the maximum relative resistance R max =R DC is The exchange-conductivity effect can be taken into account by using Eq. (3). With the typical value of exchange stiffness constant A ¼ J/m one gets d min ¼ 0:63 mm and R max =R DC ¼ 11:6 for the frequency of 15 MHz. This value is still 2.6 times larger than the experimental value (3.2) obtained for this as-quenched wire. Various Joule heating treatments were tried to improve the GMI of the glass-covered microwires. Small changes of magnetostriction constant (of the order 10 7 ) can be induced by short-range order relaxation of amorphous structure [12]. This effect can be used for a fine tuning of l s : The dependence of magnetostriction constant on the annealing current for three different samples subsequently annealed with increasing current is shown in Fig. 3. These curves are typical for Co-rich dr/dh Co Fe 4.5 Si B 15 as-quenched φ m = 29.3 µm 12.5 x H [koe] Fig. 2. FMR of as-quenched Co Fe 4.5 Si B 15 wire measured at 35.7 GHz. λ s (ppm) x = 4.35, φ m = 13 µm, t g = 5 µm x = 4.40, φ m = 20 µm, t g = 5.4 µm x = 4.45, φ m = 20 µm, t g = 11.3 µm I a (ma) Fig. 3. Magnetostriction constant as a function of annealing current. GMI [%] Co Fe 4.5 Si B 15 f m = 29.3 µm t g = 16.2 µm 70 ma/10 min I a [ma] H [A/m] low-magnetostrictive amorphous alloys. After a slow increase at lower annealing temperatures and a distinct maximum, a sharp decrease is observed near the glass transition temperature. The magnitude of the total change of l s depends on the initial short-range order of amorphous structure, which is closely related to the quenching rate. The behavior of hysteresis loops clearly reflects the observed change of l s : With increasing heating current I a the slope of initially sheared loop first increases. When l s changes to positive the loop becomes rectangular. When the magnetostriction constant second time passes through zero the loop again becomes shared and its slope sharply decreases. This indicates that the magnetoelastic coupling is controlled mainly by l s while the internal stress remains practically unchanged. As has been expected, Joule heating can improve the GMI of microwires with very low negative magnetostriction. The GMI curve of the thick Co Fe Si B 15 wire, annealed for 10 min with 70 ma, measured at 15 MHz, is shown in Fig. 4. The dependence of GMI on annealing current I a ; measured at two different frequencies, is shown in the inset of the figure. GMI [%] 0 15 MHz 1 MHz Fig. 4. GMI of Joule-heated glass-covered microwire measured at 15 MHz with current 1 ma.

5 L. Kraus et al. / Journal of Magnetism and Magnetic Materials (2003) A broad maximum of GMI is observed near the current where l s changes sign. The value of GMIE600%, obtained here is already close to the theoretical value GMI ¼ % ðr max =R DC 1Þ ¼ 1060%: It is the highest GMI reached for amorphous materials and is comparable with the best results ever reported [15]. Finally the Joule stress-heating will be briefly mentioned. It is well known that in Co-rich amorphous alloys, magnetic anisotropy with easy plane perpendicular to the strain axis can be induced by annealing under tensile stress [16]. To induce circumferential anisotropy in glass-covered microwires, Joule heating under tensile stress has been used [14]. The GMI curves exhibit sharp maxima at the anisotropy field H K ; which is proportional to the stress applied during annealing. The Joule-heating under stress can be therefore used for the tailoring of GMI curves to particular applications. 5. Conclusion The systematic investigation of Co-rich amorphous glass-covered microwires has shown that by the careful choice of alloy composition and subsequent heat treatment, very large GMI effect can be obtained. Based on these investigations the following recipe of preparation of glass-covered microwires for GMI applications can be suggested: First, the alloy composition should be chosen so that a small negative magnetostriction (in the range 0 to ) is obtained. Then annealing (either Joule or conventional) should be used to tune l s close to zero. Stress annealing can also be used for inducing additional transverse magnetic anisotropy, which determines the positions of the maxima on GMI curves. Acknowledgements The work was supported by the Ministry of Education, Youth and Sports of the Czech Republic under the Programme KONTAKT ME 355 (2000). References [1] E.P. Harrison, G.L. Turney, H. Rowe, Nature 135 (1935) 961. [2] E.P. Harrison, G.L. Turney, H. Rowe, H. Gollop, Proc. Roy. Soc. 157 (1937) 451. [3] L. Kraus, J. Magn. Magn. Mater. 195 (1999) 764. [4] H. Chiriac, T.A.! Ovari, Prog. Mater. Sci. 40 (1996) 333. [5] W.S. Ament, G.T. Rado, Phys. Rev. 97 (1955) [6] C.E. Patton, Czech J. Phys. B 26 (1976) 925. [7] D. Men!ard, A. Yelon, J. Appl. Phys. 88 (2000) 379. [8] D. Men!ard, M. Britel, P. Ciureanu, A. Yelon, J. Appl. Phys. 84 (1998) [9] K.R. Pirota, L. Kraus, M. Knobel, P. Pagliuso, C. Rettori, Phys. Rev. B 60 (1999) [10] L. Kraus, A.N. Anisimov, J. Magn. Magn. Mater. 58 (1986) 107. [11] J.P. Sinnecker, et al., J. Phys. IV France 8 (1998) Pr [12] J.M. Barandiar!an, et al., Phys. Rev. B 35 (1987) [13] R. Gemperle, L. Kraus, J. Schneider, Czech J. Phys. B 28 (1978) [14] L. Kraus, M. Knobel, S.N. Kane, H. Chiriac, J. Appl. Phys. 85 (1999) [15] K.R. Pirota, L. Kraus, H. Chiriac, M. Knobel, J. Magn. Magn. Mater. 221 (2000) L243. [16] O.V. Nielsen, IEEE Trans. Magn. Mag-21 (1985) 2008.