Journal of Science: Advanced Materials and Devices (2016) 388e392 Contents lists available at ScienceDirect Journal of Science: Advanced Materials and Devices journal homepage: www.elsevier.com/locate/jsamd Original Article Estimation of the frequency and magnetic field dependence of the skin depth in Co-rich magnetic microwires from GMI experiments Arcady Zhukov a, b, c, *, Ahmed Talaat a, b, Mihail Ipatov a, b, Alexandr Granovsky d, Valentina Zhukova a, b n, 20009, Spain Dpto de Fís Mater., UPV/EHU, San Sebastia Dpto de Física Aplicada, EUPDS, UPV/EHU, 20018, San Sebastian, Spain c IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain d Faculty of Physics, Lomonosov Moscow State University, 11991, Moscow, Russian Federation a b a r t i c l e i n f o a b s t r a c t Article history: Received 23 July 2016 Received in revised form August 2016 Accepted August 2016 Available online 15 August 2016 We studied giant magnetoimpedance (GMI) effect in magnetically soft amorphous Co-rich microwires in the extended frequency range From obtained experimentally dependences of the GMI ratio on magnetic field at different frequencies we estimated the penetration depth and its dependence on applied magnetic field and frequency © 2016 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Keywords: Magnetic glass-coated microwires Amorphous materials Giant magnetoimpedance effect Soft magnetic properties Taylor-Ulitovsky technique Introduction Studies of amorphous soft magnetic materials attract attention during last three decades owing to excellent soft magnetic properties, enhanced mechanical and corrosion properties and fast preparation method [1,2] Amorphous wires present quite peculiar magnetic properties such as magnetic bistability related to the single and large Barkhausen jump and Giant Magneto Impedance effect [3,4] From the viewpoint of applications of soft magnetic amorphous materials so called “Giant Magneto Impedance effect” (GMI) recently attracted special attention This GMI effect defined as the large change of the electrical impedance of a magnetic conductor when is subjected to an axial dc magnetic field, H [4e6] It has been recognized that the large sensitivity of the total impedance of a soft magnetic conductor at low magnetic fields and high frequencies of the driven ac current originates from the dependence of the transverse magnetic permeability upon the dc magnetic field n, 20009, * Corresponding author Dpto de Fís Mater., UPV/EHU, San Sebastia Spain E-mail address: arkadi.joukov@ehu.es (A Zhukov) Peer review under responsibility of Vietnam National University, Hanoi and skin effect Large GMI effect (up to 600%) has been reported for Co-based amorphous glass-coated microwires with nearly zero magnetostriction value [6] This extremely high magnetic field sensitivity allows to use soft magnetic materials for creation of sensitive and cheap magnetic sensors and magnetometers [6e13] Consequently studies of different magnetic wires have attracted considerable attention of researchers and engineers along many years [4e13] Perfectly cylindrical symmetry is quite favorable for achievement of high MI effect [4e6,14,15] As reported elsewhere GMI effect exhibited by amorphous wires is quite sensitive to external stimuli, such as applied stress, temperature that enables them for detection of stresses and/or temperature variation [13,16] On the other hand it is well-known, the penetration depth, d, of conductor depends on the current frequency For observation of high MI effect the penetration depth must be smaller than the magnetic wires diameter [4e6] Moreover, the penetration depth can be evaluated from the GMI effect [17] In this evaluation it was assumed that the changes in the real component of the impedance (in-phase component) are due only to changes in the effective area where the AC-current flows as a consequence of the skin effect http://dx.doi.org/10.1016/j.jsamd.2016.08.002 2468-2179/© 2016 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) A Zhukov et al / Journal of Science: Advanced Materials and Devices (2016) 388e392 It should be proposed method of the penetration depth evaluation is only meaningful when the penetration depth, d, is smaller than the wire radius, r, or what is equivalent RAC > RDC (in fact the penetration depth should be infinitively large at the frequency f ¼ 0) As mentioned previously [17] for a simple estimation of the penetration depth at high enough frequencies proposed approach is sufficient for a qualitative interpretation the GMI-response of the magnetic wire-element and possible use of this element in sensors Recently most attention is paid to magnetic glass-coated microwires with diameter of magnetic metallic nucleus of few mm [6,14,15] This tendency of the miniaturization of the magnetic sensors is demanded by the industries for the most modern applications [6] As described elsewhere the diameter reduction must be associated with the increasing of the optimal MI frequency range: a tradeoff between dimension and frequency is required in order to obtain a maximum MI effect [18] Therefore recently GMI effect in thin magnetic wires at GHz frequency range has been studied [14,15] Recently we modified the experimental facility that allowed us to extend the frequency range and measure GMI effect at GHZ frequencies [14,15] and reported that in soft magnetic amorphous microwires the GMI ratio above 100% can be observed even at GHz frequencies band [14,15] Consequently we present our recent studies on the penetration depth of the alternating current flowing through the magnetically soft conductor caused by the applied static magnetic field in thin amorphous wires 389 Si14.5Mo1.7 microwires is shown Fig 1a This microwire also presents rather high GMI effect in as-prepared state (Fig 1b) As discussed elsewhere [4e6,14,15]the magnetic field dependence of GMI ratio is affected b y the magnetic anisotropy When the samples present transversal magnetic anisotropy the double peaks magnetic field DZ/Z (H) dependence takes place Consequently the double peaks magnetic field DZ/Z (H) dependence observed for Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7 microwire must be associated to the transversal magnetic anisotropy observed in Fig 1a Maximum GMI ratio, DZ/Zmax z 320% can be observed varying the frequency (Fig 1b) A frequency dependence of DZ/Zmax presents the frequency range where the highest DZ/Zmax can be observed (Fig 1c) For the metallic nucleus diameter, d z 10.5 mm the optimum frequency for the GMI effect is about 200 MHz (see Fig 1b) Material and methods We studied various Co-rich (Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7, Co67.71Fe4.28Ni1.57Si11.24B12.4Mo1.25C1.55 and Co69.2Fe4.1B11.8Si13.8C1.1) with different metallic nucleus diameter, d, and total microwire diameter, D, produced by the modified Taylor-Ulitovsky method described elsewhere [14,15] We have measured the magnetic field dependence of impedance, Z, and GMI ratio, DZ/Z, for as-prepared samples and after heat treatments We used a specially designed micro-strip sample holder described elsewhere [14,15] The sample holder was placed inside a sufficiently long solenoid that creates a homogeneous magnetic field, H The sample impedance, Z, was measured using a vector network analyzer from reflection coefficient S11 The magneto impedance ratio, DZ/Z, has been defined as: DZ=Z ¼ ½ZðHÞ À ZðHmax Þ$100=ZðHmax Þ; (1) An axial DC-field with a maximum value Hmax up to kA/m was supplied by magnetizing coils The frequency range for the diagonal impedance component has been measured from MHz up to GHz As described above the diameter reduction must be associated with the increasing of the optimal MI frequency range: a tradeoff between dimension and frequency is required in order to obtain a maximum MI effect [18] Consequently we measured GMI effect at different frequencies Hysteresis loops have been measured by fluxmetric method previously used by us for similar studies [19] We represent the normalized magnetization, M/M0 versus magnetic field, H, where M is the magnetic moment at given magnetic field and M0 is the magnetic moment of the sample at the maximum magnetic field amplitude, Hm The sample length was 10 cm Experimental results and discussion All Co-rich microwires present linear hysteresis loops As an example the hysteresis loop of as-prepared Co67Fe3.85Ni1.45B11.5 Fig Hysteresis loop (a), GMI ratio (b) and frequency dependence of DZ/Zmax (c) measured in Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7 microwire with d z 10.5 mm 390 A Zhukov et al / Journal of Science: Advanced Materials and Devices (2016) 388e392 The origin of the maximum on DZ/Zmax (f) dependences has been discussed elsewhere [14,20,21] There are few reasons for the optimum frequency for the DZ/Zmax i) It might be understood from the following: as can be seen from Fig 1b the magnetic field of the GMI peaks, Hm, increases with frequency, f Therefore if the frequency is high enough and the maximum applied DC magnetic field, Hmax is fixed (in our case Hmax ¼ 25000 A/m), Hm becomes comparable with Hmax Consequently for a given value of maximum applied magnetic field, Hmax, the optimum frequency for highest GMI ratio takes place ii) On the other hand, Hm value is associated with the magnetic anisotropy field and therefore one can expect different Z/Zmax (f) dependences for microwires with different r-ratios iii) As recently discussed the decreasing of the GMI effect at high frequencies can be explained considering that the magnetic structure and the anisotropy can be different inside the microwire and near the surface This difference can be attributed to the existence of the interfacial layer between the metallic nucleus and glass coating recently reported for glasscoated microwires [20] Indeed if the chemical composition of the interfacial layer is considerably different from the metallic nucleus than the effective magnetic anisotropy field and magnetic permeability closer to the surface can be different from those in the inner part of metallic nucleus [20] It is worht mentioning that the penetration depth, d, of conductor decreases increasing the AC current frequency Therefore the impedance values at H ¼ increase with increasing of the AC current frequency As mentioned above, from DZ/Z(H) dependences it is possible to estimate the penetration depth at different frequencies using the model previously described in ref [17] considering that the changes in the real component of the impedance are related to changes in the effective area where the AC-current flows as a consequence of the skin-effect In this model the penetration depth, d, as a function of the ratio RDC/RAC (RDC is the DC-resistance of the wire, and RAC is the real component of the impedance), can be expressed as: h i d ¼ r À ð1 À RDC =RAC Þ1=2 ; (2) where r is the wire radius Consequently we measured DZ/Z(H) dependences for various Co-rich microwires at elevated frequencies and tried to estimate the d (H) dependences Thus for all studied samples (Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7, Co67.71Fe4.28Ni1.57Si11.24B12.4Mo1.25C1.55 and Co69.2Fe4.1B11.8Si13.8C1.1)) a considerable GMI effect is observed for GHz frequencies (see Figs 2e4) Obtained d (H) dependences demonstrate that at high frequencies the minimum penetration depth of studied microwires depends on the metallic nucleus diameter, d, and on the composition From obtained d (H) dependences we evaluated d -values and dependence of minimum d -values on frequency (see Figs 2c, 3c and 4c) For Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7 microwire (d ¼ 17.4 mm) dmin is about 2.2 mm (Fig 3c) For the case of Co67.71Fe4.28Ni1.57Si11.24B12.4Mo1.25C1.55 microwire the minimum calculated penetration depth is below 0.5 mm for high frequencies (Fig 4b) As can be appreciated from Figs 2ce4c minimum d -values, d min, decrease with increasing the frequency and for Co67.71Fe4.28Ni1.57Si11.24B12.4Mo1.25C1.55 microwire at frequency, f, above GHz d min, z0.33 mm (Fig 4c) Fig Z(H) dependence (a), calculated d (H) dependences (b) and d min(f) dependence estimated for different frequencies from eq (2) for Co69.2Fe4.1B11.8Si13.8C1.1microwire (d ¼ 25.6 mm, D ¼ 30.2 mm) Consequently obtained minimum penetration depth for studied Co-rich microwires can be few times smaller than the microwires diameter Used method of the penetration depth estimation is meaningful when the penetration depth, d, is smaller than the wire radius, r, or what is equivalent RAC > RDC (in fact the penetration depth should be infinitively large at the frequency f ¼ 0), i.e at high enough frequencies On the other hand at high enough frequencies the magnetic permeability decreases and therefore GMI effect in its classical interpretation must be negligible As discussed elsewhere the magnetic permeability at GHz frequencies, the magnetization rotation is strongly influenced by the gyromagnetic effect [14,15,19] On the other hand, the penetration depth, d, of conductor depends on the current frequency Therefore proposed method for A Zhukov et al / Journal of Science: Advanced Materials and Devices (2016) 388e392 Fig Z(H) dependence (a), calculated d (H) dependences (b) and d min(f) dependence estimated for different frequencies from eq (2) of Co67Fe3.85Ni1.45B11.5Si14.5Mo1.7 microwires (d ¼ 17.4 mm) evaluation of the penetration depth in which it is considered that the changes in the real component of the impedance (in-phase component) are due only to changes in the effective area where the AC-current flows as a consequence of the skin effect must be still valid for high frequency regime It is worth mentioning that recently we reported on observation of the interfacial layer in Fe and Co-rich glass-coated microwires [20] with thickness of about 0.5 mm Consequently considering low penetration depth evaluated for the case of some of studied microwires we can assume that the interface layer can affect the features of the GMI effect at GHz frequencies The chemical composition and hence the magnetization and magnetostriction coefficient in the interface layer therefore can be different from the inner part of the magnetic nucleus Therefore the interface layer can affect the features of the GMI effect at GHz frequencies 391 Fig Z(H) dependence (a), calculated d (H) dependences (b) and d min(f) dependence estimated for different frequencies from eq (2) of Co67.71Fe4.28Ni1.57Si11.24B12.4Mo1.25C1.55 microwires (d ¼ 10 mm, D ¼ 13.8 mm) Conclusions We measured the GMI effect and frequency dependence of the GMI ratio and evaluated frequency dependence in Co-rich microwires From obtained experimentally dependences of GMI ratio on magnetic field and different frequencies we estimated the skin depth and its dependence on applied magnetic field and frequency We discussed origin of the optimum frequency for studied microwires considering the difference of the magnetic structure and the magnetic anisotropy inside the microwire and near the surface Acknowledgments This work was supported by Spanish MINECO under MAT201347231-C2-1-P and the Russian Science Foundation under the 16-19- 392 A Zhukov et al / Journal of Science: Advanced Materials and Devices (2016) 388e392 10490 grant Technical and human support provided by SGIker (UPV/EHU, MICINN, GV/EJ, ERDF and ESF) is gratefully acknowledged References [1] J Durand, in: H Beck, H.-J Giintherodt (Eds.), Magnetic Properties of Metallic Glasses in Topics in Applied Physics Volume 53, Glassy Metals II Atomic Structure and Dynamics, Electronic Structure, Magnetic Properties, SpringerVerlag, Berlin Heidelberg New York Tokyo, 1983 [2] G Herzer, 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evaluated for the case of some of studied... magnetostriction coefficient in the interface layer therefore can be different from the inner part of the magnetic nucleus Therefore the interface layer can affect the features of the GMI effect at GHz