Sensors and Actuators A 119 (2005) 384–389 Skin-effect and circumferential permeability in micro-wires utilized in GMI-sensors Henryk K. Lachowicz a,∗ , Karin L. Garcia b , Marek Ku´ zmi´ nski a , Arcady Zhukov c,d , Manuel V´ azquez b a Institute of Physics, Polish Academy of Sciences, Al. Lotnik´ ow 32/46, 02-668 Warszawa, Poland b Instituto de Ciencias de Materiales, CSIC, 28049 Cantoblanco, Madrid, Spain c Dpto. F´ ısica de Materiales, Fac. Qu´ ımica, UPV/EHU, Apdo. 1072, 20080 San Sebasti´ an, Spain d “TAMag Iberica” S.L., Parque Tecnol´ ogico de Miram´ on, Paseo Mikeltegi 52, 1 a Planta, 20009 San Sebasti ´ an, Spain Received 10 August 2004; received in revised form 8 October 2004; accepted 9 October 2004 Available online 18 November 2004 Abstract The penetration depth of the skin-effect and circumferential permeability have been calculated for a magnetic micro-wire of the nominal composition Co 67 Fe 3.85 Ni 1.45 Mo 1.7 Si 14.5 B 11.5 displaying large giant magnetoimpedance (GMI) effect. For these calculations a simple model was applied in which a rough assumption was made that the changes of the real component of the impedance are due only to changes in the effective cross-section of the wire for the AC-current. The evolution of both, the penetration depth and circumferential permeability, is presented as a function of the applied DC-axial field at various frequencies of the AC-current, flowing along the wire. These quantities are calculated using the experimental data of the real component of the micro-wire impedance. A comparison of the experimental data obtained for the imaginary component of the impedance with those calculated by the model, shows that the latter gives only a qualitative agreement with the measured dependencies. © 2004 Elsevier B.V. All rights reserved. Keywords: Amorphous micro-wires; Giant magnetoimpedance; Skin-effect; Penetration depth; Circumferential permeability 1. Introduction The giant magnetoimpedance (GMI) effect [1–3] mani- fests itself by huge changes in the impedance of an elec- trically conducting magnetic element, usually in a form of a magnetically soft thin ribbon, tiny wire, thin film or film structures, submitted to a simultaneous action of an external longitudinal DC-magnetic field and a transverse or circular (in the case of wires) AC-field generated by an AC-current of the R.F.-frequency flowing through the magnetic conductor. During the recent years, numerous results of intense studies on the GMI-phenomenon, both of the basic and applied na- ture, were reported. Owing to them, the physical background ∗ Corresponding author. Tel.: +48 22 843 5212; fax: +48 22 843 0926. E-mail address: henryk.lachowicz@ifpan.edu.pl (H.K. Lachowicz). of the GMI-phenomenon is now generally recognized (see e.g. [4]). Moreover, this effect is actually widely utilized in a numerous sensitive sensors of various physical quantities (see e.g. [5]). Magnetic element most frequently used in these sensors is an amorphous wire of very small diameter (from 1 to around 100 m). The composition of these wires is similar to those of metallic glasses, Co- or Fe-rich alloys. Since GMI effect is mainly observed in nearly-zero magnetostrictive ma- terials, for application in sensors utilizing this effect, usually Co-rich wires are used. Fe-rich wires are assigned in general to sensors based on magnetoelastic phenomena, although re- cently GMI effect has been also observed in Fe-rich wires after special heat treatment [6]. Recently, thin micro-wires coated with glass (ordinary Pyrex-type), produced using the so-called Taylor–Ulitovsky method [7,8] are often utilized in sensors. Since the thermal expansion coefficient of the glass 0924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2004.10.017