Low-field hysteresis in the magnetoimpedance of amorphous microwires M. Ipatov,* V. Zhukova, A. Zhukov, J. Gonzalez, and A. Zvezdin Departamento de Física de Materiales, Facultad de Qímicas, Universidad del País Vasco, San Sebastián, Spain Received 14 January 2010; revised manuscript received 8 March 2010; published 19 April 2010 The phenomena of low-field hysteresis of the magnetoimpedance MIin zero-magnetostrictive amorphous wires are studied theoretically and experimentally. We developed a mathematical model for magnetization reversal and impedance field dependence. The presented model considers the low-field hysteresis and the effect of circular bias magnetic field. It is demonstrated that the hysteresis originates from a nonzero angle between the anisotropy easy axis and transversal plane. The bias field, which is produced by current running through the wire, considerably affects the MI dependence making it anhysteretic and highly asymmetric. The validity of the model is confirmed by the experiments. The main characteristics of the studied amorphous wire such as anisotropy field H A , angle between the anisotropy easy axis with the transversal direction , and Gilbert damping constant G were obtained from the experiment in accordance with the presented model. DOI: 10.1103/PhysRevB.81.134421 PACS numbers: 75.47.-m, 75.30.Gw, 75.50.Kj, 75.60.Jk I. INTRODUCTION The giant magnetoimpedance effect GMIconsists of significant change of the impedance of a magnetically soft conductor upon the application of an external magnetic field. The GMI effect is intrinsically related with magnetic softness and requires low magnetic anisotropy constant and high cir- cumferential magnetic permeability. In particular, these con- ditions are fulfilled in magnetically soft amorphous wires with low and negative magnetostriction constant s -10 -7 . 1 It was reported the sensitivity to magnetic field as high as 1 Oe Ref. 2and up to hundreds of percents of the impedance changes in amorphous wires 1,3,4 that, combined with low cost and simple fabrication method, have made them very attractive for prospective application where local- ized weak magnetic field is especially important such as bio- medical, geological, environmental, navigation, and indus- trial highly sensitive magnetic field sensing. Recently a novel family of amorphous wires with reduced dimensionality—glass-coated microwires consisting on much thinner metallic ferromagnetic nucleus usually of the order of 1–30 mcoated by glass—has been developed. 4,5 These microwires fit much better for utilization in magnetic sensors mostly because of their thinner dimensions and therefore lower effect of demagnetizing stray fields. At cer- tain conditions such microwires exhibit quite good magnetic softness, high GMI Refs. 5 and 6and stress-impedance 7 effects. Another emerging application of amorphous microwires is tunable and self-sensing composite materials with micro- wave electromagnetic properties depending on the imped- ance of the microwires embedded in the dielectric matrix. 812 The use of microwires with high GMI and stress impedance effects in composites gives the possibility to realize the ma- terials which dielectric permittivity is determined by the structural scaling, external stimuli or internal state of the material. For example, a material with self-monitoring prop- erties could be able to evidence invisible structural damages, defects, excessive loadings, local stress, and temperature dis- tribution, thus considerably facilitating the in situ health monitoring of large scale objects such as infrastructure bridges, buildings, etc.. Obviously, for both GMI applications in magnetic field sensors and tunable composites, the highly sensitive MI and its low hysteresis are required. Consequently, improvement of these parameters is essential for these applications. At the same time, the hysteresis up to 100 A/m or even higher was found in amorphous microwires 13 that considerably limit the sensor’s precision. 14 Though the MI effect has been rather extensively studied over the last two decades, most of the performed investiga- tions were devoted to MI in high fields above 1 kA/m. To the best of our knowledge, the problem of low-field hyster- esis in amorphous wires was consider only in a few works. 15,16 It these papers it was shown that the MI hyster- esis is related with static circumferential magnetization and the application of circumferential dc bias field H B is required to suppress this hysteresis. Nevertheless, a complete model describing all aspects of MI dependence such as hysteresis, asymmetry induced by the bias field, influence of anisotropy constant, and so on has not been given. Thus, rigorous theo- retical and experimental studies of MI effect with consider- ation for the low-field anomalies are of considerable interest and importance. In the paper we developed the mathematical model for the magnetization reversal and MI field dependence for zero- magnetostrictive amorphous microwires and compared it with the experiment. The paper is organized as follows. First, we considered the equilibrium magnetization state in the sur- face layer of the wire. We assume ia nonzero angle be- tween the anisotropy easy axis and transversal plane and ii the presence of a dc circular field that is created by the bias current. Second, the tensors of magnetic permeability and surface impedance are discussed. Finally, the model is com- pared with the experimental measurements from which the main characteristics of the microwire such as anisotropy field H A , angle between the anisotropy easy axis with the trans- versal direction , and Gilbert damping constant G were obtained. II. MAGNETIC STRUCTURE The outer shell of amorphous glass-coated microwires with vanishing magnetostriction is characterized by the cir- PHYSICAL REVIEW B 81, 134421 2010 1098-0121/2010/8113/1344218©2010 The American Physical Society 134421-1