Modeling of asymmetric giant magnetoimpedance in amorphous ribbons with a surface crystalline layer

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Abstract

A model describing the asymmetric giant magnetoimpedance (GMI) in field-annealed amorphous ribbons is proposed. It is assumed that the ribbon consists of an inner amorphous core and surface hard magnetic crystalline layers. The model is based on a simultaneous solution of linearized Maxwell equations and Landau–Lifshitz equation. The coupling between the surface layers and the amorphous core is described in terms of an effective bias field. Analytical expressions for the frequency and field dependences of the ribbon impedance are found. The calculated dependences are in a qualitative agreement with results of experimental studies of the high-frequency asymmetric GMI in field-annealed amorphous ribbons.

Introduction

The giant magnetoimpedance (GMI) effect implies a significant change in the impedance of a soft magnetic conductor with the variation of an external magnetic field. The effect has been observed in different soft magnetic materials and has attracted a great deal of interest due to a possible use in various applications (see, e.g., Refs. [1], [2], [3] and references therein). The sensitivity and linearity for the magnetic field are the most important parameters in practical applications of GMI for magnetic sensors. An asymmetric behavior of the GMI profile is desirable because of this requirement. In this connection, much attention has been paid recently to the asymmetric GMI effect.

The asymmetric GMI has been observed first for twisted Co-based amorphous wires with DC bias current superimposed on the driving current [4]. A similar effect has been studied later in as-quenched amorphous ribbons [5] and wires [6]. Another method of producing the asymmetric GMI profile consists of applying an axial AC bias field to a sample [7]. However, these two methods have some limitations in applications, such as electrical power consumption.

Recently, a very large asymmetric GMI profile has been observed in Co-based amorphous ribbons annealed in air, in the presence of a weak magnetic field [8], [9], [10], [11], [12]. It has been shown that the asymmetry of the GMI profile is related to the hard magnetic crystalline layer, which appears due to the surface crystallization of a ribbon after the field annealing [9], [13], [14]. Although the effect has been studied experimentally quite well, the satisfactory theoretical explanation is still missing. An attempt to explain the asymmetric GMI in field-annealed ribbons in the framework of the quasi-static model [15] has not been very successful [16]. This model describes some basic features of the asymmetric GMI, however, it cannot explain the frequency dependence of the impedance. Moreover, the effect of the crystalline layer thickness is not taken into account in the model. More recently, a phenomenological model of the asymmetric GMI based on a solution of Maxwell equations and Landau–Lifshitz equation for semi-infinite ribbon with surface spin-pinning condition has been proposed [17]. Taking into account the exchange interactions and neglecting the anisotropy field, the problem of the impedance calculation reduces to a numerical solution of a differential equation for the magnetic field distribution in the ribbon. The model describes qualitatively the asymmetric GMI observed in experiments, however, a complex numerical procedure to calculate the impedance is required.

In this paper, we propose another model, which allows one to explain main features of the high-frequency asymmetric GMI in field-annealed ribbons. The model is based on a simultaneous solution of Maxwell equations together with Landau–Lifshitz equation for a ribbon of a finite thickness consisting of an amorphous core and two outer crystalline layers. The coupling between the surface layers and the amorphous core is considered in terms of an effective bias field. Neglecting a domain structure and exchange interactions, the analytical expression for the impedance is obtained, and the field and frequency dependences of the impedance are analyzed.

Section snippets

Ribbon impedance

Let us consider a ribbon of thickness D consisting of an inner amorphous core of thickness d and two outer crystalline layers at the ribbon surface occurring after field annealing. The AC current I=I0exp(-iωt) flows along the ribbon (along z-axis), and the external DC magnetic field He is parallel to the current. The coordinate system is chosen so that the AC field induced by the current is parallel to the y-axis. A sketch of the coordinate system is shown in Fig. 1. It is assumed that the

Results and discussion

Fig. 2 shows the ribbon impedance as a function of the external magnetic field He at the current frequency f=ω/2π=5MHz for different values of the bias field Hb. The saturation magnetization, the unidirectional anisotropy field, the uniaxial anisotropy field and the damping parameter of the ribbon are taken as 4πM=7000Gs, Hu=300Oe, Ha=2Oe and α=0.1, respectively. For simplicity, we assume that the conductivity of the crystalline layers is equal to that of the amorphous core, σ1=σ2.

It follows

Conclusions

In this paper, the rotational model to calculate the impedance of the ribbon consisting of an amorphous core and two hard magnetic crystalline layers is developed. In the framework of the model, analytical expressions for the impedance are found taking into account the influence of the effective bias field occurring due to the interaction between the amorphous and the crystalline layers. The results of calculations allow one to describe main features of the field and frequency dependences of

Acknowledgements

This work was supported by the Korea Science and Engineering Foundation through ReCAMM. N.A Buznikov would like to acknowledge the support of the Brain Pool Program.

References (22)

  • M. Vazquez

    J. Magn. Magn. Mater.

    (2001)
  • M. Knobel et al.

    J. Magn. Magn. Mater.

    (2002)
  • L. Kraus

    Sensors Actuators A

    (2003)
  • S.H. Song et al.

    J. Magn. Magn. Mater.

    (2000)
  • K.J. Jang et al.

    J. Magn. Magn. Mater.

    (2000)
  • C.G. Kim et al.

    J. Magn. Magn. Mater.

    (2002)
  • E.E. Shalyguina et al.

    Physica B

    (2003)
  • E.E. Shalyguina et al.

    J. Magn. Magn. Mater.

    (2003)
  • N.A. Usov et al.

    J. Magn. Magn. Mater.

    (1998)
  • L. Kraus

    J. Magn. Magn. Mater.

    (1999)
  • T. Kitoh et al.

    IEEE Trans. Magn.

    (1995)
  • Cited by (0)

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