A model for exchange-biased asymmetric giant magneto-impedance in   amorphous wires
  A model describing the exchange-biased asymmetric giant magneto-impedance in Joule-heated amorphous wires is proposed. It is assumed that the Joule heating results in the formation of a surface hard magnetic crystalline layer, and the asymmetric giant magneto-impedance is related to the exchange coupling between the amorphous and crystalline phases. The coupling between the surface layer and the amorphous bulk is described in terms of an effective bias field. The model is based on a simultaneous solution of linearizied Maxwell equations and the Landau-Lifshitz equation. The calculated field and frequency dependences of the wire impedance are in a qualitative agreement with results of the experimental study of the asymmetric giant magneto-impedance in Joule-heated Co-based amorphous wires. 
N.A. Buznikov, S.S. Yoon, C.G. Kim, C.O. Kim