Modeling of asymmetric giant magnetoimpedance in amorphous ribbons with   a surface crystalline layer
  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 linearizied 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 giant GMI in field-annealed amorphous ribbons. 
N.A. Buznikov, C.G. Kim, C.O. Kim, S.S. Yoon