Field-dependent surface impedance tensor in amorphous wires with two   types of magnetic anisotropy: helical and circumferential
  This paper concerns the theoretical and experimental investigation of the magneto-impedance (MI) effect in amorphous wires in terms of the surface impedance tensor. Physical concepts of MI and problems of significant practical importance are discussed using the results obtained. The theoretical analysis is based on employing the asymptotic-series expansion method of solving the Maxwell equations for a ferromagnetic wire with an ac permeability tensor of a general form associated with magnetisation rotation. The magnetic structure-dependent impedance tensor is calculated for any frequency and external magnetic field, and is not restricted to the case when only strong skin-effect is present. This approach allows us to develop a rigorous quantitative analysis of MI characteristics in wires, depending on the type of magnetic anisotropy, the magnitude of dc bias current, and an excitation method. The theoretical model has been tested by comparing the obtained results with experiment. For the sake of an adequate comparison, the full impedance tensor is measured in CoFeSiB and CoSiB amorphous wires having a circumferential and helical anisotropy, respectively, by determining the S21 parameter. In cases, when the rotational dynamics is responsible for the impedance behaviour, there is a reasonable agreement between the experimental and theoretical results. Such effects as the ac biased asymmetrical MI in wires with a circumferential anisotropy, the transformation in MI behaviour caused by a dc current (from that having a symmetric hysteresis to an asymmetric anhysteretic one) in wires with a helical anisotropy are discussed. 
D.P. Makhnovskiy, L.V. Panina, and D.J. Mapps (University of Plymouth,   UK)