The off-diagonal magneto-impedance in Co-based amorphous ribbons was measured using a pick-up coil wound around the sample. The ribbons were annealed in air or in vacuum in the presence of a weak magnetic field. The evolution of the first and second harmonics in the pick-up coil voltage as a function of the current amplitude was studied. At low current amplitudes, the first harmonic dominates in the frequency spectrum of the voltage, and at sufficiently high current amplitudes, the amplitude of the second harmonic becomes higher than that of the first harmonic. For air-annealed ribbons, the asymmetric two-peak behaviour of the field dependences of the harmonic amplitudes was observed, which is related to the coupling between the amorphous phase and surface crystalline layers appearing after annealing. For vacuum-annealed samples, the first harmonic has a maximum at zero external field, and the field dependence of the second harmonic exhibits symmetric two-peak behaviour. The experimental results are interpreted in terms of a quasi-static rotational model.It is shown that the appearance of the second harmonic in the pick-up coil voltage is related to the anti-symmetrical distribution of the transverse field induced by the current. The calculated dependences are in a qualitative agreement with the experimental data.Recently, the generation of the second harmonic in the off-diagonal magnetoimpedance in Co-based amorphous ribbons annealed in air in the presence of a weak magnetic field has been reported [24]. In this paper, we present the results of the study of the nonlinear off-diagonal magneto-impedance in Co-based amorphous ribbons annealed in air or in vacuum. The evolution of the first and second harmonics in the pick-up coil voltage with an increase of the current amplitude is analysed. It is demonstrated that formation of the surface crystalline layers in air-annealed samples changes drastically the behaviour of the harmonics. The experimental results are described in the framework of a quasi-static rotational model.

A model describing the exchange-biased asymmetric giant magneto-impedance in Jouleheated 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 magnetoimpedance 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.