Field-dependent surface impedance of a bilayer film with an antisymmetric bias magnetization

The evolution of magneto-impedance (MI) behavior under the effect of an antisymmetric transverse bias field is studied in a bilayer film with in-plane anisotropy directed at an angle $\mathrm{\pm \alpha }$ with respect to the current flow. By symmetry, this case is similar to MI in a helically magnetized wire, but in contrast to the wire, permits an analytical consideration at any frequencies in terms of the surface impedance tensor $\mathrm{\zeta ̂.}$ The longitudinal diagonal component of $\mathrm{\zeta ̂}$ contributes to the voltage between the ends of the sample, whereas the off-diagonal component related to the inverse Wiedemann effect indicates that the current flow induces a circular electric field or a coil voltage. A strong skin effect existing at certain high frequencies causes the surface impedance to become an explicit function of the ac permeability and the stable magnetization direction both of which can be sensitive to a dc magnetic field. Without the dc bias, the plots of impedance versus longitudinal field exhibit a symmetric hysteresis. With increasing bias field, the hysteresis area shifts and shrinks, and finally disappears, resulting in highly sensitive asymmetric impedance plots. Such behavior is in line with that reported for a twisted amorphous wire excited by a sharp current pulse involving low and high frequency harmonics.