Anomalous field dependence of magnetoresistance in magnetic multilayers based on the Fibonacci sequence

The discovery of giant magnetoresistance and concomitant effects such as oscillatory exchange coupling in magnetic multilayers was the starting point of the spintronics era. In the present study, a multilayer of Fe and Cr was designed, using the Fibonacci sequence for the growth of the non-magnetic spacers. Using the gradient method we simulated the magnetic field dependence of these nanostructures for in-plane magnetic fields. The simulations included magnetocrystalline anisotropy for the [100] and [110] directions, as well as bilinear and biquadratic exchange coupling. The resultant magnetization and magnetoresistance behavior shows unusual behavior, such as a Devil's staircase for the magnetization and increasing magnetoresistance with increasing applied magnetic fields. When the ratio of the biquadratic to bilinear coupling exceeds 30{\%} the magnetic field response is expected to show even fractal behavior. These numerical simulations will also be compared to experimental measurements on samples prepared with nominally the same thicknesses.