Anomalous Magnetoresistance in Fibonacci Multilayers
  The present paper theoretically investigates magnetoresistance curves in quasiperiodic magnetic multilayers for two different growth directions, namely [110] and [100]. We considered identical ferromagnetic layers separated by non-magnetic layers with two different thicknesses chosen based on the Fibonacci sequence. Using parameters for Fe/Cr multilayers, four terms were included in our description of the magnetic energy: Zeeman, cubic anisotropy, bilinear and biquadratic couplings. The minimum energy was determined by the gradient method and the equilibrium magnetization directions found were used to calculate magnetoresistance curves. By choosing spacers with a thickness such that biquadratic coupling is stronger than bilinear coupling, unusual behaviors for the magnetoresistance were observed: (i) for the [110] case there is a different behavior for structures based on even and odd Fibonacci generations; and more interesting, (ii) for the [100] case we found magnetic field ranges for which the magnetoresistance increases with magnetic field. 
L. D. Machado, C. G. Bezerra, M. A. Correa, C. Chesman, J. E. Pearson   and A. Hoffmann
cond-mat.mes-hall