Hofstadter-type energy spectra in lateral superlattices defined by   periodic magnetic and electrostatic fields
  We calculate the energy spectrum of an electron moving in a two-dimensional lattice which is defined by an electric potential and an applied perpendicular magnetic field modulated by a periodic surface magnetization. The spatial direction of this magnetization introduces complex phases into the Fourier coefficients of the magnetic field. We investigate the effect of the relative phases between electric and magnetic modulation on band width and internal structure of the Landau levels. 
Rolf R. Gerhardts, Daniela Pfannkuche and Vidar Gudmundsson