Field-Induced SDW and Butterfly Spectrum in Three Dimensions

Landau’s quantization for incompletely nested Fermi surfaces is known to give rise to magnetic-field-induced spin-density waves(FISDW) in two-dimensional organic metals. Here we show that three-dimensional(3D) systems can have 3D-specific series of FISDW phases as energetically stable states, for which we clarify how and why they appear as the magnetic field is tilted. Each phase is characterized by quantized Hall effect for each of ${\sigma }_{xy}$ and ${\sigma }_{zx}$ that reside on a fractal spectrum like Hofstadter’s butterfly.