Threshold Current of Domain Wall Motion under Extrinsic Pinning,   $\beta$-Term and Non-Adiabaticity
  Threshold current of domain wall motion under spin-polarized electric current in ferromagnets is theoretically studied based on the equation of motion of a wall in terms of collective coordinates. Effects of non-adiabaticity and a so-called $\beta$-term in Landau-Lifshitz equation, which are described by the same term in the equation of motion of a wall, are taken into account as well as extrinsic pinning. It is demonstrated that there are four different regimes characterized by different dependence of threshold on extrinsic pinning, hard-axis magnetic anisotropy, non-adiabaticity and $\beta$. 
Gen Tatara, Toshihiko Takayama, Hiroshi Kohno, Junya Shibata,   Yoshinobu Nakatani and Hidetoshi Fukuyama