Analytic description of domain-wall deformation caused by the Oersted field in current-driven domain-wall motion

We report here an analytic prediction of the domain-wall (DW) tilting caused by the Oersted field in the current-driven DW motion along ferromagnetic nanowires that have perpendicular magnetic anisotropy. By adopting the variational principle for energy minimization, the DW tilting angle is determined as a function of the current density with a finite threshold current density, above which the DW becomes elongated along the nanowire with two narrow domains at its edges. These results predict the minimum data bit size as well as the maximum current density needed for realizing stable DWs in DW-mediated nanodevices.