  The interfacial Dzyaloshinskii-Moriya interaction (DMI) of a heavy metal
(HM)/ferromagnetic (FM) metal heterostructure is vital to the current-induced
domain wall motion (CIDWM) at an ultrahigh velocity. However, strong DMI also
tilts the moving domain wall (DW) plane, and the mechanism for this tilting is
not quite clear. In this work, we have found that this tilting may be
understood based on a micromagnetic calculation from a microscopic dynamical
perspective. The DMI-induced antisymmetric moment structure at the two
boundaries of the track needs to be paid attention. In the early stage of CIDWM
induced by spin-orbit torque, this antisymmetry is destroyed. Afterwards, the
moments at the two boundaries experience distinct rotation processes with
different energy paths towards their final stable antisymmetric moment
structure. This results in different initial velocities of the local DW regions
at the two boundaries. In mathematics, this distinct DW dynamical progresses at
the two boundaries can be approximately revealed by modifying the initial
conditions for solving the Thiele equations.
