We report on the time-resolved investigation of current- and field-induced domain wall motion in perpendicularly magnetized microwires exhibiting asymmetric exchange interaction by means of scanning transmission x-ray microscopy using a time step of 200 ps. Dynamical domain wall velocities on the order of 50-100 m s$^{-1}$ were observed. The improvement in the temporal resolution allowed us to observe the absence of incubation times for the motion of the domain wall, together with indications for a negligible inertia. Furthermore, we observed that, for short current and magnetic field pulses, the magnetic domain walls do not exhibit a tilting during its motion, providing a mechanism for the fast, tilt-free, motion of magnetic domain walls.
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