  Using magnetic force microscopy and micromagnetic simulations, we studied the
effect of Oersted magnetic fields on the chirality of transverse magnetic
domain walls in Fe$_{20}$Ni$_{80}$/Ir bilayer nanostrips. Applying nanosecond
current pulses with a current density of around $2\times10^{12}$ A/m$^2$, the
chirality of a transverse domain wall could be switched reversibly and
reproducibly. These current densities are similar to the ones used for
current-induced domain wall motion, indicating that the Oersted field may
stabilize the transverse wall chirality during current pulses and prevent
domain wall transformations.
