  We show that the Dzyaloshinskii-Moriya interaction (DMI) can lead to a
tilting of the domain wall (DW) surface in perpendicularly magnetized magnetic
nanotracks when DW dynamics is driven by an easy axis magnetic field or a spin
polarized current. The DW tilting affects the DW dynamics for large DMI and the
tilting relaxation time can be very large as it scales with the square of the
track width. The results are well explained by an analytical model based on a
Lagrangian approach where the DMI and the DW tilting are included. We propose a
simple way to estimate the DMI in a magnetic multilayers by measuring the
dependence of the DW tilt angle on a transverse static magnetic field. Our
results shed light on the current induced DW tilting observed recently in Co/Ni
multilayers with inversion asymmetry, and further support the presence of DMI
in these systems.
