  The surface energy of a magnetic Domain Wall (DW) strongly affects its static
and dynamic behaviours. However, this effect was seldom directly observed and
many related phenomena have not been well understood. Moreover, a reliable
method to quantify the DW surface energy is still missing. Here, we report a
series of experiments in which the DW surface energy becomes a dominant
parameter. We observed that a semicircular magnetic domain bubble could
spontaneously collapse under the Laplace pressure induced by DW surface energy.
We further demonstrated that the surface energy could lead to a geometrically
induced pinning when the DW propagates in a Hall cross or from a nanowire into
a nucleation pad. Based on these observations, we developed two methods to
quantify the DW surface energy, which could be very helpful to estimate
intrinsic parameters such as Dzyaloshinskii-Moriya Interactions (DMI) or
exchange stiffness in magnetic ultra-thin films.
