  The Dzyaloshinskii-Moriya interaction (DMI) causes domain walls in
perpendicular magnetized systems to adopt a homochiral configuration by winding
in the same direction for both Up-Down and Down-Up walls. The topology of these
domain walls is then distinct from the uniformly magnetized state. When two
domain walls approach each other and are in close proximity they form winding
pairs, stabilized by a dipolar repulsion. This can result in the formation of
360 {\deg} stable domain walls, whose stability is directly related to the
magnitude of the additional dipolar interaction resulting from the spin
structure governed by the DMI. Application of an external magnetic field can
overcome the dipolar repulsion of the winding pairs and result in the
annihilation of the domain walls, which is studied here in a combined
theoretical and experimental effort. We present an extended analytical model
that studies the interaction and modification of the dipolar interaction of the
domain wall pairs under the application of in-plane and out-of-plane magnetic
fields. We realize the experiment in a system of
Ta/Co$_{20}$Fe$_{60}$B$_{20}$/MgO and observe that the results are in agreement
with the behavior predicted by the analytical model. To compare and understand
these results, we perform micromagnetic calculations to gauge the validity of
the analytics and also include the full dipolar interactions which are present
due to the device geometry. We find that our numerical and experimental studies
are in agreement and that the DMI indeed provides an additional stability
mechanism against annihilation of DWs, which is potentially useful in dense
memory storage applications. Beyond implications for domain walls,
understanding the interaction is an important step to understand and control
the interaction of many spin structures that contain domain walls, such as
skyrmions.
