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.
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