a) Change of the magnetoresistance as a function of the external magnetic field measured at a current of I=−14 mA. As indicated by the arrows, the red curve is obtained when the field is swept from positive to negative values and the black curve for the opposite sweep direction. The magnetic field is applied in the sample plane. The insets symbolically show the magnetization states of the two ferromagnetic layers at different fields, as obtained by micromagnetic simulations. The green arrows mark in which parts of the curve the magnetization states shown by the insets occur. The white arrows display the magnetization direction, and the blue–orange colour coding represents the in-plane component of the magnetization parallel to the external field direction. ( b) Dependence of the magnetoresistance change on the external field calculated from the simulations. ( c) Four examples of OV–DV states with the labelling convention used in the manuscript. The labels b and t refer to the bottom and top discs, respectively. CCW and CW denote counter-clockwise and clockwise vorticity, while the red/grey arrows display the core polarities. ( d) Scheme of the preparation sequence for DV states with opposite vorticities. At large external field B both discs are saturated (orange dot). When reducing the field to zero in the presence of a positive current, the DV state with equal vorticities is obtained (green polygon). Then, the direction of the current is reversed. By increasing the external field to the point marked by the blue square, the vortex is expelled from the top disc. Once this configuration is obtained, decreasing the external field to zero nucleates a vortex in the top disc. This vortex has a vorticity opposite to that of the vortex in the bottom disc because the Oersted field was reversed along with the sample current. The resistance R shows a maximum at the point marked by a yellow star.