Control of magnetic vortex circulation in one-side-flat nanodisk pairs by in-plane magnetic filed

In a nanodisk made of soft ferromagnet, the magnetic vortex structure are highly stabilized, and the circulation directions of the vortices are naturally binary (either clockwise (CW) or counter-clockwise (CCW)), which can be associated with one bit of information, and thus the magnetic vortices have been of great interest recently. A vortex-circulation-based memory requires the perfect controllability of the circulation direction. From the circulation point of view, there are four possible ground states in a nanodisk pair: (CCW, CCW), (CCW, CW), (CW, CCW) and (CW, CW). In a perfect circular nanodisk, CW and CCW states are degenerate because of the high symmetry of the system. However, the circulation of the magnetic vortex is known to be controlled by introducing the asymmetry. It has been reported that the magnetic vortices with opposite (the same) circulations are realized in one-side-flat disk pair. That means in one-side-flat nanodisk pair only the control of two of these four ground states is possible, eg., (CCW, CW), (CW, CCW) or (CCW, CCW), (CW, CW). We found that the reversal of the magnetic vortex circulation is affected by the nanodisk thickness as well. By further introducing another asymmetry, different thickness, the control of the four circulation ground states is achieved in a nanodisk pair. In this work, the controllability of the four ground states in a nanodisk pair was numerically investigated via micromagnetic simulations. The results show that in a single one-side-flat nanodisk, there exists a preferred rotational sense at the remanent state after the nanodisk is saturated by the external magnetic field, applied parallel to the flat edge of the nanodisk. The shape anisotropy is the primary cause of this phenomenon. We further found that the obtained rotational senses of the magnetization in the vortex state in nanodisks with the same geometrical parameters but different thickness (20 nm and 50 nm) are opposite for the same direction of the externally applied field. This is attributed to the competition between the demagnetization field energy and the exchange energy during the vortex formation. The method we proposed provides a simple means of controlling the vortex state that can thus become a useful tool for designing vortex-based devices.