Geometric symmetry and size-dependent skyrmion phase transitions in magnetic nanostructures

We investigate the interplay of geometric symmetry, size, and external magnetic fields in regulating individual skyrmion states within magnetic nanostructures. By analyzing nanodisks, nanosquares, and nanorectangles, we demonstrate that rotational symmetry in nanodisks enables rich topological phase transitions, from ferromagnetic states to skyrmions, skyrmioniums, and multi-states, as their diameter increases. In contrast, square and rectangular structures exhibit suppressed topological complexity due to corner-induced demagnetization effects and reduced symmetries. Under perpendicular magnetic fields, nanodisks show field-driven transitions between skyrmionium and skyrmion states. By leveraging asymmetry, square and rectangular nanostructures stabilize skyrmions over a broader parameter range than nanodisks. These findings highlight geometric symmetry as a critical design parameter for tailoring skyrmion stability and functionality in spintronic applications such as multi-state memory and reconfigurable logic devices.