Fig. 1: Dependence of ramified stripe-morphology on nucleation domains.

Numerical solutions of the Landau–Lifshitz–Gilbert equation with the periodical boundary conditions and A = 10 pJ m⁻¹, D = 6 mJ m⁻², K = 0.49 MJ m⁻³, M_s = 0.58 MA m⁻¹ for a sample of 300 nm × 300 nm × 0.4 nm. A, D, K, and M_s are exchange stiffness constant, the Dzyaloshinskii–Moriya interaction coefficient, easy-axis anisotropy, and saturation magnetization, respectively. a–c are different initial configurations of a disk of diameter 20 nm (a), a hexagon of side length 10 nm (b) and a square of length 20 nm (c). d–f are intermediate states at 0.3 ns with irregular shapes. g–i are the final stable patterns with irregular ramified stripes. Skyrmion charge density ρ is encoded by colours (the blue for positive and the red for negative) while the grayscale encodes m_z. The dark black lines denote m_z = 0. The positive and negative charges exist respectively only around convex and concave areas. The spin profile across the stripes at the green ⓝ is considered. j–l are the evolution of total energy E_total and topological skyrmion number Q (t is in the logarithmic scale). Q reaches the skyrmion number 1 within 1 ps. Clearly, the skyrmion number is a constant and the total energy is negative and approaches a constant almost independent from the initial configurations.