Fig. 1: An ordinary magnetic skyrmion and a square-shaped magnetic skyrmion.

a Top-view schematic of the simulation geometry. l denotes the spacing between two adjacent parallel defect lines. w denotes the width of the defect line. n denotes the number of unit square patterns along the x and y directions. The total side length of the ferromagnetic layer equals n ⋅ l + (n + 1) ⋅ w. K and K_d stand for the perpendicular magnetic anisotropy constants for the unmodified areas and defect lines, respectively. The defect lines with reduced K_d are indicated by yellow lines. The thickness of the ferromagnetic layer is fixed at 1 nm. b Illustration of a relaxed ordinary round-shaped skyrmion with the topological charge of Q = 1 at the center of a sample with K_d/K = 1. The side length of the sample equals 106 nm. The relaxed skyrmion diameter d_sk equals 16 nm, which is indicated by the black line. The color scale represents the out-of-plane magnetization component m_z, which has been used throughout the work. c Illustration of a relaxed square-shaped skyrmion with Q = 1 at the center of a sample with K_d/K = 0.2. Here, l = 30 nm, w = 4 nm, and n = 3. The side length of the sample equals 106 nm. The relaxed skyrmion diameter d_sk equals 38 nm, as indicated by the black line. d Top view of the sample with K_d/K = 1, corresponding to (b). e Top view of the sample with K_d/K = 0.2, corresponding to (c).