Figure 2

Magnetic phase diagram and characteristics of magnetic phases. (a) \(\Gamma\)-H magnetic phase diagram for the model in Eq. (6) in the unit of J. The 3Q-I, 3Q-II, 3Q-III, SkX-2, SkX-1, 3Q-Ch, 1Q conical, and FP represent the triple-Q I, triple-Q II, triple-Q III, \(n_{\mathrm{sk}}=2\) SkX, \(n_{\mathrm{sk}}=1\) T-SkX, triple-Q chiral, single-Q conical, and fully polarized states, respectively. In the hatched region, energies for several magnetic states are degenerate and it is difficult to determine the phase boundaries. (b–g) Snapshots of the spin configurations in (b) 3Q-I for \(\Gamma =0.075\) and \(H=0.4\), (c) 3Q-II for \(\Gamma =0.075\) and \(H=1.3\), (d) SkX-2 for \(\Gamma =0.2\) and \(H=0\), (e) SkX-1 for \(\Gamma =0.2\) and \(H=1\), (f) 3Q-III for \(\Gamma =0.075\) and \(H=1.6\), and (g) 3Q-Ch for \(\Gamma =0.2\) and \(H=1.4\). The arrows and contour denote the xy and z components of the spin moments, respectively. The square root of in-plane and out-of-plane spin structure factors in the Brillouin zone are shown in upper and lower panels, respectively, where the dashed circles highlight \(\pm {\varvec{Q}}_1\), \(\pm {\varvec{Q}}_2\), and \(\pm {\varvec{Q}}_3\) and the \({\varvec{q}}=0\) component is removed for better visibility. (h–m) Real-space distributions of the skyrmion density \(\Omega _R\) for the spin configurations in (b–g), respectively. (n) H dependences of the magnetization (red square) and spin scalar chirality (blue circle) for \(\Gamma =0.075\) (filled symbols) and \(\Gamma =0.2\) (open symbols).