Figure 1

(a) and (b) show $M\text{−}H$ curves (squares) and $dM/dH$ (triangles) for a $d=26.7$ nm film for increasing (red filled points) and decreasing (blue open points) magnetic fields. (a) $T=42$ K and $K_u/K_0=0.02$, and (b) $T=15$ K and $K_u/K_0=0.22$. The elliptic skyrmion $\left(\mathcal{S}\mathcal{k}\right)$, helicoid $\left(\mathcal{H}\right)$, elliptic cone $\left(\mathcal{C}\right)$, and ferromagnetic $\left(\mathcal{F}\right)$ regions are labeled. (c) Numerical calculations of $M\left(H\right)$ for $K_u/K_0=0.22$. The dashed light-blue line represents the helicoid phase, solid green line represents the conical phase, dotted navy line represents the skyrmion phase, and the thick black line follows the most energetically favorable state. The inset shows calculations for $K_u/K_0=0.02$.Reuse & Permissions

Figure 2

Static susceptibility in increasing and decreasing field sweeps for the 26.7-nm MnSi film at various temperatures. Consecutive curves are offset by 200 kA/m/T for clarity. Dashed lines show the transition fields selected at each temperature.Reuse & Permissions

Figure 3

(a) The critical field data for five different film thicknesses collapses into four groups that correspond in increasing field to $H_{\beta }$ (turquoise), $H_{\alpha 1}$ (orange), $H_{\alpha 2}$ (green), and $H_{\mathrm{sat}}^{\parallel }$ (navy). The two open symbols correspond to temperatures where plateaus in $dM/dH$ exist in place of peaks. $H_{S1}$ and $H_{S2}$ bound the region of stable elliptic skyrmions. The dashed lines define the boundary for metastable helicoids $H_h$ and elliptic skyrmions $H_{S3}$. (b) Elliptic skyrmion lattice produced by an in-plane magnetic field $\mathbf{H}$ and a uniaxial hard axis along $\mathbf{n}$. (c) The equilibrium distribution of the magnetization component along the skyrmion axis calculated for $K_u/K_0$ = 0.22 and different values of the applied field. For $H/H_D>0.8$ the lattice transforms into a set of isolated skyrmions.Reuse & Permissions

Figure 4

The in-plane field $H\text{−}T$ phase diagram for a $d=26.7$ nm MnSi film for increasing (filled red) and decreasing field (open blue) extracted from Fig. 2. The open black diamonds are obtained from the peaks in Fig. 5. The out-of-plane saturation fields $H_{C2}^{\perp }$ that we used to calculate the anisotropy are also included (black hexagons). The phases at intermediate temperatures are labeled with $\mathcal{H}$ (helicoid), $\mathcal{S}k$ (elliptic skyrmion), and $\mathcal{F}$ (ferromagnet).Reuse & Permissions

Figure 5

The temperature dependence of the static susceptibility for a 26.7 nm thick sample measured in fixed fields ranging from 0.010 to 0.6 T. The dashed lines show the transition temperatures selected at each field, which are plotted in Fig. 4.Reuse & Permissions