fig2

Figure 2. Hopfion under geometric constriction. (A) Mid-plane cross-sections of hopfions in circular nanodisk with d = 150 nm. (B) Simulated phase-shift image and (C) under-focused LTEM image of hopfion shown in (A) for viewing directions along the z-axis. (D) In-plane magnetic component distribution reconstructed by solving the transport-of-intensity equation. (E-H) Magnetization structures stabilized in elliptical nanodisks with different short axis lengths at the mid-plane. (I-L) Results of simulated under-focused LTEM images in elliptical nanodisks corresponding to hopfions in (E-H).