Fig. 5

Images of freely moving textures away from the influence of the defect lines in the system from Fig. 4 with \(\Delta =21\) nm and \(j=2.6\times 10^{10}\) A m\(^{-2}\) where a hopfion to toron transformation occurs. (a–d) Hopfion motion, with no Hall angle, \(\theta =0^\circ\), before the transformation at (a) \(t=0\) ns, (b) \(t=5.1\) ns, (c) \(t=9.6\) ns, and (d) \(t=14.1\) ns. (e–h) Dipole string, or toron, motion, with a Hall angle of \(\theta =43^\circ\) after the transformation at (e) \(t=40.8\) ns, (f) \(t=45.3\) ns, (g) \(t=49.8\) ns, and (h) \(t=54.3\) ns. The velocity of the hopfion is roughly \(v=2.7\) m s\(^{-1}\), and that of the dipole string is roughly \(v=1.1\) m s\(^{-1}\). Arrows indicate the direction of motion. The colors represent the \({\bf{m}}\) direction, with the color given by the angle between \(m_y\) and \(m_x\), and the brightness given by the \(m_z\) value, following the colormap presented in Fig. 1.