Fig. 1: Skyrmion braid in a chiral magnet.
From: Magnetic skyrmion braids
a–d Skyrmion braid comprising six skyrmion strings represented by isosurfaces of mz = 0. The color modulation at the edges of the box indicates the presence of the conical phase. (see inset in a). The equilibrium state for each value of applied magnetic field (\({{{{{{{{\bf{B}}}}}}}}}_{{{{{{{{\rm{ext}}}}}}}}}| | {\hat{{{{{{{{\bf{e}}}}}}}}}}_{{{{{{{{\rm{z}}}}}}}}}\)) is found by using energy minimization (see “Methods”), on the assumption of periodic boundary conditions in the xy plane, free surfaces in the third dimension, and a sample thickness of t = 1440 nm. The presence of bumps on the isosurfaces results from the magnetization modulations in the surrounding conical phase. These bumps become less pronounced with increasing Bext, as the cone phase approaches a field-polarized state. e Dependence of twist angle on distance to the lower surface for the five skyrmions that wind around a central sixth skyrmion. The angles φi(z) are measured from the x axis, as indicated in c. The dotted lines are linear fits for each φi(z) dependence. f Dependence of the average twist angle \(\langle {{\Delta }}\varphi \rangle =\frac{1}{5}{\sum }_{i}\left[{\varphi }_{i}(0)-{\varphi }_{i}(t)\right]\) on the applied magnetic field. g Dependence of the average twist angle 〈Δφ〉 on sample thickness t. The solid circles in f, g are obtained from numerical calculations, while the lines are used to guide the eye.
