Magnetic D-brane solitons: skyrmion strings ending on a Néel wall in chiral magnets

Abstract

Magnetic skyrmions extended to three dimensions form string-like objects whose fundamental role remains largely unexplored. We show that skyrmion strings can terminate on a Néel-type domain wall (DW), realizing a magnetic analogue of a Dirichlet(D)-brane soliton. While an isolated Néel DW tends to rotate into a Bloch DW, the Néel DW is stabilized when a skyrmion string ends on it. Unlike field-theory D-branes, the Bloch-type DMI produces linear rather than logarithmic DW bending, and the strings retain finite width far from the DW, circumventing singular behavior. Furthermore, the repulsive interaction between strings allows periodic multi-junction solutions, yielding a square lattice of alternating strings and local DW deformations. These results establish magnetic skyrmion strings as fundamental strings that can end on a D-brane.

Figures (3)

• Figure 1: String-DW junctions (trumpets) for various strength of the DMI $\kappa=0.35$ (blue), $0.4$ (red), $0.45$ (magenta), $0.5$ (yellow). The slope of the linear bending is nearly linearly proportional to $\kappa$.
• Figure 2: String-DW junction with $\kappa=0.5$. Arrows are mapped from $\mathbf{n}$ to $\mathbf{x}$ and the colors are in one-to-one correspondence with the arrows: $n_1=1\mapsto$ red, $n_2=1\mapsto$ green, $n_1=-1\mapsto$ cyan, $n_2=-1\mapsto$ magenta, $n_3=1\mapsto$ white and $n_3=-1\mapsto$ black. The inlet and the bottom are horizontal cross sections, whereas the top is a vertical cross section of the string-DW junction.
• Figure 3: Multi-string-DW junctions with $\kappa=0.4$. Periodic boundary conditions are imposed in the $x$- and $y$-directions. Left panel: the two isosurfaces corresponding to $n_3=1/2$ (red) and $n_3=-1/2$ (green). Right panel: the corresponding details of the entire field using arrows, which are mapped from $\mathbf{n}$ to $\mathbf{x}\in\mathbb{R}^3$ and the colors corresponding to the arrows are described in Fig. \ref{['fig:stringjuncspin']}. In the top-part of the configuration, the spins circle counter-clockwise corresponding to skyrmion strings, whereas in the bottom-part of they circle clockwise corresponding to anti-skyrmion strings.