Skyrmion engineering with origami

Abstract

Skyrmion structures play critical roles in solid-state systems involving electric, magnetic and optical fields. Previous approaches to the study of skyrmions have involved specific structures in magnetic materials, liquid crystals and polymers in addition to two-dimensional arrays used for electrical control. These methods have encountered limitations and constraints on both the microscopic and macroscopic scales related to the physical properties of materials. The present work demonstrates an origami-based skyrmion engineering strategy that suggests a new approach to topological control. This technique utilizes the unique properties of orientational origami, combining polarization techniques with rotationally symmetric, periodically folded designs. This strategy enables the transformation of flat sheets into three-dimensional structures with associated changes in optical topology, similar to the characteristics of proteins. Topological defects such as misalignments and dislocations in folded molecularly oriented sheets lead to the creation of skyrmion clusters at boundaries having different orientational orders. The strategy reported herein involves the construction of unique metamaterial platforms that could provide new applications for twistronics in graphene and photonic crystals.

Fig. 1

The topological metamorphosis concept. (a) The origami geometry net. The mountain and valley folds are indicated by red and blue lines. The direction (φ = 0°) of the molecular orientational order of the sheet are represented here by the eight colored arrows. (b) Both ends, as indicated by line C, of the molecular-oriented sheet connected with non-oriented tape. (c) The sheet is folded into a valley fold at point O to form an angle θ and is then mountain-folded at points A and B to create a single blade. A unit is defined by the dimensions t, a and b and the angle θ (see Extended Data Figs. 1b and 1c). (d) Eight blades were designed and individually folded. Depending on the folding method, these structures transitioned to the first mode (d1) or the second mode (d2). (e) An enlarged view of blade number 3 as seen from the front of the flat fold depicted in the right column of (d1). Note that the interior of each blade is divided into eight elements. The origami was constructed via the rotationally symmetric assembly of the four elements enclosed within the red box. (f) The output polarization was calculated based on the folding structure of the four elements and the orientated directions of the overlapped sheets.

Fig. 2

Generation of a topological skyrmion using origami (a) The origami geometry net having 24 blades (mountain and valley folds are indicated by red and blue lines). When both ends of the structure shown in (a1) are glued together, a ring-shaped primary structure (a2) is formed. Repeated mountain and valley folds along the creases yield the flat fold shown in (a4) via the structure shown in (a3). (b). (a4) presents a front view of the red area, representing a single blade, which can be divided into as many as 28 elements depending on the folding process (Extended Data Fig. 2b). Consisting of eight basic elements, numbered 1, 2, 14, 19, 23, 26–28 (all of which are shown in grey in Extended Data Fig. 2b), this assembly can undergo rotational transformation to achieve axisymmetric optical properties, allowing these properties to be spatially determined. This figure indicates the number of sheets stacked in elements from 1 to 28 based on the folding structure. (c) Elements 1 to 28 can have up to 13 molecularly oriented sheets superimposed on one another. The direction of the orientational order of the molecularly oriented sheets resulting from this superposition is mapped in two dimensions. (d) The distributions of the ellipticity (d1) and the azimuth (d2) of the output polarization are mapped with an incident linear polarization of 0°. Here, the magnitude of the orientation order possessed by the molecular-oriented sheet was set to a retardance of Δ. The result of the azimuth at Δ = 180° is shown in (d3). (e) Interestingly, the ellipticity became zero (e1) and the azimuth varied linearly (e2). Two-dimensional mappings demonstrated a polarization topology having a polarization order of 2 with respect to the angle. (f) An origami produced by a retardation film. (g1–g6) Light intensity distributions imaged while rotating the achromatic quarter-wave plate in 30° intervals. (h) The analysis results: ellipticity (h1), orientation (h2), ellipticity and azimuth distributions along the white dashed lines in (h2). The ellipticity was almost zero whereas the azimuth changed in a staircase-like manner, resulting in a higher order skyrmion (h3).

Fig. 3

Topological metamorphosis through origami transformation (a) The topological mode transformation of origami with 24 blades. When this geometry net is modified with mountain and valley folds, the topological mode changes. If two mountain fold in the geometry net in (a1) are set to flat, a topology with mode m = 2 is generated (a2). If three mountain fold positions are changed from mountain fold to valley fold, a mode m = 3 topology shape is formed (a3). An investigation of the polarization morphology associated with the topological mode of the origami produced the results shown in (b1–c2). The 2D maps of ellipticity and azimuth at mode m = 2 (b1, b2) and the 2D maps of ellipticity and azimuth at mode m = 3 (c1, c2) are shown. A more detailed inspection of the azimuth distribution at mode m = 2 reveals that a ± 1/2 topological vortex associated with a second-order polarization was generated, thus producing skyrmion clusters. Scar bar is 20 mm.

Fig. 4

Skyrmion structures with a polarization vortex of ± 1/2 order. (a) Enlarged views of the image in Fig. 2h2, showing CW (clockwise) (a1) and CCW (counter-clockwise) (a2) images. (b) The angle variations of the azimuth along the white dashed lines in (a1) and (a2) are shown: a 180° change in the azimuth of the polarization was obtained for a single revolution. The number of such changes was investigated with the results shown in Figs. 2 and 3. (c) Distributions of the number of skyrmion clusters with ± 1/2-order vortices caused by metamorphosis of the origami. The folding structure exhibits the fewest defects when in the first-order topological mode, as this mode was the most stable. Conversely, defects were most prevalent when the topological mode was of the second order during the metamorphosis of the origami metamaterials because this structure was the least stable. Pixel size is 0.35 mm in (a1) and (a2).