Evolution and competition between chiral spin textures in nanostripes with D2d symmetry

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Science Advances  04 Dec 2020:
Vol. 6, no. 49, eabc0723
DOI: 10.1126/sciadv.abc0723
  • Fig. 1 Spin textures in oriented nanostripes.

    (A) SEM image of the host material after the nanostripes have been formed and lifted out by FIB. [010] and [1¯10] oriented nanostripes that were fabricated from (A) are shown in the SEM images in (B) and (C). (D and E) Bright-field TEM images of portions of nanostripes with indicated widths and crystallographic axes. (F and G) Lorentz TEM images of the magnetic texture at zero field in the two nanostripes that show the formation of helices whose Q-vectors are oriented along the [100] and [010] directions, in both cases. (H) Schematic representation of a magnetic antiskyrmion, where the color encodes the orientation of the magnetic moments. The Bloch parts of the antiskyrmion are along the family of {10} directions (orange), while the Néel parts are along the {11} directions. (I and J) LTEM images of antiskyrmion chains measured in magnetic fields of 187 and 273 mT, respectively, oriented perpendicular to the plane of the nanostripes. The bright and dark regions correspond to the antiskyrmions’ Bloch parts oriented along {10}. (K and L) Micromagnetic simulations of the spin textures in nanostripes with orientations corresponding to those in (I) and (J), respectively. The color code represents the direction of the moment within each cell used in the simulation. The same color code has been used throughout the paper: black along +z, white along –z, and the hue colors stand for in-plane orientations with respect to the [100] direction (e.g., blue arrows always point along the [100] direction).

  • Fig. 2 Helix formation upon decreasing the magnetic field.

    In the left column, the magnetic field is decreased starting from 316 mT in (A) corresponding to the ferromagnetic phase. (B) At 227 mT, a single helix segment forms along the [010] direction (along the nanotrack), elongates, and finally extends over the whole stripe region in (C) at 208 mT. (D) At 183 mT, a second helix segment forms, which elongates in (E) at 134 mT. (F) At 88 mT, a third segment forms. (G) At zero field, the ground state is formed: three parallel helix segments along the nanostripe. In the right row, the magnetic field is decreased under tilting of the sample by ~21°. (H) The starting configuration is again the ferromagnetic phase at 316 mT. (I) At 272 mT, noncollinear spin textures already form at higher magnetic fields. An irregular chain of antiskyrmions has formed. (J) At 245 mT, more of those have formed and the chain is rather periodic. (K) At 233 mT, they begin to elongate along the [100] direction (perpendicular to the nanotrack direction). (L) At 224 mT, a mixed state has formed. (M) At zero field, the magnetic texture is not perfectly ordered. (N) At small negative fields, a periodic helical state is formed. Using this tilted field, the helical segments are oriented along the [100] direction rather than [010].

  • Fig. 3 Antiskyrmion and helix formation upon increasing the magnetic field.

    On the left side, the starting configuration (A) is a helical phase with helix segments along [010]. (B to E) The three individual segments shrink and disappear one after another upon increasing the magnetic field as indicated. In the middle column, the helix segments are initially oriented along the [100] direction, the narrow width of the nanostripe (F). (G) Again, they shrink, but this time, antiskyrmions form in (H) at 200 mT. (I) At 215 mT, the antiskyrmions annihilate. (J) At 225 mT, the ferromagnetic phase is restored. In the right column, the initial configuration (K) is a mixed helical state with Q-vectors along [100] and [010]. (L) At 158 mT, the helix segments shrink. (M) At 236 mT, the interaction of them leads to segments of different sizes along [100]. (N) Once the helix segment at the bottom right edge has disappeared, the smaller segments expand upon relaxation. (O) Even at 283 mT, the antiskyrmion on the very left has a slightly different contrast compared to the other antiskyrmions. This is because small deformations along [100] and [010] are still present, corresponding to the initial helix type. (P to R) Results of micromagnetic simulations exemplarily showing the metastability of (P) a mixture of one and two horizontal helix segments, (Q) a chain of antiskyrmions, and (R) a mixture of horizontal and vertical helix segments (see Materials and Methods for details).

  • Fig. 4 Single and double chains of antiskyrmions.

    In the left column, the starting configuration (A) are helix segments that are elongated along the [100] direction, which is oriented at an angle φ ≈ − 28° with respect to the racetrack direction. (B) Upon increasing the field, the helix segments shrink, until few antiskyrmions are formed in (C) at 187 mT. (D) For fields above 201 mT, almost all segments have turned into antiskyrmions so that a chain of antiskyrmions is present in (E). (F) At 253 mT, the antiskyrmions annihilate, until the ferromagnetic phase is restored. In the middle column, the procedure is changed. This time, the sample is reversibly tilted by 30° to provide a temporal in-plane field component before each image is taken. (G to I) At low fields, the magnetic texture mainly exhibits a helical phase, like in the left column. (J) However, at 200 mT, a double row of antiskyrmions forms because of temporary application of in-plane field component. (K) At 237 mT, the number of antiskyrmions reduces and a single chain is restored. At 254 mT, the sample becomes ferromagnetic in (L). In (M), the numbers of antiskyrmions (aSk) for the two scenarios are compared for different field strengths (red is without in-plane field; black is with in-plane field). Blue shows results for a larger tilting angle. The corresponding LTEM images are shown in the Supplementary Materials (fig. S1). In (N to Q), the generation of an antiskyrmion chain starting from a mixed helical phase is shown. Like in the left column, the magnetic field is not tilted in this this case. On the right side, results of micromagnetic simulations are shown. Both helix types from (N) shrink and form antiskyrmions in (Q).

  • Fig. 5 Evolution of single and double antiskyrmion chains upon decreasing the field.

    In the left column, (A) the starting configuration is a ferromagnet. (B) The field is simply decreased, leading to the generation of antiskyrmions. (C to G) The antiskyrmions elongate until a helical phase is restored. In the right column, the starting configuration is again a ferromagnet. (H) This time, the field is reduced under reversible tilting of the sample by 30° to provide a temporal in-plane magnetic field. This again allows the stabilization of antiskyrmions. (I) They survive at 211 mT without elongation. (J) At 192 mT, a double chain of antiskyrmions forms. (K to M) When the field is decreased from here, these double chains of antiskyrmions elongate. (N) At zero field, the helical phase is restored. (O and P) The elongation process of an antiskyrmion chain is shown in micromagnetic simulations at different external fields. (Q and R) When more antiskyrmions are placed in the sample, a double chain of antiskyrmions is stabilized that elongates similar to the experiments.

  • Fig. 6 Antiskyrmions versus elliptical skyrmions in a nanostripe along the [1¯10] direction.

    In (A), the initial configuration is shown consisting mainly of antiskyrmions (indicated by red triangles) and only showing three elliptical skyrmions that are elongated along the [010] direction and one elliptical skyrmion that is elongated along the [100] direction (both indicated by blue triangles). In (B), the sample was reversibly tilted to provide a small in-plane field along the [100] direction. The result is mainly elliptical skyrmions. Most of them are elongated along the [100] direction. In (C to F), the same procedure is repeated but with larger tilting angles: The number of antiskyrmions increases with tilt angle. For a few nano-objects, it is difficult to determine whether it is a skyrmion or an antiskyrmion. In these cases, we did not add a marker. In (G), the coexistence of elliptical Bloch skyrmions and antiskyrmions in a single chain is shown as a result of a micromagnetic simulation. (H) Simulated LTEM contrast of the spin texture shown in (G).

Supplementary Materials

  • Supplementary Materials

    Evolution and competition between chiral spin textures in nanostripes with D2d symmetry

    Jagannath Jena, Börge Göbel, Vivek Kumar, Ingrid Mertig, Claudia Felser, Stuart Parkin

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