Unconventional domain-wall pairs and interacting Bloch lines in a Dzyaloshinskii-Moriya multilayer thin film

Bloch lines (BLs) play a key role in determining the static and dynamic behavior of chiral domain walls and skyrmions in multilayer films with a significant Dzyaloshinskii-Moriya interaction (DMI). Here, using in situ Lorentz phase microscopy, we reveal a type of spin texture termed a type-II domain-wall pair (DWP), stabilized in DMI multilayer thin films with BLs. For a type-II DWP, the Bloch components of each complementary domain wall are parallel, implying opposite chirality. We find that type-II DWPs preferentially form through bifurcation of a type-I DWP and require the formation of at least two BLs. We demonstrate a distinct phase jump associated with type-II DWPs, and further we reveal the role they play in the formation of mixed-character skyrmions where the Bloch component can be of either left- or right-handed chirality.

Figure 1

Introduction to imaging type-I and type-II domain regions with Lorentz phase microscopy (LPM). (a) Definition of the type-I and type-II DWP structure with corresponding schematics of their expected Lorentz and phase image contrast. The derivative relationships between the phase, magnetic induction, and Lorentz intensity are displayed from the overfocus imaging condition. The calculated line-profiles were carried out using an extension of Eq. (2) that accommodates 360° domains. (b) Micromagnetic simulations of type-I and type-II domains with corresponding Lorentz contrast simulations (369 μm) performed with MUMAX and MALTS, respectively. For all simulations, the input parameters match either measured or calibrated values. The kink in the type-II DWP phase line scan corresponds to the DWP out-of-plane core. (c) Schematic of the Co/Pd, $N=30$ sample studied in this work. (d) Experimental demonstration of the contrast generated by the four possible domain configurations showing the difference images and phase contrast for type-I and type-II domain regions. The blue and red circular arrows designate right- and left-handed Bloch chirality.

Figure 2

Fresnel contrast of type-II 360° domain regions. (a)–(d) Difference images of a representative region that contains both type-I and type-II regions acquired at varying defocus magnitude. There is a noticeable jump in the background contrast level from the area between two type-II DWPs. (e) Line scans of the difference image intensity to show the contrast overlap that occurs as the defocus is increased. The broadening of the apparent domain width is designated with colored lines. All difference, phase, and induction images in the following figures were acquired at a defocus magnitude of 369 μm. (f) Schematic that demonstrates the type-I to type-II DMP spin structure transition that can be derived from the difference image contrast.

Figure 3

Shown is the prevalence and preferential formation mechanism of type-II domain regions. (a) Difference images of a typical state observed from the Co/Pd $N=30$ sample upon lowering the applied field from a saturated state. The applied field is 306 mT, where the white boxes correspond to the type-I and type-II examples in Fig. 1. (b) Phase image identifying the preferential formation of type-II domain regions through bifurcation of a type-I domain that are designated by red arrows, with other formation pathways highlighted by a blue and green arrow. Part (c) shows enlarged examples of the variations of type-II domain regions. The first, highlighted in red, demonstrates the formation of a type-II domain through bifurcation of a type-I domain. For the region highlighted in green, a single type-II domain folds over itself while the region highlighted by the blue arrow demonstrates a type-II region that forms in unattached, neighboring domains. Pair formation of type-II domain regions is observed for all large-area cases.

Figure 4

Demonstration of the connection between BLs and stray fringing fields for two situations. (a), (c), (e) Simulated Fresnel, phase, and colored phase gradient images from a BL in a DWP turning from type-I (bottom) to type-II (top); (b), (d), (f) corresponding experimental images. For this case, the flux protruding from the BL is clearly resolved in the form of a “flair” at the bottom left corner of (f), and in agreement with the simulation in (e). The location of the BL is highlighted with a white box. (g), (i), (k) Simulated Fresnel, phase, and colored phase gradient images from two DWPs facing each other, each containing a BL, and each transitioning from type-I to type-II, although at different positions along their length; (h), (j), (l) corresponding experimental images. The areas of interest for comparison are highlighted with a red box. Note in this case the opposite color of the two BL flairs, blue on the right, red on the left, in agreement with the experimental image and denoting opposite chirality. Also notice the weak green shade of the region inside the two DWPs that is emphasized with gray arrows, reflecting the stray field established between the BLs, also clearly visible in the experimental image.

Figure 5

An investigation of the persistence and evolution of type-II domain regions. A phase image series acquired on the same area shows that type-II domain regions form early in the nucleation process and persist to high applied fields where skyrmion nucleation occurs. Further, it reveals the distinct and varied dynamic nature of the BL pair interaction, which is focused on in (b). The white box in the image from 310 mT designates the areas displayed in Fig. 4, while the white box in the 482 mT image designates the area displayed in Fig. 5. (b) The red and blue boxes in the phase image from 310 mT highlight two different type-II domain regions. The white arrows indicate the location of the BLs essential for the formation of a type-II domain. As the field is decreased, the BL pairs are dynamic with an attractive character displayed by the region highlighted with the red box and a repulsive character shown in the region highlighted with the blue box. Part (c) demonstrates the behavior of type-II domain regions at high applied fields where skyrmion formation occurs. At the highest applied field (523 mT), skyrmion (sky.) nucleation is observed and, further, it shows an unpaired type-II domain that enables direct comparison with the simulation shown in Fig. 1. Line scans of type-I domain regions confirm the consistency of the retrieved phase, while the line scan of the type-II domain agrees with the phase gradient surrounding type-II domains.

Figure 6

Illuminating interactions that can occur between BL pairs. (a) Phase image acquired at 482 mT showing the interactions between type-II domains and BLs that is also displayed as part of Fig. 4. (b) Enlarged image of the area of interest in (a). (c) Line scan acquired from the region shown with a white dotted line in Fig. 4. There is a clear phase gradient between the two domains (D1, D2), which corresponds with a stray field interaction (SFI) shown in (d). Induction map with a corresponding schematic in (e) of the region highlighted by the blue boxes in (a). The gray arrows indicate regions where there is an electron phase gradient and reveals interactions that can occur between BL pairs and type-II domains.

Figure 7

Probing the role that type-II domain regions play on skyrmion formation. (a) Difference images acquired from the same area at high fields where skyrmion nucleation occurs. An expanded image series on skyrmion nucleation is shown in the Supplemental Material. The red and blue boxes highlight type-II domains that nucleate skyrmions upon increased applied field and type-II DWP annihilation. Parts (b) and (c) show schematic representations of the difference images shown in (a). The type-II domains are of the same structure, yet they nucleate skyrmions of opposite chirality, which suggests there are additional energetics that can influence skyrmion chirality in mixed-character DMI multilayer thin films.