Introduction

Magnetic films with a quality factor exceeding 1 show perpendicular magnetic anisotropy (PMA) that favors magnetization in two directions (up or down) perpendicular to the film1. Recently, the formation of magnetic topological defects in PMA systems has drawn much interest because topological defects can present a topologically protected magnetization texture known as a magnetic skyrmion2,3,4. Because of their distinct topological properties2,3,4,5,6,7,8, skyrmions are treated as ideal information carriers for memory9,10, logic11,12, and neuromorphic devices13. Skyrmions have been observed in various magnetic systems14,15, even at room temperature16. Furthermore, skyrmions have been intentionally created using diverse methods, including a pulsed local magnetic field14 or spin-orbit torque (SOT)-based perturbation17,18,19. However, to date, skyrmions have only been discovered in extremely narrow ranges of material parameters. For example, more than ten multilayers of [heavy metal/ferromagnet/heavy metal] are required to induce a large dipole field20, and the ability to control the thickness within 0.1 nm or less is essential for achieving a particular PMA value5,21. Furthermore, these creations of magnetic skyrmions reported thus far are mostly based on the local skyrmion nucleation process occurring at defects with reduced anisotropy, which disturbs their motion after creation and thereby increases the critical threshold for driving skyrmions. These restrictions in creating skyrmions are one of the challenging issues in skyrmion research. In addition, several works have reported the creation of multiple bubble domains after applying a tilted magnetic field, where the specific mechanism remains unclear22,23. Furthermore, although several reports have demonstrated a nearly perfect skyrmion lattice in helimagnets24,25, a universal way of creating a large number of skyrmions in a typical PMA film system is not yet available. Therefore, for further in-depth research on magnetic topological physics and realization of a skyrmion application device, more generalized skyrmion generation, as well as a detailed creation mechanism, is needed.

Here, we present a universal method for magnetic skyrmion generation with experimental proof of the microscopic mechanism of skyrmion generation. The current results provide a solution to the unclear mechanism in several works22,23 that reported the creation of multiple bubble domains after applying a tilted magnetic field. More importantly, the presented method can be applied to samples with a much broader range of material parameters, such as PMA and the Dzyaloshinskii–Moriya interaction (DMI)26,27, compared with previous works. For example, we succeeded in generating many skyrmions even in a high-PMA sample. To date, it is known that such high-PMA samples show large domains27 and do not produce individual skyrmions. We believe that by solving the critical problems that have been hampering skyrmion research and applications, our findings will open new pathways for skyrmion-based information processing devices and will help us understand the fundamental physics of skyrmion generation and annihilation.

The stack of our sample (SiO2/W/CoFeB/Ta/MgO/Ta) with PMA is shown in Fig. 1a, where the PMA originates from the CoFeB/MgO interface28,29. To manipulate the PMA in this sample, we inserted a Ta wedge layer between CoFeB and MgO. Unlike the PMA, the total summed magnetization of this system was dominated by the volume of CoFeB, and it barely depended on the insertion of a Ta layer. As a result, it is possible to observe the effect of PMA manipulation by measuring the magnetic domain patterns as a function of the Ta thickness (see Figs. S1, S2 for PMA measurement and Figs. S3, S4 for saturation magnetization measurement). In addition, as the DMI comes from the interface between the W and CoFeB layers, the insertion of a Ta layer does not significantly change the DMI (see Figs. S5, S6). The upper images of Fig. 1b present typical domain patterns observed by a magneto-optic Kerr effect microscope at several sample positions having different PMA strengths. Light gray indicates upward (+z) magnetization, and dark gray indicates downward (–z) magnetization. These magnetization states consist of an equal number of up and down domains, and both exhibit a certain width (λ0 in Fig. 1b), which can be clearly shown by a fast Fourier transform (see Fig. S7). This type of magnetization state is known as the “stripe domain”30,31.

Fig. 1: Stripe, bubble, and uniform states and their transition due to a perpendicular magnetic field.
figure 1

a Sample structure: SiO2/W (5 nm)/Co2Fe6B2 (1.3 nm)/Ta (0.12–0.14 nm)/MgO (1 nm)/Ta (2 nm). Pink arrows denote possible domain magnetization directions in the CoFeB layer. b Typical magnetization state at several sample positions with zero magnetic field (upper images) (light gray represents +z magnetization, dark gray represents –z magnetization). The lower images are bubble domain states. c Stripe disappearance field and bubble disappearance field as a function of the zero-field strip width. The orange- and green-colored regions are expected regions where the bubble and stripe states, respectively, are at the GME. d Changes in the magnetization state as a function of the perpendicular field at a narrow-stripe (λ0 = 1.3 μm) position. e Magnetization state change as a function of the perpendicular field at a wide-stripe (λ0 = 2.6 μm) position. A blue (red) circle indicates the disappearance of the stripe (bubble) domains. A green square represents the transformation from the uniform state to the stripe state.

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The stripe domain has been considered a precursor for the creation of magnetic skyrmions. In the simplest example, application of a perpendicular magnetic field (Hz in Fig. 1a) can stabilize the bubble state compared to the stripe state. As a result, in a moderate Hz range, the bubble state becomes the global minimum energy (GME) state. A further increase in Hz causes the uniform magnetization state to become the GME state due to the Zeeman energy. Interestingly, all Hz ranges for stabilizing the stripe, bubble, and uniform states are normalized by a certain Hz value at which the bubbles disappear (Hz,B)30,31. Roughly, the stripe domain, bubble and uniform states are at the GME in the regions from 0 to 0.5 Hz,B, 0.5Hz,B to Hz,B and Hz,B to infinity, respectively. Thus, most studies on skyrmions try to use stripe domain states to create skyrmions. However, to date, these attempts at changing the stripe domains into the bubble state have been limited to narrow stripes.

We will show why creating bubble domains fails for wide stripes under Hz. We measured the minimum field strength (Hz,S) to erase all the stripe domains. The values of Hz,S were obtained at several sample positions with different values of λ0. We performed the same experiments with initial bubble domain states, as shown in Fig. 1b, to obtain Hz,B. These Hz,S and Hz,B values are plotted in Fig. 1c (blue and red circles). From the measured Hz,B values, the regions where the stripe and bubble states were the GME states (the orange and green areas in Fig. 1c, respectively) could be estimated30,31,32. It is worth noting that the measurement of Hz,B indicated by red filled circles has never been achieved for wide-stripe domains. Remarkably, the overall results of Fig. 1c are separated at λ0 = 1.7 μm. For λ0 < 1.7 μm (narrow stripes), increasing Hz cuts all stripe domains into bubble domains at Hz,S, and the bubble domains are maintained before reaching the uniform state. Figure 1d shows the sequential change in the magnetization state with Hz at a narrow-stripe position (λ0 = 1.3 μm). Increasing Hz leads to a state change of stripe–bubble–uniform. Blue and red circles between images indicate stripe-bubble and bubble-uniform transitions, respectively. Decreasing Hz also induces uniform–bubble–stripe transitions, by nucleation of bubble domains and their elongation. However, in wide stripes (λ0 > 1.7 μm), we cannot see such a stripe–bubble–uniform transition because all bubble domains already disappeared at a much smaller field than Hz,S. Therefore, we cannot form a bubble state by changing Hz in wide stripes. Figure 1e presents this failure for a wide stripe (λ0 = 2.6 μm); only a strip–uniform transition occurred at large Hz values (indicated by a blue circle). When Hz was reduced, the bubble domains did not nucleate within the range of the bubble GME state. Instead, the stripe domain grew to fill the entire area under the reduced magnetic field, which is the stripe domain GME state. This event is indicated by a green square in Fig. 1e, c.

To address the question of why bubbles are not easily formed in a wide-stripe domain state, we examined the effect of an in-plane magnetic field (Hx). We prepared an initial stripe domain state at zero field. We turned on Hx and captured the domain image; then, we turned off Hx and captured the image again. Repeating these procedures with increasing Hx resulted in the sequential images shown in Fig. 2a. A reduced stripe width was observed with the application of Hx. However, the stripe width was recovered to the initial width after turning off Hx. The field-off states showed no isolated domain up to 0.34 kOe, and the domain states looked similar to the initial state. Therefore, we can expect that Hx induces continuous deformation of the stripe structure by adding narrower stripes (red lines in Fig. 2a) to the original stripe structure (white lines in Fig. 2a).

Fig. 2: Effect of an in-plane magnetic field on the stripe domain state.
figure 2

a Sequential images of the magnetization state with varying in-plane magnetic field. b Variation in the stripe domain width as a function of the in-plane field at several sample positions. Hk indicates the strength of the PMA converted to the magnetic field value (see Supplementary Note 1 for measurements of Hk). Black dots indicate the critical values for isolated domain generation at each position (see Supplementary Note 6). The inset shows the definition of the stripe width, the in-plane field direction, and a schematic image of the domain wall structure. The dotted line represents λ = 1.7 μm.

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Interestingly, a discontinuous deformation occurred after applying Hx above 0.45 kOe. The initial stripe structures almost disappeared, and isolated domains were created (red boxes in Fig. 2a). Further application of Hx produced stripe domains almost parallel to the x-direction but still left isolated domains. Therefore, the formation of isolated domains can be considered to be strongly related to the stripe width. Thus, we plotted the stripe width (λ) as a function of Hx, as shown in Fig. 2b, at several sample positions with different stripe widths (λ0). The value of λ is defined along the y-axis (inset of Fig. 2b). The logarithm of the stripe width shows a linear dependence on Hx (see Supplementary Note 5).

Our finding is a universal value of the stripe width that creates isolated domains regardless of the initial stripe width. The creation of isolated domains was confirmed by zero-field domain images (see Figs. S8, S9 for the detailed procedure). The results of the required Hx and λ at each position are plotted together in Fig. 2b (black open circles). All the width values are in the range of 1.5–1.8 μm, and this range is almost the same as the reference value (1.7 μm) for dividing the narrow stripes and the wide stripes in Fig. 1c. We expect that sufficiently narrow-stripe domains can be cut into small segments and create isolated domains, as shown in Fig. 1d. Thus, it can be seen that the width of the stripe is an important variable in determining the instability of the stripe domain.

The application of an additional field Hz during the stripe-cutting process can leave only bubble domain states. It is clear that Hx does not distinguish between +z and –z domains, so the numbers of +z and –z isolated domains after application of Hx are almost equal (Fig. 2a). In addition, the isolated domains made in this way have irregular shapes and sizes with low density. However, the additional Hz can select only one of the +z and –z domains due to the Zeeman energy. As a result, it is expected that as many bubbles of one polarity are formed as possible, and a dense circular bubble state is created for close packing. Figure 3a shows typical domain patterns at zero field after the simultaneous application of Hx and Hz to the values presented at the center of the squares for 1 s. To obtain these results, we prepared initial well-connected stripe states using Hz for every single image. When Hx was <0.54 kOe, a larger Hz created uniform magnetization states, and Hz = 0 induced stripe states. This result is similar to those for the wide stripe shown in Fig. 1e. When Hx exceeded 0.54 kOe, the creation of isolated domains was observed, as were bubble-filled states. The isolated domain number (bubble number) at a larger Hz is much larger than that of the Hz = 0 state. Therefore, the application of simultaneous Hx and Hz can cause the bubble-filled states to be the GME states. As a result, the bubble state can be created by simultaneously applying Hx and Hz in a wide-stripe domain sample.

Fig. 3: Magnetization state pattern changes under the combination of an in-plane field and a perpendicular field.
figure 3

a Zero-field magnetization states after application of the magnetic field. The values of Hx and Hz at the center of each image are the applied field values. b Convergence of normalized isolated domain numbers as a function of field application time for different initial states. Filled dots at time 0 represent different initial states marked in a. Red, blue, and green filled dots indicate the well-connected stripe state, -z bubble-filled state, and +z bubble-filled state, respectively. c Magnetization state changes when the magnetic field is applied for a longer time after the number of isolated domains converges.

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The detailed process of isolated domain creation will be discussed next. We prepared three different initial domain states, namely, a well-connected stripe state, a + z bubble-filled state, and a –z bubble-filled state (the colored dots in Fig. 3a). A magnetic field (μ0Hz = 2.8 Oe, μ0Hx = 0.52 kOe) was applied for a certain time, and after that, the isolated domains under zero field were counted. The number of ±z isolated domains was N±, and Nmax was the total number of isolated domains of the initial bubble-filled states. The ratio (N_–N+)/Nmax is plotted in Fig. 3b as a function of the field application time. All data exponentially converged to a single value after 2 s. Further application of the field did not change N±, although the detailed domain images were not the same. The domain states with additional application of the field are shown in Fig. 3c. Thus, we believe that the converged state is a thermal equilibrium state.

Because of the thermal energy, domain walls randomly fluctuate from an equilibrium position33. A schematic situation for this state is shown in Fig. 4a. The domain wall is perturbed by thermal energy and could have a different shape (gray dashed lines) over time. If two adjacent walls are far apart (wide stripes), it is difficult for domain walls to collide with each other (Fig. 4a)31. Note that the domain wall magnetization can also have a certain chiral structure due to the DMI. The DMI generates an effective magnetic field (HDMI, cyan arrows in Fig. 4a) in the domain wall. In our system, the interface between W and CoFeB is a meaningful source of the DMI34,35, and it adopts the (+z)–(+y)–(–z)–(–y)–(+z) chiral structure in the y-direction and the (+z)–(+x)–(–z)–(–x)–(+z) chiral structure in the x-direction. This chiral magnetization texture can also enhance the stripe stability.

Fig. 4: Detailed magnetization states during the stripe–bubble transition.
figure 4

a–h Schematic images of magnetization states; pink arrows indicate magnetization directions. a Initial wide-stripe state. b Narrow-stripe state due to the application of sufficient Hx. c–d Two possible switching patterns. e Formation of an isolated domain with –z magnetization by the switching process shown in (c). f–h Formation of the skyrmion state. The magnetization state in the yellow box shows the Bloch line configuration. The green-boxed magnetization state represents the skyrmion state. i–o Sequential images of magnetization states of the wide-stripe domain under application of the magnetic field.

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Applying Hx reduces the stripe width, and two adjacent domain walls will have more chances of colliding with each other. When these domain walls collide, the form of the domain may change. As shown in Fig. 4b, the domain wall collisions can take two forms (Fig. 4b, red and blue boxed areas). Figure 4c, d depicts these two possible domain pattern change processes. In Fig. 4c, the –z domain connected in the x-direction becomes the +z domain connected in the y-direction. By contrast, Fig. 4d shows the process in which the +z domain connected in the x-direction is transformed into the –z domain connected in the y-direction. If there is no Hz, then these two pattern change processes occur equally. However, a nonzero Hz breaks the symmetry in the +z and –z domains; thus, Hz selects only one of these two collision processes. Thus, the magnetization state in Fig. 4b is converted to that in Fig. 4e under +Hz. This process creates an isolated domain with –z magnetization (the yellow dot in Fig. 4e). If \(H_x \gg H_{{\mathrm{DMI}}}\), then all domain wall magnetizations are aligned along Hx, and thus, the chiral-induced stability disappears. The isolated domain in Fig. 4e is not a skyrmion because a skyrmion consists of vectors in all directions2, but there is no –x magnetization vector in this figure. If Hx is reduced, then the magnetization direction of the magnetic domain wall is aligned along the HDMI direction (Fig. 4e–g). This continual deformation of the magnetization state inevitably forms a Bloch line in the domain wall (yellow box in Fig. 4g)36. Such a Bloch line contains an opposite magnetization to HDMI. When HDMI (cyan arrow in Fig. 4g) is high enough to switch this opposite magnetization or another effect, such as thermal fluctuation, reverses this magnetization, the bubble domain becomes a skyrmion (Fig. 4h).

Figure 4i–o depicts sequential magnetization state images showing the conversion process from the initial wide stripes to the bubble-filled state as a function of field application. Figure 4i shows the initial wide stripes with λ0 = 4.9 μm that are too wide to observe the stripe cutting process. Applying sufficient Hx reduces λ to 1.2 μm, and then, the stripe is ready to be broken up (Fig. 4j). The additional Hz allows breakage of the –z stripe domain into –z bubble domains (Fig. 4k, l). Then, by turning off Hx and Hz at the same time, the bubble-filled state remains. Reducing Hx to zero increases the stripe width as well as the bubble size, and reducing Hz also assists the expansion of bubble domains30,31 to finally produce the bubble-filled state, as shown in Fig. 4m-o (see Fig. S10 for constant Hx). This is an impossible result with narrow-stripe domains because a thermal fluctuation easily finds the GME state. However, in the wide-stripe domain state, the thermal fluctuations have difficulty changing the magnetization state, so the bubble-filled state exists as a local minimum energy state even in the absence of magnetic fields.

Whether the formed bubble is a skyrmion cannot be confirmed by the domain image but is indirectly confirmed by checking the current-induced motion because when the bubble has a skyrmion texture, it is moved by a current37,38,39. The images in Fig. 5a are sequential images of bubble motion after turning a current on in the y-direction with μ0Hz = 7 Oe (also see Supplementary Video 1). Hz removed many bubble domains and left a few with quasi-uniform size because compressed domains can easily reach the local minimum energy state (circular bubble domain) due to their small size. Bubble domains that move in the y-direction are identified by colored squares. From these results, we think that the spin textures shown are likely to be skyrmions. In addition, it is worth noting that the current for bubble motion is extremely low (5 × 108Am−2), which can indicate that the observed skyrmions are not domains nucleated from point defects and are therefore freely mobile.

Fig. 5: Application of the creation method of bubble domains.
figure 5

a Current-induced motion of magnetization states. Constant current flow in the y-direction. The current density is 5.0 × 108 A m−2, and μ0Hz = 7 Oe. b–d Magnetization states of SiO2/Ta (3 nm)/Co4Fe4B2 (1.1 nm)/MgO (1.5 nm)/Ta (2 nm). b Large circular domain formation. c Stripe domain state under μ0Hx = 2.1 kOe. d Zero-field magnetization state after application of μ0Hx = 3 kOe and μ0Hz = 10 Oe.

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Ours is a universal method for skyrmion creation because bubble-filled states can be created as a seed for skyrmions in arbitrary PMA samples. When the PMA strength is sufficiently large, the stripe width exceeds the finite sample size. Such samples are no longer called stripe domains but large domain samples27. It is important that the presented method is applicable to large domains because the domain wall energy reduction by Hx is a universal phenomenon in PMA samples. A sample showing a large domain is presented in Fig. 5b. The application of Hz switches the magnetization at reduced PMA defects first, and then, the reversed domain expands in all directions, forming a large circular domain (Fig. 5b). However, the application of Hx can create observable stripe domains. Figure 5c shows a magnetization state with μ0Hx = 2.1 kOe. Figure 5d shows an example of a zero-field state after application of μ0Hx = 3 kOe and μ0Hz = 10 Oe. It is clear that a bubble-filled state can be created even in a large domain sample.

We have shown that in a prototypical PMA material, CoFeB, a large number of magnetic skyrmions can be easily created by applying a magnetic field tilted from the in-plane direction at room temperature. Our proposed method for the creation of multiple skyrmions can be applied to generic PMA materials and thus overcomes the limitations of previous methods with a narrow range of material parameters. However, we have demonstrated that skyrmions were created using an external magnetic field, where the key parameter determining the instability of the stripe domain is not the field but the width of the stripe. From the point of view of applications, the important parameter, the skyrmion density, is also determined by the stripe width (see Fig. S11). Therefore, through control of the width of the stripes by electrical means (e.g., PMA and DMI control using an electric field40,41), we can create skyrmions without a magnetic field in the future. Our findings will not only facilitate the development of skyrmion-based spintronic devices by offering a universal generation method for multiple magnetic skyrmions but also trigger fundamental research on the hitherto underestimated role of domain instability in the skyrmion phase and its neighboring phases.