Deformation of Néel-type skyrmions revealed by Lorentz transmission electron microscopy

Néel-type magnetic skyrmions have recently attracted significant interest because of their fundamental interest and application potential in next generation spintronic devices.^1–17 Néel-type skyrmions have been observed in a wide range of [heavy metal I/ferromagnet/heavy metal II (or oxide)]_n hetero-structured stacks, in which they are created and stabilized by the interplay of Dzyaloshinskii-Moriya interaction (DMI), dipole interaction, magnetic anisotropy, exchange interaction, and the external magnetic field.^2,3,18–21 In particular, the DMI from the strong spin–orbit interaction at the interfaces plays a key role in the formation of skyrmions.^22,23 However, the typical DMI strength in multilayer stacks is usually less than ∼2 mJ/m² and difficult to be further increased.^{7,15,21,24,25} Thus, in actual applications, the best tunable parameter would be the magnetic anisotropy, which could be easily controlled by changing the thickness of the ferromagnetic layer.^26–28 

To investigate the intriguing physics of skyrmions and to explore the potential applications, many techniques have been employed such as magnetic force microscopy (MFM),^14,21,29 X-ray magnetic circular dichroism (XMCD),³ polar magneto-optical Kerr effect (MOKE) microscopy,^8,18 and Lorentz transmission electron microscopy (L-TEM).^11,27,30 L-TEM is one of the most useful tools due to its capability to directly observe the skyrmions with high spatial resolution and to in situ study their dynamics upon the application of different stimuli.^{11,13,26,27,31} As it is well known, the magnetic contrast of Néel-type skyrmions in films appears in L-TEM images only after tilting the sample to produce the projection of the curl of the magnetization to the beam propagation direction. Consequently, a small fraction of the applied magnetic field along the beam axis will inevitably produce an in-plane magnetic field to the tilted sample.¹¹ For the samples with a strong perpendicular magnetic anisotropy (PMA), this small in-plane magnetic field has a negligible effect on the skyrmion spin texture, leading to a dark-bright contrasted circular disk in the L-TEM images as shown in many publications.^11,26,28 For samples with a weak PMA, the same in-plane field should have a pronounced effect to deform the spin texture of skyrmions.^{18,27,32–34} To date, there has been a lack of experimental study on the effect of such skyrmion deformation on the L-TEM images, leading to a potential misinterpretation of the skyrmion structure from the L-TEM images. In this paper, we fabricated [Pt/Co(t nm)/Ta]₂₀ multilayer samples. By varying the thickness of the Co layer, the easy axis changes from the out-of-plane direction to the in-plane direction. Surprisingly, a dark-bright-dark-bright (DBDB) double contrasted pattern is observed as the defocus length is decreased from Δf = −5 to −2 mm. The inner bright-dark contrasted pattern becomes more evident for the thicker Co sample in which the easy magnetization axis tilts more toward the in-plane direction. A closer analysis, by combing MFM experiments, micromagnetic simulations, and micromagnetic analysis to Lorentz TEM simulation (MALTS),³⁵ demonstrates that new features are caused by the deformed Néel-type skyrmions due to the in-plane component of the applied field.

The multilayer stacks of Ta(3 nm)/[Pt(1.5 nm)/Co(t nm)/Ta(1 nm)]₂₀ with t = 1.8, 2.0, and 2.2 were deposited using a DC magnetron sputtering system, as shown schematically in Fig. 1(a). Figure 1(b) shows the high resolution, high-angle annular dark-field scanning transmission electron microscopy (HADDF-STEM) image of the cross section of a multilayer with t = 2.2. It is evident that the quality of the multilayer structured sample is high, which guarantees the repeatability and quality of the measured results. Figures 1(c)–1(e) show the normalized out-of-plane and in-plane magnetic hysteresis loops of the films measured at 300 K from the three samples. It is clearly seen that the saturation field of the out-of-plane loops increases, whereas the saturation field for the in-plane curve decreases with increasing t. The change in saturation fields suggests that the easy axes of the magnetization changes from the out-of-plane in the t = 1.8 sample to the in-plane direction in the t = 2.2 sample. A systematically micromagnetic simulation (see the details in the supplementary material, SI1) of a 1-μm-diameter disk [Fig. 2(a)] reveals that skyrmions could be created in a uniaxial magnetocrystalline anisotropy K_u range from a value slightly smaller than 4.87 × 10⁶ J/m³ to a value slightly larger than 4.87 × 10⁶ J/m³. K_u = 4.87 × 10⁶ J/m³ in our simulation corresponds to the effective anisotropy constant K_eff = 0 J/m³ according to the equation $Keff=Ku−12μ0Ms2$⁠, where positive and negative K_eff represent the PMA and in-plane magnetic anisotropy (IMA), respectively. With the increasing DMI constant, the range of K_u for the creation of skyrmions extended rapidly.

To study the creation and spin textures of the skyrmions in samples with different directions of the magnetic easy axis, L-TEM imaging was carried out by using a FEI Titan Cs Image TEM in Lorentz mode. To image Néel-type skyrmions, the samples have to be tilted, and thus, an in-plane field will be simultaneously applied to the sample.¹¹ We first studied the sample with t = 1.8, which possess positive K_eff. The skyrmions are created by increasing the out-of-plane field from zero to 1.6 kOe with a tilt angle of θ = 5°. Figure 2(b) shows the L-TEM images of the created skyrmions taken at defocus lengths Δf = −5 and −2 mm, respectively, with a high magnification of ×9100 (about 4 times of ∼×2100 that used in Ref. 27). It can be seen that, similar to typical Néel-type skyrmion images reported in many other literature studies,^{11,13,26–28} very clear dark-bright contrasted patterns were observed at the defocus of Δf = −5 mm. However, with the decreasing defocus value to Δf = −2 mm, a faint and tiny bright-dark contrasted pattern appeared in the center of the dark-bright disks, forming a DBDB contrasted disk. As it is well known, a large defocus length may lead to loss of some information of fine/weak structures in the image of the microscope. With the decreasing defocus length to −2 mm, some fine structures that cannot be observed at Δf = −5 mm may be observed. Thus, we speculate that there may be some special spin texture existing inside the columnar skyrmions in the multilayer sample or the spin texture is probably not a Néel-type skyrmion at all. To uncover the spin texture that may lead to the DBDB contrasted images, we further performed similar measurements using samples with t = 2.0 and 2.2 at different defocus values (see the details in the supplementary material, SI2). Figure 2(c) shows the L-TEM image of the sample with t = 2.2 taken at a defocus of Δf = −2 mm. Similarly, additional features (bright-dark contrast) are also observed in the L-TEM images of the sample with t = 2.2 at the smaller defocus. More importantly, with increasing t from 1.8 to 2.2, the additional bright-dark contrast becomes clearer and more prominent.

To understand the origin of the additional bright-dark contrast in the L-TEM images, we try to reconstruct the magnetization distributions using a phase reconstruction technique based on a transport of intensity equation (TIE)³⁶ (see details in the supplementary material, SI3). However, the reconstructed spin texture does not match any spin textures experimentally observed previously. As we know, the results obtained from TIE analysis reflect the component of magnetic flux density normal to the electron beam, which includes the information of both the magnetization and the stray field, averaged through the sample thickness along the beam direction.³⁷ Therefore, the TIE analysis results may not be consistent with actual magnetization, and Ref. 37 proved that a type-II bubble can be reconstructed to a bi-skyrmion by TIE analysis. Moreover, the tilting of the sample makes the reconstruction work more complex. Thus, we may not able to identify the spin texture only based on the TIE analysis of the L-TEM images.

To reveal the origin of the DBDB contrast in the L-TEM image, we simulated different kinds of spin textures using the MuMax3 software package³⁸ and then simulated the corresponding L-TEM contrast using the MALTS code.³⁵ According to the simulations, we find that there are three types of spin textures that could lead to similar L-TEM contrast as observed in Fig. 2. They are (1) type-II magnetic bubble,^30,37 (2) Néel-type skyrmionium,³⁹ and (3) Néel-type skyrmion as shown in Fig. 3(a). Figures 3(b) and 3(c) show the corresponding simulated L-TEM contrast obtained at tilt angles of θ = 0° and θ > 0°. It can be seen that the type-II magnetic bubble can lead to an L-TEM image with DBDB contrast even without tilting the sample because of the Bloch-type domain wall. After tilting the sample with a small angle, the changes in the contrast are not detectable. Strikingly contrast to what we observed in the images of the type-II magnetic bubble, no contrast patterns can be observed in the images of both the Néel-type skyrmion and Néel-type skyrmionium if the samples are not tilted, being in agreement with that reported in literature studies.^11,27,31 Therefore, a type-II magnetic bubble can be easily distinguished from the Néel-type spin textures.

A Néel-type skyrmionium (also called the 2π-skyrmion⁴⁰) can be understood as a composited skyrmion, in which one skyrmion sits in the center of a second skyrmion with reversed magnetization. The corresponding L-TEM image [Fig. 3(c)] for θ > 0 is very similar to what we observed (Fig. 2). Interestingly, the TIE analysis (Fig. S4) based on the experimental results looks like a tilted skyrmionium too. Therefore, the DBDB contrasted images might be originated from the Néel-type skyrmionium. For Néel-type skyrmions, if we ignore the influence of the in-plane field on the deformation of skyrmion texture as done in most of the previous studies,^11,27 an L-TEM image with bright-dark contrast is obtained from the simulation, which is similar to the previous experimentally observed one.¹¹ However, if the PMA of the film is not that strong, the spins at the skyrmion boundary will rotate toward the direction of the in-plane field as shown in the inset of the last figure of Fig. 3(c) (see details in the supplementary material, SI4), which will lead to the appearance of DBDB contrast in the simulated L-TEM image. Again, the DBDB contrasted images may also be originated from Néel-type skyrmions due to the in-plane magnetic field.

To identify the spin texture that is of Néel-type or Bloch-type, we imaged the lattice of the spin textures using L-TEM at tilting angles of 0° and 5° as shown in Fig. 4(a) (see L-TEM images for different tilt directions in the supplementary material, SI5). It can be seen that the DBDB contrasts along the rotation axis appeared for θ = 5°, whereas almost no contrast can be observed without tilting the sample. Thus, we confirm that the spin texture is of Néel-type and can exclude the probability of the type-II magnetic bubble.

Based only on the L-TEM images, it is difficult to distinguish the Néel-type skyrmion from the Néel-type skyrmionium, as their L-TEM images are very similar. MFM is among the most effective techniques to characterize the skyrmions with a very high spatial resolution.¹⁴ We thus performed the MFM experiments on the sample with t = 2.2. Before the MFM measurements, the spin texture lattice was created first in L-TEM. We find that, once created, the lattice was stable even after switched off the field (the lattice is unchanged even after more than three months). Figure 4(b) shows the 3D view of the MFM image of the lattice at zero field. It is evident that each spin-texture forms a smooth image and that no fine structure can be observed. Particularly, no evidence of skyrmionium in which one small skyrmion sitting in another larger skyrmion was found. Thus, we further excluded the existence of Néel-type skyrmioniums.

Now, we are almost sure that the spin textures we observed are the Néel-type skyrmions whose magnetization are distorted by the in-plane field during the observation using L-TEM. To examine and understand how the in-plane field affects the L-TEM contrast of a skyrmion in our multilayers, we imaged the sample of t = 2.2, which hosted the skyrmion lattice at zero field, again using L-TEM. A series of images were obtained at a defocus length of Δf = −2 mm during the external (with a tilting angle of 5°) magnetic field is increased from 0 to 2.5 kOe. It can be seen from Fig. 4(c) that the size of the skyrmions decreased from 180 nm to 78 nm as the magnetic field was increased from 0 to 2.5 kOe. Insets of Fig. 4(c) show four typical L-TEM images taken during the field increasing process. At zero fields, where the in-plane field is also zero, the L-TEM image of a skyrmion is a circular disk composed of dark up part and bright bottom part. With the increasing magnetic field, where the in-plane magnetic field also increases simultaneously, the additional bright-dark contrasted pattern appears gradually and becomes more evident inside the dark-bright contrasted disk. With further increasing field, the skyrmion sizes become so small that the contrast becomes blurry, but the DBDB contrasted pattern still exists until the skyrmions vanish to a ferromagnetic state. Moreover, we also simulated the L-TEM images of the skyrmion lattice in materials with different magnetic anisotropies (see the supplementary material, SI6) and L-TEM images of a deformed skyrmion at different defocus values (see the supplementary material, SI7). All these simulation results are consistent with our experimental results. Thus, we could come to a conclusion that it is the in-plane field that induces the additional dark-bright contrast inside.

In conclusion, we have investigated the L-TEM images of skyrmions created in [Pt/Co/Ta]₂₀ multilayers with different Co layer thicknesses, in which the easy magnetization axis changes from the out-of-plane for the 1.8 nm sample to the in-plane for the 2.2 nm one. Interestingly, we observed an additional bright-dark contrasted pattern inside the previously reported dark-bright contrast in the L-TEM image at a smaller defocus value and larger magnification at a tilt angle of only 5°. These additional bright-dark contrasts become more evident in the sample with thicker Co layers. Through a thorough analysis by combining the L-TEM, MFM, micromagnetic simulations, and MALTS analysis, we confirm that the characteristic L-TEM images with dark-bright-dark-bright contrasts in our samples are from the deformed Néel-type skyrmion by the in-plane component magnetic field, with the deformed spin texture consisting of a pure Néel-type skyrmion and a small percentage type-II bubble. It is the latter that is responsible for the additional bright-dark contrasts in the L-TEM image. Our results prove that the L-TEM image of a Néel-type skyrmion may be very similar to that of a type-II bubble or Néel-type skyrmionium due to the small in-plane magnetic field, especially for samples with an easy magnetization axis toward the in-plane direction.

See the supplementary material for the simulated phase diagram of the magnetic domain configurations, L-TEM images taken at different defocus values, reconstruction of the spin textures using TIE analysis, L-TEM images for different tilt directions, in-plane field induced deformation of Néel-type skyrmions, simulated L-TEM images in materials with different magnetic anisotropy and simulated L-TEM images of a deformed skyrmion at different defocus values.

This publication is based on research supported by the King Abdullah University of Science and Technology (KAUST), the Office of Sponsored Research (OSR), under Award Nos. OSR-2016-CRG5-2977 and CRF-2015-SENSORS-2708, and the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-05CH11231 (van der Waals heterostructures program, KCWF16). J.W.Z. acknowledges the support by the National Natural Science Foundation of China (Grant No. 51801087). This research used the resources of Shaheen II at the King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia.