Letter Cite This: Nano Lett. XXXX, XXX, XXX−XXX
pubs.acs.org/NanoLett
Stable Magnetic Skyrmion States at Room Temperature Confined to Corrals of Artificial Surface Pits Fabricated by a Focused Electron Beam Takao Matsumoto,*,† Yeong-Gi So,‡ Yuji Kohno,§ Yuichi Ikuhara,†,¶ and Naoya Shibata†,¶ †
Institute of Engineering Innovation, School of Engineering, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan ‡ Department of Materials Science, Graduate School of Engineering Science, Akita University, 1-1 Tegata Gakuen-machi, Akita 010-8502, Japan § JEOL Limited, 1-2, Musashino 3-chome, Akishima, Tokyo 196-8558, Japan ¶ Nanostructures Research Laboratory, Japan Fine Ceramic Center, 2-4-1 Mutsuno, Atsuta-ku, Nagoya 456-8587, Japan S Supporting Information *
ABSTRACT: Stable confinement of elemental magnetic nanostructures, such as a single magnetic domain, is fundamental in modern magnetic recording technology. It is well-known that various magnetic textures can be stabilized by geometrical confinement using artificial nanostructures. The magnetic skyrmion, with novel spin texture and promise for future memory devices because of its topological protection and dimension at the nanometer scale, is no exception. So far, skyrmion confinement techniques using large-scale boundaries with limited geometries such as isolated disks and stripes prepared by conventional microfabrication techniques have been used. Here, we demonstrate an alternative technique confining skyrmions to artificial nanostructures (corrals) built from surface pits fabricated by a focused electron beam. Using aberration-corrected differential phase contrast scanning transmission electron microscopy, we directly visualized stable skyrmion states confined at a room temperature to corrals made of artificial surface pits on a thin plate of Co8Zn8Mn4. We observed a stable single-skyrmion state confined to a triangular corral and a unique transition into a triple-skyrmions state depending on the perpendicular magnetic field. Furthermore, we made an array of stable single-skyrmion states by using concatenated triangular corrals. Artificial control of skyrmion states with the present technique should be a powerful way to realize future nonvolatile memory devices using skyrmions. KEYWORDS: Magnetic skyrmion, geometrical confinement, room temperature, focused electron beam, aberration-corrected differential phase contrast STEM
M
agnetic skyrmions1−6 are promising for use in future innovative memory devices because of their topological stability at nanometer-scale dimensions. For practical applications, however, several key issues must be explored. In particular, artificial control of skyrmions is an important issue for future applications. Generally, stable confinement of elemental magnetic nanostructures, such as a single magnetic domain, is fundamental in modern magnetic recording technology.7 It is well-known that various magnetic textures can be stabilized by geometrical confinement using artificial © XXXX American Chemical Society
nanostructures, and the skyrmion is no exception. So far, direct nanofabrication techniques such as focused ion beam (FIB) milling have been used to fabricate nanodisks of FeGe (Curie temperature Tc ≈ 280 K), and magnetic field-driven transitions of skyrmion cluster states have been directly visualized by Lorentz transmission electron microscopy (TEM).8 It should Received: September 15, 2017 Revised: January 11, 2018
A
DOI: 10.1021/acs.nanolett.7b03967 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters be noted, however, that such skyrmion cluster states were stable only at a temperature much lower than the Tc (100 K; T/Tc ≈ 0.36). They were unstable at a higher temperature (220 K; T/ Tc ≈ 0.79) because of strong thermal fluctuations. Thus, dynamic transition between skyrmion cluster states with different numbers of skyrmions were observed. A combination of electron-beam lithography and ion-beam etching was also used to demonstrate that isolated skyrmions can be stabilized at room temperature in nanodisks and nanostripes of (Ir/Co/ Pt)10 multilayers.9 Epitaxial metal growth with shadow mask10 and electron beam evaporation with ultraviolet (UV) lithography11 were also used to fabricate arrays of micronsized Co disks to create artificial skyrmion at room temperature. Recently, a wedge-shaped FeGe nanostripe with a width ranging from 45 to 150 nm, i.e., from below to above the helical period of bulk FeGe (70 nm), was fabricated by FIB milling, and the morphology and nucleation of magnetic skyrmions in such a strongly confined geometry was directly visualized by electron holography.12 It was found that strongly confined skyrmions were able to adopt a wide range of deformation. These conventional studies used rather large-scale boundaries to stabilize skyrmions. However, atomic-scale defects, such as atomic impurities, dislocations, and grain boundaries,13 also influence skyrmions as manifested by lattice distortions and large deformations of individual skyrmions. Such influence is closely related with the pinning of magnetic moments by defects. First-principles calculations within the density functional theory (DFT) have shown that the pinning energy of skyrmion in MnSi can be tuned by substituting one site of Mn or Si with different elements.14 In a study of the effect of randomly distributed atomic impurities on the current-driven motion of skyrmion by numerical simulations, the motion of skyrmion lattice was shown to be insensitive to impurity pinning.15 Significantly, the particle-like skyrmions are deformed during the motion to avoid the impurities. Also, current-induced motion of a single skyrmion in a confined nanotrack in the presence of a defect (notch) was studied numerically,16,17 and it was demonstrated that skyrmions move around the defect unaffected by pinning. Capturing of a skyrmion with a hole at the nanometer length scale was studied by solving the Landau−Lifshitz−Gilbert (LLG) equation in the presence of an electric current density.18 In that study, skyrmion-defect interaction was described by an effective potential with both repulsive and attractive components depending on the magnetic field. As an example, the strength of the pinning potential of a 10 nm diameter hole in a FeGe film with a thickness of 50 nm in a magnetic field of 0.2 T was estimated to be sufficiently large to ensure thermal stability. Despite these numerous theoretical investigations; however, there have been very few attempts to fabricate artificial defects at the nanometer length scale to control a skyrmion lattice19 or individual skyrmion.20 In the present study, we first fabricate isolated defects at the nanometer length scale on a thin plate of Co8Zn8Mn4 (Tc ≈ 300 K)21−23 by using a focused electron beam and investigate the interaction of skyrmions with the defects by using aberration-corrected differential phase contrast scanning transmission electron microscopy (DPC STEM).13,24−26 We then demonstrate unique stable skyrmion states confined to triangular corrals made by using a focused electron beam. In addition to using plan-view STEM and energy dispersive X-ray (EDX) to characterize a thin-plate specimen, we find from cross-sectional observations that each of the defects created by
Figure 1. Interactions of skyrmions with isolated artificial surface pits at a room temperature (295 K) under a perpendicular magnetic field of 59.9 mT visualized by aberration-corrected DPC STEM. The defects were created by positioning a fixed-focused electron beam at four laterally separated positions. (a) Reconstructed in-plane magnetic field vector map, (b) in-plane magnetic field intensity, (c) pseudocolor magnetic helicity image, and (d) simultaneously obtained ADF image. Skyrmions with counterclockwise rotation are imaged as bright disks, while surface pits are imaged as dark spots in magnetic helicity images in (c). Surface pits are imaged with such faint contrast in the ADF image that they are indicated by yellow arrows in panel d.
the focused electron beam consists of a pair of top (beam entrance) and bottom (beam exit) surface pits. Thus, skyrmions are confined to a corral built from the periodic array of top and bottom surface pits. Lastly, we discuss the interaction of the skyrmion lattice with the artificial defects on the basis of Monte Carlo simulations. DPC STEM images clearly demonstrate the interaction of skyrmions with isolated artificial surface pits (Figure 1). These images were recorded under a perpendicular magnetic field of 59.9 mT at a room temperature (295 K; T/Tc ≈ 0.98) after four surface pits were sequentially fabricated by positioning a focused electron beam at separated lateral positions of the thin plate (The whole process of the fabrication of four surface pits is shown in Figure S1). The separation was much larger than the skyrmion size (∼120 nm). The direction of the applied magnetic field was parallel to the incident electron beam as indicated by a crossed circle in Figure 1d. As explained in detail in Figure S2, skyrmions and surface defects can be distinguished unambiguously in Figure 1a−c. In the magnetic helicity image, skyrmions with counterclockwise rotation are imaged as bright disks, while surface pits are imaged as dark spots (Figure 1c). In the annular dark field (ADF) image; however, only surface pits are imaged, and they are imaged with such faint contrast that they are indicated in Figure 1d by yellow arrows. When an isolated surface pit was fabricated inside the lattice, the lattice deformed and individual skyrmions were positioned off-center with respect to the surface pits. As shown in Figure 1, subsequent fabrications of additional three isolated surface pits produced similar results. We next observed the behaviors of skyrmions when we fabricated a rectangular corral built of more closely arranged surface pits. The separation was nearly equal to or smaller than the skyrmion size. When the first surface pit of the corral was B
DOI: 10.1021/acs.nanolett.7b03967 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 2. Interactions of skyrmions with a rectangular corral composed of a series of isolated surface pits created by a fixed-focused electron beam. (a−c) Magnetic helicity images and (d−f) simultaneously obtained ADF images. When the first surface pit, indicated by yellow arrowheads, was created (panels a and d), the initial regular skyrmion lattice, created under a perpendicular magnetic field of 59.9 mT at room temperature (295 K) was deformed by the interaction of individual skyrmions with the defect. After the construction of the rectangular corral was completed (panels b and e), a total of 27 individual skyrmions were confined to the corral. When the perpendicular magnetic field was decreased to the residual field of the objective lens, the skyrmion lattice outside of the corral disappeared, while individual skyrmions, including several strongly deformed ones, were confined to the corral (panels c and f).
fabricated, as indicated by a yellow arrowhead in Figure 2a,d, the initially regular skyrmion lattice was slightly deformed, and individual skyrmions were positioned off-center with respect to the surface pit. After the entire rectangular corral was constructed (Figure 2b,e), 27 individual skyrmions were confined to the corral. The whole process of the construction is shown in Figure S3 and Movie S1. When the perpendicular magnetic field was decreased to the residual field of the objective lens (∼20 mT), the skyrmion lattice outside of the corral disappeared, while individual skyrmions, including several strongly deformed ones as reported in a supercooled state of the same material,23 remained inside and along the periphery of the corral (Figure 2c,f). The numbers of skyrmions confined to the corral under a residual magnetic field of the objective lens varied in several repeated experiments. In the example shown in Figure 2c, it appears that 14 skyrmions remain inside and 7 skyrmions remain along the periphery of the corral. It should be emphasized that what are observed in Figure 2c are not helical stripes but deformed skyrmions (see Figure S9). In addition, we fabricated an additional surface pit (indicated by a red arrow) near the center of the rectangular corral as shown in Figure 3. Again, several circular skyrmions and largely elongated skyrmions were formed in the modified corral. Note that the skyrmions are clearly separated from the surface pits as indicated by yellow arrows, confirming that what are observed are not helical stripes but skyrmions stabilized inside the corral under the low magnetic field. In addition, it appears that at least two circular skyrmions (indicated by white arrows) are separated from the elongated skyrmions near the additional surface pit. Such a surface pit-mediated nucleation of skyrmion will be reported elsewhere. One can also see that the surface pits were positioned off-center with respect to individual skyrmions. A similar tendency was reported in previous literature on the pinning of individual skyrmion by atomic-scale defects in PdFe bilayer on Ir (111).19 In that report, scanning tunneling microscopy (STM) revealed that the
Figure 3. Influence of an additional surface pit fabricated near the center of the corral as shown in Figure 2. (a) Horizontal deflection and (b) vertical deflection DPC STEM images. (c) Reconstructed in-plane magnetic field vector map, (d) in-plane magnetic field intensity, (e) pseudocolor magnetic helicity image, and (f) simultaneously obtained ADF image. The additional surface pit is indicated by red arrows. Several circular skyrmions and strongly elongated skyrmions were confined to the rectangular corral. Note that the magnetic spin texture is clearly separated by the surface pits as indicated by yellow arrow, confirming that what are observed are not helical stripes but skyrmions stabilized inside the corral, even under a low magnetic field.
pinning sites, presumed to be single Fe atoms in the Pd layer, were usually found off-center with respect to the skyrmions. To investigate the interaction of skyrmions with much more closely arranged and smaller surface pits, we used a much more finely focused electron beam with atomic-scale lateral dimensions by exciting the objective lens with the aid of aberration-correction technology. We fabricated an 800 nm equilateral triangular corral composed of surface defects and C
DOI: 10.1021/acs.nanolett.7b03967 Nano Lett. XXXX, XXX, XXX−XXX
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However, variable numbers of skyrmions are allowed when the physical conditions, such as temperature or magnetic field, are changed. In movies demonstrating a transition from a singleskyrmion state to a triple-skyrmions state (Movies S2 and S3), it appears as if a single skyrmion split into three skyrmions. Careful examinations, however, revealed that the single skyrmion and triple skyrmions actually have the same skyrmion number: 1. Hence, this transition is not a splitting of single skyrmion having the skyrmion number 1 into three skyrmions having the skyrmion number of 1/3. It is simply the increase of numbers of skyrmions inside the corral. We are presuming two possible sources for two such additional skyrmions. One possibility is that they came from outside the corral, and the other is that they existed along the sides of the triangle as kinds of target skyrmions.27 Faint triangular contrasts surrounding the central skyrmion seen in Figure 4a,b may be evidence for the latter. A closely related phenomenon in which geometric confinement plays an important role as well is that superconducting magnetic vortices merge into a giant vortex state from dense multivortex states in isolated islands of a type II superconductor (Pb) grown on Si(111) with lateral sizes of a few coherence lengths.28 In this case, in contrast, the flux of the merged giant vortex is the total flux of the individual vortices. Such a difference highlights the topological stability of skyrmion, a property that the superconducting vortices are lacking. In addition, the superconducting island is completely isolated, whereas both inside and outside of the corrals of surface pits are composed of the same material in the present study. A numerical study suggested that magnetic skyrmion with a high skyrmion number cannot exist as a static stable excitation.29 However, another analogous confinement method for an electron, a typical quantum object with particle-wave duality, using artificial closed structures (corrals) at the atomic length scale was achieved by using a scanning tunneling microscope (STM).30 Surface state electrons on copper (111) were confined to a corral built from iron adatoms. Although a magnetic skyrmion is not a quantum object with the particlewave duality, it is interesting to discuss the present results from a “particle-like or wave-like” point of view.31 From numerous theoretical and experimental investigations, it is commonly understood that a skyrmion lattice with a long-range order has a wave-like nature and thus can be viewed as a superposition of three helical waves.32 However, a skyrmion has an apparent particle-like nature. This duality can be found in the deviation from a circular shape to a combination of an axially symmetric core and hexagonally disturbed edges in the long-range order skyrmion lattice phase.33 Our observation that a two-skyrmion state was not evident as a stable configuration suggests that an individual skyrmion or skyrmion cluster in the triangular corral can be viewed as the superposition of spin waves of three different q vectors (triple-q mechanism). Judging from the relative configuration of triple skyrmions with respect to the triangle (Figure 4c,d), q vectors are constrained perpendicular to the three sides of the triangle. In contrast, parallel q vectors with crystal edges25 and the coexistence of perpendicular and parallel q vectors with respect to edges depending on crystalline anisotropy5 or external magnetic field34 were reported. Detailed analysis of the mechanism of stabilization, as well as systematic investigation of various geometries, is beyond the scope of this letter. Here, we just note that the stable geometric confinement of a ferromagnetic vortex in a trigonal cobalt fine particle with 300 nm sides and 55 nm thickness visualized by electron
Figure 4. Stable skyrmion state at a room temperature (295 K) in an 800 nm equilateral triangular corral of linear surface defects fabricated by scanning a focused electron beam. (a,c) In-plane magnetic field vector map and (b,d) field intensity. (a,b) An apparent singleskyrmion state was created under a perpendicular magnetic field of 59.9 mT. (c,d) The single-skyrmion state turned into a stable tripleskyrmion state under the residual field of the objective lens (∼20 mT). The transition was monitored by changing the objective lens current gradually, as shown in Figure S4 and Movies S2 and S3. The transition occurred in a very narrow range of perpendicular magnetic field (40.0 ± 1.0 mT). No two-skyrmion state was evident during the transition.
then observe their influence on skyrmions. Each side of the triangle was a sequence of tiny surface pits with diameters of a few nanometers separated by ∼10 nm (see Figure S5). DPC STEM images (Figure 4a,b) clearly demonstrate a stable single skyrmion state located at the center of the corral at a room temperature (295 K) under the perpendicular magnetic field of 59.9 mT. Under the residual field of the objective lens, the single-skyrmion state turned into a triple-skyrmion state, as shown in Figure 4c,d. The transition from the single-skyrmion state to the triple-skyrmion state occurred in a very narrow range of perpendicular magnetic field (40.0 ± 1.0 mT). More details of the transition are shown in Figure S4 and Movies S2 and S3). Intriguingly, a two-skyrmion state was not evident during the transition. Moreover, no helical magnetic state was observed inside the triangular corral under the residual field of objective lens (∼20 mT). The true ground state under the exactly zero bias field is yet to be confirmed, though. However, a single-skyrmion state becomes unstable under an increasing magnetic field and vanishes above 77 mT (see Figure S4x,y). It is interesting to discuss the present results in terms of the skyrmion number6 and numbers of skyrmions. The skyrmion number is defined as: NSk =
1 4π
⎛
∬ n⃗·⎜⎝ ∂∂nx⃗
×
∂n ⃗ ⎞ ⎟d x d y ∂y ⎠
(1)
where n⃗ is the unit vector in the direction of the local magnetization, and the integral is taken over two-dimensional space. Because the skyrmion number is an integer and conserved in a continuous transformation under constant physical conditions, the creation and annihilation of skyrmions with changing skyrmion number is usually prohibited. This characteristic is termed as the topological stability of skyrmions. D
DOI: 10.1021/acs.nanolett.7b03967 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters holography35 is induced by a similar but different mechanism. In the ferromagnetic fine particle, magnetic moments align parallel with each side of a triangle to minimize magnetostatic energy. At the center of the particle, however, they are forced to interfere, creating a vortex. In the present chiral magnetic material, however, helical magnetic moments propagate perpendicular to each side, and they interfere in the whole area of the triangle. As a result, the triple-skyrmion state as well as the single-skyrmion state can be stably realized. This triple-q mechanism, together with the interactions between individual skyrmions and surface pits, should be responsible for the unique transition between single-skyrmion and triple-skyrmion states. Our present observations suggest that a skyrmion may have a wave-like nature even if it does not form a lattice with long-range order. Furthermore, to investigate the dependence of the number of stable skyrmions on the lateral size of the corral, we fabricated a 440 nm equilateral triangular corral with the surface pits. Each of its side was a sequence of tiny surface pits with 2 nm diameters on average and separated by 10 nm (Figure 5a,b). Inside the 440 nm corral, a stable skyrmion “bit” was created even at a higher room temperature (300 K; T/Tc ≈ 1) very close to the Curie temperature of the material under perpendicular magnetic fields below 55 mT (Figure 5c−e) down to a residual magnetic field of the objective lens. Furthermore, we made an array of single-skyrmion states that were stable at 300 K under a residual perpendicular magnetic field (∼20 mT) in a row of alternately concatenated upright and inverted 440 nm equilateral triangular corrals (Figure 5f− h). This showed that such specifically configured equilateral triangular corrals can be used to create a track of stable skyrmion “bits”. To understand the present results, it is important to characterize the nature of the defects fabricated by a focused electron beam. We first present results of structural and chemical characterizations of the surface pits by using plan-view TEM amd STEM and STEM EDX analysis techniques as shown in Figures S5 and S6. We confirmed that the linear surface defects are built of a sequence of separated tiny surface pits (Figure S5). Their diameters and the separation depend on the conditions of fabrication, such as probe size and exposure time, and also on the thickness of the thin plate at the irradiated region, but their typical diameter is 5 nm and they are typically separated by 10 nm. The low-angle annular dark field (LAADF) image (Figure S6b), which is more sensitive to local strains, exhibits highly localized contrast along the three sides of the triangle. This suggests that the influence of strain fields accompanying the artificial surface pits should be, if any, quite localized in the immediate vicinity of the pits. Although there is no localized precipitation of specific atomic components, particularly cobalt atoms with larger magnetic moment (Figure S6d−f), there may be an edge effect producing an inhomogeneous magnetic field in the vicinity of surface pits when the thin plate specimen is subjected to an external magnetic field. Such an inhomogeneous magnetic field can be the origin of the interaction between skyrmions and surface pits depending on the perpendicular magnetic field. To characterize the nature of the defects more in detail, we observed cross-sectional views of the surface pits. It should be noted, however, the thin plate specimen shown here is not exactly the same as the one used to investigate the interaction of skyrmions and surface defects. We usually use a standard ionthinning method to prepare thin plate specimens to observe
Figure 5. Stable skyrmion “bits” created in a 440 nm equilateral triangular corral and a track of stable skyrmion “bits” at 300 K, very close to the Curie temperature of the material (Tc ≈ 300 K), in a row in which upright and inverted equilateral triangular corrals are alternately concatenated under a residual perpendicular magnetic field. (a) Plan-view ADF STEM image of a 440 nm triangular corral fabricated in a thinner area of the plate with mostly the same conditions. Part of the boxed area with a white square is enlarged in the inset. Because of the digital scanning of the electron beam, it can be seen that the corral is composed of a sequence of surface pits. (b) Enlarged ADF STEM image of a typical surface pit. Although the plate was too thick for true atomic-resolution observation, the orientation of the crystal unit cell can be distinguished by the hexagonal Co atomic columns viewed along the [111] zone axis, which continues into the center of the surface pit. The diameter of the pit is a few nanometers, and such pits are separated along the edge of the triangle by the same distance. A stable skyrmion bit was created in a 440 nm triangular corral at a room temperature (300 K) close to the Curie temperature of the material (Tc ≈ 300 K). (c) Reconstructed in-plane magnetic field vector map, (d) the magnetic helicity image, and (e) simultaneously obtained ADF image. Stable skyrmion states in a track composed of an alternating sequence of upside-down triangular corrals are clearly observed. (f) In-plane magnetic field vector map, (g) magnetic helicity image, and (h) ADF image of the triangular track.
skyrmions to minimize surface damage and ensure surface quality, but it is extremely difficult to prepare a cross-sectional specimen from such a thin plate by the ion thinning method. We therefore fabricated the cross-sectional specimen by using a E
DOI: 10.1021/acs.nanolett.7b03967 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 6. Cross-sectional STEM characterizations of dummy surface pits fabricated by a focused electron beam. (a) Plan-view STEM ADF image showing several linear surface pits created by a focused electron beam on a thin plate specimen of Co8Zn8Mn4. Note that this dummy thin plate specimen was prepared by FIB milling, while the thin plate specimen shown in Figures 1−5 was prepared by using standard ion thinning method. Inset is a selected-area electron diffraction pattern showing the [111] zone axis. There are four kinds of pits (indicated in panels A−D). Those indicated by panel A were fabricated with the condition used to create the 800 nm triangular corral shown in Figure 4, while those indicated by panel B were fabricated using the condition used to create the 440 nm triangular corrals shown in Figure 5. (b) Pseudocolor STEM ADF image of the cross-sectional thin plate specimen picked up from the part designated by a yellow rectangle in panel a. The top (beam entrance) surfaces of the four linear surface pits are labeled A−D, while the bottom (beam exit) surfaces of the defects are labeled A′−D′. Directions of the focused electron beam are indicated by arrows. (c) A slightly higher magnification image containing only A−A′ and B−B′ cross-sections. Higher magnification images of the top surface, inside, and bottom surface along the A−A′ cross-section are shown in panels d−f, respectively, with unmagnified pseudocolor images in each inset.
FIB technique. The major difference between the two specimen preparation techniques should be the thickness of the surface damage layer. Through a careful examination, we found that both top and bottom damage layers in the specimen fabricated by FIB were as thick as 15 nm, whereas those of the ionthinned specimen are presumed to be thinner. In this additional experiment, we fabricated four linear surface pits (indicated as A−D in the plan view in Figure 6a). The linear surface pits indicated as A were fabricated using the same beam condition used when we created the 800 nm triangular corral as shown in Figure 4, while those indicated as B were fabricated using the beam condition used when we created the 440 nm triangular corral shown in Figure 5. As demonstrated in the crosssectional views shown in Figure 6b−f, the defect on the top (beam entrance) crystalline surface (indicated by A) is actually a pit with a diameter and depth of 5 nm (Figure 6d), while the defect on the bottom (beam exit) damage layer (indicated by A′) is larger than that on the top surface (Figure 6f). After all, it proved that the defects are a pair of surface defects, one on the top surface of the thin plate and the other on the bottom surface of the thin plate. Whether surface sputtering by a focused electron beam occurs on either surface of the thin plate
specimen depends on the material and electron-optical conditions, as previously reported in the literature.36 However, no apparent nanometer length scale damage along the path of the focused electron beam is evident (Figure 6e; higherresolution images and EDX analysis are shown in Figures S7 and S8). Nevertheless, whether any defects at the atomic scale along the focused electron beam path may contribute to the confinement must be carefully investigated in our future work. Finally, we discuss the influence of defects by using numerical simulations based on the Metropolis Monte Carlo method.37 We used the Hamiltonian38,39 defined for twodimensional coordinates r = (x,y) as: H = −J ∑ Mr ·(M r + ex + Mr + ey) r
− + ∑ (Mr × Mr + ex ·ex + Mr × Mr + ey ·ey) r
− B ·∑ Mr − ( ∑ M zr2 r
r∈I
(2)
where Mr is the local magnetic moments, defined as Mr ≡ −:r /ℏ (Sr represents the local spin at r), and J , D, F
DOI: 10.1021/acs.nanolett.7b03967 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 7. Monte Carlo simulations of skyrmion lattice in the presence of (a) no defects and (b) one, (c) five, and (d) nine defects. Positions of the defects are indicated by yellow filled circles. Individual skyrmions are positioned off-center around defects, which is consistent with the present experimental results. Skyrmion lattices in the presence of a triangular corral under different magnetic fields are shown in panels e−h. The numbers of skyrmions inside the triangle decreased sequentially from 3 to 1 when the magnetic field is increased from panels e to h. Note that two skyrmions confined to the triangular corral are observed in panel g, which is not consistent with the present experimental results.
and A are, respectively, the ferromagnetic exchange interaction constant, the Dzyaloshinskii-Moriya interaction constant, and the uniaxial anisotropy interaction constant. The last term is the Zeeman interaction with the magnetic field B. Here, ex and ey are, respectively, unit vectors in the x and y direction, and I denotes positions of the defects. We simply assume that the local magnetic moments at defects are fixed parallel with the applied magnetic field (other details of the parameters used in the present simulation are described in the Materials and Methods section in the Supporting Information). Similar assumptions were also used in the work reported in previous literature. As shown in Figure 7a−d, individual skyrmions are positioned off-center with respect to defects, which is consistent with the present experimental results and also with the previous numerical simulations. Thus, most of the present experimental results can be explained if we assume the off-center pinning of skyrmions by the artificial surface pits. However, the number of skyrmions confined to the triangular corral decreases sequentially from 3 to 1 as the magnetic field is increased (Figure 7e−h). Note that the two-skyrmion state is confined to the triangular corral, as shown in Figure 7g, which is not consistent with the present experimental results (Figures 4 and 5). This suggests that a more complicated form of interaction between defects and skyrmions, such as the one with repulsive and attractive components depending on the magnetic fields,18 rather than the simple assumption, must be included in the Hamiltonian (eq 2). In conclusion, a FIB might be usable to fabricate surface defects at the nanometer length scale on a specimen. Although a FIB has been used to make artificial skyrmions and antiskyrmions by controlling the perpendicular anisotropy of continuous Co/Pt multilayer films,40 we think that a focused electron beam is advantageous in terms of minimum probe size and less secondary effect, such as an extended dislocation network concomitant with columnar defects fabricated by a focused ion beam.41 We expect the present technique should be
a convenient and powerful way to control magnetic skyrmions, enabling patterning with versatile geometries such as a spiral and even more complicated shapes, offering novel confinement techniques not achieved by conventional methods.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b03967. Additional details on materials and methods. Figures showing sequential magnetic helicity and ADF images, schematics, plan-view STEM and EDX characterizations, cross-sectional STEM and EDX characterization, partially reconstructed DPC STEM images (PDF) A movie showing the sequential observations of the magnetic skyrmion state inside the rectangular corral created by a focused electron beam as shown in Figures 2 and S3 (MOV) A movie showing the sequential observations of the magnetic skyrmion state inside the rectangular corral created by a focused electron beam as shown in Figures 4 and S4 (MOV) Movie S2 repeated several times back and forth at a faster speed focused on the triangular part only (MOV)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Takao Matsumoto: 0000-0003-0775-8423 Naoya Shibata: 0000-0003-3548-5952 G
DOI: 10.1021/acs.nanolett.7b03967 Nano Lett. XXXX, XXX, XXX−XXX
Letter
Nano Letters Author Contributions
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T.M., Y.S., and N.S. designed and conducted the TEM and STEM experiments, processed images, and wrote the manuscript. Y.S. prepared bulk polycrystalline Co8Zn8Mn4. N.S. and Y.K. developed the aberration-corrected DPC STEM system. T.M. coded a program for Monte Carlo simulations running on MATLAB. Y.I. discussed the results. N.S. directed the study. All authors read and commented on the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors acknowledge Ms. M. Nakabayashi at The University of Tokyo for preparation of thin plate specimen. We also acknowledge Mr. H. Oshikawa and Mr. I. Tokita at The University of Tokyo for their technical assistance. Dr. H. Sawada at JEOL Ltd. is acknowledged for his initial efforts to develop DPC STEM at The University of Tokyo. This work was supported by the Japan Science and Technology Agency SENTAN and Precursory Research for Embryonic Science and Technology. A part of this work was conducted at the Research Hub for Advanced Nano Characterization, The University of Tokyo, supported under “Nanotechnology Platform” (project No. 12024046) sponsored by MEXT, Japan. N.S. acknowledges supports from the JSPS KAKENHI Grant number 26289234 and the Grant-in-Aid for Scientific Research on Innovative Areas “Nano Informatics” (grant number 25106003) from JSPS.
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DOI: 10.1021/acs.nanolett.7b03967 Nano Lett. XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.nanolett.7b03967 Nano Lett. XXXX, XXX, XXX−XXX
