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Field-Free Manipulation of Skyrmion Creation and Annihilation by Tunable Strain Engineering
Chun Feng,* Fei Meng, Yadong Wang, Jiawei Jiang, Nasir Mehmood, Yi Cao, Xiaowei Lv, Feng Yang, Lei Wang, Yongkang Zhao, Shuai Xie, Zhipeng Hou,* Wenbo Mi,*
Yong Peng, Kaiyou Wang, Xingsen Gao, Guanghua Yu, and Junming Liu
Creation and annihilation of skyrmions are two crucial issues for constructing skyrmion-based memory and logic devices. To date, these operations were mainly achieved by means of external magnetic, electrical, and optical modula- tions. In this work, we demonstrated an effective strain-induced skyrmion nucle- ation/annihilation phenomenon in [Pt/Co/Ta]n multilayers utilizing the shape memory effect of a TiNiNb substrate. A tunable tensile strain up to 1.0% can be realized in the films by thermally driving phase transition of the substrate, which significantly decreases the nucleation field of skyrmions by as many as 400 Oe and facilitates the field-free manipulation of skyrmions with the strain. Such a strain effect can be attributed to the synergetic interplay of the planar magnetic moment twirling and decrement of interfacial Dzyaloshinskii–Moriya interaction.
In addition, the strain tunability is found to be strongly related to the strain direc- tion due to magnetoelastic interaction. These findings provide a novel strategy for developing strain-assisted skyrmion-based memory and logic devices.
DOI: 10.1002/adfm.202008715
Prof. C. Feng, F. Meng, L. Wang, Y. Zhao, S. Xie, Prof. G. Yu School of Materials Science and Engineering
University of Science and Technology Beijing Beijing 100083, P. R. China
E-mail: [email protected]
Y. Wang, Dr. N. Mehmood, Dr. Z. Hou, Prof. X. Gao, Prof. J. Liu Guangdong Provincial Key Laboratory of Optical Information Materials and Technology & Institute for Advanced Materials
South China Academy of Advanced Optoelectronics South China Normal University
Guangzhou 510006, P. R. China E-mail: [email protected]
Y. Wang, Dr. N. Mehmood, Dr. Z. Hou, Prof. X. Gao, Prof. J. Liu National Center for International Research on Green Optoelectronics South China Normal University
Guangzhou 510006, P. R. China J. Jiang, Prof. W. Mi
Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparation Technology
School of Science Tianjin University Tianjin 300354, P. R. China E-mail: [email protected]
Dr. Y. Cao, Prof. K. Wang
State Key Laboratory of Superlattices and Microstructures Institute of Semiconductors
Chinese Academy of Sciences Beijing 100083, P. R. China X. Lv, Prof. Y. Peng
Key Laboratory for Magnetism and Magnetic Materials of Ministry of Education
Lanzhou University Lanzhou 730000, P. R. China Dr. F. Yang
State Key Laboratory of Heavy Oil Processing China University of Petroleum-Beijing Beijing 102249, P. R. China
Prof. J. Liu
Laboratory of Solid State Microstructures Nanjing University
Nanjing 211102, P. R. China
research communities because of its exotic physics and potential applications in spintronics.[1–3] This topological object was first discovered in non-centrosymmetric bulk crystals, in which the broken crystal symmetry generated a bulk Dzyaloshin- skii–Moriya interaction (DMI) that not only stabilized the skyrmion phase, but also endowed it with a fixed chirality.[4]
Later studies revealed that skyrmions could also be stabilized in a variety of magnetic multilayers intercalating non- magnetic heavy metal layers, in which DMI was intrinsically generated by the interface asymmetry.[5–9] Since DMI in magnetic multilayers is sensitive to the interface quality, film constitution, and spin−orbit coupling strength the corre- sponding skyrmion phase is readily tun- able which provides an important base for device application.
More importantly, the magnetic multilayers are highly com- patible with modern nano-manufacturing techniques, which facilitate nanoscale device integration. From the perspective
The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adfm.202008715.
1. Introduction
Magnetic skyrmion, a topologically non-trivial swirling spin configuration, has attracted tremendous attention from
to the strain tuning scheme for not only its energy-efficient feature, but also intriguing magnetoelastic responses. For example, Shibata et al. reported that a mechanical strain as low as 0.3% in the chiral FeGe crystal could induce a large dis- tortion of skyrmion lattice up to 20% at 94 K.[18] The sensitive response of skyrmion lattice to strain demonstrates a prom- ising alternative for constructing a strain-mediated spintronic device.
Despite its significance, the experimental realization of strain-manipulation of skyrmions has remained relatively limited and mostly focused on bulk single crystals. Obviously, skyrmion manipulation in magnetic multilayers is more desir- able for practical applications. The key challenge for realizing this is how to apply large enough strain on the multilayers to overcome the energy barrier between skyrmion and other magnetic states. The most effective approach is to combine magnetic multilayers with a deformable substrate, such as the polymer-based flexible substrate or ferroelectric substrate.
However, flexible substrates generally have large Young’s modulus mismatch with metallic magnetic films, which can severely hinder effective strain transfer to the film.[19,20] Fur- thermore, the strain produced by the flexible substrate is often volatile, which is unfavorable for practical applications.
On the other hand, the strain generated from the ferroelec- tric substrates may be non-volatile, but the achievable max- imum strain is only in the order of thousandths.[21–23] It is thus urgently desirable to develop a new strain manipulation strategy that can exert not only a large strain on the film, but also one that is non-volatile.
Shape memory alloys (SMA) are a family of smart materials that can produce non-volatile deformation as large as 6–8%
driven by the martensite/austenite phase transformation.[24,25]
Moreover, Young’s moduli of common metallic SMA are com- parable with that of the magnetic films, facilitating effective strain transfer in tuning the electronic structure of the film significantly.[26,27] In this study, we successfully realized strain- manipulated creation and annihilation of skyrmions in [Pt/Co/
Ta]n multilayers by temperature control of the phase transition in a TiNiNb-SMA substrate. The strain effectively promoted the creation of skyrmion by lowering the nucleation field from 400 Oe to zero. By a combination of experimental and theoretical analyses, we demonstrated that the strength of interfacial DMI and the angle between the strain and the initial alignment of stripe domains play crucial roles in the strain-modulated skyrmions.
high-density skyrmions can be observed in the film at an out- of-plane magnetic field of 700 Oe using Lorentz transmission electron microscopy (LTEM), as displayed in Figure 1c. These observations clearly demonstrate that the deposited [Pt/Co/Ta]12 film is of good quality. Then, in-plane and non-volatile uniaxial strains were applied to the film by controlling the martensite/
austenite transition of SMA substrate through temperature (T) manipulation. As illustrated in Figure 1d, a martensite structure of the pre-stretched SMA substrate will transform to austenite by elevating the temperature (I→II), resulting in a compressive strain. Conversely, an inverse phase transformation can be ini- tiated by cooling the SMA from stage III to IV, generating a tensile strain. Details about the strain generation process are described in Experimental Section. The maximal strain strength (ε) generated in the substrate was tunable by adjusting the pre- stretching amount of the substrate (see Figure S1, Supporting Information). Such a strain was subsequently transferred into the film due to a strong mechanical coupling between the SMA substrate and the film. The corresponding film strains (εL) to the substrate strains ε are displayed in Figure 1e, and the blue line shown in the graph is a guide for the eye. Notably, a consid- erable lattice strain (εL) up to 1.0% can be transferred to the top surface of the film for ε = 1.8% in the substrate, which provides an important basis for the strain manipulation of skyrmions.
2.2. Strain Effects on Skyrmion Nucleation
Strain effects on skyrmion nucleation were further investi- gated using magnetic force microscopy (MFM). To reduce the influence of the magnetic field created by MFM tip, a low- moment magnetic tip with less than 100 Oe was used. Prior to the MFM measurements, a large in-plane magnetic field of 2 T was pre-applied to the as-deposited film to align initial magnetic domains (marked with a red arrow) along the strain direction (marked with a blue arrow), as schematically shown in Figure 2a. Then, an out-of-plane magnetic field (H) was applied to induce nucleation of skyrmions. Figure 2b illus- trates the variation of magnetic domain structures with H at different substrate strains ε. In the initial state (ε = 0%, H = 0 Oe), only stripe domains were observed in the film, an indica- tion that the magnetic field generated by the MFM tip was not enough to induce the nucleation of skyrmion directly. Here- after, the alignment direction of the initial stripe domains is referred to as the initial domain orientation. By increasing H,
the stripe domains first fractured into small pieces and then transformed into skyrmions, owing to a delicate interplay of the interfacial DMI, magnetic anisotropy, dipolar interac- tion, and Zeeman interaction.[29–31] The critical magnetic field (Hcri), in which the stripe domains began to transform into skyrmions, was determined to be about 700 Oe for the current sample. When a compressive strain ε of −2.7% was applied, we observed a striking change in the field-dependent domain evo- lution during which the stripe domains directly transformed into out-of-plane ferromagnetic domains without the formation of any skyrmions (see the first row of Figure 2b). This result suggests that the compressive strain can strongly suppress the nucleation of skyrmions. However, when a tensile strain was applied, a completely different process was observed. As in the third row of Figure 2b, it was observed that Hcri decreased from 700 Oe at the strain-free state to 500 Oe at ε = 0.9%.
By further increasing ε to 1.8%, an even lower Hcri of ≈400 Oe could be reached. This result clearly demonstrates that a tensile strain can significantly decrease the energy barrier between stripe domain and skyrmions, which promotes the nucleation of skyrmions. Based on the MFM results, we sum- marized a ε-H phase diagram of skyrmions in Figure 2c. The dashed boundary line between the light blue and green regions shifts downward with the strengthening of the tensile strain, and it moves upward with an increase of the compressive strain. These results suggest that the tensile strain promotes skyrmion nucleation, whereas the compressive strain sup- presses it. Notably, we obtained a similar variation of Hcri with
ε in different samples, which suggests these results are uni- versal (see Figure S2, Supporting Information). Furthermore, we studied the variation of average skyrmion size as a func- tion of tensile strain (see Figure S3, Supporting Information).
Clearly, the skyrmion size slightly decreased from ≈115 nm at ε = 0% to 95 nm at ε = 1.8%. This result implies that an increasing tensile strain tends to reduce the skyrmion size to a certain extent. Notably, both these features of high magne- toelastic response and sub-100 nm size are beneficial for devel- oping the high-density memory and logic devices.
To investigate if the nucleation field of skyrmions can be lowered below 100 Oe or even to zero field, the repetition number of [Pt/Co/Ta]n was decreased from 12 to 8 to increase transferred strain in films and lower Hcri at the strain-free state.
As shown in Figure 3a, Hcri of the as-deposited film was indeed lowered from 700 Oe for [Pt/Co/Ta]12 to 400 Oe for [Pt/Co/Ta]8. When a tensile strain of substrate up to 1.8% was applied along the initial domain orientation, Hcri decreased drastically from 400 to 0 Oe (Figure 3b). Notably, no matter how we varied the tip-sample distance or reversed the tip magnetization, the mor- phology of skyrmions at H = 0 Oe changed little. This result clearly demonstrates the stabilization of skyrmions regardless of the MFM tip stray field, implying that the tensile strain can induce the skyrmion nucleation without the magnetic field of the MFM tip. Moreover, the strain effect is non-volatile at room temperature because the substrate deformation can be stably sustained in the range of −50 to 50 °C (see Figure 1d).
Based on these observations, we can draw the conclusion that Figure 1. Sample structure and strain control. a) Schematic diagram of the sample structure. b,c) HAADF and LTEM images of the as-deposited Ta(10 nm)/
[Pt(3 nm)/Co(2.3 nm)/Ta(1.9 nm)]12 film. d) Representative thermal expansion curve of the NiTiNb-SMA substrate. Dimensions of the SMA substrate can be manipulated by temperature-controlled martensite/austenite phase transitions. Insets depict the schematic lattice structures at different stages.
e) Film strain at surface εL shows strong dependence on the substrate strain ε, where εL is measured using a strain gauge. The connecting blue line serves as a guide for the eye.
a field-free, non-volatile creation and annihilation of skyrmion may be achieved by alternately applying and releasing the ten- sile strain in a temperature-mediated manner, which is critical for developing strain-assisted skyrmion-based memory and logic devices.
On the other hand, we found that the strain effects were strongly influenced by the angle between the strain and initial magnetic domain. As demonstrated above, the tensile strain decreased Hcri significantly when the strain was applied parallel to the initial domain orientation (Figure 3b). However, when
Figure 3. Optimized strain effect for field-free manipulation of skyrmions. Schematic diagram of strain implementation on a [Pt/Co/Ta]8 film and cor- responding MFM images, in which the red and blue arrows denote the initial domain orientation and strain direction, respectively. The scale bar in the MFM image is 500 nm. a) strain-free; b) tensile strain is parallel to the initial domain; and c) tensile strain is perpendicular to the initial domain.
The substrate strain ε is fixed at 1.8%.
Figure 2. Strain-tuned magnetic structure. a) Schematic diagram of strain and initial magnetic domain in the magnetic multilayer film on SMA sub- strate, in which the red and blue arrows denote the initial domain orientation and strain direction, respectively. b) Typical strain-dependent MFM images of the [Pt/Co/Ta]12 film. The scale bar in the image is 500 nm. The red dotted line represents the critical magnetic field in which the stripe domains begin to transform into skyrmions. The insets display the schematic spin arrangements of different types of domain. The FM represents a ferromagnetic domain with all the spins aligning parallelly. c) Magnetic phase diagram as a function of H and ε depicted based on the MFM results. The regions in light blue, green, red, and dark blue represent the magnetic configuration composed of the stripe domain, the combination of stripe and skyrmions, the complete skyrmions, and the ferromagnetic domain, respectively.
the strain was exerted perpendicularly to the initial domain ori- entation, Hcri did not show much variation (Figure 3c). These results indicate that the strain effect is not only associated with the strain strength, but it is also sensitive to the strain direction.
2.3. Discussion
We now discuss the physical mechanism underlying the strain effects. Generally, the strain manipulation of skyrmions in the magnetic multilayers mainly originates from the strain modi- fication of magnetic anisotropy and interfacial DMI.[1–3] Here, the variation of magnetic anisotropy with the strain was first explored. Since the films used in our experiment possessed an apparent in-plane anisotropy (see Figure S4, Supporting Infor- mation), we measured the in-plane angle-dependent magneto- optical Kerr curves to reveal the strain effect on the magnetic moment distribution of the film. Notably, the strain was par- allel along the initial domain direction (x axis), seen as the blue arrow in Figure 4a. An in-plane magnetic field (HM) was then applied during the magneto-optical Kerr measurement.
Figure 4b summarizes the Kerr signal variation of the [Pt/
Co/Ta]12 film at a remanence state with the angle (θ) between HM and the y axis. In the strain-free state, the Kerr signal was maximal at θ = 80° and minimal at θ = 0°, an indication that the as-deposited film had a magnetic anisotropy with an easy magnetization axis nearly parallel to the x axis. When a tensile strain was applied along the x axis, the maximal Kerr signal emerged at θ = 40° for ε = 0.9% and θ = 20° for ε = 1.8%. This result suggests that the tensile strain can change the magnetic anisotropy significantly, in which the easy axis rotates from the initial direction to the vertical direction (as schematically depicted in Figure 4c). As we know, applied uniaxial strain will introduce additional magnetoelastic energy into the magnetic system. This energy can be expressed as Kε = −3/2λsσcos2α,[32]
where λs is the magnetostriction constant, σ is the stress, and α is the angle between the stress axis and magnetic moment.
Since λs for Co film is negative,[33,34] Kε turns minimum when
the magnetic moment is perpendicular to the tensile strain axis (i.e., α = 90°). That is to say, the magnetic moment tends to align perpendicularly to the tensile strain. Thus, the magnetic moment rotated toward the vertical direction (y axis) when the strain was parallel to the initial magnetic moment, which tog- gled a planar rotation of the stripe domains at a certain degree, as illustrated in Figure 2a. The planar twirling of the magnetic moment reduced the uniaxial anisotropy energy of the film with respect to the initial moment direction; namely, the twirling decreased the absolute value of the magnetic anisotropy energy (Keff) between x and z directions (see Figure S4f, Supporting Information). Regarding the dynamics, the magnetic moment twirling may generate an extra torque-like interaction on the ini- tial stripe domains, which facilitates the breakage of the stripe domain and the further transition to skyrmions. This point is supported by previous simulation work on CoFeB, though the value of λs is opposite to that of [Pt/Co/Ta]n.[35] Therefore, the tensile strain decreased Hcri significantly when the strain was parallel to the initial domain. Conversely, the perpendicularly exerted tensile strain sustained the initial magnetic moment alignment because α was already 90°, resulting in the strength- ening of the uniaxial anisotropy along the initial moment direc- tion. Thus, the stripe domain was fixed and stretched along the initial direction (Figure 3c), which made the breakage of the stripe domain more difficult and suppressed skyrmion forma- tion. Therefore, the magnetic moment alignment is strongly associated with the strain implementation direction due to the magnetoelastic interaction, which leads to the anisotropic tun- ability of strain to the magnetic domain.
On the other hand, strain may alter the interfacial DMI of the multilayer, which can also affect the manipulation of skyr- mions. We now explore the strain effects on DMI tunability.
The value of DMI constant (D) can be experimentally deter- mined based on the domain wall energy (σDW) obtained from stripe domain width measurements in MFM images and Keff,[5]
as detailed in Figure S5 and Note S1, Supporting Information.
Figure 5a presents the variation of D as a function of strain. It is clearly evident that D decreased with the increasing tensile Figure 4. Influence of magnetic anisotropy evolution on domain tunability. a) Schematic diagram of the magneto-optical Kerr measurement, in which θ is the angle between measuring field HM and y axis. The substrate strain ε (marked with a red arrow) is applied in parallel to the initial domain direction (marked with a blue arrow), and this direction is defined as the x axis. b) θ-dependent variation of Kerr signal of the [Pt/Co/Ta]12
film at the remanence state, in which the arrows indicate the maximal Kerr signal for each strain state. c) Schematic evolution of the easy axis with the strain application.
strain and enhanced by increasing the compressive strain.
Such a variation of D with the strain is consistent with previous work,[36] suggesting that our results are reliable. We then per- formed micromagnetic simulations to clarify the role of D in the observed strain manipulation of skyrmions. Details about the simulations are presented in the Experimental Section.
During simulation, we calculated magnetization dynamics at D = 0.8 mJ m−2 (a corresponding value established in the strain- free state) to describe the magnetic field-induced nucleation process of skyrmions with zero strain. As shown in Figure 5b, the simulated results qualitatively agreed with our experimental observations, indicating that our theoretical model is rea- sonable. Subsequently, the D value was varied based on the experimentally established D–ε relationship in which the ten- sile strain reduced the D value while the compressive strain increased D. In Figure 5b, it is evident that the magnetic field required for the nucleation of skyrmions significantly decreased from 800 Oe at D = 0.8 mJ m−2 (strain-free state) to 200 Oe at D = 0.2 mJ m−2 (under tensile strain). In addition, if the D value increases from 0.8 to 1.0 mJ m−2 (under compressive strain), the nucleation field of skyrmions will also increase. These results are highly in consistent with the experimental observa- tions as shown in Figures 2 and 3. Therefore, we can conclude that the heightened tensile strain leads to a drop in DMI, which reduces the energy barrier for the nucleation of skyrmions and
promotes their formation in lower magnetic fields. By contrast, the increased compressive strain results in an enhancement of DMI, which in turn increases the energy barrier and sup- presses the nucleation of skyrmions.
We further carried out first-principles calculations to gain insights into the strain-modified DMI from the point view of the material electronic structure. The model and spin chirality configuration in the calculations are presented in Figure 5c.
First, the DMI strength (d) of the model was calculated using equation d = (EACW − ECW)/m, where m is a coefficient depending on the wavelength of cycloid, and EACW and ECW represent the total energies of anticlockwise and clockwise chirality spin con- figurations, respectively. Then, the micromagnetic DMI coeffi- cient D was obtained using the formula D=3 2 /(d N aF 2), where a is the face-centered-cubic Co lattice constant and NF represents the number of magnetic atomic layers. Figure 5d illustrates the strain-dependent d and D values of the Co/Pt bilayer, Co/Ta bilayer, and Pt/Co/Ta trilayer. Due to the same chirality in Co/Pt and Co/Ta bilayers, the net d and D values of the Pt/Co/
Ta trilayer were obtained by subtracting the result of the Co/Pt bilayer from that of the Co/Ta bilayer. Clearly, D for the Pt/Co/Ta trilayer decreases with increasing the tensile strain while it increases with the strengthening of compressive strain. Such a trend is in line with the experimental observations as shown in Figure 5a. Notably, with an increase in tensile strain, the D Figure 5. Strain-related DMI tunability. a) Experimentally observed D variation with strain. The connecting line in the graph is a guide for the eye.
b) Micromagnetic simulation demonstrates that the domain structure evolution dependence on D and H. Area for each image is 2 µm × 2 µm.
c) Schematic diagram of spin chirality of Co/Pt and Co/Ta used to calculate DMI. The arrows indicate the direction of the magnetic moment. EACW
and ECW represent the total energies of anticlockwise and clockwise chirality spin configurations, respectively. d) Calculated DMI strength d and D of the Co/Pt bilayer, Co/Ta bilayer, and Pt/Co/Ta trilayer based on first-principles calculations. Positive d represents a clockwise chirality spin structure.
e,f) Atomic layer resolved spin-orbit-coupling energy difference between anticlockwise and clockwise chirality spin configurations (ΔESOC) with the strain. g) d orbit resolved ΔESOC matrix elements of neighboring Pt 1 atom layer at the Pt/Co interface, in which the red arrow represents the dz2-dxz
orbital hybridization of Pt.
of the Co/Pt bilayer obviously increases, whereas that of the Co/Ta bilayer only varies slightly. This observation implies that the strain mainly modifies the DMI at the Co/Pt interface and consequently decreases the net DMI of the Pt/Co/Ta trilayer.
To reveal the respective DMI contributions of the Pt, Co, and Ta layers at the interfaces, an atomic-layer resolved spin-orbit- coupling energy difference calculation between anticlockwise and clockwise chirality spin configurations (ΔESOC) was per- formed,[8,37] as displayed in Figures 5e,f. The positive ΔESOC rep- resented a positive contribution to DMI and possessed a clock- wise chirality. As the tensile strain increases, ΔESOC of the first Pt layer at the Pt/Co interface increases remarkably while the ΔESOC of the Co/Ta interface changes marginally. Therefore, the strain-induced evolution of the Pt layer is responsible for the DMI decrement in the Pt/Co/Ta trilayer. To reveal further the electronic origin of the strain effect, the d orbit resolved ΔESOC matrix elements of the first Pt atomic layer at the Pt/Co interface were calculated (Figure 5g). Clearly, the out-of- plane dz2-dxz orbital hybridization of Pt (marked with the red arrow), which negatively contributes to ΔESOC, is weakened by increasing the tensile strain, leading to the DMI increment at the Co/Pt interface and a net DMI decrement in the Pt/Co/Ta trilayer. Notably, the strain has a negligible effect on the orbital hybridization of Co and has very weak influence on ΔESOC (see Figure S6, Supporting Information). These findings elucidate that strain affects the out-of-plane orbital hybridization of Pt by changing the interatomic distances, which leads to effective tunability on the interfacial DMI of the multilayer film.
Moreover, the tensile strain was found to be able to reduce the skyrmion size to some extent. This result is possibly associated to the strain-induced variations of D and Keff. According to the previous report,[38] the skyrmion size (R) is mainly determined by the formula
16 2 2 2
R D A
AK D K
π π
= − where A and K are the
exchange stiffness and magnetic anisotropy energy, respectively.
In our experiments, tensile strains lead to decreases in both D and the absolute value of Keff (see Figure 5a and Figure S4f, Sup- porting Information). We can find that the variations of D and Keff make contrary contributions to the skyrmion size: the decrement of D reduces the R value while the decrement of the absolute value of Keff increases the R value. We propose that their respec- tive contribution may be comparable, resulting in a slight reduc- tion of the skyrmion size with increasing the tensile strain.
3. Conclusions
In this work, we realized an effective strain control of skyrmion nucleation and annihilation in [Pt/Co/Ta]n multilayers by using the shape memory effect in the underlying metallic substrates.
The strain effects can be derived from the interplays of interfa- cial DMI evolution and magnetic anisotropy variation. On the one hand, tensile strain can effectively reduce the interfacial DMI by tuning the orbital hybridization of Pt, which lowers the nucleation barrier of skyrmions and promotes the formation of skyrmions. On the other hand, strain can also induce substan- tial variations on the magnetic anisotropy via magnetoelastic coupling, which is strongly related to the strain direction and resulted in anisotropic magnetic domain modulation. With
the synergetic effect of DMI decrement and magnetic anisot- ropy modification, the nucleation field of skyrmions can be sig- nificantly decreased and a field-free manipulation of skyrmion creation is achieved. These findings not only provide a novel strategy for developing strain-assisted skyrmion-based memory devices, but also help to enrich the topological spintronics by clarifying the electronic origin of skyrmion-elastic coupling.
3.1. Outlook
Since SMA can be fabricated into films by magnetron sputtering to generate a considerable strain with suitable processing, we anticipate to be able to deposit Pt/Co/Ta mul- tilayers on a SMA film in a magneton sputtering system and then realize the strain-induced field-free manipulation of skyrmion by controlling the martensite transition in the SMA films. Notably, the nanoscale composite multilayers are highly compatible with modern nano-manufacturing techniques, facilitating nanoscale device integration. Therefore, it is quite possible to use such a configuration to construct strain-assisted skyrmion-based memory and logic devices. Moreover, the strain-controlled magnetic moment approach can also facilitate the development of functional devices, such as magnetic logic components, artificial synapses, and magnetoresistive random access memories.[39,40]
4. Experimental Section
Sample Preparation: Prior to the film deposition, a Ni45Ti45Nb10-SMA sheet with 0.5 mm thickness was pre-stretched to induce a reoriented martensite phase, which was set as the Stage I shown in Figure 1d.
Then, the SMA sheet was carefully polished to reach a surface roughness of about 1 nm. Two subsequent film deposition and processing steps were used to reach the different strain states in the film: 1) Compressive strain: Ta(10 nm)/[Pt(3 nm)/Co(2.3 nm)/Ta(1.9 nm)]n multilayers (n = 8 or 12) were first deposited on the SMA sheet in Stage I using a magnetron sputtering. Then, a compressive strain was transferred onto the film by heating the substrate to 200 °C to drive the martensite to austenite transformation (I→II in Figure 1d), accompanied by a lattice shrinkage and a compressive deformation in the SMA. 2) Tensile strain:
the pre-stretched SMA sheet was post-heated to induce the compressive deformation (I→II), after which the SMA sheet reached Stage III at room temperature. Then, the [Pt/Co/Ta]n multilayers were deposited on the SMA sheet at Stage III in Figure 1d by using magnetron sputtering.
After the film deposition, the samples were further cooled to −100 °C to trigger an inversed phase transformation (III→IV in Figure 1d), which produced a tensile strain in the film. The maximal substrate strain ε can be tuned by changing the pre-stretching amount. Five representative ε values (−2.7%, 0%, 0.9%, 1.2%, and 1.8%) were chosen. Prior to the strain application by controlling the temperatures, an in-plane magnetic field of 2T was applied to the as-deposited sample to induce a uniform domain orientation. Both the film deposition and heating process were completed in a vacuum better than 3 × 10−5 Pa, and an Ar gas pressure was maintained at 0.45 Pa.
Sample Characterization: The lattice strain on the film surface was measured using a strain gauge. The HAADF image of a typical film was obtained using transmission electron microscopy (FEI Tecnai G2 F20 at 200 kV), and the corresponding domain structure was characterized by another transmission electron microscope (Tecnai-F30) using a Lorentz mode at room temperature. During the LTEM measurements, the sample stage was tilted at a 30° angle from the horizontal plane.
DMI was calculated using the constrained method in the Vienna ab initio simulation package.[37] Г-centered Monkhorst–Pack schemes with k-point meshes of 12 × 12 × 1 and 6 × 12 × 1 were used for the primary cell and supercell of the Co/heavy metal interface, respectively.
Micromagnetic Simulation: The domain structure evolution in the films was simulated using the Mumax3 software package based on the Landau–Lifshitz–Gilbert equation.[44,45] In the simulation, a 2 × 2 µm2 square system of 12 repetitions of a trilayer stack consisting of Pt (3 nm), Co (2.3 nm), and Ta (1.9 nm) by applying the 2D periodic boundary conditions and the mesh size of 4 × 4 nm2 was used. The saturation magnetization (MS), the Keff, the exchange constant (A), and the temperature (T) were chosen to be 7.03 × 105 A m−1, −40 kJ m−3, 1.7 × 10−11 J m−1,[46] and 300 K, respectively. The initial magnetization state was set to be the parallel stripe domain structure. To match the simulation conditions with a polycrystalline sample, the disordered film was considered by using a grain size of 30 nm and anisotropy constant and magnetic anisotropy axis variations of 10%. The exchange coupling between grains was set at 90%.
Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.
Acknowledgements
The authors acknowledge the financial support from the National Key Research and Development Program of China (Nos. 2019YFB2005800 and 2020YFA0309300), the National Science Foundation of China (Nos. 51871017, 51871018, 51871161, 51901081, and 52071025), the Beijing Natural Science Foundation (No. 2192031), the Fundamental Research Funds for the Central Universities (No. FRF-TP-19-011B1), the Science and Technology Program of Guangzhou (No. 202002030052), the Science and Technology Innovation Team Program of Foshan (No. FSOAA-KJ919-4402-0087), and the Foundation of Beijing Key Laboratory of Metallic Materials and Processing for Modern Transportation.
Conflict of Interest
The authors declare no conflict of interest.
Data Availability Statement
All relevant data that support the plots within this paper are available from the corresponding author upon reasonable request.
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