Abstract
Chiral magnetic domain walls are of great interest because lifting the energetic degeneracy of left and righthanded spin textures in magnetic domain walls enables fast currentdriven domain wall propagation. Although two types of magnetic domain walls are known to exist in magnetic thin films, Bloch and Néelwalls, up to now the stabilization of homochirality was restricted to Néeltype domain walls. Since the driving mechanism of thinfilm magnetic chirality, the interfacial Dzyaloshinskii–Moriya interaction, is thought to vanish in Blochtype walls, homochiral Bloch walls have remained elusive. Here we use realspace imaging of the spin texture in iron/nickel bilayers on tungsten to show that chiral domain walls of mixed Blochtype and Néeltype can indeed be stabilized by adding uniaxial strain in the presence of interfacial Dzyaloshinskii–Moriya interaction. Our findings introduce Blochtype chirality as a new spin texture, which may open up new opportunities to design spin–orbitronics devices.
Introduction
The formation of magnetic domains and domain walls (DWs) results from the interplay between the exchange interaction, the dipolar interaction and magnetic anisotropy. In perpendicularly magnetized thinfilm systems, DWs can be classified as two canonical types: in Bloch walls, the spin rotates like a helical spiral around an axis which is parallel or antiparallel to the DW normal, whereas in Néel walls the spin rotates like a cycloidal spiral. A magnetic film is called chiral when the rotational sense of these spirals is the same in all DWs. In nonchiral films, both rotation senses exist in different sections of DWs, with the same probability overall. The conventional textbook view predicts nonchiral Bloch walls as the ground state in magnetic thin films^{1,2,3}. In this picture chirality, that is, one preferred spin rotational sense in DWs, does not emerge because the magnetic energy contributions are all symmetric with respect to the rotation direction between to spins.
An asymmetric exchange interaction term, known as the Dzyaloshinskii–Moriya interaction (DMI), can be induced when inversion symmetry is broken in the system^{4,5}. The inversion symmetry can break in the lattice (bulk DMI) or at surfaces and interfaces (interfacial DMI) of magnetic films^{6,7,8}. The DMI term between two atomic spin S_{i} and S_{j} on neighbouring atomic sites i and j can be written as E_{DM}=−D_{ij}·(S_{i} × S_{j}), where D_{ij} is the DMI vector. In the case of interfacial DMI, D_{ij} is restricted to be perpendicular to the position vector r_{ij}=r_{i}−r_{j} (refs 6, 7, 8, 9). For this reason, interfacial DMI alone can only stabilize Néeltype chiral spin textures, such as cycloidal spin spirals^{10,11,12}, skyrmions^{13,14} or chiral Néel walls^{15,16,17}. In Blochtype spin textures, the crossproduct (S_{i} × S_{j}) is parallel to the position vector r_{ij} and E_{DM} vanishes, consequently Bloch walls are usually nonchiral.
It was recently found that chiral Néel walls in film and multilayer structures enable fast currentdriven DW motion and spin texturedependent DW propagation direction^{15,18,19,20,21}. A numerical study also predicts that introducing chirality of Bloch walls into magnetic films can extend possibilities to manipulate DW propagation behaviours to new geometries^{18}. Developing experimental evidence that allows us to tailor the spin structure of chiral DWs via interfacial DMI^{6,22} is crucial for engineering methods to control current or fielddriven DW dynamics in film and multilayer structures, since these phenomena hold great potential for information storage and spintronics. In particular, direct observations of DW spin structure under the combined effects of interfacial DMI and inplane uniaxial anisotropy are still missing.
In the following, we demonstrate how the introduction of inplane uniaxial anisotropy allows us to tailor the DMIstabilized chiral DW spin textures. We focus on Fe/Ni bilayer grown on W(110) substrates, where the very large spin Hall angle of tungsten^{23} is combined with twofold symmetry at the (110) interface and perpendicular magnetic anisotropy of the magnetic layer^{24,25,26}. Using spinpolarized lowenergy electron microscopy (SPLEEM)^{27,28,29}, we observe anisotropic chiral DW spin structures with mixed components of chiral Bloch and chiral Néelcharacter. We find that, as a function of the relative orientation of the DWs with respect to the [001] substrate surface direction, the Fe/Ni/W(110) system features chiral Néel walls, mixed chiral walls containing both Néel and Bloch components or nonchiral Bloch walls. The chirality of the Néel wall components is always lefthanded, whereas the chirality of the Bloch wall components is either left or righthanded. Blochcomponent handedness as well as the ratio of the Bloch versus Néel components depends on the orientation relationship between the DW direction and the substrate lattice. Supported by Monte Carlo simulations, we propose that the origin of anisotropic chirality is the interplay between the DMI, the dipolar interaction and the inplane uniaxial anisotropy. Our findings experimentally demonstrate the Blochtype chirality as a new type of chiral spin texture stabilized by interfacial DMI, which may open up new opportunities to design spin–orbitronics devices.
Results
Visualizing chiral DWs
Within DWs in perpendicularly magnetized systems, spins usually rotate from one domain to another in one of the four basic spin textures, which are Bloch or Néel walls with left or righthanded chirality. Figure 1 shows sketches of a lefthanded (a) and righthanded (b) chiral Néel wall and a lefthanded (c) and righthanded (d) chiral Bloch wall. Experimentally, chirality in magnetic DWs can be determined by imaging threedimensional spin textures. Figure 2 shows a SPLEEM measurement of the DW spin structure in a Fe/Ni bilayer grown on W(110) substrate. The structure of the thin film is sketched in Fig. 2a, and a typical compound SPLEEM image (see Methods) is shown in Fig. 2b where blue/yellow indicates magnetization components along [1–10]/[−110] and cyan/red indicates components along [001]/[001]. In this rendering scheme, all DWs are highlighted in colour and, in Fig. 2b, we notice that all DWs are either cyan or red, which means that the inplane components of all DWs are either parallel or antiparallel to W[001], even though the directions of DWs are oriented along all possible directions within the film plane. These findings are reproduced in all images of other areas of this and a number of additional samples (see Supplementary Fig. 1). This indicates that the inner spin structure of DWs in the Fe/Ni/W(110) system is coupled to the direction of the DW with respect to the W[001] lattice direction.
To understand the micromagnetic properties of these DWs, we analyse the spin texture of the DWs in more detail. We start by identifying the image pixels on the centerlines of all DWs in a representative set of SPLEEM images (see Methods). At all centrelinepixels of all the DWs, we measure the local direction of the magnetization, expressed as the magnetization unit vector m, and the direction of the inplane normal vector n of the DW. We represent these data in terms of two angles: to capture the DW orientation, we define the angle φ as the angle of the normal vector n of the DW with respect to the W[001] lattice direction, and to capture the local DW spin texture, we define the angle α as the angle between the magnetization unit vector m and the inplane normal vector n of the DW; the geometry of these angles is sketched in Fig. 2c. The magnitude of the angle α indicates whether the wall is in Bloch configuration (α=±90°) or in Néelconfiguration (α=0° or α=180°)^{17}. Our measurements show that not only do both of these DW types occur, but there are also parts of the DWs which exhibit mixed types (for example, α=±45°). We notice that the magnitude of the angle α, and thus the type of the wall, is a function of the orientation of the wall φ. Figure 2d reproduces SPLEEM images cropped from Fig. 2b to show DW sections, highlighted by dashed lines, where certain DW orientations are prevalent (red and blue arrows in the SPLEEM images indicate directions of DW magnetization unit vector m and DW normal vector n within these DW sections). Next to these images, Fig. 2e–h shows histograms of the angle α at DW sections with corresponding orientations. Key points for these data demonstrated are as follows: when DW tangential direction is parallel to [1–10], that is, φ=0°±3°, then the histogram plotted in Fig. 2e shows that the angle α is scattered about a narrow distribution centred near 0°, confirming that these DWs are Néel type with lefthanded chirality^{17}. When φ=90°±3° (DW tangential direction is parallel to [001], Fig. 2f), then the distribution of α has two peaks with comparable heights centred at −90° and +90°, indicating right and lefthanded Bloch wall sections. This distribution corresponds to the conventional case of nonchiral Bloch walls^{17}. The distribution for φ=−45°±3° is shown in Fig. 2g, where a peak showing a narrow distribution of the angle α appears at ~+45°. Although this is clearly a chiral spin structure, it neither corresponds to chiral Néel wall^{15,16,17} nor to nonchiral Bloch wall^{1,2,3,16,17}. This DW spin texture can be understood as a superposition of the lefthanded chiral Néel structure and lefthanded chiral Bloch structure, that is, as in Néel walls the spin vector tilts towards the inplane normal direction of the DW while, at the same time, it rotates around the DW normal as it does in Bloch walls. We will refer to this texture as a mixed DW. Similarly, when φ=45°±3°, as shown in Fig. 2h, then the single peak at −45° indicates a mixed chiral wall type composed of a lefthanded Néel component and a righthanded Blochcomponent.
Quantitative picture of anisotropic chirality
To analyse the orientationdependent DW structure systematically, we test how Blochtype chirality evolves from lefthanded to nonchiral to righthanded chiral order as seen, for example, in Fig. 2f–h. A twodimensional histogram reproduced in Fig. 3a shows the statistical likeliness of DW spin configurations α and DW orientations φ; on our colour scale, rare α/φ combinations are darker and common α/φ combinations are brighter. To guide interpretation, Fig. 3b shows the sketches of DW configurations corresponding to the α−φ histogram plotted in Fig. 3a. As defined in the inset in Fig. 2, red arrows in Fig. 3b indicate the inplane direction of magnetization inside the DW and blue arrows correspond to the DW normal n. Vertical cuts along green dashed lines through the twodimensional histogram in Fig. 3a correspond to the histograms of α as shown in Fig. 2e–h. The bright regions in Fig. 3a (emeraldcoloured regions in Fig. 3b) represent the most common DW spin textures found experimentally. The most prominent feature in this histogram is a diagonal streak in the lower half. This streak forms for two reasons. First, in this region of the histogram, the orientations of inplane components of DW magnetization (red arrows) are aligned with inplane uniaxial magnetic anisotropy K_{u}, that is, parallel to the W[001] direction. Second, the Néel components of spin textures in the lower half of the histogram (−90°<α<90°) are always left handed. By contrast, a similar diagonal steak is suppressed in the upper half of the histogram (90°<α<270°) because, although a corresponding region exists where DW magnetization is aligned with K_{u}, the Néel components of spin textures in this part of the histogram are righthanded and thus energetically unfavourable as a result of the DMI of this system. Besides the prominent diagonal steak, six additional DW textures are observed where both α and φ are right angles (four bright regions in the four corners of the histogram and two bright regions where α=90° and φ=±90°). These α/φ combinations correspond to pure Bloch textures. The fact that for φ=−90° and +90° we simultaneously observe textures with α=90° (lefthanded) and with α=−90° or α=270° (righthanded) indicates that the system is achiral in the limit of pure Bloch texture.
To clarify how the system evolves from homochirality for most α/φ combinations to nonchiral Bloch textures at φ=−90° and +90° we quantify the magnetic chirality of mixed DWs by decomposing the magnetization into Bloch and Néel components. By plotting the projections of the magnetization unit vector onto the DW tangent and normal directions the twodimensional histogram shown in Fig. 3a can be converted into separate histograms of the Bloch and Néel components: for all points on DW centrelines, the projection of the local magnetization unit vector onto the DW tangent, given by sin(α), contributes to the Blochtype histogram and the projection onto the DW normal direction, given by cos(α), contributes to the Néeltype histogram. The resulting histograms are shown in Fig. 4a,b. From these data, we can quantify average chiralities γ_{B} and γ_{N} of the Blochtype components and Néeltype components by averaging the magnetization projections over all angles α.
The sign of the average chiralities γ_{B} and γ_{N} reflects rotational sense and, following the conventions used by Heide et al.^{30}, the Blochtype component is called lefthanded (righthanded) for positive (negative) γ_{B}, and the Néeltype component is lefthanded (righthanded) for positive (negative) γ_{N}. Figure 4c plots the dependence of γ_{B} and γ_{N} on φ, the angle between the DW normal and K_{u}. The average Néel chirality is always positive and follows a cosine curve (light blue dashed line), indicating that Néel components of DW spin textures in this system are always lefthanded, regardless of the orientation of local DW sections. The average Bloch chirality of DW spin textures follows a sin curve (dark blue dashed line) in the middle region of the plot, where the magnitude of φ is less than ~60°. This indicates that Bloch wall spin texture can be either lefthanded or righthanded, depending on the orientation of the DW with respect to the substrate induced anisotropy K_{u}. The sinusoidal φdependence suggests that left and righthanded Bloch components occur with equal likeliness in this system, similar to the case of nonchiral magnets where the DMI can be neglected. Yet this system is clearly different from nonchiral magnets, in which case one would expect the quantities plotted in Fig. 4c to scatter about the flat line where average chirality vanishes, γ=0 (purple dashed line). By contrast, the sinusoidal dependence of average chirality on φ is a result of the anisotropic DMI in the Fe/Ni/W(110) system. Here Bloch chirality gradually vanishes when φ approaches ±90° (ref. 16). The gradual deviation from sinusoidal behaviour is interesting because, given that the DMI stabilizes the Blochtype chirality, measuring how the system evolves from mixed chiral textures at small φ to nonchiral Bloch DWs at φ=±90° offers a way to estimate the strength of the DMI (see Supplementary Note 1).
A model for the origin of anisotropic chirality
Prior work on a similar system, Fe/8 monolayer Ni/W(110), established that inplane anisotropic strain due to lattice mismatch^{31} gives rise to an inplane uniaxial magnetic anisotropy K_{u} with easy axis along W[001], through magnetoelastic contributions to the magnetic anisotropy^{25}. We also confirmed the presence of uniaxial anisotropy K_{u} by SPLEEM observations on thicker inplane magnetized Fe/Ni films, where the orientation of magnetization of the inplane domains is always parallel or antiparallel to the W[001] direction. Thus, in these systems, spin structure inside the DWs is a result of interplay between the exchange interaction, the interfacial DMI, the dipolar interaction, the perpendicular magnetic anisotropy, as well as K_{u}. The interfacial DMI favours chiral Néel DWs, and the dipolar interaction favours nonchiral Bloch DWs. Because of its twofold symmetry, uniaxial anisotropy itself does not influence the chirality of the DWs. However, K_{u} provides an additional force favouring alignment of the magnetization within DWs towards the easy magnetization axis [001]. This additional force lifts the left/righthanded degeneracy of Blochtype spin structures whenever DWs are at a nonzero angle with respect to the [001] direction.
Simulation for the anisotropic DW
To test this model and clarify the role of K_{u} in a DMI system, we performed Monte Carlo simulations^{32,33}. A twodimensional Heisenberg model was constructed to simulate DW configurations in the presence of the interfacial DMI and K_{u} (see Supplementary Note 1). Figure 5a shows typical simulated DWs. The coloured bars represent straight DW segments, each in a different orientation φ, that is, we sweep the angle φ by changing the easy axis of K_{u} with respect to the DW orientation. As φ varies from 0° to 90°, simulated DWs evolve from chiral Néeltype wall to nonchiral Blochtype DWs. Quantitative values for the average chiralities γ_{B} and γ_{N} of the Néel and Bloch components can be derived from simulation results. Results are shown in Fig. 5b, where the φ dependence of γ_{B} and γ_{N} nicely reproduces the experimental results (see also Supplementary Fig. 2b). The simulated results suggest that this type of Blochcomponent chirality may be a general feature of DMI systems with uniaxial inplane anisotropy, beyond Fe/Ni/W(110).
Towards a homochiral Blochtype component
In the measurements reported above, both left and righthanded DW segments coexist within each sample, and the handedness of the chiral Bloch component in DWs in this system is solely determined by the DW orientation φ. This suggests the possibility that the system might be driven into a homochiral state if one can experimentally confine the directions of the DW orientation. One possibility to tune DW orientations might be to fabricate nanowires on W(110). For energetic reasons, DWs in nanowires tend to be oriented orthogonal to the wire direction. By controlling nanowire orientation with respect to the lattice orientation of the tungsten crystal, it may be possible to select preferred DW orientations and thus preferred handedness (and weight) of the Bloch component. Another way to control DW orientations is to exploit the interaction of atomic surface steps with DWs. Results on related thinfilm systems have shown how substrate step arrays can be used to orient DWs^{34,35}. We have confirmed the viability of this approach. Preparing thinner Fe/Ni bilayers, we find that most of the DWs are aligned along surface step directions, as shown in Fig. 6. Evaluating all DWs in this image shows that the histogram of the angle α has only one peak at −40°, indicating that the Blochtype chirality in these DWs is righthanded homochiral. Considering that direction and density of atomic surface steps can be controlled by polishing substrates at controlled vicinal angles near the (110) lattice plane, this result suggests that it is indeed possible to prepare Fe/Ni/W(110) structures featuring homochiral DW with tailored Blochcomponent spin textures.
Our experimental results on iron/nickel bilayers epitaxially grown on (110) tungsten surfaces demonstrate that anisotropic chiral magnetism can be stabilized by combining the interfacial DMI with inplane uniaxial anisotropy. Under these conditions, a family of DW spin textures is stabilized: chiral Néeltype DWs, chiral mixedtype DWs composed of Néel and Bloch components and nonchiral Blochtype DWs. The handedness of the Blochtype component is a function of DW orientation with respect to the substrate lattice, which provides unique opportunities to systematically study in detail the transition between chiral DWs and nonchiral DWs to further understand the interplay between the DMI, magnetic anisotropy and the dipolar interaction.
These experimental observations demonstrate how the Blochtype chirality emerges as a new type of DW spin texture when the interfacial DMI is combined with magnetic anisotropy, thus adding a new degree of freedom to tailor a diverse family of chiral spin textures. The results introduce rich possibilities to influence DW dynamics by combining intrinsic phenomena such as spin Hall effects^{18,19,20,21,36,37}, Rashba effects^{18,36,38,39} or the DMI^{15,18}, not only with magnetoelastically induced anisotropy (as we have shown in this work), but also with piezoinduced strain^{40,41}, nanowire shapeinduced anisotropy^{42} or external magnetic fields^{19,20,21,43,44}, which may open up new opportunities to design spin–orbitronics devices.
Methods
Sample preparation
The W(110) substrate was cleaned by flashing at 1,950 °C in 3 × 10^{−8} Torr O_{2} and final annealing at 1,900 °C under ultrahigh vacuum with base pressure 4 × 10^{−11} Torr. Fe and Ni film thickness was calibrated by monitoring lowenergy electron microscopy (LEEM) image intensity oscillations associated with atomic layerbylayer growth. Fe and Ni layers were grown at 300 K by electron beam evaporation, and the sample was annealed to 900 K for several minutes after growth of one monolayer Ni to develop a wellordered interface^{24,25}.
Image vector field analysis
Two LEEM images, I_{+p}(i, k) and I_{−p}(i, k), are acquired with spin of the illuminating electron beam aligned and antialigned with a chosen polarization axis p. We typically use image integration times of 1 s. The LEEM images are used to calculate a SPLEEM asymmetry A_{p}(i, k)=(I_{+p}(i, k)−I_{−p}(i, k))/(I_{+p}(i, k)+I_{−p}(i, k)). The asymmetry value A_{p}(i, k) at pixel coordinates (i, k) within a SPLEEM image is proportional to the projection of the magnetization vector m(i, k) of the sample on the chosen polarization axis p, A_{P}(i, k)~(m(i, k)·p). We choose three orthonormal vectors x, y and z to form a cartesian coordinate system with z being normal to the sample surface. From sets of three SPLEEM images shown in Supplementary Fig. 3a–c, each with p set to be parallel to one of the three components of the sample surface coordinates, the direction of magnetization unit vector m can be determined at all pixel coordinates. To obtain lownoise threedimensional vector fields A(i, k) used for this study, we aligned and averaged 40 such images for the component in the outofplane direction (z) and 100 each for the inplane directions (x, y). To represent these vector images in colour, we mapped the inplane angle on hue and the outofplane component to the brightness of the image (Supplementary Fig. 3d). For higher contrast within DWs, the contrast range of the outofplane domains was reduced to 50%. The centrelines of the DWs were determined by thresholding at A_{z}(i, k)=0 and subtracting the thresholded image from its binary dilation. The DW normal vectors were determined by applying Gaussian blur with a width of 2px and then evaluating the twodimensional gradient on the centreline. To determine the direction of m(i, k), we evaluated and normalized m(i, k)=(A_{x}(i, k),A_{y}(i, k),0)/(A_{x}(i, k)^{2}+A_{y}(i, k)^{2})^{1/2} so that the blur of the strong signal of the z component overlapping with the DW does not add noise to the data. Determining m(i, k) from singlepixel centrelines and from three, five and sevenpixelwide ribbons straddling the DW centrelines, we had found that the histograms, characterizing DW magnetization direction as a function of the angles α and φ come out nearly identical; therefore, we use DW centre line pixels in the analysis.
Additional information
How to cite this article: Chen, G. et al. Unlocking Blochtype chirality in ultrathin magnets through uniaxial strain. Nat. Commun. 6:6598 doi: 10.1038/ncomms7598 (2015).
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Acknowledgements
We acknowledge Dr Colin Ophus for helpful discussions. Experiments were performed at the Molecular Foundry, Lawrence Berkeley National Laboratory, supported by the Office of Science, Office of Basic Energy Sciences, Scientific User Facilities Division, of the U.S. Department of Energy under Contract No. DEAC02—05CH11231. This work was also supported by the National Research Foundation of Korea Grant funded by the Korean Government (2012R1A1A2007524), by the National Key Basic Research Program (No. 2015CB921401 and No. 2011CB921801) and the National Science Foundation (No. 11434003 and No. 11474066) of China, by National Science Foundation DMR1210167 and NRF through Global Research Laboratory project of Korea.
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Contributions
G.C. was responsible for the concept of the experiment and carried out the measurements. A.K.S. supervised the SPLEEM facility. A.T.N. developed and implemented algorithms for the quantitative analysis of SPLEEM data. G.C., A.T.N., A.K.S., Y.W. and Z.Q.Q. analysed and interpreted the results. S.P.K. performed the Monte Carlo simulations. C.W. supervised the Monte Carlo simulations. H.Y.K. contributed to the development of the simulation code. G.C. and A.K.S. prepared the manuscript. All authors commented on the manuscript.
Corresponding authors
Correspondence to Gong Chen or Andreas K. Schmid.
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Supplementary Figures 13, Supplementary Note 1 and Supplementary References (PDF 627 kb)
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Nature Materials (2018)

Elastic moduli and Poisson's ratio of 2dimensional magnetic skyrmion lattice
Journal of Applied Physics (2017)
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