Unlocking Bloch-type chirality in ultrathin magnets through uniaxial strain

Abstract

Chiral magnetic domain walls are of great interest because lifting the energetic degeneracy of left- and right-handed spin textures in magnetic domain walls enables fast current-driven domain wall propagation. Although two types of magnetic domain walls are known to exist in magnetic thin films, Bloch- and Néel-walls, up to now the stabilization of homochirality was restricted to Néel-type domain walls. Since the driving mechanism of thin-film magnetic chirality, the interfacial Dzyaloshinskii-Moriya interaction, is thought to vanish in Bloch-type walls, homochiral Bloch walls have remained elusive. Here we use real-space imaging of the spin texture in iron/nickel bilayers on tungsten to show that chiral domain walls of mixed Bloch-type and Néel-type can indeed be stabilized by adding uniaxial strain in the presence of interfacial Dzyaloshinskii-Moriya interaction. Our findings introduce Bloch-type chirality as a new spin texture, which may open up new opportunities to design spin-orbitronics devices.

ARTICLE

Received 24 Jun 2014 | Accepted 10 Feb 2015 | Published 23 Mar 2015

Gong Chen1, Alpha T. NDiaye1, Sang Pyo Kang2, Hee Young Kwon2, Changyeon Won2, Yizheng Wu3, Z.Q. Qiu4 & Andreas K. Schmid1

Chiral magnetic domain walls are of great interest because lifting the energetic degeneracy of left- and right-handed spin textures in magnetic domain walls enables fast current-driven domain wall propagation. Although two types of magnetic domain walls are known to exist in magnetic thin lms, Bloch- and Nel-walls, up to now the stabilization of homochirality was restricted to Nel-type domain walls. Since the driving mechanism of thin-lm magnetic chirality, the interfacial DzyaloshinskiiMoriya interaction, is thought to vanish in Bloch-type walls, homochiral Bloch walls have remained elusive. Here we use real-space imaging of the spin texture in iron/nickel bilayers on tungsten to show that chiral domain walls of mixed Bloch-type and Nel-type can indeed be stabilized by adding uniaxial strain in the presence of interfacial DzyaloshinskiiMoriya interaction. Our ndings introduce Bloch-type chirality as a new spin texture, which may open up new opportunities to design spinorbitronics devices.

DOI: 10.1038/ncomms7598

Unlocking Bloch-type chirality in ultrathin magnets through uniaxial strain

1 NCEM, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA. 2 Department of Physics, Kyung Hee University, Seoul 130-701, Korea. 3 Department of Physics, State Key Laboratory of Surface Physics and Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai 200433, Peoples Republic of China. 4 Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA. Correspondence and requests for materials should be addressed to G.C. (email: mailto:[email protected]

Web End [email protected] ) or to A.K.S. (email: mailto:[email protected]

Web End [email protected] ).

NATURE COMMUNICATIONS | 6:6598 | DOI: 10.1038/ncomms7598 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 1

& 2015 Macmillan Publishers Limited. All rights reserved.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7598

The formation of magnetic domains and domain walls (DWs) results from the interplay between the exchange interaction, the dipolar interaction and magnetic aniso

tropy. In perpendicularly magnetized thin-lm systems, DWs can be classied 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 Nel walls the spin rotates like a cycloidal spiral. A magnetic lm is called chiral when the rotational sense of these spirals is the same in all DWs. In non-chiral lms, both rotation senses exist in different sections of DWs, with the same probability overall. The conventional textbook view predicts non-chiral Bloch walls as the ground state in magnetic thin lms13. 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 DzyaloshinskiiMoriya interaction (DMI), can be induced when inversion symmetry is broken in the system4,5. The inversion symmetry can break in the lattice (bulk DMI) or at surfaces and interfaces (interfacial DMI) of magnetic lms68. The DMI term between two atomic spin Si and Sj on neighbouring atomic sites i and j can be written as EDM Dij (Si Sj), where Dij is the

DMI vector. In the case of interfacial DMI, Dij is restricted to be perpendicular to the position vector rij ri rj (refs 69). For

this reason, interfacial DMI alone can only stabilize Nel-type chiral spin textures, such as cycloidal spin spirals1012, skyrmions13,14 or chiral Nel walls1517. In Bloch-type spin textures, the cross-product (Si Sj) is parallel to the position

vector rij and EDM vanishes, consequently Bloch walls are usually non-chiral.

It was recently found that chiral Nel walls in lm and multilayer structures enable fast current-driven DW motion and spin texture-dependent DW propagation direction15,1821. A numerical study also predicts that introducing chirality of Bloch walls into magnetic lms can extend possibilities to manipulate DW propagation behaviours to new geometries18. Developing experimental evidence that allows us to tailor the spin structure of chiral DWs via interfacial DMI6,22 is crucial for engineering methods to control current- or eld-driven DW dynamics in lm 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 in-plane uniaxial anisotropy are still missing.

In the following, we demonstrate how the introduction of in-plane uniaxial anisotropy allows us to tailor the DMI-stabilized chiral DW spin textures. We focus on Fe/Ni bilayer grown on

W(110) substrates, where the very large spin Hall angle of tungsten23 is combined with two-fold symmetry at the (110) interface and perpendicular magnetic anisotropy of the magnetic layer2426. Using spin-polarized low-energy electron microscopy (SPLEEM)2729, we observe anisotropic chiral DW spin structures with mixed components of chiral Bloch- and chiral Nel-character. We nd 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 Nel walls, mixed chiral walls containing both Nel and Bloch components or non-chiral Bloch walls. The chirality of the Nel wall components is always left-handed, whereas the chirality of the Bloch wall components is either left- or right-handed. Bloch-component handedness as well as the ratio of the Bloch- versus Nel- 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 in-plane uniaxial anisotropy. Our ndings experimentally demonstrate the Bloch-type chirality as a new type of chiral spin texture stabilized by interfacial DMI, which may open up new opportunities to design spinorbitronics devices.

ResultsVisualizing 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 Nel walls with left- or right-handed chirality. Figure 1 shows sketches of a left-handed (a) and right-handed (b) chiral Nel wall and a left-handed (c) and right-handed (d) chiral Bloch wall. Experimentally, chirality in magnetic DWs can be determined by imaging three-dimensional 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 lm 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 [110]/[ 110] and cyan/red indicates com

ponents along [001]/[00-1]. 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 in-plane 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 lm plane. These ndings 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.

Figure 1 | Schematic of chiral DWs. Sketch of left-handed (a) and right-handed (b) chiral Nel walls in perpendicularly magnetized thin lm, directions of arrows correspond to the magnetization direction. The spin structure of the DW is simplied by highlighting the in-plane component in the centreof the walls. Sketch of left-handed (c) and right-handed (d) chiral Bloch walls in a perpendicularly magnetized thin lm.

2 NATURE COMMUNICATIONS | 6:6598 | DOI: 10.1038/ncomms7598 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

& 2015 Macmillan Publishers Limited. All rights reserved.

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7598 ARTICLE

[001]

[1-10]

1.5 ML

Fe

[001]

10 ML

Ni

n

m

W

Bloch Right h.

Nel Left h.

Bloch Left h.

Nel Right h.

Bloch Right h.

=0

=90

Pixel count

=45

=45

90 270

0

90

180

()

Figure 2 | Real-space observation of anisotropic chiral DWs in a Fe/Ni bilayer. (a) Prole sketch of Fe/Ni bilayer grown on W(110) substrate. (b) Compound SPLEEM image, colourized DW highlights the in-plane orientation of the magnetization inside the DW; scale bar, 1 mm.

(c) Denition of angles a and f, m indicates the in-plane component of the DW, blue arrow indicates normal vector n, grey arrow indicates W[001]

direction. (d) Examples of different DW orientations, data are cropped from b. DW tangent directions are indicated by white dashed lines, scale bars are 100 nm. (eh) f-dependent histograms of angle a in DW centre, counted pixel-by-pixel in four SPLEEM compound images including b. The histograms are normalized with respect to the total number of evaluated states. Left h., left-handed; ML, monolayer; right h., right-handed.

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 centreline-pixels of all the DWs, we measure the local direction of the magnetization, expressed as the magnetization unit vector m, and the direction of the in-plane normal vector n of the DW. We represent these data in terms of two angles: to capture the DW orientation, we dene the angle f 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 dene the angle a as the angle between the magnetization unit vector m and the in-plane normal vector n of the DW; the geometry of these angles is sketched in Fig. 2c. The magnitude of the angle a indicates whether the wall is in Bloch conguration (a 90) or in Nel

conguration (a 0 or a 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, a 45). We notice that the magnitude of the angle a, and thus

the type of the wall, is a function of the orientation of the wall f. 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. 2eh shows histograms of the angle a at

DW sections with corresponding orientations. Key points for these data demonstrated are as follows: when DW tangential direction is parallel to [110], that is, f 03, then the

histogram plotted in Fig. 2e shows that the angle a is scattered about a narrow distribution centred near 0, conrming that these DWs are Nel type with left-handed chirality17. When f 903 (DW tangential direction is parallel to [001], Fig. 2f),

then the distribution of a has two peaks with comparable heights centred at 90 and 90, indicating right- and left-handed

Bloch wall sections. This distribution corresponds to the conventional case of non-chiral Bloch walls17. The distribution for f 453 is shown in Fig. 2g, where a peak showing a

narrow distribution of the angle a appears at B 45. Although

this is clearly a chiral spin structure, it neither corresponds to chiral Nel wall1517 nor to non-chiral Bloch wall13,16,17. This DW spin texture can be understood as a superposition of the left-handed chiral Nel structure and left-handed chiral Bloch structure, that is, as in Nel walls the spin vector tilts towards the in-plane 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 f 453, as shown in Fig. 2h, then the single peak at 45

indicates a mixed chiral wall type composed of a left-handed Nel component and a right-handed Bloch-component.

Quantitative picture of anisotropic chirality. To analyse the orientation-dependent DW structure systematically, we test how Bloch-type chirality evolves from left-handed to non-chiral to right-handed chiral order as seen, for example, in Fig. 2fh. A two-dimensional histogram reproduced in Fig. 3a shows the statistical likeliness of DW spin congurations a and DW orientations f; on our colour scale, rare a/f combinations are darker and common a/f combinations are brighter. To guide interpretation, Fig. 3b shows the sketches of DW congurations corresponding to the a f histogram plotted in Fig. 3a. As

dened in the inset in Fig. 2, red arrows in Fig. 3b indicate the in-plane direction of magnetization inside the DW and blue arrows correspond to the DW normal n. Vertical cuts along green dashed lines through the two-dimensional histogram in Fig. 3a correspond to the histograms of a as shown in Fig. 2eh. The bright regions in Fig. 3a (emerald-coloured 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 in-plane components of DW magnetization (red arrows) are aligned with in-plane uniaxial magnetic anisotropy Ku, that is, parallel to the W[001]

direction. Second, the Nel components of spin textures in the lower half of the histogram ( 90oao90) are always left

NATURE COMMUNICATIONS | 6:6598 | DOI: 10.1038/ncomms7598 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 3

& 2015 Macmillan Publishers Limited. All rights reserved.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7598

handed. By contrast, a similar diagonal steak is suppressed in the upper half of the histogram (90oao270) because, although a corresponding region exists where DW magnetization is aligned with Ku, the Nel components of spin textures in this part of the histogram are right-handed 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 a and f are right angles (four bright regions in the four corners of the histogram and two bright regions where a 90

and f 90). These a/f combinations correspond to pure

Bloch textures. The fact that for f 90 and 90 we

simultaneously observe textures with a 90 (left-handed) and

with a 90 or a 270 (right-handed) indicates that the

system is achiral in the limit of pure Bloch texture.

To clarify how the system evolves from homochirality for most a/f combinations to non-chiral Bloch textures at f 90 and 90 we quantify the magnetic chirality of mixed DWs by decomposing the magnetization into Bloch- and Nel- components. By plotting the projections of the magnetization unit vector onto the DW tangent- and normal directions the two-dimensional histogram shown in Fig. 3a can be converted into separate histograms of the Bloch and Nel components: for all points on DW centrelines, the projection of the local magnetization unit vector onto the DW tangent, given by sin(a), contributes to the Bloch-type histogram and the projection onto the DW normal direction, given by cos(a), contributes to the Nel-type histogram. The resulting histograms are shown in Fig. 4a,b. From these data, we can quantify average chiralities gB and gN of the

Bloch-type components and Nel-type components by averaging the magnetization projections over all angles a.

The sign of the average chiralities gB and gN reects rotational sense and, following the conventions used by Heide et al.30, the

Bloch-type component is called left-handed (right-handed) for positive (negative) gB, and the Nel-type component is left-handed (right-handed) for positive (negative) gN. Figure 4c plots the dependence of gB and gN on f, the angle between the DW normal and Ku. The average Nel chirality is always positive and follows a cosine curve (light blue dashed line), indicating that Nel components of DW spin textures in this system are always left-handed, 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 f is less than B60. This indicates that

Bloch wall spin texture can be either left-handed or right-handed, depending on the orientation of the DW with respect to the substrate induced anisotropy Ku. The sinusoidal f-dependence suggests that left- and right-handed 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 non-chiral magnets, in which case one would expect the quantities plotted in Fig. 4c to scatter about the at line where average chirality vanishes, g 0 (purple dashed

line). By contrast, the sinusoidal dependence of average chirality on f is a result of the anisotropic DMI in the Fe/Ni/W(110)

system. Here Bloch chirality gradually vanishes when f approaches 90 (ref. 16). The gradual deviation from sinusoidal behaviour is interesting because, given that the DMI stabilizes the Bloch-type chirality, measuring how the system evolves from mixed chiral textures at small f to non-chiral Bloch

DWs at f 90 offers a way to estimate the strength of the

DMI (see Supplementary Note 1).

0

Number

Max

270

Bloch Right h.

Mixed

270

Mixed

180

Nel Right h.

Nel Left h.

Bloch Right h.

180

Mixed

90

Bloch Left h.

90

()

()

Mixed

0

0

90

0

90 90 45 45 90

()

90

45 45 90

0

()

Figure 3 | Distribution of anisotropic DW chirality in a/ space.(a) Two-dimensional histogram of experimental DW magnetization data in a f space derived from four SPLEEM compound images including Fig. 2b.

Colour bar corresponds to the number of pixels on DW centrelineswith a given f and a. Green dashed lines correspond to the histograms in

Fig. 2eh. (b) Sketch of DW congurations with respect to DW orientation, in a f space: each circle contains a black and a white domain, blue arrows

show DW normal vectors n, red arrows show orientation of in-plane magnetization of the DWs, grey arrows show direction of Ku. Emerald-coloured regions highlight the preferred congurations realized in the Fe/Ni/W(110) system (that is, left-handed DMI and Ku along [001]).

Left h., left-handed; right h., right-handed.

Bloch-type

(+1)

(1)

Nel-type

270

90 90

270 (+1)

1.0

180

180

0.5

()

90

Number

()

90

Number

0.0

0

0

0.5

N B

Non-chiral

(1)

1.0

90 45 0 45 90

Figure 4 | Quantifying Nel- and Bloch chirality. Histograms of Bloch wall chirality (a) and Nel wall chirality (b) in a f space. (c) f-dependent chirality

of Nel-type (gN) and Bloch-type (gB) components, 1 corresponds to right-handed and 1 corresponds to left-handed.

45 0 45 90

90 90 45 0 45 90

N, B(normalized)

() () ()

4 NATURE COMMUNICATIONS | 6:6598 | DOI: 10.1038/ncomms7598 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

& 2015 Macmillan Publishers Limited. All rights reserved.

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7598 ARTICLE

A model for the origin of anisotropic chirality. Prior work on a similar system, Fe/8 monolayer Ni/W(110), established that in-plane anisotropic strain due to lattice mismatch31 gives rise to an in-plane uniaxial magnetic anisotropy Ku with easy axis along

W[001], through magneto-elastic contributions to the magnetic anisotropy25. We also conrmed the presence of uniaxial anisotropy Ku by SPLEEM observations on thicker in-plane magnetized Fe/Ni lms, where the orientation of magnetization of the in-plane 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 Ku. The interfacial DMI favours chiral Nel DWs, and the dipolar interaction favours non-chiral Bloch DWs. Because of its two-fold symmetry, uniaxial anisotropy itself does not inuence the chirality of the DWs. However, Ku provides an additional force favouring alignment of the magnetization within DWs towards the easy magnetization axis [001]. This additional force lifts the left-/right-handed degeneracy of Bloch-type spin structures whenever DWs are at a non-zero angle with respect to the [001] direction.

Simulation for the anisotropic DW. To test this model and clarify the role of Ku in a DMI system, we performed Monte Carlo simulations32,33. A two-dimensional Heisenberg model was constructed to simulate DW congurations in the presence of the interfacial DMI and Ku (see Supplementary Note 1). Figure 5a shows typical simulated DWs. The coloured bars represent straight DW segments, each in a different orientation f, that is, we sweep the angle f by changing the easy axis of Ku with respect to the DW orientation. As f varies from 0 to 90, simulated DWs evolve from chiral Nel-type wall to non-chiral Bloch-type DWs. Quantitative values for the average chiralities gB and gN of the Nel- and Bloch- components can be derived from simulation results. Results are shown in Fig. 5b, where the f dependence of gB and gN nicely reproduces the experimental results (see also Supplementary Fig. 2b). The simulated results suggest that this type of Bloch-component chirality may be a general feature of DMI systems with uniaxial in-plane anisotropy, beyond Fe/Ni/ W(110).

Towards a homochiral Bloch-type component. In the measurements reported above, both left- and right-handed 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 f. This suggests the possibility that the system might be driven into a homochiral state if one can experimentally conne the directions of the DW orientation. One possibility to tune DW orientations might be to fabricate nano-wires 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 thin-lm systems have shown how substrate step arrays can be used to orient DWs34,35. We have conrmed the viability of this approach. Preparing thinner Fe/Ni bilayers, we nd 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 a has only one peak at

40, indicating that the Bloch-type chirality in these DWs is right-handed 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 Bloch-component 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 in-plane uniaxial anisotropy. Under these conditions, a family of DW spin textures is stabilized: chiral Nel-type DWs, chiral mixed-type DWs composed of Nel- and Bloch components and non-chiral Bloch-type DWs. The handedness of the Bloch-type 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 non-chiral DWs to further understand the interplay between the DMI, magnetic anisotropy and the dipolar interaction.

These experimental observations demonstrate how the Bloch-type 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 inuence DW dynamics by combining intrinsic phenomena such as spin Hall effects1821,36,37, Rashba effects18,36,38,39 or the DMI15,18, not only with magnetoelastically induced anisotropy (as we have shown in this work), but also with piezo-induced strain40,41,

1.0

=0

=30

Ku

DW

0.5

=60

=90

N, B(normalized)

0.0

0.5

N B

1.0 90

45

50

45

90

()

Figure 5 | Monte Carlo simulation. (a) Monte Carlo simulation results with variable DW orientation f. White and black regions correspond to perpendicularly magnetized domains, coloured region in between corresponds to DW, and orientation of in-plane component of the DW is highlighted by colour wheel. (b) f-dependent chiralities gN and gB derived from the simulation, 1 corresponds to right-handed and 1 corresponds to left-handed.

NATURE COMMUNICATIONS | 6:6598 | DOI: 10.1038/ncomms7598 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 5

& 2015 Macmillan Publishers Limited. All rights reserved.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7598

[001]

[1-10]

Nel

Bloch Left h.

Right h.

Bloch Left h.

Nel Right h.

Bloch Right h.

1

Number (normalized)

2.1 ML

Fe

4 ML

Ni

W

0

90

0

90

180

270

()

Figure 6 | Homochiral Bloch-component walls. (a) Sketch of Fe/Ni bilayer grown on W(110) substrate. (b) Compound SPLEEM image highlighting the direction of DW in-plane magnetization. The colour wheel indicates the direction of in-plane magnetization on the DWs. White arrows additionally show the in-plane spin orientations in the DWs; scale bar, 1 mm. (c) Histogram of angle a in DW counted pixel-by-pixel in (b) shows a single peak pointing at

B 40. Left h., left-handed; right h., right-handed.

nanowire shape-induced anisotropy42 or external magnetic elds1921,43,44, which may open up new opportunities to design spinorbitronics devices.

Methods

Sample preparation. The W(110) substrate was cleaned by ashing at 1,950 C in 3 10 8 Torr O2 and nal annealing at 1,900 C under ultrahigh vacuum

with base pressure 4 10 11 Torr. Fe and Ni lm thickness was calibrated by

monitoring low-energy electron microscopy (LEEM) image intensity oscillations associated with atomic layer-by-layer 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 well-ordered interface24,25.

Image vector eld analysis. Two LEEM images, Ip(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 timesof 1 s. The LEEM images are used to calculate a SPLEEM asymmetryAp(i, k) (Ip(i, k) I p(i, k))/(Ip(i, k) I p(i, k)). The asymmetry value

Ap(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, AP(i, k)B(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. 3ac, 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 low-noise three-dimensional vector elds A(i, k) used for this study, we aligned and averaged 40 such images for the component in the out-of-plane direction (z) and 100 each for the in-plane directions (x, y). To represent these vector images in colour, we mapped the in-plane angle on hue and the out-of-plane component to the brightness of the image (SupplementaryFig. 3d). For higher contrast within DWs, the contrast range of the out-of-plane domains was reduced to 50%. The centrelines of the DWs were determined by thresholding at Az(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 two-dimensional gradient on the centreline. To determine the direction of m(i, k), we evaluated and normalized m(i, k)

(Ax(i, k),Ay(i, k),0)/(Ax(i, k)2 Ay(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 single-pixel centrelines and from three-, ve- and seven-pixel-wide ribbons straddling the DW centrelines, we had found that the histograms, characterizing DW magnetization direction as a function of the angles a and f come out nearly identical; therefore, we use DW centre line pixels in the analysis.

References

1. Hubert, A. & Schafer, R. Magnetic Domains: The Analysis of Magnetic Microstructures (Springer, 1998).

2. Chikazumi, S. Physics of Ferromagnetism (Oxford Univ. Press, 1999).3. Yafet, Y. & Gyorgy, E. M. Ferromagnetic stripe domains in an atomic monolayer. Phys. Rev. B 38, 91459151 (1988).

4. Dzyaloshinskii, I. E. A thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241255 (1958).

5. Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 9198 (1960).

6. Fert, A. Magnetic and transport properties of metallic multilayers. Mat. Sci. Forum 5960, 439480 (1990).

7. Crpieux, A. & Lacroix, C. DzyaloshinskiiMoriya interactions induced by symmetry breaking at a surface. J. Magn. Magn. Mater. 182, 341349 (1998).

8. Fert, A., Cros, V. & Sampaio, J. Skyrmions on the track. Nat. Nanotechnol. 8, 152156 (2013).

9. Vedmedenko, E. Y., Udvardi, L., Weinberger, P. & Wiesendanger, R. Chiral magnetic ordering in two-dimensional ferromagnets with competing Dzyaloshinsky-Moriya interactions. Phys. Rev. B 75, 104431 (2007).

10. Bode, M. et al. Chiral magnetic order at surfaces driven by inversion asymmetry. Nature 447, 190193 (2007).

11. Ferriani, P. et al. Atomic-scale spin spiral with a unique rotational sense: Mn monolayer on W(001). Phys. Rev. Lett. 101, 027201 (2008).

12. Meckler, S. et al. Real-space observation of a right-rotating inhomogeneous cycloidal spin spiral by spin-polarized scanning tunneling microscopy in a triple axes vector magnet. Phys. Rev. Lett. 103, 157201 (2009).

13. Heinze, S. et al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713718 (2011).

14. Romming, N. et al. Writing and deleting single magnetic skyrmions. Science 341, 636639 (2013).

15. Thiaville, A. et al. Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic lms. Europhys. Lett. 100, 57002 (2012).

16. Chen, G. et al. Novel chiral magnetic domain wall structure in Fe/Ni/Cu(001) lms. Phys. Rev. Lett. 110, 177204 (2013).

17. Chen, G. et al. Tailoring the chirality of magnetic domain walls by interface engineering. Nat. Commun. 4, 2671 (2013).

18. Khvalkovskiy, A. V. et al. Matching domain-wall conguration and spin-orbit torques for efcient domain-wall motion. Phys. Rev. B 87, 020402(R) (2013).

19. Ryu, K.-S., Thomas, L., Yang, S.-H. & Parkin, S. S. P. Chiral spin torque at magnetic domain walls. Nat. Nanotechnol. 8, 527533 (2013).

20. Emori, S., Bauer, U., Ahn, S.-M., Martinez, E. & Beach, G. S. D. Current-driven dynamics of chiral ferromagnetic domain walls. Nat. Mater. 12, 611616 (2013).

21. Torrejon, J. et al. Interface control of the magnetic chirality in CoFeB|MgO heterosctructures with heavy metal underlayers. Nat. Commun. 5, 4655 (2014).

22. Fert, A. & Levy, P. M. Role of anisotropic exchange interactions in determining the properties of spin-glasses. Phys. Rev. Lett. 44, 15381541 (1980).

23. Pai, C.-F. et al. Spin transfer torque devices utilizing the giant spin Hall effect of tungsten. Appl. Phys. Lett. 101, 122404 (2012).

24. Sander, D. et al. Structure and perpendicular magnetization of Fe/Ni(111) bilayers on W(110). J. Appl. Phys. 81, 47024704 (1997).

25. Meyerheim, H. L. et al. Spin reorientation and structural relaxation of atomic layers: pushing the limits of accuracy. Phys. Rev. Lett. 93, 156105 (2004).

26. Lee, J.-S. et al. Interfacial nanostructure induced spin-reorientation transition in Ni/Fe/Ni/W(110). Phys. Rev. B 83, 144420 (2011).

27. Rougemaille, N. & Schmid, A. K. Magnetic imaging with spin-polarized low-energy electron microscopy. Eur. Phys. J. Appl. Phys. 50, 20101 (2010).

28. Ding, H. F., Schmid, A. K., Li, D., Guslienko, K. Y. & Bader, S. D. Magnetic bistability of Co nanodots. Phys. Rev. Lett. 94, 157202 (2005).

6 NATURE COMMUNICATIONS | 6:6598 | DOI: 10.1038/ncomms7598 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

& 2015 Macmillan Publishers Limited. All rights reserved.

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7598 ARTICLE

29. El Gabaly, F. et al. Imaging spin-reorientation transitions in consecutive atomic Co layers on Ru(0001). Phys. Rev. Lett. 96, 147202 (2006).

30. Heide, M., Bihlmayer, G. & Blgel, S. Dzyaloshinskii-Moriya interaction accounting for the orientation of magnetic domain in ultrathin lms: Fe/ W(110). Phys. Rev. B 78, 140403(R) (2008).

31. Sander, D., Schmidthals, C., Enders, A. & Kirschner, J. Stress and structure of Ni monolayers on W(110): The importance of lattice mismatch. Phys. Rev. B 57, 14061409 (1998).

32. Kwon, H. Y. & Won, C. Effects of DzyaloshinskiiMoriya interaction on magnetic stripe domains. J. Magn. Magn. Mater. 351, 815 (2014).

33. Kwon, H. Y. et al. A Study of the stripe domain phase at the spin reorientation transition of two-dimensional magnetic system. J. Magn. Magn. Mater. 322, 27422748 (2010).

34. Ramchal, R., Schmid, A. K., Farle, M. & Poppa, H. Spiral-like continuous spin-reorientation transition of Fe/Ni bilayers on Cu(100). Phys. Rev. B 69, 214401 (2004).

35. Klein, C., Ramchal, R., Farle, M. & Schmid, A. K. Direct imaging of spin-reorientation transitions in ultrathin Ni lms by spin-polarized low-energy electron microscopy. Surf. Interface Anal. 38, 15501553 (2006).

36. Kim, J. et al. Layer thickness dependence of the current-induced effective eld vector in Ta|CoFeB|MgO. Nat. Mater 12, 240245 (2013).

37. Haazen, P. P. J. et al. Domain wall depinning governed by the spin Hall effect. Nature Mater 12, 299303 (2013).

38. Miron, I. M. et al. Current-driven spin torque induced by the Rashba effect in a ferromagnetic metal layer. Nat. Mater. 9, 230234 (2010).

39. Miron, I. M. et al. Fast current-induced domain-wall motion controlled by the Rashba effect. Nat. Mater. 10, 419423 (2011).

40. Lei, N. et al. Strain-controlled magnetic domain wall propagationin hybrid piezoelectric/ferromagnetic structures. Nat. Commun. 4, 1378 (2013).

41. De Ranieri, E. et al. Piezoelectric control of the mobility of a domain wall driven by adiabatic and non-adiabatic torques. Nat. Mater. 12, 808814 (2013).42. Koyama, T. et al. Observation of the intrinsic pinning of a magnetic domain wall in a ferromagnetic nanowire. Nat. Mater. 10, 194197 (2011).

43. Rushforth, A. W. Domain wall motion driven by spin Hall effectTuning with in-plane magnetic anisotropy. Appl. Phys. Lett. 104, 162408 (2014).

44. Franken, J. H., Herps, M., Swagten, H. J. M. & Koopmans, B.

Tunable chiral spin texture in magnetic domain-walls. Sci. Rep. 4, 5248 (2014).

Acknowledgements

We acknowledge Dr Colin Ophus for helpful discussions. Experiments were performed at the Molecular Foundry, Lawrence Berkeley National Laboratory, supported by the Ofce of Science, Ofce of Basic Energy Sciences, Scientic User Facilities Division, of the U.S. Department of Energy under Contract No. DE-AC0205CH11231. 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 DMR-1210167 and NRF through Global Research Laboratory project of Korea.

Author 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.

Additional information

Supplementary Information accompanies this paper at http://www.nature.com/naturecommunications

Web End =http://www.nature.com/ http://www.nature.com/naturecommunications

Web End =naturecommunications

Competing nancial interests: The authors declare no competing nancial interests.

Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/

Web End =http://npg.nature.com/ http://npg.nature.com/reprintsandpermissions/

Web End =reprintsandpermissions/

How to cite this article: Chen, G. et al. Unlocking Bloch-type chirality in ultrathin magnets through uniaxial strain. Nat. Commun. 6:6598 doi: 10.1038/ncomms7598 (2015).

NATURE COMMUNICATIONS | 6:6598 | DOI: 10.1038/ncomms7598 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 7

& 2015 Macmillan Publishers Limited. All rights reserved.