REPORT◥

MAGNETISM

Chirally coupled nanomagnetsZhaochu Luo1,2*, Trong Phuong Dao1,2,3, Aleš Hrabec1,2,3,Jaianth Vijayakumar2, Armin Kleibert2, Manuel Baumgartner3, Eugenie Kirk1,2,Jizhai Cui1,2, Tatiana Savchenko2, Gunasheel Krishnaswamy3,Laura J. Heyderman1,2*, Pietro Gambardella3*

Magnetically coupled nanomagnets have multiple applications in nonvolatile memories,logic gates, and sensors. The most effective couplings have been found to occur betweenthe magnetic layers in a vertical stack. We achieved strong coupling of laterally adjacentnanomagnets using the interfacial Dzyaloshinskii-Moriya interaction. This coupling ismediated by chiral domain walls between out-of-plane and in-plane magnetic regions anddominates the behavior of nanomagnets below a critical size. We used this concept torealize lateral exchange bias, field-free current-induced switching between multistatemagnetic configurations as well as synthetic antiferromagnets, skyrmions, and artificialspin ices covering a broad range of length scales and topologies. Our work provides aplatform to design arrays of correlated nanomagnets and to achieve all-electric control ofplanar logic gates and memory devices.

Engineering the coupling between magneticelements is central to fundamental advancesin magnetism and spintronics. The dis-covery of interlayer coupling between twoferromagnetic layers separated by a non-

magnetic spacer, caused by the Ruderman-Kittel-Kasuya-Yosida interaction, has led to therealization of synthetic antiferromagnets (1–3)and the discovery of giant magnetoresistance(4, 5). Similarly, the exchange bias between fer-romagnetic and antiferromagnetic layers (6) iswidely used to stabilize the magnetic referencelayer in spin valves and magnetic tunnel junc-tions (7, 8). These couplings are highly effectivein vertically stacked structures. However, inorder to realize two-dimensional (2D) networksof nanoscale magnetic elements, it is desirableto engineer effective lateral couplings in a con-trollable way. So far, this has been achieved byexploiting long-range dipolar interactions (9–12).However, the dipolar interaction is nonlocal andscales inversely with the volume of the magnets,which limits its use in applications that involvenanometer-sized structures and thin films.Here, we demonstrate an alternative mech-

anism with which to control the lateral couplingbetween adjacent magnetic nanostructures. Ourconcept is based on the interfacial Dzyaloshinskii-Moriya interaction (DMI),HDM= –Dij · (mi ×mj),which embodies the antisymmetric exchangecoupling between two neighboring magneticmoments mi and mj induced by the spin-orbit

interaction in a structurally asymmetric en-vironment (13, 14). In contrast to the symmetricexchange interaction, which favors a parallelalignment of the magnetic moments, the DMI

favors an orthogonal orientation of mi relativeto mj, with a fixed chirality given by the di-rection of the Dzyaloshinskii-vector Dij. At theinterface between amagnetic layer and a heavymetal, the DMI can be strong enough to inducethe formation of noncollinear spin textures suchas spin spirals (15) and skyrmions (16, 17). Often,however, the competition between the DMI, theexchange interaction, and themagnetic anisotropyin thin films with out-of-plane (OOP) magnetiza-tion results in the formation of chiral domainwalls separating large regions with uniform upor down magnetic moments (18, 19). In thesesystems, the DMI also plays a crucial role indetermining the direction and speed of current-induced domain wall motion (20–23). We ex-ploited the DMI to control the lateral couplingbetween OOP and in-plane (IP) magnetic struc-tures (Fig. 1A) and demonstrate distinct phe-nomena associated with such chirally couplednanomagnets.We fabricated arrays of nanomagnets that

combine strong DMI with regions exhibiting IPand OOP magnetic anisotropy. The arrays werefabricated from Pt (6 nm)/Co (1.6 nm)/AlOx tri-layers patterned by means of electron beamlithography and Ar ion milling (24). Here, AlOx

refers to an Al layer that is oxidized in anoxygen plasma. Such magnetic trilayers have alarge DMI (25, 26) as well as tunable magneticanisotropy, which is IP or OOP depending on

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1Laboratory for Mesoscopic Systems, Department ofMaterials, ETH Zurich, 8093 Zurich, Switzerland. 2PaulScherrer Institut, 5232 Villigen PSI, Switzerland. 3Laboratoryfor Magnetism and Interface Physics, Department ofMaterials, ETH Zurich, 8093 Zurich, Switzerland.*Corresponding author. Email: zhaochu.luo@psi.ch (Z.L.);laura.heyderman@psi.ch (L.J.H.); pietro.gambardella@mat.ethz.ch (P.G.).

OOP regionChiral domain wall

IP region

OO eg o

M1

M2

D12

M1

M2

D12Pt

Co

Pt

Co

HDM = D12 (m1 m2)

Magnetic field

16°

X-rays V

Hext

A

B C

D

500 nm 500 nm

500 nm

Fig. 1. Chiral coupling between OOP and IP magnets. (A) Schematics of the coupledmagnetization states favored by the DMI in adjacent OOP and IP regions of a Pt/Co/AlOx trilayer.(B) Scanning electron micrograph of coupled OOP-IP elements fabricated by means of electron-beam lithography. Red and blue colors indicate regions with OOP and IP magnetization, respectively.(C) X-PEEM image with bright and dark magnetic contrast in the OOP regions corresponding to ↓and ↑ magnetization, respectively. The dark gray contrast in the IP regions corresponds to →magnetization, determined by taking images at different sample orientations with respect to thex-ray direction (24). The direction of the incident x-rays and the IP magnetic field used forprealignment are indicated with arrows. (D) Schematic of an OOP-IP element fabricated on top of aHall cross for electrical measurements.

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the degree of oxidation of the Co/Al interface(fig. S1) (27), and are widely used as a modelsystem for the study of current-induced switch-ing and domain wall motion in spintronic de-vices (28, 29). A scanning electron micrographof an array of Co elements, each consisting ofadjacent IP and OOP regions, is shown in Fig. 1B.The size and shape of the IP magnetized regionis controlled by covering the Al with a thin Taprotective layer to prevent oxidation during theoxygen plasma process.X-ray photoemission electron microscopy

(X-PEEM) images provide first evidence thatthe magnetizations of the OOP and IP regionsare coupled and that this coupling is chiral. If themagnetization of the IP region points to the right(“→”), after saturation with an IP magnetic field,OOP regions on the left and right of the IP regionpoint down (“↓”) and up (“↑”), respectively (Fig.1C). The relative orientation between OOP andIP parts is thus either ↓→ or→↑, which agreeswith the left-handed chirality expected from thenegative sign of the DMI in Pt/Co/AlOx (25). Asexpected, reversing the direction of the IP fieldleads to the observation of ↑← and←↓ coupling(fig. S8).To further analyze the chiral coupling be-

tween OOP and IP regions, we measured the

anomalous Hall resistance of OOP-IP Co/AlOx

elements fabricated on top of a Pt Hall cross(Fig. 1D) as a function of external magnetic field.Because the anomalous Hall effect is propor-tional to the z-component of the magnetization,these measurements reflect the state of the OOPregion, with the IPmagnetization preset by an IPfield applied parallel to y. For an external fieldHext//z, we found that the hysteresis loop of theOOP region shifts by more than 200 Oe towardpositive or negative fields for right or left orienta-tion of the IP magnetization, respectively (Fig.2A). These opposite shifts indicate that the DMIstrongly favors the ↓→ and ↑← configurations,resulting in an effective exchange bias fieldHbias,whose sign can be tunedby presetting the orienta-tion of the IP magnetization. Hence, the chiralcoupling demonstrated here provides a methodwith which to realize large hysteresis bias inlateral structures.When the external field is applied IP, Hext//y,

we additionally find that the OOP region switchesdirection simultaneouslywith the IP region (Fig. 2,B and C, and fig. S3). Starting from the DMI-stable↑← configuration, the OOP region switches fromup to down as the IP field switches the IP mag-netization from ← to →, thus avoiding the un-favorable ↑→ configuration. This observation

implies that the energy associatedwith the chiralcoupling is larger than the energy of the barrierto switch the OOP region, so that the directionof the IP magnetization effectively controlsthe OOP magnetization. If the applied magneticfield is tilted in the y-z plane, the field can alsoinduce the switching of the OOP region, whichthen biases the IP magnetization. Therefore,depending on the coercivity of the OOP and IPregions and on the tilt angle q of the externalfield, we observed switching between differentmultistate magnetic configurations (Fig. 2B). Ifboth the OOP and IP field components of theapplied magnetic field assisted the DMI-favoredconfigurations, we observed bistable switch-ing between the ↓→ and ↑← states (type I be-havior, similar toHext//y). By contrast, if the twofield components preferred theDMI-unfavored ↓←and ↑→ configurations, we observed switchingbetween all the four possible combinations ofstates, with the sequence determined by the rela-tive amplitude of the IP and OOP magnetic fieldcomponents (type II and type III behavior).The switching of the OOP-IP elements can be

modeled with two coupled OOP and IP macro-spins (24), where the energy of each configura-tion (E↑→, E↓→, E↑←, and E↓←) is given by thesum of the Zeeman energy and the energy

Luo et al., Science 363, 1435–1439 (2019) 29 March 2019 2 of 5

-600 -300 0 300 600

Rxy

Hz (Oe)

Hbias=+230 Oe

5 m

Hbias=-230 Oe

=

Type III

Type II

Type I

Rxy

-1000 -500 0 500 1000H (Oe)

20 m

0 100 2000

2

4

w (nm)

Single domainEnergy scaling

HK (k

Oe)

Type III

Type II

Type I

2 m

A B C

D

E

-600 -300 0 300 600

-300

0

300

Hy (Oe)

Hz (O

e)

H*z+

H*z-

H*y

10º20º30º40º50º60º65º

70º

75º

80º

90º

100º110º120º130º140º150º160º170º

Fig. 2. Exchange bias and field-induced switching of chirally coupledOOP-IP elements. (A) OOP magnetization as a function of Hz for the OOP-IP element shown in Fig. 1D for the magnetization in the IP region pointing→ and ←. The hysteretic jumps of the anomalous Hall resistance Rxy

indicate switching of the OOP magnetization. The linear increase of Rxy

with field is caused by the gradual tilt of the IP magnetization toward the zaxis. (B) Magnetic hysteresis loops for a magnetic field tilted in the y-zplane for various tilt angles q. (C) Multistate switching configurations III, II,and I corresponding to the hysteresis loops for q = 30°, 70°, and 140° shown

in (B). (D) Critical switching field H*z+ (black triangles), H*z– (red squares),and H*y (blue circles) of the OOP region. The lines are fits according tothe macrospin model described in the text, with errors indicated by theshaded regions. (E) Boundaries of the single-domain behavior (blackline) and chiral-coupling (red line) as a function of the OOP magneticanisotropy field HK and element size w. The red and black points aredetermined from micromagnetic simulations. The shaded area indicatesthe range of parameters for which chiral coupling determines themagnetic configuration.

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associated with the DMI between the magneticmoments of the OOP and IP regions, MOOP andMIP: E = –(MOOP + MIP) · Hext – D · (MOOP ×MIP). Assuming that the OOP and IP magnetiza-tion switch whenever the energy difference be-tween two configurations is larger than theenergy barrier for magnetization reversal DEOOPand DEIP, respectively, the critical switchingfields for the OOP and IP regions are given by

H*z± = (DEOOP ± EDM)/2MOOP and H*y = (DEIP +EDM)/2MIP, respectively, where EDM is the chiralcoupling energy. As expected from the model,the switching fields of theOOP regiondeterminedexperimentally lie on horizontal and vertical linesof anHz-Hy diagram (Fig. 2D). We therefore iden-tify these lines as the critical fields H*z± and H*y.From these data, we determined the value of EDM

= 3.5 ± 0.3 eV and the DMI constant D = –0.9 ±

0.1 mJ/m2, which is in good agreement withprevious estimates of the DMI in Pt/Co/AlOx

(25).Because EDM is proportional to the length lx of

the quasi-1D domain wall separating the OOPand IP regions, whereas DEOOP is proportional tothe area lxw, where w is the width of the OOPregion (Fig. 2E, inset), the ratioEDM/DEOOPº 1/wincreases when decreasing the dimensions of the

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Magnetic field

X-rays

16°

-800 -400 0 400 800

Rxy

Hz (Oe)

2 m

AFM

FM

FM

-200 -100 0 100 200-600

-300

0

300

600Hz (O

e)

Hy (Oe)

100 200 3000

20

40

60

80

100

(%)

(nm)

A B

F

I

C

E

G D

H

2

3

4

5

6

1

2

34

6 1

5

2

3

4

5

6

1

Fig. 3. Lateral synthetic antiferromagnets based on chiral coupling.(A) Scanning electron micrograph of coupled OOP-IP-OOP elements and(B) corresponding X-PEEM image. The stable magnetic configuration ofthe OOP-IP-OOP element is ↓ → ↑ after prealignment of the IP regionwith an IP field pointing →. (C) Magnetic hysteresis of an OOP-IP-OOPelement as a function of Hz for two opposite orientations of theIP spacer. The six possible magnetic configurations are shown. (D) Hz

versus Hy phase diagram of the OOP-IP-OOP element used for (C). The redand blue dots are the critical fields delimiting the antiferromagnetic andferromagnetic alignments, respectively, of the two OOP regions. In thewhite shaded area, the configuration depends on the history of themagnetization. (E) Probability of correlated switching resulting in anti-ferromagnetically aligned OOP regions as a function of the length ly of theIP spacer. Saturating fields are applied, first –Hy and then –Hz, beforeapplying a field Hz and measuring the magnetic state of the element. Each

data point is averaged over 41 different elements. (Insets) MFM imagesof OOP-IP-OOP elements with ly = 50 and 300 nm. The bright and darkMFM contrast corresponds to ↑ and ↓ magnetizations, respectively.(F) Scanning electron micrograph and X-PEEM image of a chain structureincluding five OOP regions, which align antiparallel after a field has beenapplied perpendicular to the chain (parallel to the lowest IP region).(G) MFM images of synthetic skyrmions with one, two, four, and five IPrings after saturation with a magnetic field –Hz. (H) MFM image of anartificial spin system consisting of OOP elements on a square lattice actingas Ising-like moments coupled by means of IP spacers after saturatingwith a magnetic field –Hz. Antiferromagnetic domains are shaded in greenand purple. (I) MFM image of an artificial kagome spin system aftersaturating with a magnetic field –Hz. The green and purple arrows indicatethe orientation of the magnetization of the OOP vertices. All X-PEEMand MFM images have been recorded at zero field. Scale bars, 500 nm.

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element.Hence, below a critical size, themagneticbehavior of the OOP region is predominantlydetermined by the chiral coupling. The boun-daries that delimit this region are defined byEDM/DEOOP >1 and the single-domain conditionw < wSDº

ffiffiffiffiffiffiffi

HKp

, where wSD and HK are thecritical single-domain dimension and the OOPeffective anisotropy field, respectively. Theseboundaries are shown in Fig. 2E together withthe results of micromagnetic simulations thatprovide additional support to our model (fig.S10) (24). A similar reasoning can be applied tomodel the influence of the OOP magnetizationon the IP magnetization, taking into accountthat the IP anisotropy is shape-dependent. Thefavorable scaling of EDM/DEOOP and EDM/DEIP

toward reduced dimensions means that chiralcoupling can be exploited to control the mag-netization of small systems. In our case, thethermal stability factor is EDM/kBT ≈ 140 atroom temperature, where kB is the Boltzmannconstant and T is the temperature, so the widthw of the patterned element can be reduced downto 35 nm while retaining a thermal stabilitylarger than 40 kBT.We now illustrate possible applications of

chiral coupling. First, we discuss the fabricationof tailor-made laterally coupled synthetic anti-ferromagnetic structures, skyrmions, and artificialspin systems. As a starting point, we consideredtwo separate OOP regions that are coupled byan IP spacer. X-PEEM imaging revealed that thestatic orientation of two OOP elements con-nected by an IP spacer is antiparallel and that, ifthe IP magnetization is preset with a magneticfield to the right, the OOP-IP-OOPmagnetizationis ↓→↑ (Fig. 3, A and B), which is in agreementwith the left-handed chirality imposed by theDMI. The behavior of these structures was char-acterized by their anomalous Hall resistance inan applied field (Fig. 3C). To differentiate the twoOOP regions, one side was made smaller thanthe other. For Hext//z, the flat curve between the

two shifted hysteresis loops in Fig. 3C indicatesthat the OOP regions are coupled antiparallel atlow field, whereas the parallel orientation canonly be enforced by magnetic fields larger than400 to 600 Oe. The ↑↓ and ↓↑ antiferromagneticstates at zero magnetic field were set by pre-aligning the IP magnetization to be ← or →,respectively. The antiferromagnetic state atzero field was achieved independently of theinitial orientation and amplitude of the field.Similar to the OOP-IP element, all the possiblecombinations of states 1 to 6 shown in Fig. 3Ccan be reached by changing the direction of thefield in the y-z plane (Fig. 3D).As long as the IP spacer retains a mono-

domain state, the two OOP elements effectivelyinteract with each other. Thus, reversing themagnetization of one OOP element with a fieldHext//z causes the reversal of the IP spacer andsubsequently the reversal of the other OOP ele-ment. In addition, magnetic force microscopy(MFM) measurements (Fig. 3E) demonstratethat the effective antiferromagnetic couplingbetween the OOP elements is a function of theIP spacer length ly, leading to correlated reversalevents for ly < 300 nm and a nearly 100% cor-related switching probability for ly ≤ 50 nm.These measurements were performed on struc-tures that include two OOP elements with dif-ferent sizes, so that the largest element switcheswith, and the smallest element switches against,the external fieldHz. OOP-IP-OOP structures withly > 1 mm (fig. S11A) and curvilinear geometries(fig. S11C) also have alternate up- and down-magnetized OOP regions. However, in such cases,the IP regionsmight assume amultidomain con-figuration and can effectively be replaced withtwo separate IP connectors. These two shortsections can then be used to control the OOPmagnetization in a nonlocal way. For all thesestructures, we found that the effective antifer-romagnetic interaction mediated by chiral cou-pling is orders of magnitude stronger than the

dipolar coupling between magnets of the samesize and separation (fig. S6).Coupled OOP and IP elements can be further

used as building blocks of more complex spinsystems that have a well-defined symmetry andtopology. In Fig. 3F, a linear chain that consistsof five OOP and IP regions is shown with alter-nating OOPmagneticmoments. Such a structurecan be used to propagate magnetic informationfrom one end of the chain to the other. SyntheticNéel skyrmions can also be realized by couplingconcentric OOP rings with 50-nm-wide circularIP spacers (Fig. 3G). By patterning more IP rings,we can create skyrmionic structures that do nothave a counterpart in unpatterned thin films, witha topological charge that alternates between ±1and 0 (so-called skyrmioniums or target skyrm-ions) depending on the number of rings. Suchstructures might be of interest to study high-frequency excitations of skyrmions as well as forthe generation and transmission of spinwaves inmagnonic crystals. Last, strongly coupled artifi-cial spin systems, with Ising-like OOP elementsconnected by IP elements, can be created. Exam-ples with the OOP elements arranged on a squareand a kagome lattice are given in Fig. 3, H and I,respectively. The correlated Ising-like momentslead to the spontaneous formation of domainswith antiferromagnetic ordering for the squarelattice and frustrated behavior for the kagomelattice with highly degenerate low energy states.Another interesting application concerns the

current-induced switching ofmagnetic elements,which is a basic requirement for the all-electricaloperation of integrated nonvolatile magneticmemory and logic devices. Our measurementsshow that the OOP and IP regions can be sim-ultaneously switched by an electric current flowingin the Pt/Co layer, orthogonal to the IP magne-tization (Fig. 4). The switching is caused by thecurrent-induced spin-orbit torques that originatefrom the spin Hall and interface effects found inferromagnets adjacent to heavy metal layers

Luo et al., Science 363, 1435–1439 (2019) 29 March 2019 4 of 5

Fig. 4. Field-free current-induced magneti-zation switching of OOP-IP elements.(A) Schematic of the current-inducedswitching of an OOP-IP element. The devicegeometry is shown in Fig. 1D; the area of theOOP region is about 120 by 120 nm. (B)Magnetization loops as a function of appliedcurrent for different values of Hy. The mea-surements are performed by injecting 50-ms-long current pulses and measuring theanomalous Hall resistance Rxy after eachpulse. Changes in Rxy indicate switching ofthe OOP region. The switching at zero field issymmetric with respect to the current,whereas Hy > 0 helps to switch the OOP region↓ and decrease the negative switching current,and Hy < 0 helps to switch the OOP region ↑and decrease the positive switching current.(C) Critical switching current ISW as a functionof Hy. The range of parameters leading todeterministic switching between ↑ and ↓states is shaded in red.

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(28–31). Such electrical switching cannot be im-plemented in dipolar-coupledmagnetic elements,which are usually too thick to be manipulated byspin torques. Moreover, the chiral coupling en-ables entirely field-free switching of the OOPmagnetization, which is difficult to achieve inisolated OOP elements (32–36). In Fig. 4B, weshow that the OOP region switches determi-nistically in zero field for a current ISW = 5 mAinjected parallel to x. Applying a field Hext//±yalong the IP easy axis leads to a decrease or in-crease of the switching current, which is propor-tional toHext (Fig. 4C). We interpret this behavioras the field assisting or counteracting the reversalof the IP magnetization that is driven by thedamping-like component of the spin-orbit torque.This suggests that the current drives the switch-ing of the IP magnetization (30, 37) and that thereversal of the OOP region is a consequence ofthe chiral coupling. Because the current densitythat is required to switch the IPmagnetization istypically lower than that required by the OOPmagnetization (fig. S5C) (37, 38), OOP-IP coupledstructures offer an efficient and scalable ap-proach to field-free switching ofmagnetic devices,which is furthermore compatible with the ma-terials and processes currently used in the fab-rication of magnetic memories.The coupled OOP-IP building blocks dem-

onstrated here can be used to fabricate syn-thetic antiferromagnets with linear and curvedgeometries, synthetic skyrmions, and artifi-cial spin ices. Indeed, the spontaneous forma-tion of the ground state after magnetizationin an athermal artificial spin ice network re-flects the strong nearest-neighbor interactionsin these systems, which is likely to lead to in-teresting frustrated behavior. Furthermore,the multiplicity of magnetic states that can bestabilized in OOP-IP elements combined withall-electric synchronous switching opens a routefor the realization of nanomagnet logic gatesand memory devices as well as for the designof electrically reconfigurable magnonic crys-

tals, which can be used to manipulate the prop-agation of spin waves in synthetic media orprovide a controlled modulation of the mag-netic stray field in hybrid materials, such asferromagnet/semiconductor and ferromagnet/superconductor heterostructures.

REFERENCES AND NOTES

1. P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky, H. Sowers,Phys. Rev. Lett. 57, 2442–2445 (1986).

2. S. S. Parkin, N. More, K. P. Roche, Phys. Rev. Lett. 64,2304–2307 (1990).

3. R. A. Duine, K. J. Lee, S. S. P. Parkin, M. D. Stiles, Nat. Phys.14, 217–219 (2018).

4. M. N. Baibich et al., Phys. Rev. Lett. 61, 2472–2475 (1988).5. G. Binasch, P. Grünberg, F. Saurenbach, W. Zinn, Phys. Rev. B

Condens. Matter 39, 4828–4830 (1989).6. J. Nogués, I. K. Schuller, J. Magn. Magn. Mater. 192, 203–232

(1999).7. B. Dieny et al., Phys. Rev. B Condens. Matter 43, 1297–1300

(1991).8. S. S. Parkin et al., J. Appl. Phys. 85, 5828–5833 (1999).9. R. P. Cowburn, M. E. Welland, Science 287, 1466–1468

(2000).10. A. Imre et al., Science 311, 205–208 (2006).11. R. F. Wang et al., Nature 439, 303–306 (2006).12. L. J. Heyderman, R. L. Stamps, J. Phys. Condens. Matter 25,

363201 (2013).13. I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241–255 (1958).14. T. Moriya, Phys. Rev. 120, 91–98 (1960).15. M. Bode et al., Nature 447, 190–193 (2007).16. S. Heinze et al., Nat. Phys. 7, 713–718 (2011).17. A. Fert, N. Reyren, V. Cros, Nat. Rev. Mater. 2, 17031

(2017).18. M. Heide, G. Bihlmayer, S. Blügel, Phys. Rev. B 78, 140403

(2008).19. J. P. Tetienne et al., Nat. Commun. 6, 6733 (2015).20. A. Thiaville, S. Rohart, E. Jue, V. Cros, A. Fert, Europhys. Lett.

100, 57002 (2012).21. S. Emori, U. Bauer, S. M. Ahn, E. Martinez, G. S. Beach,

Nat. Mater. 12, 611–616 (2013).22. K. S. Ryu, L. Thomas, S. H. Yang, S. Parkin, Nat. Nanotechnol.

8, 527–533 (2013).23. F. Ummelen, H. Swagten, B. Koopmans, Sci. Rep. 7, 833

(2017).24. Materials and methods are available as supplementary

materials.25. M. Belmeguenai et al., Phys. Rev. B 91, 180405 (2015).26. H. Yang, A. Thiaville, S. Rohart, A. Fert, M. Chshiev,

Phys. Rev. Lett. 115, 267210 (2015).27. S. Monso et al., Appl. Phys. Lett. 80, 4157–4159 (2002).28. I. M. Miron et al., Nature 476, 189–193 (2011).

29. M. Baumgartner et al., Nat. Nanotechnol. 12, 980–986(2017).

30. L. Liu et al., Science 336, 555–558 (2012).31. K. Garello et al., Nat. Nanotechnol. 8, 587–593 (2013).32. G. Yu et al., Nat. Nanotechnol. 9, 548–554 (2014).33. S. Fukami, C. Zhang, S. DuttaGupta, A. Kurenkov, H. Ohno,

Nat. Mater. 15, 535–541 (2016).34. Y. W. Oh et al., Nat. Nanotechnol. 11, 878–884 (2016).35. A. van den Brink et al., Nat. Commun. 7, 10854 (2016).36. K. Cai et al., Nat. Mater. 16, 712–716 (2017).37. S. Fukami, T. Anekawa, C. Zhang, H. Ohno, Nat. Nanotechnol.

11, 621–625 (2016).38. K. S. Lee, S. W. Lee, B. C. Min, K. J. Lee, Appl. Phys. Lett. 102,

112410 (2013).39. Z. Luo et al., Data from: Chirally coupled nanomagnets,

Zenodo (2019).40. A. Vansteenkiste et al., AIP Adv. 4, 107133 (2014).

ACKNOWLEDGMENTS

We thank A. Weber, H. Arava, and V. Guzenko for technical supportwith sample fabrication. Funding: This work was supportedby the Swiss National Science Foundation through grants 200021-153540, 200020-172775, and 200021-160186. J.C. has receivedfunding from the European Union’s Horizon 2020 research andinnovation program under the Marie Skłodowska-Curie grantagreement 701647. Part of this work was carried out at theSurface/Interface: Microscopy beamline of the Swiss Light Source.Author contributions: This work is a partnership that was ledjointly and equally by the L.J.H. and P.G. groups. Z.L., T.P.D., L.J.H.,and P.G. conceived the work and designed the experiments;Z.L. fabricated the samples and performed the electricalmeasurements with the support of T.P.D. and E.K.; Z.L. analyzedand interpreted the data from the electrical measurements withthe help of T.P.D. and P.G.; Z.L., J.V., A.K., T.P.D., J.C., M.B.,T.S., and G.K. performed the X-PEEM measurements, which wereinterpreted by Z.L., J.V., and A.K.; A.H. performed themicromagnetic simulations; and Z.L., P.G., and L.J.H. workedon the manuscript together. All authors contributed to thediscussion of the results and the manuscript revision. Competinginterests: The authors declare no competing interests. Dataand materials availability: All data used in this Report hasbeen deposited in the Zenodo public database (39). Themicromagnetic simulations were performed by using the opensource code MuMax3 (40).

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/363/6434/1435/suppl/DC1Materials and MethodsSupplementary TextFigs. S1 to S15References (41, 42)

17 July 2018; accepted 26 February 201910.1126/science.aau7913

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Chirally coupled nanomagnets

Jizhai Cui, Tatiana Savchenko, Gunasheel Krishnaswamy, Laura J. Heyderman and Pietro GambardellaZhaochu Luo, Trong Phuong Dao, Ales Hrabec, Jaianth Vijayakumar, Armin Kleibert, Manuel Baumgartner, Eugenie Kirk,

DOI: 10.1126/science.aau7913 (6434), 1435-1439.363Science 

, this issue p. 1435Scienceable to engineer more-complex magnetic structures such as skyrmions and frustrated magnets.orientation of the magnetization in adjacent domains. Using the coupling between the domains, the researchers wereinteracted laterally through the so-called Dzyaloshinskii-Moriya interaction, which determined the relative sign and

trilayers that had alternating in-plane and out-of-plane magnetizations. The regionsxmagnetic domains in Pt/Co/AlO engineeredet al.Artificial magnetic structures can offer a variety of functionalities in spintronics devices. Luo

Magnetic building blocks in two dimensions

ARTICLE TOOLS http://science.sciencemag.org/content/363/6434/1435

MATERIALSSUPPLEMENTARY http://science.sciencemag.org/content/suppl/2019/03/27/363.6434.1435.DC1

REFERENCES

http://science.sciencemag.org/content/363/6434/1435#BIBLThis article cites 41 articles, 3 of which you can access for free

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