Emergence of robust 2D skyrmions in SrRuO3 ultrathin film without the capping layer

Byungmin Sohn,1, 2 Bongju Kim,1, 2, ∗ Se Young Park,1, 2 Hwan Young Choi,3 Jae Young Moon,3 Taeyang Choi,4

Young Jai Choi,3 Tae Won Noh,1, 2 Hua Zhou,5 Seo Hyoung Chang,4, † Jung Hoon Han,6, ‡ and Changyoung Kim1, 2, §

1Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea2Center for Correlated Electron Systems, Institute for Basic Science, Seoul 08826, Korea

3Department of Physics, Yonsei University, Seoul 03722, Korea4Department of Physics, Chung-Ang University, Seoul 06974, Korea

5Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA6Department of Physics, Sungkyunkwan University, Suwon 16419, Korea

(Dated: October 4, 2018)

Magnetic skyrmions have fast evolved from a novelty, as a realization of topologically protectedstructure with particle-like character, into a promising platform for new types of magnetic storage(See refs. 1–5 for recent reviews). Significant engineering progress was achieved with the synthe-sis of compounds hosting room-temperature skyrmions in magnetic heterostructures6–11, with theinterfacial Dzyaloshinskii-Moriya interactions (DMI) conducive to the skyrmion formation. Herewe report findings of ultrathin skyrmion formation in a few layers of SrRuO3 grown on SrTiO3

substrate without the heavy-metal capping layer. Measurement of the topological Hall effect (THE)reveals a robust stability of skyrmions in this platform, judging from the high value of the criticalfield ∼ 1.57 Tesla (T) at low temperature. THE survives as the field is tilted by as much as 85◦

at 10 Kelvin, with the in-plane magnetic field reaching up to 6.5 T. Coherent Bragg Rod Analysis,or COBRA for short, on the same film proves the rumpling of the Ru-O plane to be the sourceof inversion symmetry breaking and DMI. First-principles calculations based on the structure ob-tained from COBRA find significant magnetic anisotropy in the SrRuO3 film to be the main sourceof skyrmion robustness. These features promise a few-layer SRO to be an important new platformfor skyrmionics, without the necessity of introducing the capping layer6–11 to boost the spin-orbitcoupling strength artificially.

Starting with the first experimental observation of theskymion lattice in the bulk crystal of MnSi12 and thethin-film chiral magnet Fe1−xCoxSi13, numerous sight-ings of skyrmions both as a collective lattice or in amor-phous forms have been reported. Interesting recent direc-tions in the efforts are the synthesis of various magneticmultilayer structures in which the magnetic crystal itselfis devoid of inversion symmetry breaking and yet its engi-neered interfacial or multilayer structure induces it exter-nally, resulting in the so-called interfacial DMI that playsa pivotal role in stabilizing the Neel-type skyrmions14.An important breakthrough in this regard is the works ofrefs. 15 and 16, which reported an evidence of skyrmionformation through the observation of THE in the EuOthin film and the SrRuO3-SrIrO3 heterostructure. Thework was immediately taken up by other groups, result-ing in the creation of room-temperature skyrmions inthe Ir/Fe/Co/Pt multilayer10. The key underlying de-sign strategy has been the heavy-metal capping layer thatpurportedly boosts the spin-orbit coupling necessary forthe DMI. Such structures are inevitably quite compli-cated, however, due to the participation of many atomsand geometrical factors, and could be detrimental to re-alization of actual application10,17.

SrRuO3 (SRO), a well-known and heavily studied itin-erant ferromagnet with many exotic properties, was re-cently shown to be a platform for skyrmion formationas well16. However, it was tacitly believed that thespin-orbit coupling in SRO would be too small to haveskyrmions and that a capping layer with an heavier ele-

ment was necessary. As we show now, even the simple,few-layer magnetic structure of SRO without the cap-ping layer proves to be an adequate platform for theskyrmion formation. The idea is that the intrinsic fer-romagnetism of the metallic SRO, together with the in-terfacial DMI endowed by the interface to the vacuum,might be sufficient to stabilize the skyrmions. Unlike theearlier demonstration of atomic-scale skyrmions by the Featomic layer deposited on the Ir substrate18, our ultra-thin SRO film maintains the conductive property, mak-ing it possible to utilize THE as a probe of the skyrmionformation. Figure 1a illustrates the schematic geome-try of our electronic transport setup and the phase di-agram in the plane of (µ0H‖, µ0H⊥) at 10 K for the 4unit-cell (u.c.) SRO film, as deduced from the Hall ef-fect measurement data. The two components refer to thein-plane (µ0H‖) and out-of-plane (µ0H⊥) magnetic field,respectively. As one can see, there exists a marked in-crease in the magnetic field window of stability for theskyrmions as the tilt angle θ = tan−1(H‖/H⊥) grows. Itwill be carefully shown that several factors - extreme twodimensionality of the film, magnetic anisotropy, break-ing of inversion symmetry through rumpling of the Ru-Oplane - contribute serendipitously to the robustness ofskyrmions both in terms of its stability under high mag-netic field and under the tilting, holding the promise thatthis simple device can be a practical new platform forskyrmionics.

The Hall resistivity in the SRO thin film consists ofthree terms, ρxy = ρOHE + ρAHE + ρTHE, namely the or-

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FIG. 1. Phase diagram of 4 u.c. SRO ultrathin film under the field tilt. (a) Phase diagram in the plane ofparallel (µ0H‖) and perpendicular (µ0H⊥) components of the external magnetic field. Color plots represent the measured Hallresistivity values at 10 K with the ordinary Hall effect contribution subtracted. Assignments of the phases are ferromagnetic(FM), Skyrmion (Sk), and spin-polarized (SP), respectively. The low-field phase is ferromagnetic (see the SupplementaryInformation (SI) for experimental indication of ferromagnetism in 4 u.c. SRO). The spin-polarized phase is induced by theexternal magnetic field. (Inset) Schematics of our experiment with the tilt angle indicated by θ. (b) Columnar triangular latticeof skyrmions realized in sufficiently thick magnetic films. (c) Two-dimensional skyrmions realized in ultrathin film geometry.

dinary Hall effect (OHE), anomalous Hall effect (AHE)and THE. The OHE contribution is subtracted in all thedata shown in the paper. The Hall resistivity measuredat various temperatures for 4-7 u.c. is shown in Fig.2a for external magnetic field applied perpendicular tothe film. As illustrated in Fig. 2b, THE exists as clearhumps, and disappears near the coercive field where AHEundergoes a sign change. Both AHE and THE are clearlyvisible for 4 and 5 u.c. SRO, whereas only AHE occursin the case of 6 and 7 u.c. structures. As the temper-ature decreases in 4 and 5 u.c. SRO, THE is startingto appear together with AHE below the Curie tempera-ture Tc, which is determined from the differentiation ofthe temperature-dependent ρxx(T ) (see the supplemen-tary information, SI, for the method). At the lowest mea-sured temperature of 2 K, THE persists over the 1.6−2.6T range, showing that the skyrmion phase in SRO thinfilm is extremely robust compared to other materials thathost skyrmions over much weaker fields13,19.

In order to see if the hump feature is indeed from THE,

we look for a distinct feature of the skyrmion phase,that is, the reduction in the Hall effect in the movingskyrmion phase. When skyrmions get de-pinned and setin motion by the electric current, conduction electronssee the moving skyrmion as a magnetic flux in motion,and experience the transverse voltage drop according toFaraday’s law. The result is the reduction in the Hall re-sistivity ρxy

1,4,20,21. We increased the driving currentby more than an order of magnitude and observed agradual decrease in THE signal as shown in Fig. 2c, asexpected in the moving skyrmion phase. The observedreduction in THE was sudden in the case of skyrmionlattice20, implying the collective de-pinning of the en-tire skyrmion lattice above the threshold current20. Hereit is more gradual, without an obvious signature of thede-pinning transition. In this regard, we note the re-cent magnetic force microscopy image of skyrmions inthe Ir/Fe/Co/Pt multilayer revealing an amorphous dis-tribution of skyrmions10, presumably due to pinning byrandom potential. In such situations skyrmions in shal-

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FIG. 2. THE in ultrathin SRO film under the perpendicular external magnetic field. (a) Hall effect measurementas a function of the perpendicular field µ0H at various temperatures for 4 - 7 u.c. SRO after subtraction of the ordinary Halleffect. The red (blue) arrow indicates the positive (negative) sweep direction of the external magnetic field. Both AHE andTHE are observable on 4, 5 and 6 u.c. SRO, while only AHE is observed for 7 u.c. SRO. (See SI for enlarged view of theHall data in the 6 u.c. SRO) (b) An enlarged plot of the Hall effect measured for 5 u.c. SRO at 30 K. The curves containcontributions from both AHE and THE, while the humps are due to the THE16. (c) Hall effect measurement on 4 u.c. SROat 10 K depending on electric current. THE is decreasing as the current increases while the AHE part remains constant, in amanifestation of the skyrmion Hall effect20. (d) Phase diagram of 5 u.c. SRO in the (T, µ0H) plane. Color plots represent themeasured (anomalous + topological) Hall resistivity values.

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FIG. 3. Tilt-angle dependence of THE for 4 u.c. SRO. (a) Schematics of the angle-dependent Hall effect measurement.External magnetic field is tilted at an angle θ from the film normal. (b) Typical Hall resistivity data (here shown for θ = 0)under the field sweep. Hc1 is defined by the intersection of two extrapolations shown as black dotted lines. Hc2 is definedas the field value at which the Hall resistivity values under the positive and negative sweeps coincide. ∆(µ0H) is defined asthe difference µ0Hc2 − µ0Hc1. (c), (d) Hall resistivity at various angles of field inclination. The same data is plotted usingthe x-axis of (c) total external magnetic field µ0H, and (d) out-of-plane magnetic field µ0H⊥. (e) Schematics of the easy-axisanisotropy serving as the effective magnetic field µ0Ha. The net effective magnetic field is obtained as the vector sum of µ0Ha

and the external magnetic field µ0H. As a result, the magnetization orientation ϕ differs from the external field orientation.(f) Fit to the experimentally extracted tilt-angle-dependent critical field Hc2(θ) using the model equation (2). A good fit isobtained with µ0Ha = 2.8 T.

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lower wells get de-pinned first, followed by those in deeperand deeper wells, resulting in a smooth decrease of THEas in our data. Still, the overall film quality is very highas evidenced by further measurements detailed in the SI,which was found to be essential in observing the THE.

By using the Hall resistivity data, an overalltemperature-field phase diagram for 5 u.c. SRO can beobtained as shown in Fig. 2d for the magnetic field ori-ented perpendicular to the film. The topology of thephase diagram is similar to those obtained previously inthe SrRuO3-SrIrO3 bilayer16, and also to the thin-filmchiral magnet Fe1−xCoxSi13 and FeGe19. On the otherhand, the actual critical field strengths for the destruc-tion of the skyrmion phase is much bigger in our SROultrathin film.

A surprising aspect of the skyrmion phase in ultrathinSRO is its exceptional stability under the tilting of themagnetic field (Fig. 1a). As shown schematically in Fig.3a, the Hall resistivity at 10 K for 4 u.c. SRO was mea-sured with the magnetic field tilted at an angle θ fromthe normal to the thin film. Earlier experiment on EuOfilm found the destruction of skyrmion order at θ & 10◦

inclination of external magnetic field from the normal15.Similar field-tilt measurement on the easy-plane polarmagnet GaV4Se8 found θc ≈ 60◦ to be the critical angleof inclination22 before the cycloidal phase replaced theskyrmion phase. By comparison, the THE signal in ourSRO ultrathin film survives for θ as large as 85◦ - themaximal angle of inclination under which it was possibleto measure THE.

The Hall effect data under the external magnetic fieldtilting are plotted in two different ways in Fig. 3c and3d, using either the total magnetic field (µ0H) or the per-pendicular field (µ0H⊥) as the variable for the plot. Ateach angle of inclination one can define two critical fieldsHc1(θ) and Hc2(θ), associated with the onset and disap-pearance of THE, respectively (see Fig. 3b and the cap-tion below for their definitions). The region of skyrmionstability is then defined as ∆(µ0H) ≡ µ0Hc2 − µ0Hc1

for a given angle of inclination. In the first case whereµ0H is used, Hc1(θ), Hc2(θ), and ∆(µ0H) all increasedcontinuously as the tilt angle increases. In the other caseusing µ0H⊥ as the plot variable, they decreased with θ.Compared to similar field-tilt experiments in (easy-plane)EuO15, (easy-axis) GaV4S8

22, (easy-plane) GaV4Se823,

and FeGe24, the ultrathin SRO shows an exceptionallywide region of skyrmion stability under the field tilt.

Based on the transport data supporting the existenceof skyrmions in ultrathin SRO, we may ask now if one canalso understand the origin of skyrmion formation and thesource of their unique stability in this platform. Belowwe give various experimental and theoretical supports toaddress these issues.

Some key insights into the origin of skyrmion formationand its stability in the SRO film were available from thesurface X-ray scattering measurements combined withCoherent Bragg Rod Analysis (COBRA)25,26. Figure 4agives the schematics of the 4 u.c. SRO thin film grown

on the STO(001) substrate. The COBRA method, beingone of the effective phase-retrieval techniques in ultrathinfilms, is capable of providing the three-dimensional elec-tron density profile and accurate atomic positions (seeMethods for details of the measurements). One can seein Fig. 4b the overall two-dimensional electron densityprofiles of the 4 u.c. SRO and the STO layers in the(100) plane at the Ru, Ti, and O atoms. Electron den-sities in some of the individual Ti-O2 and Ru-O2 planesare shown in Fig. 4c in greater detail.

Intriguingly, the SRO ultrathin film on the STO sub-strate maintains the tetragonal structure (a0a0c−)27 (SeeSI for the low energy electron diffraction data), mean-ing that the octahedral tilt angle is zero while the ro-tation about the c-axis (by angle γ) is allowed. Theother significant aspect of the COBRA findings is thecation(Ru)-oxygen rumpling, measured by the displace-ment δ of the Ru atom out of the Ru-O2 plane. Figure4d and 4e give pictorial definitions of γ and δ. Boththese quantities have been measured for the individualSRO and STO layer as shown in Fig. 4f and 4g. The Rudisplacement is as much as 0.2A at the top layer. By con-trast, the bulk SRO and thick SRO films grown on STOsubstrates at the room temperature or lower exhibit or-thorhombic (a+c−c−) or orthorhombic-like (monoclinic,a+b−c−) structure, respectively, and the lack of cation-oxygen rumpling28–30.

A significant ionic displacement of the SRO ultrathinfilm observed by COBRA accounts for the breaking ofinversion symmetry and the consequent appearance ofDMI in the SRO thin film, which is a key factor inthe skyrmion formation. As displayed in Fig. 4d, thedirection of the DMI vector, D12, is perpendicular tothe Ru(spin S1)-O-Ru(S2) plane and its strength pro-portional to the cation(Ru)-oxygen rumpling length δ31.Other features of the COBRA measurement such as theelongation of the lattice and the enhanced rotation angleγ in the ultrathin layer are discussed in SI.

With the lattice parameters and oxygen rotation anglesprovided by COBRA, we have performed first-principlescalculation of the 4 u.c. SRO. Previous study sug-gested that as the thickness of the SRO thin film be-comes smaller, the easy axis of the magnet tends toalign with the normal direction due to the magneticanisotropy32. Our calculation gives an estimate of theeasy-axis anisotropy toward the normal direction to thefilm of order of 0.56 meV for the 4 u.c. SRO (see Methodsfor details of the calculation). The tilt-angle-dependentHall effect of 4 and 5 u.c. SRO thin films we measuredwas consistent with such easy-axis anisotropy.

According to the simple model we present now, suchanisotropy plays a crucial role in stabilizing the skyrmionphase under the large tilting of the magnetic field. Forsimplicity we focus on the estimate of the upper criticalfield Hc2 associated with the destruction of skyrmions infavor of fully spin-polarized state. A typical estimationof Hc2 assumes the field direction normal to the planewhere skyrmions form1,4,14, and has to be modified to

6

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SrTiO3 substrate SrRuO3

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bc

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b

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d

e

f

g

b

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SrTiO3 substrate SrRuO3

Sr Ti Ru O

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c

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Z height (Å)

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FIG. 4. Coherent Bragg rod analysis of 4 u.c. SRO thin-film. (a) A crystal model of SRO on the STO substrate. Agreen (red) dot indicates Sr (O) atom. The blue (gray) dots indicate the octahedron formed by Ti (Ru) atoms. (b) Electrondensity contour plot of STO substrate and 4 u.c. SRO thin-film in (100) plane measured at 30 K. (c) Electron density contourplots on B-site atoms for several Ti and Ru layers. (d) A schematic plot of the cation rumpling length δ, measured from thecenter of the octahedron to the Ru atom, and the corresponding DMI vector (D12). (e) SRO atomic structure within theab-plane with the octahedral rotation angle γ between Ru atom and O atom. (f) Layer-dependent cation-oxygen rumpling ∆of the STO substrate and the SRO thin film measured by COBRA. (i) Layer-dependent octahedral rotation angle γ of the STOsubstrate and the SRO thin film. Blue dotted horizontal line indicates the average of octahedral rotation angle for the STOsubstrate.

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accommodate the effect of in-plane field.Due to the field tilting, the average magnetic moment

also has the normal and in-plane components. We as-sume that only the normal component undergoes a twistthat gives rise to the skyrmion texture. Due to the ex-treme two dimensionality of the sample, the in-planemoment has “no room to twist” and must remain uni-form. Furthermore, the magnetic anisotropy we discov-ered from first-principles calculation can be viewed asan effective magnetic field (denoted Ha in Fig. 3e) thatfavors the alignment of the moment in the normal direc-tion. Hence we can write the total effective magnetic fieldµ0Heff(θ) = µ0(Ha+H cos θ,H sin θ) at a given tilt angleθ. The average magnetization m(θ) = (m⊥(θ),m‖(θ)) isaligned with the effective field m ∝ µ0Heff , as schemati-cally shown in Fig. 3d. Due to the anisotropy field, theangle of inclination ϕ of the magnetization lags behindthat of the external field θ as (see Fig. 3e)

cosϕ =Ha+H cos θ√

(Ha+H cos θ)2+(H sin θ)2. (1)

Thus we have m⊥ = m cosϕ for the normal componentof the total magnetization m.

Usually the nucleation energy of the skyrmion scalesas the square of the magnetic moment, while the Zee-man energy does so linearly. Thus the critical fieldHc2, obtained as the competition between the two en-ergy scales, must scale linearly with m⊥, since we areassuming that only the normal component undergoes askyrmionic twist. We therefore expect that the normalcomponent of the upper critical field at a given angle ofinclination θ should scale with cosϕ in the above formula:Hc2,⊥(θ) = Hc2(θ = 0) cosϕ.

Figure 3f shows the plot of Hc2,⊥(θ) based on suchtheoretical consideration, which shows excellent matchto the experimentally determined upper critical fieldsHc2,⊥(θ) assuming the zero-inclination critical fieldµ0Hc2(θ = 0) = 1.57 T and the anisotropy field µ0Ha =2.8 T as inputs. Our simple picture works well even fortilting angle as large as θ = 85◦. The anisotropy fieldHa = 2.8 T is somewhat smaller than the estimatedanisotropy energy of 0.56 meV (corresponding to ∼ 5T in magnetic field assuming two units of Bohr magne-ton for the Ru magnetic moment) obtained from densityfunctional theory calculation.

The transition in the material selection from the bulkcrystal12 to the thin-film form13 of the chiral magnet ush-ered in a drastic improvement in the temperature stabil-ity of the skyrmion and opened up the potential routeto “skyrmionics” where this topological bits can serve asinformation coding devices. Now with the fabrication ofultrathin SRO, we have shown that skyrmions not onlyform, but possess extra stability in terms of magneticfield ranges and inclinations. The common wisdom33 ofhaving a heavy-metal layer as a necessary ingredient toboost the DMI in order to host the skyrmion phase is,to say the least, being challenged by our observation. A

much simpler structure of a few-layer SRO grown on topof STO has the DMI originating from the Ru-O rum-pling and the magnetic anisotropy that helps with theskyrmion’s stability.

ACKNOWLEDGMENTS

This work is supported by IBS-R009-G2 through theIBS Center for Correlated Electron Systems. J. H. wassupported by Samsung Science and Technology Foun-dation under Project Number SSTF-BA1701-07. T.C.and S.H.C. were supported by Basic Science ResearchProgram through NRF (2016K1A3A7A09005337). Theuse of the Advanced Photon Source at the ArgonneNational Laboratory was supported by the US DOEunder Contract No. DE-AC02-06CH11357. PPMSmeasurements were supported by the National Centerfor Inter-University Research Facilities (NCIRF) atSeoul National University in Korea. The work at YonseiUniversity was supported by the NRF Grant (NRF-2016R1C1B2013709, NRF-2017K2A9A2A08000278,2017R1A5A1014862 (SRC program: vdWMRC center),and NRF-2018R1C1B6006859).

Methods

Thin-film growth by pulsed laser depositionSrRuO3 ultrathin films were grown on top of TiO2-

terminated single crystal SrTiO3 substrate by pulsedlaser deposition (PLD) technique. The TiO2-terminatedSrTiO3 single crystal substrate was prepared by deion-ized (DI) water etching and in-situ pre-annealing at 1300K for 90 minutes with oxygen partial pressure (PO2),5×10−6 Torr. Epitaxial SrRuO3 thin film was depositedwith PO2=100 mTorr at 1000 K. A KrF Excimer laser(wavelength = 248 nm) was delivered on SrRuO3 targetwith 1-2 J/cm2 and repetition rate of 2 Hz. The entiregrowth was monitored by reflection high-energy electrondiffraction (RHEED). (See SI for further details on filmgrowth).

Electric transport and magnetization measure-ment

A 60 nm-thick Au top electrode with a hall bar geom-etry was prepared on top of SRO thin film by E-beamevaporator. Electric transport measurement was car-ried out by the Physical Property Measurement System(PPMS), Quantum Design Inc.. The magnetic propertysuch as magnetization versus temperature and externalmagnetic field was performed along in-plane and out of-plane direction by SQUID magnetometery.

COBRA methodX-ray scattering measurements were performed at Sec-

tor 33-BM-C of the Advanced Photon Source at ArgonneNational Laboratory. The samples were characterized at30 K using a closed-cycle He cryostat (Displex). The

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crystal truncation rods were measured with a Pilatus100K area detector at an x-ray energy at 21.0 keV. Thebackground were removed using the area detector. Thecrystal truncation rod (CTR) measurements were takenat 30 K in order to elucidate the detailed atomic structureof ultrathin SRO film. All the specular and off-specularCTR measurements were quantified using the COBRAmethod. The complex structure factors from measuredCTR intensities were able to determine the electron den-sity distribution with sub-Angstrom resolution using aFourier transformation and iterative procedures.

First-principles calculationsWe performed first-principles DFT calculations

with the generalized gradient approximation plus U(GGA+U) method using the Vienna ab-initio simulationpackage34,35. The projector augmented wave method36

was used with pseudopotentials contain 6 valenceelectrons for O (2s22p4), 12 for Ti (3s23p63d24s2),10 for Sr (4s24p65s2), and 14 for Ru (4p64d75s1).The Perdew-Becke-Erzenhof parametrization37 for theexchange-correlation functional and the rotationallyinvariant form of the on-site Coulomb interaction38

were used with U = 1.4 and J = 0.4 eV for the Ru-dorbitals39,40 and U = 4 and J = 0.68 eV for Ti-dorbitals41–43. Our choice of U and J values correctlyreproduced the ferromagnetic metallic ground state ofthe bulk SRO with magnetization of 1 µB/Ru alignedin plane consistent with experimental observations44,45.The parameter also reproduce the ferromagnetic metallicground state of thin-film geometry of SRO with the mag-netic anisotropy favoring the out-of-plane direction. Weused the energy cutoff of 500 eV and k-point sampling on

a 8×8×1 grid with a√

2×√

2 in-plane unit cell to includea0a0c− octahedral rotation of SRO/STO heterostruc-ture. In order to calculate the magnetic anisotropyof the film, we used (SrTiO3)4/(SrRuO3)4-vacuumconfiguration with experimental atomic positions inwhich an additional SrO layer was added to have SrOterminated surfaces for both ends and a vacuum of 15A was used. The magnetic anisotropy was calculatedwith spin-orbit coupling by comparing the total energyper Ru ion calculated with the magnetic moments fixedalong the c-axis with that along the a-axis.

Author contributionsB.K. conceived the project. B.S. and B.K. conductedthe thin film growth, device fabrication, magneticmeasurement and data analysis. B.S., B.K., H.C. andJ.M. performed the electric transport measurement.S.P. performed the first-principles calculation, and J.H.contributed to the modeling of magnetic anisotropyeffect. T.C, H.Z. and S.H.C. performed the surface x-rayscattering measurements using the COBRA technique.J.H. led the preparation of the manuscript with contri-butions from B.S., B.K., S.P., S.H.C., and C.K.. B.K.and C.K. led the project.

Additional informationSupplementary information is available in the online ver-sion of the paper. Correspondence and requests for ma-terials should be addressed to B.S. and C.K.

Competing financial interestsThe authors declare no competing financial interests.

∗ Electronic address: bongju@snu.ac.kr† Electronic address: cshyoung@cau.ac.kr‡ Electronic address: hanjh@skku.edu§ Electronic address: changyoung@snu.ac.kr1 Nagaosa, N., Tokura, Y. Topological properties and dy-

namics of magnetic skyrmions. Nat. Nanotech. 8, 899-911(2013).

2 Liu, J. P., Zhang, Z., Zhao, G. Skyrmions: topologicalstructures, properties, and applications (CRC Press, 2016).

3 Jiang, W., Chen, G., Liu, K., Zang, J., Velthuis, S. G. E.,Hoffmann, A. Skyrmions in magnetic multilayers. Phys.Rep. 704, 1-49 (2017).

4 Han, J. H. Skyrmions in Condensed Matter (Springer,2017).

5 Fert, A., Reyren, N., Cros, V. Magnetic skyrmions: ad-vances in physics and potential applications. Nat. Rev.Mater. 2, 17031 (2017).

6 Moreau-Luchaire, C. et al. Additive interfacial chiral in-teraction in multilayers for stabilization of small individ-ual skyrmions at room temperature. Nat. Nanotech. 11,444-448 (2016).

7 Boulle, O. et al. Room-temperature chiral magneticskyrmions in ultrathin magnetic nanostructures. Nat. Nan-

otech. 11, 449-454 (2016).8 Yu, G. et al. Room-temperature creation and spin-orbit

torque manipulation of skyrmions in thin films with engi-neered asymmetry. Nano. Lett. 16, 1981-1988 (2016).

9 Woo, S. et al. Observation of room-temperature magneticskyrmions and their current-driven dynamics in ultrathinmetallic ferromagnets. Nat. Mater. 15, 501-506 (2016).

10 Soumyanarayanan, A., Raju, M., Gonzales Oyarce, A. L.,Tan, A. K. C., Im, M.-Y., Petrovic, A. P., Ho, P. Khoo,K. H., Tran, M., Gan, C. K., Ernult, F., Panagopou-los, C. Tunable room-temperature magnetic skyrmions inIr/Fe/Co/Pt multilayers, Nat. Mat. 16, 898-904 (2017).

11 Maccariello, D. et al. Electrical detection of single mag-netic skyrmions in metallic multilayers at room tempera-ture. Nat. Nanotech. 13, 233-237 (2018).

12 Muhlbauer, S. et al. Skyrmion lattice in a chiral magnet.Science 323, 915-919 (2009).

13 Yu, X. Z. et al. Real-space observation of a two-dimensionalskyrmion crystal. Nature 465, 901-904 (2010).

14 Bogdanov, A., Hubert, A. Thermodynamically stable mag-netic vortex states in magnetic crystals. J. Mag. Mag. Mat.138, 255-269 (1994).

15 Ohuchi, Y. et al. Topological Hall effect in thin films of

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the Heisenberg ferromagnet EuO. Phys. Rev. B 91, 245115(2015).

16 Matsuno, J., et al. Interface-driven topological Hall effectin SrRuO3-SrIrO3 bilayer. Sci. Adv. 2, e1600304 (2016).

17 Koretsune, T., Kikuchi, T., Arita, R. First-Principles Eval-uation of the Dzyaloshinskii-Moriya Interaction. J. Phys.Soc. Jpn. 87, 041011 (2018).

18 Heinze, S. et al. Spontaneous atomic-scale magneticskyrmion lattice in two dimensions. Nat. Phys. 7, 713-718(2011).

19 Yu, X. Z. et al. Near room-temperature formation of askyrmion crystal in thin-films of the helimagnet FeGe. Nat.Mater. 10, 106-109 (2011).

20 Schulz, T. et al. Emergent electrodynamics of skyrmionsin a chiral magnet. Nat. Phys. 8, 301-304 (2012).

21 Zang, J., Mostovoy, M., Han, J. H., Nagaosa, N. Dynamicsof skyrmion crystals in metallic thin films. Phys. Rev. Lett.107, 136804 (2011).

22 Kezsmarki, I. et al. Neel-type skyrmion lattice with con-fined orientation in the polar magnetic semiconductorGaV4S8. Nat. Mat. 14, 1116-1122 (2015).

23 Bordacs, S. et al. Equilibrium skyrmion lattice groundstate in a polar easy-plane magnet. Sci. Rep. 7:7584(2017).

24 Wang, C. et al. Enhanced stability of the magneticskyrmion lattice phase under a tilted magnetic field in atwo-dimensional chiral magnet, Nano. Lett. 17, 2921-2927(2017).

25 Zhou, H. et al. Anomalous expansion of the copper-apical-oxygen distance in superconducting cuprate bilay-ers. PNAS 107, 8103-8107 (2010).

26 Shin, Y. J. et al. Interface control of ferroelectricity in anSrRuO3/BaTiO3/SrRuO3 capacitor and its critical thick-ness. Adv. Mater. 29 1602795 (2017).

27 Chang, S. H. et al. Thickness-dependent structure phasetransition of strained SrRuO3 ultrathin films: The role ofoctahedral tilt. Phys. Rev. B 84, 104101 (2011).

28 Koster, G. et al. Structure, physical properties, and ap-plications of SrRuO3 thin films. Rev. Mod. Phys. 84 253(2012).

29 Vailionis, A., Siemons, W., Koster. G. Room temperatureepitaxial stabilization of a tetragonal phase in ARuO3 (A =Ca and Sr) thin films. App. Phys. Lett. 93, 051909 (2008).

30 Gao, R. et al. Interfacial octahedral rotation mismatch con-trol of the symmetry and properties of SrRuO3. ACS Appl.Mater. Interfaces 8 14871-14878 (2016).

31 Cheong, S. W., Mostovoy, M. Multiferroics: a magnetictwist for ferroelectricity. Nat. Mater. 6 13-20 (2007).

32 Schultz, M. et al. Magnetic and transport properties ofepitaxial films of SrRuO3 in the ultrathin limit. Phys. Rev.B 79, 125444 (2009).

33 Jiang, W. et al. Mobile Neel skyrmions at room tempera-ture: status and future. AIP Advances 6, 055602 (2016).

34 Kresse, G., Furthmuller, J. Efficient iterative schemes forab initio total-energy calculations using a plane-wave basisset. Phys. Rev. B 54, 11169 (1996).

35 Kresse, G. , Joubert, D. From ultrasoft pseudopotentialsto the projector augmented-wave method. Phys. Rev. B59, 1758 (1999).

36 Blochl, P. E. Projector augmented-wave method. Phys.Rev. B 50, 17954 (1994).

37 Perdew, J. P., Burke, K., Ernzerhof, M. Generalized gradi-ent approximation made simple. Phys. Rev. Lett. 77, 3865(1996).

38 Liechtenstein, A. I., Anisimov, V. I. Zaanen, J. Density-functional theory and strong interactions: Orbital order-ing in Mott-Hubbard insulators. Phys. Rev. B 52, R5467(1995).

39 Kim, B., Min, B. I. Termination-dependent electronic andmagnetic properties of ultrathin SrRuO3 (111) films onSrTiO3. Phys. Rev. B 89, 195411 (2014).

40 Rondinelli, J. M. et al. Electronic properties of bulk andthin film SrRuO3: Search for the metal-insulator transi-tion.

41 Zhong, Z., Kelly, P. J. Electronic-structure-induced recon-struction and magnetic ordering at the LaAlO3/SrTiO3

interface. Europhys. Lett. 84, 27001 (2008). Phys. Rev. B78, 155107 (2008).

42 Jang, H. W. et al., Metallic and insulating oxide interfacescontrolled by electronic correlations. Science 331, 886-889(2011).

43 Okatov, S., Poteryaev, A., Lichtenstein, A. Structural dis-tortions and orbital ordering in LaTiO3 and YTiO3. Eu-rophys. Lett. 70, 499-505 (2005).

44 Kanbayasi, A. Magnetic Properties of SrRuO3 Single Crys-tal II. J. Phys. Soc. Jpn. 44, 89-95 (1978).

45 Bushmeleva, S. N., Pomjakushin, V. Yu., Pomjakushin, E.V., Sheptyakov, D. V., Balagurov, A. M. Evidence for theband ferromagnetism in SrRuO3 from neutron diffraction.J. Mag. Mag. Mat. 305, 491-496 (2006).

46 Jones, C. W., Battle, P. D., Lightfoot, P., Harrison, W.T. A. The structure of SrRuO3 by time-of-flight neutronpowder diffraction. Acta Cryst. C45, 365-367 (1989).

47 Xia, J. et al. Critical thickness for itinerant ferromagnetismin ultrathin films of SrRuO3. Phys. Rev. B 79, 140407(R)(2009).