Current-driven dynamics and inhibition of the

Current-driven dynamics and inhibition of the skyrmion Hall effect of ferrimagnetic skyrmions in GdFeCo films

Seonghoon Woo,1†* Kyung Mee Song,1,2† Xichao Zhang,3 Yan Zhou,3 Motohiko Ezawa,4 S. Finizio,5 J. Raabe,5 Jun Woo Choi,1,6 Byoung-Chul Min,1,6 Hyun Cheol Koo,1,7 and Joonyeon Chang1,6 1

Center for Spintronics, Korea Institute of Science and Technology, Seoul 02792, Korea

2

Department of Physics, Sookmyung Women’s University, Seoul 04130, Korea

3

School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen

518172, China 4

Department of Applied Physics, University of Tokyo, Hongo 7-3-1, Tokyo 113-8656, Japan

5

Swiss Light Source, Paul Scherrer Institut, 5232 Villigen, Switzerland

6

Department of Nanomaterials Science and Engineering, Korea University of Science and

Technology, Daejeon 34113, Korea 7

KU-KIST Graduate School of Converging Science and Technology, Korea University,

Seoul 02792, Korea † These authors contributed equally to this work. * Authors to whom correspondence should be addressed: [email protected]

Magnetic skyrmions are swirling magnetic textures with novel characteristics suitable for future spintronic applications. Recent studies confirmed the room-temperature stabilization of skyrmions in ultrathin ferromagnets. However, such ferromagnetic skyrmions show undesirable topological effect, the skyrmion Hall effect, which leads to their current-driven motion towards device edges, where the skyrmions could easily be annihilated by topographic defects. Recent theoretical studies have predicted enhanced functionality and behaviour for antiferromagnetically exchange-coupled skyrmions. Here we present, for the first time, the stabilization of such skyrmions and their current-driven dynamics in ferrimagnetic GdFeCo films. By utilizing element-specific X-ray imaging, we find that the skyrmions in the Gd and FeCo sublattices are antiferromagnetically exchange-coupled. We further confirm that ferrimagnetic skyrmions can move at a velocity of ~60 m s-1 with significantly reduced skyrmion Hall angle, θSkHE < 10°. Our findings open the door to ferrimagnetic and antiferromagnetic skyrmionics while providing key experimental evidences of recent simulations.

Page 2 of 23

Magnetic skyrmions are non-trivial topological objects1,2 that have been greatly highlighted recently, mainly due to their unique and fascinating topological characteristics suitable for future spintronic applications such as skyrmion-based racetrack memory.3–5 Magnetic skyrmions can be stabilized in the presence of a strong Dzyaloshinskii-Moriya interaction (DMI),6,7 which prefers non-collinear spin orientation between neighbouring magnetic moments. Recent investigations have revealed that, in structures where ultrathin ferromagnets

are

interfaced

with

large

spin-orbit

coupling

materials,

such

as

Ta/CoFeB/MgO,8 Pt/Co/Ir,9 Pt/Co/MgO,10 Pt/Co/Ta and Pt/CoFeB/MgO,11 the interfacial DMI can be strong enough to stabilize the chiral skyrmion structure at room temperature. It has also been shown that room-temperature skyrmions can move along magnetic tracks upon the injection of an electrical current,8,11 which indicates that the skyrmions can be adopted in practical devices.5 However, unlike theoretical predictions, room-temperature ferromagnetic skyrmions have shown relatively slow and pinning-dominated current-driven dynamic behaviours.8,11,12 More importantly, ferromagnetic skyrmions show an inevitable topological effect, namely, the skyrmion Hall effect,13–16 where the magnetic skyrmions do not move collinear to the current flow direction but acquire a transverse motion due to the appearance of a topological Magnus force acting upon the non-zero topological charge: ground-state ferromagnetic skyrmions have a topological charge (Q) of either Q = 1 or -1. To avoid this issue, theoretical studies have suggested that the skyrmion Hall effect can be suppressed by balancing the topological Magnus force in antiferromagnetically exchange-coupled skyrmions, in materials such as (synthetic-)antiferromagnets or compensated ferrimagnets, in which the net topological charge is zero.17–19 Moreover, simulations have shown that currentdriven dynamic behaviours could further be enhanced for skyrmions with zero topological charge.17,19,20 Along with the recent interest in antiferromagnets resulting from their intrinsic ultrafast dynamics and insensitivity to disturbing magnetic fields,21 these advantages in skyrmion dynamics have generated an intense interest in antiferromagnetic chiral skyrmion textures in such systems. However, the actual observation of such skyrmions has so far remained elusive. In this article, we present the first observation of stable 150-nm-diameter ferrimagnetic skyrmions and their characteristic current-driven behaviours at room temperature. [Pt (3 nm)/Gd25Fe65.6Co9.4 (5 nm)/MgO (1 nm)]20 multilayer stacks (hereafter Pt/GdFeCo/MgO) based on ferrimagnetic Gd25Fe65.6Co9.4 with perpendicular magnetic anisotropy (PMA) were studied. In amorphous GdFeCo alloy, Gd and FeCo represent two antiferromagnetically exchange-coupled collinear magnetic sublattices originating from the Page 3 of 23

antiparallel magnetic coupling between the rare-earth Gd 4f and 5d spin moments and the transition-metal Fe and Co 3d spin moment.22,23 The relatively small amount of Co, ~9.4 %, is present to control the PMA, so that the 5-nm-thick Gd25Fe65.6Co9.4 has PMA.23–25 For the last few decades, this ferrimagnetic alloy has been investigated mainly for the purpose of ultrafast optical magnetization reversal or magneto-optical recording due to its strong magneto-optical effect.25,26 Recent studies have shown that chiral Néel-type domain walls may be present in GdFeCo nanowires27, implying that GdFeCo might show chiral spin textures such as skyrmions. However, the direct observation of chiral magnetic skyrmions (or any other chiral textures) in such ferrimagnetic material has never been achieved up to now. In our multilayer stack, the Pt heavy metal underlayer is used to induce a strong DMI that stabilizes chiral magnetic textures. The sizable internal de-magnetization field of the 20repetition multilayer stack effectively drives as-grown the magnetization state into the multidomain state (see Supplementary Information S1 for its hysteresis behaviours and the top left panel in Figure 1a for its as-grown multi-domain state). Using vibrating sample magnetometry (VSM) measurements, we confirm that our GdFeCo film exhibits its magnetization compensation point, TM, at roughly 450 K (see Supplementary Information S2 for details), thus, our magnetic devices remain at an uncompensated ferrimagnetic state throughout all the room-temperature X-ray measurements. To reveal the nature of ferrimagnetic skyrmions in our system, we first performed element-specific scanning transmission X-ray microscopy (STXM) in the presence of an external perpendicular magnetic field, Bz. Figure 1a shows the STXM images of the domain structure in a patterned 2.5-µm-wide and 5-µm-long Pt/GdFeCo/MgO film with increasing external magnetic field from Bz = 0 mT to Bz = 130 mT. The upper and lower panels show corresponding STXM images taken at the absorption edges of Fe (L3-edge) and Gd (M5edge), respectively. In these STXM images, bright and dark contrasts correspond to upward (+Mz) and downward (-Mz) magnetization directions, respectively. At Bz = 0 mT, a labyrinth stripe domain state with the average domain width of ~220 nm is achieved. Moreover, it is immediately obvious that STXM images at Fe- and Gd-absorption edges show opposite contrast, revealing their expected antiferromagnetic spin ordering within the GdFeCo alloy. Note that, since the measurements are conducted at room temperature, which is lower than the compensation point TM, the magnetic moment of Gd aligns parallel with the external magnetic field while the moment of Fe aligns in an anti-parallel fashion.25 As the magnetic field increases, fewer domains remain and magnetic configurations become less complex. Eventually, by reaching a magnetic field of Bz = 130 mT, we observe multiple isolated Page 4 of 23

skyrmions, and it is evident that the Gd and Fe magnetic moments are still antiferromagnetically exchange-coupled within these skyrmions, therefore confirming that we observed ferrimagnetic skyrmions. In these skyrmions, the net topological charge vanishes, Q = 0, while the skyrmions themselves maintain a sizable net magnetization because we carried out the measurements at room temperature (300 K < TM). The high spatial resolution (~25 nm) of STXM allows us to measure the diameter of the observed skyrmions as discussed in Supplementary Information S3, and we find that the average skyrmion diameter at Bz = 130 mT is roughly ~150 nm, which is as small as the skyrmions found in ferromagnetic multilayers with a large DMI value, 1.5 ~ 2 mJ m-2, studied in Refs. [9,11]. We later confirm that our skyrmions exhibit a left-handed Néel-type chirality by observing their current-driven behaviours. Figure 1b schematically illustrates the orientation of the antiferromagnetically exchange-coupled internal magnetic moments within the observed ferrimagnetic skyrmion structure. Having established that ferrimagnetic skyrmions can form at a finite external field in this material, we next study their electric current-induced dynamics in the magnetic track. Figure 2a shows a schematic drawing of our ferrimagnetic track and electric contacts patterned on a 100-nm-thick Si3N4 membrane for transmission X-ray measurements. The actual scanning electron microscopy (SEM) micrograph of our device is also included, and two indicated areas within the image, (i) and (ii), are used to analyse current-driven skyrmion behaviours shown in Fig. 2b and 2c, respectively. In Fig. 2b and 2c, each STXM image was acquired after injecting current pulses. 20~40 repetition of current pulses, with the current density of |ja| = 2.31×1011 A m-2 and pulse duration of 1.8 ns, were applied (see Supplementary Information S4 for details on the electronic connections and the actual pulse shape). The pulse polarity, defined by the electric current flow direction, is indicated in the figure as red and blue pulse-shaped arrows. Fig. 2b first shows a sequence of STXM images of skyrmions stabilized by a magnetic field of Bz = 130 mT in region (i). Three skyrmions move towards the current flow direction on the track for the first two pulses. Afterwards, only one skyrmion freely moves while the other skyrmions remain stationary at a fixed position, evidently pinned by a defect, for the rest of pulse applications. Note that only mobile skyrmions are colour-circled, and thus, the left-most skyrmion, which has remained immobile throughout the pulse applications, is not separately indicated with another colour. We then reversed the magnetic field to Bz = -130 mT and investigated region (ii) on the same track, as shown in Fig. 2c. Among the three skyrmions observed at the initial state, only one could be freely displaced forward and backward along the current flow direction, whereas the other Page 5 of 23

two skyrmions remain immobile, implying the presence of strong pinning effects. With these observations shown in Fig. 2b and 2c, three important observations on the skyrmion physics within ferrimagnetic material can be drawn. First and most importantly, our investigation reveals that ferrimagnetic skyrmions can also be displaced by electric currents at room temperature just as the ferromagnetic skyrmions8,11. This observation serves as the very first experimental demonstration of the current-driven motion of antiferromagnetically exchangecoupled magnetic skyrmions. Moreover, we identify that relatively strong skyrmion pinning, which was observed for crystalline metallic Co and negligible for amorphous CoFeB,11 exists within our amorphous GdFeCo alloy. We speculate that an inhomogeneous material composition over the same track may have caused the skyrmion pinning, which is very sensitive to the local material parameter variation. Lastly, we show that the skyrmion propagation direction is along the current flow direction (against the electron flow) for both +Mz-core and -Mz-core skyrmions, and this same directionality agrees well with the spin Hall current-driven motion of homochiral left-handed Néel-type hedgehog-like skyrmions stabilized by interfacial DMI in Pt/ferromagnet thin films.11,15 This implies that the interfacial DMI at the Pt/GdFeCo interface plays a crucial role in stabilizing skyrmions and also driving them on the track in our ferrimagnetic structure. However, in Fig. 2b and 2c, we witness that a highly mobile skyrmion cannot move when it finds itself between two pinned skyrmions, probably due to the inter-skyrmion repulsion. Thus, when we observed multiple skyrmions present within a small area (see Fig. 2), we were not able to extract either skyrmion velocity or its topological effect, that is, the skyrmion Hall effect. To avoid the inter-skyrmion interaction and also local skyrmion pinning potentials, we then localized a single skyrmion in a pinning-free area of the device and analyzed its current-driven behaviours by applying back-and-forth current pulses as shown in Fig. 3. Figure 3a shows consecutive STXM images after applying 20 ~ 40 bursts of the current pulses of varying amplitudes, 0.93×1011 A m-2 ≤ |ja| ≤ 3.94×1011 A m-2, and a fixed singlepulse-duration of 1.8 ns. For the burst-mode current injections, a low-duty-cycle train of current pulses was used to provide enough cooling and relaxation time to our ferrimagnetic track and avoid possible over-heating. It is first evident that a skyrmion moves freely within the pinning-free area, which allows us to analyse the pulse amplitude-dependent skyrmion velocity and its skyrmion Hall angle, as plotted in Fig. 3b and 3c, respectively. To correctly calculate the distance and angle between two images, we have performed imagedisplacement correction using the edge between our magnetic track and Au electrode. We first observe a critical current density |jc| = 0.93×1011 A m-2, below which no skyrmion Page 6 of 23

displacement is observed. Thus the threshold current density observed for our ferrimagnetic skyrmions is much smaller compared to that of ferromagnetic skyrmions with few nanoseconds pulse-length, |jc| ~ 2×1011 A m-2. It should also be noted that the pulse duration, 1.8 ns, used to displace our ferrimagnetic skyrmions were few times shorter than the pulse length used to displace ferromagnetic skyrmions; a 6-ns-long pulse was used for Pt/Co or Pt/CoFeB.11 Moreover, the skyrmion velocity approaches ~60 m s-1 at |ja| ~ 4×1011 A m-2, which is comparable to the maximum velocity achieved for amorphous pinning-free metallic ferromagnetic CoFeB at similar current densities.11 Most strikingly, as shown in Fig. 3c, we observe a very small skyrmion Hall angle, θSkHE < 10°, which is significantly lower than the skyrmion Hall angles, θSkHE > 30°, observed for ferromagnetic skyrmions in Ta/CoFeB/MgO and Pt/CoFeB/MgO structures.14,15 As a large skyrmion Hall effect results in more nonprecise and even invalid information delivery due to the additional transverse motion, we believe that our ferrimagnetic multilayers can serve as an important magnetic material for such future skyrmionic devices that could replace conventional ferromagnets with enhanced mobility and accuracy. It is noteworthy that the skyrmion Hall angles were measured to be negative for |ja| = 1×1011 A m-2 and |ja| = 1.3×1011 A m-2 in the experiment. The reason is that the skyrmion dynamics is primarily dominated by pinning sites at low current densities, showing a zig-zaglike motion, which is similar to the creep motion of ferromagnetic skyrmions in low-currentdensity regime caused by the pinning potential.12,14 The remnant finite skyrmion Hall angle, θSkHE ~ 10°, results from the uncompensated magnetic moments between Gd and FeCo at 300 K < TM, even with compensated topological charge, Q = 0 (see Supplementary Information S5 and subsequent simulation results for details). Therefore, by adjusting material compositions and lowing the compensation temperature to near room-temperature, it should be possible to realize negligible skyrmion Hall angle in ferrimagnetic GdFeCo films. Moreover, recent experimental reports reveal that the damping-like spin-transfer torque generated by the spin Hall effect, which essentially propels skyrmions, can be significantly enhanced near the magnetization compensation temperature in ferrimagnetic materials such as GdFeCo28 or TbCo29, implying that skyrmion dynamics can further be enhanced in a composition-adjusted material with compensated magnetization. For comparison, we also simulated the current-driven dynamics of a ferrimagnetic skyrmion in a checkerboard-like two-sublattice spin system based on the G-type antiferromagnetic structure with simple square lattices,17,18 where the two sublattices, corresponding to Gd and FeCo, are coupled in a ferrimagnetic manner with a net saturation Page 7 of 23

magnetization, while each sublattice is ferromagnetically ordered. Simulations were performed with both models: with and without pinning defects (see Methods for more modelling details). Here, we first used a damping coefficient of α = 0.5, which was also used for similar structures in previous reports11,15, for the simulation given in Fig. 3b and 3c. Since the skyrmion Hall angle is inversely proportional to the damping coefficient (see Supplementary Information S6), using a relatively large damping coefficient in the simulation could reduce the skyrmion Hall angle at a given current density, leading to a good reproduction of the experimental observation. Figure 3b shows the simulated skyrmion velocity as a function of the current density. It is first obvious that simulation results show excellent qualitative and quantitative agreement with experimental observations, revealing that the ferrimagnetic skyrmion velocity is linearly proportional to the driving current density. Moreover, the calculated skyrmion velocities are very similar for both models, implying that the presence of a moderate pinning effect in ferrimagnetic system minimally influences on the skyrmion velocity unlike its ferromagnetic counterpart.11 We also calculated the skyrmion Hall angle as a function of the current density as shown in Fig. 3c. Although the simulated skyrmion Hall angle is slightly larger than the experimental observation, it should be noted that the quantitative difference falls within the error range of only few degrees. The skyrmion Hall angle in the model without pinning defects is independent of the current density, however, the skyrmion Hall angle in the model with certain pinning defects obviously increases with increasing current density and approaches to the constant value calculated with the pinning-absent model. This linear increase is qualitatively consistent with our experimental observations and also with previous report14, indicating the existence of certain pinning effects due to impurities or defects in the real material. Nevertheless, as discussed above, the finite remnant angle can be easily eliminated with the compensated ferrimagnets, leading to the realization of the straight translational motion of magnetic skyrmions. In order to understand the remanent skyrmion Hall effect in the Q = 0 ferrimagnetic skyrmions and to provide more general explanations for ferrimagnetic skyrmions in ferrimagnetic or antiferromagnetic material system, we have also derived an analytical solution using the conventional Thiele equation as discussed in Supplementary Information S5. For the validation of the analytical model, Figure 4 summaries the comparison between the numerical simulation and analytical solution of the ferrimagnetic skyrmion dynamics driven by a spin Hall current in ferrimagnetic models with different values of the damping coefficient. As shown in Fig. 4a, the simulated skyrmion velocity driven by a certain current density is inversely proportional to the damping coefficient, which can also be wellPage 8 of 23

reproduced by the analytical solution

𝑣 = 𝑗!"#$

1 + 𝛼 ! 𝒟 ! (see Supplementary

Information S5), where jspin represents the driving force in the Thiele motion equation, and 𝒟 stands for the dissipative term. It should be noted that in order to apply the Thiele equation approach to the ferrimagnetic system, we assumed Q = 1 in the Thiele equation solutions when the studied ferrimagnetic system has a certain net saturation magnetization. The reason is that a ferrimagnetic skyrmion having Q = 0 is composed of two sublattice skyrmions with opposite topological charge, however, the topological Magnus force acted in opposite directions cannot be cancelled due to the presence of the net saturation magnetization, leading to the ferrimagnetic skyrmion dynamics similar to that of a ferromagnetic skyrmion with |Q| = 1. The use of Thiele equation in describing a ferrimagnetic skyrmion is also supported by the fact that ferrimagnets can be considered as ferromagnets as long as the intensity of the external stimulus does not perturb the interaction between the two underlying sublattices30. Indeed, at the compensation temperature where the net saturation magnetization of the ferrimagnetic system equals zero, the Q in the Thiele equation should be equal to zero, straightforwardly yielding zero skyrmion Hall angle. On the other hand, the simulated skyrmion Hall angle 𝜃!"#$ is also inversely proportional to the damping coefficient (see Supplementary Information S6). Figure 4d shows 1 tan 𝜃!"#$ as a function of the damping coefficient. It can be seen that 1 tan 𝜃!"#$ is proportional to the damping coefficient, which can be described by the derived analytical solution 1 tan 𝜃!"#$ = 1 𝛼𝒟 (see Supplementary Information S5). These simulation results suggest that the ferrimagnetic material with larger damping coefficient can lead to weaker skyrmion Hall effect, while larger damping coefficient will also result in smaller skyrmion velocity. In conclusion, we have, for the first time, observed and studied the stabilization and current-driven

dynamics

of

antiferromagnetically

exchange-coupled

skyrmions

in

ferrimagnetic GdFeCo films. By utilizing the element-specific X-ray imaging, we have identified that the ferrimagnetic skyrmion in the GdFeCo films are consist of two antiferromagnetically exchange-coupled skyrmions in the Gd and FeCo sublattices, which carries a topological charge of zero. We further confirm that current-driven ferrimagnetic skyrmions can move at a velocity of ~60 m s-1 with significantly reduced skyrmion Hall angle, θSkHE < 10°. With simulations and analytical approaches, we have also studied the skyrmion Hall effect of a ferrimagnetic skyrmion at different current densities and damping coefficients, which suggests that the skyrmion Hall effect of ferrimagnetic skyrmions could be greatly suppressed by increasing the damping coefficient of the material system. Our

Page 9 of 23

findings reveal the promising dynamic properties of ferrimagnetic skyrmions, and highlight the possibility to build more reliable skyrmionic devices using ferrimagnetic and antiferromagnetic materials.

Page 10 of 23

Methods Experimental details. The [Pt(3 nm)/GdFeCo(5 nm)/MgO(1 nm)]20 films were grown by DC magnetron sputtering at room temperature under 1 mTorr Ar for Pt and GdFeCo and 4 mTorr Ar for MgO at a base pressure of roughly ~2×10-8 Torr. Samples were grown on a 100-nm-thick SiN substrate and then patterned using electron beam lithography and lift-off technique. Nominally sample films were grown on SiOx/Si substrate for vibrating-sample magnetometry (VSM) measurement, and the measurement yielded material constants of µ0Hk = 0.15 T, and a net saturation magnetization MS = 4×105 A/m. All microscopy images were acquired using the STXM installed at the PolLux (X07DA) beamline of the Swiss Light Source (SLS) at the Paul Scherrer Institute in Villigen, Switzerland. The device used for the experiments was 2.5-µm-wide and 5-µm-long, which yielded an electrical resistance of ~78 Ohms measured in 2-point. This resistance reduced the impedance mismatch of the device, and allowed an almost complete transmission of 1.8-nslong short electrical pulses across the device. This was verified by simultaneously measuring the injected (through a -20 dB pickoff T) and transmitted samples with a real-time oscilloscope. Pulse current densities above ~4×1011 A m-2 led to a damage of the Au contact, which eventually limited the maximum current applied in Fig. 3. Skyrmion velocities were determined using the total displacements, measured by acquiring XMCD-STXM images before and after the injection of the pulses, and the integrated pulse time. Three to ten displacements were recorded for each pulse amplitude, and the average value and standard deviations of the individual velocity measurements are plotted in Fig. 3c. Current densities were calculated by dividing the injected current with stripe width and effective total thickness of Pt and GdFeCo. Simulation Details. The spin dynamics simulation is carried out by using the Object Oriented MicroMagnetic Framework (OOMMF) with the home-made extension modules for the periodic boundary condition.31 The model is treated as a checkerboard-like two-sublattice spin system based on the G-type antiferromagnetic structure with simple square lattices, where the two sublattices are coupled in a ferrimagnetic manner with a net spontaneous magnetization, while each sublattice is ferromagnetically ordered. The Hamiltonian is based on the classical Heisenberg model, given as ℋ = −𝐽!"

!!,!! 𝐒!

∙ 𝐒! + 𝐷

!!,!!

𝐮!" ×𝑧 ∙ 𝐒! ×𝐒! − 𝐾

!

𝐒!!

!

+ 𝐻!!" ,

(1)

Page 11 of 23

where 𝐒! represents the local spin vector reduced as 𝐒! = 𝑴! 𝑀!! at the site i, and 𝐒! !

represents the local spin vector reduced as 𝐒! = 𝑴! 𝑀! at the site j. 𝑴! and 𝑴! are the magnetization at the site i and j, respectively. 𝑀!! denotes the saturation magnetization of the !

sublattice i, while the saturation magnetization of sublattice j is defined as 𝑀! = 𝑛𝑀!! with the compensation ratio n. runs over all the nearest-neighbor sites in the two-sublattice spin system. 𝐽!" is the exchange coupling energy constant between the two spin vector 𝐒! and 𝐒! , which has a negative value (𝐽!" < 0) representing the antiferromagnetic spin ordering of the two sublattices. 𝐷 is the interface-induced DMI constant, 𝐮!" is the unit vector between spins 𝐒! and 𝐒! , and 𝑧 is the interface normal, oriented from the heavy-metal layer to the ferrimagnetic layer. 𝐾 is the PMA constant, and 𝐻!!" stands for the dipole-dipole interaction, i.e., the demagnetization effect. The time-dependent dynamics of the spin system is controlled by the Landau-LifshitzGilbert (LLG) equation augmented with the damping-like spin Hall torque, which is expressed as !𝐒! !"

= −𝛾! 𝐒! ×𝐇!"" + 𝛼 𝐒! ×

!𝐒! !"

+ 𝜏 𝐒! × 𝑝×𝐒! ,

(2)

where 𝐇!"" = − 1 𝜇! 𝑀!! ∙ 𝛿ℋ 𝛿 𝐒! is the effective field on a lattice site, 𝛾! is the Gilbert gyromagnetic ratio, and α is the phenomenological damping coefficient. The coefficient for the spin Hall torque is given as 𝜏 = 𝛾! ℏ𝑗𝜃!"

2𝜇! 𝑒𝑀!! 𝑏 , where 𝑗 is the applied charge

current density, 𝜃!" is the spin Hall angle, and 𝑏 is the thickness of the ferrimagnetic layer. 𝑝 = 𝒋×𝒛 denotes the spin polarization direction. For the simulation on the multilayer structure, we employed an effective medium approach11 with the lattice constant of 4 Å, which improves the computational speed by converting the multilayer into a two-dimensional effective model with reduced parameters. The intrinsic magnetic parameters used in the simulation are measured from our experimental samples as well as adopted from Refs. [11,15,32]: the Gilbert damping coefficient α = 0.05 ~ 0.5 (see Supplementary Information S6 for the effect of α), the inter-sublattice exchange stiffness A = -15 pJ m-1, the spin Hall angle θSH = 0.1, the DMI constant D = -2 mJ m-2, the PMA constant Ku = 0.13 MJ m-3, and the net saturation magnetization 𝑀! = 𝑀!!" − 𝑀!!" = 400  kA  m!! . The compensation ratio is defined as 𝑛 = 𝑀!!" 𝑀!!" = 0.7. We found that the skyrmion Hall angle is inversely proportional to the value of n, thus we used n = 0.7 in order to ensure a small skyrmion Hall angle which reproduces the experimental observation (see Supplementary Information S6 for the effect of n). In the experimental multilayer system, the Page 12 of 23

thickness of one ferrimagnetic layer is tm = 5 nm, the thickness of one repetition is tr = 9 nm, and the number of repetitions is nrep = 20. The effective spin Hall angle and DMI constant are reasonably acquired from Pt-based ferromagnetic heterostructures in Refs. [11,33]. For the simulation on the model with pinning defects, the defects with the size of 8 Å × 8 Å and a higher PMA (Kp = 2Ku) are randomly distributed in the whole ferrimagnetic layer. The density of the defects in the whole model equals 10%.

Page 13 of 23

References 1. Rößler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006). 2. Mühlbauer, S. et al. Skyrmion Lattice in a Chiral Magnet. Science 323, 915–919 (2009). 3. Jonietz, F. et al. Spin Transfer Torques in MnSi at Ultralow Current Densities. Science 330, 1648–1651 (2010). 4. Yu, X. Z. et al. Skyrmion flow near room temperature in an ultralow current density. Nat. Commun. 3, 988 (2012). 5. Fert, A., Cros, V. & Sampaio, J. Skyrmions on the track. Nat. Nanotechnol. 8, 152–156 (2013). 6. Dzyaloshinsky, I. A thermodynamic theory of ‘weak’ ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958). 7. Moriya, T. Anisotropic Superexchange Interaction and Weak Ferromagnetism. Phys. Rev. 120, 91–98 (1960). 8. Jiang, W. et al. Blowing magnetic skyrmion bubbles. Science aaa1442 (2015). doi:10.1126/science.aaa1442 9. Moreau-Luchaire, C. et al. Additive interfacial chiral interaction in multilayers for stabilization of small individual skyrmions at room temperature. Nat. Nanotechnol. 11, 444–448 (2016). 10. Boulle, O. et al. Room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures. Nat. Nanotechnol. 11, 449–454 (2016). 11. Woo, S. et al. Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets. Nat. Mater. 15, 501–506 (2016). 12. Hanneken, C., Kubetzka, A., Bergmann, K. von & Wiesendanger, R. Pinning and movement of individual nanoscale magnetic skyrmions via defects. New J. Phys. 18, 055009 (2016). 13. Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899–911 (2013). 14. Jiang, W. et al. Direct observation of the skyrmion Hall effect. Nat. Phys. 13, 162–169 (2017). 15. Litzius, K. et al. Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy. Nat. Phys. 13, 170–175 (2017).

Page 14 of 23

16. Chen, G. Spin-orbitronics: Skyrmion Hall effect. Nat. Phys. 13, 112–113 (2017). 17. Barker, J. & Tretiakov, O. A. Static and Dynamical Properties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature. Phys. Rev. Lett. 116, 147203 (2016). 18. Zhang, X., Zhou, Y. & Ezawa, M. Antiferromagnetic Skyrmion: Stability, Creation and Manipulation. Sci. Rep. 6, 24795 (2016). 19. Zhang, X., Zhou, Y. & Ezawa, M. Magnetic bilayer-skyrmions without skyrmion Hall effect. Nat. Commun. 7, 10293 (2016). 20. Kim, S. K., Lee, K.-J. & Tserkovnyak, Y. Self-Focusing Skyrmion Racetracks in Ferrimagnets. ArXiv170202554 Cond-Mat (2017). 21. Jungwirth, T., Marti, X., Wadley, P. & Wunderlich, J. Antiferromagnetic spintronics. Nat. Nanotechnol. 11, 231–241 (2016). 22. Taborelli, M., Allenspach, R., Boffa, G. & Landolt, M. Magnetic coupling of surface adlayers: Gd on Fe(100). Phys. Rev. Lett. 56, 2869–2872 (1986). 23. Camley, R. E. & Tilley, D. R. Phase transitions in magnetic superlattices. Phys. Rev. B 37, 3413– 3421 (1988). 24. Hansen, P., Clausen, C., Much, G., Rosenkranz, M. & Witter, K. Magnetic and magneto-optical properties of rare-earth transition-metal alloys containing Gd, Tb, Fe, Co. J. Appl. Phys. 66, 756– 767 (1989). 25. Radu, I. et al. Transient ferromagnetic-like state mediating ultrafast reversal of antiferromagnetically coupled spins. Nature 472, 205–208 (2011). 26. Ostler, T. A. et al. Ultrafast heating as a sufficient stimulus for magnetization reversal in a ferrimagnet. Nat. Commun. 3, 666 (2012). 27. Tono, T. et al. Chiral magnetic domain wall in ferrimagnetic GdFeCo wires. Appl. Phys. Express 8, 073001 (2015). 28. Ham, W. S. et al. Spin-orbit effective fields in Pt/GdFeCo bilayers. ArXiv170300995 Cond-Mat (2017).

Page 15 of 23

29. Finley, J. & Liu, L. Spin-Orbit-Torque Efficiency in Compensated Ferrimagnetic Cobalt-Terbium Alloys. Phys. Rev. Appl. 6, 054001 (2016). 30. Yuklov, V. I., Cottam, M. G. & Singh, M. R. Nonlinear dynamics of nuclear–electronic spin processes in ferromagnets. J. Appl. Phys. 85, 5627–5629 (1999). 31. Porter, D. G. & Donahue, M. J. OOMMF user’s guide, version 1.0. Natl. Inst. Stand. Technol. Interag. Rep. NISTIR 6376 32. Liu, L., Lee, O. J., Gudmundsen, T. J., Ralph, D. C. & Buhrman, R. A. Current-Induced Switching of Perpendicularly Magnetized Magnetic Layers Using Spin Torque from the Spin Hall Effect. Phys. Rev. Lett. 109, 096602 (2012). 33. Emori, S., Bauer, U., Ahn, S.-M., Martinez, E. & Beach, G. S. D. Current-driven dynamics of chiral ferromagnetic domain walls. Nat. Mater. 12, 611–616 (2013).

Page 16 of 23

Acknowledgements This work was primarily supported by Samsung Research Funding Center of Samsung Electronics under Project Number SRFC-MA1602-01. Part of this work was performed at the PolLux (X07DA) beamline of the Swiss Light Source. S.W. acknowledges the support from KIST Institutional Program. K.M.S acknowledges the support from the Sookmyung Women's University BK21 Plus Scholarship. X.Z. was supported by JSPS RONPAKU (Dissertation Ph.D.) Program. Y.Z. acknowledges the support by the National Natural Science Foundation of China (Grant No. 11574137) and Shenzhen Fundamental Research Fund under Grant No. JCYJ20160331164412545. M.E. acknowledges the support by the Grants-in-Aid for Scientific Research from JSPS KAKENHI (Grant Nos. 25400317 and 15H05854), and also the support by CREST, JST (Grant No. JPMJCR16F1). S.F acknowledges the support by the EU Horizon 2020 MAGicSky project (Grant No. 665095). J.W.C. acknowledges the travel fund supported by the National Research Foundation of Korea (NRF) funded by the MSIP (2016K1A3A7A09005418). Author Contributions S.W. designed and initiated the study. K.M.S. optimized structure, fabricated devices and performed the film characterization. S.W., K.M.S., S.F. and J.R. performed X-ray experiments using STXM at Swiss Light Source in Villigen, Switzerland. X.Z. and Y.Z. performed the numerical simulations. M.E. carried out the theoretical analysis. S.W., X.Z. and M.E. drafted the manuscript and revised it with assistance from J.W.C., B.-C.M., H.C.K. and J.C.. All authors commented on the manuscript. Author Information S.W. and K.M.S. contributed equally to this work. The authors declare no competing financial interests. Correspondence and requests for materials should be addressed to S.W. ([email protected]).

Page 17 of 23

Figure Legends Figure 1. Scanning transmission X-ray microscopy (STXM) imaging of domain structure upon magnetic field application. a, STXM images acquired by sweeping the external perpendicular magnetic field from Bz = 0 mT to Bz = 130 mT. Bright and dark contrasts correspond to magnetization oriented up (along +z) and down (along -z), respectively. Upper panel and lower panel show corresponding images acquired at the L3 and M5 absorption edges of Fe and Gd, respectively. Note that, due to longer penetration depth associated with the higher energy used for Gd, ~1189 eV, compared with that of Fe, ~709 eV, magnetic contrast under Au electrodes is visible for Gd magnetic moment imaging. b, Schematic of antiferromagnetically exchange-coupled ferrimagnetic skyrmion on a magnetic track as observed in our GdFeCo films as indicated in the red dashed-square boxes in the last image of a. Figure 2. Current-driven motion of ferrimagnetic skyrmions and the effect of skyrmion pinning. a, Schematic of STXM geometry, and a scanning electron microscopy (SEM) image of the actual device used for experiments. Sequential STXM images taken at Fe-edge showing the responses of multiple skyrmions after injecting unipolar current pulses along the track at b, Bz = 130 mT and c, Bz = -130 mT, respectively, with an pulse amplitude of |ja| = 2.31×1011 A m-2, a fixed pulse width of 1.8 ns and the burst number of 20 ~ 40. Pulse polarities are indicated as red- and blue-coloured arrows inside each image. Within STXM images, only mobile skyrmion are highlighted with coloured circles. The same skyrmion is indicated with the same colour. Figure 3. Current-driven behaviour of pinning-free ferrimagnetic skyrmions and their velocity and skyrmion Hall effect. a, Sequential STXM images taken at Fe-edge showing skyrmion displacement within a pinning-free region inside our Pt/GdFeCo/MgO track. With a fixed pulse-length of single pulse, 1.8 ns, the pulse amplitude and the number of injected pulses are changed between 0.93×1011 A m-2 ≤ |ja| ≤ 3.94×1011 A m-2, and 20 ~ 40 times, respectively. b, Experimental and simulated average skyrmion velocity of Pt/GdFeCo/MgO versus current density. c, Experimental and simulated average skyrmion Hall angle of Pt/GdFeCo/MgO versus current density. Note that pulse current densities above ~4×1011 A m-2 led the damage of the Au contact, which eventually limited the maximum applicable current to our sample. Error bars denote the standard deviation of multiple measurements. Page 18 of 23

Figure 4. Numerical and analytical solutions of the skyrmion velocity and the skyrmion Hall angle in ferrimagnets. a, The skyrmion velocity as a function of the damping coefficient at |ja| = 4×1011 A m-2. The numerical solution is fitted by analytical solution 𝑗!"#$

1 + 𝛼 ! 𝒟 ! with the use of 𝒟 = 6.76 and 𝑗!"#$ = 166.68 . 𝒟 is estimated by the

numerical integration of equation (1.17) in the Supplementary Information S5. Inset shows the G-type model used in the simulation of the ferrimagnetic system. b, 1 tan 𝜃!"#$ as a function of the damping coefficient at |ja| = 4×1011 A m-2. The numerical solution is fitted by analytical solution 1 𝛼𝒟 with the use of 𝒟 = 6.76.

Page 19 of 23

Figure 1 Seonghoon Woo et al.

Page 20 of 23

Figure 2 Seonghoon Woo et al.

Page 21 of 23

Figure 3 Seonghoon Woo et al.

Page 22 of 23

Figure 4 Seonghoon Woo et al.

Page 23 of 23