Spin-orbit torque-driven skyrmion dynamics revealed by time-resolved X-ray microscopy

Magnetic skyrmions are topologically protected spin textures with attractive properties suitable for high-density and low-power spintronic device applications. Much effort has been dedicated to understanding the dynamical behaviours of the magnetic skyrmions. However, experimental observation of the ultrafast dynamics of this chiral magnetic texture in real space, which is the hallmark of its quasiparticle nature, has so far remained elusive. Here, we report nanosecond-dynamics of a 100nm-diameter magnetic skyrmion during a current pulse application, using a time-resolved pump-probe soft X-ray imaging technique. We demonstrate that distinct dynamic excitation states of magnetic skyrmions, triggered by current-induced spin–orbit torques, can be reliably tuned by changing the magnitude of spin–orbit torques. Our findings show that the dynamics of magnetic skyrmions can be controlled by the spin–orbit torque on the nanosecond time scale, which points to exciting opportunities for ultrafast and novel skyrmionic applications in the future.

AH loops under dc-currents Idc = ±4 mA and an in-plane field Hx = 2500 Oe. (c), (d) Switching fields HSW for down-to-up (blue square) and up-to-down (red square) magnetization reversals at Hx = -2500 Oe and Hx = -4000 Oe, respectively. The center of hysteresis loop H0, which is the net effective spin-Hall field in the z direction, is shown to more clearly show the amount of AH loop shift. For each figure, the spin-Hall effective field per unit current in mA is calculated and shown. (e) The measured effective χ (= χSHEcosΦ) as a function of Hx. The measure of effective spin-Hall efficiency, χSHE, and an estimate of DMI effective field, HDMI, is indicated. DMI randomly varies between 1.5 mJ m -2 and 1.9 mJ m -2 . (b) Initial skyrmion state at equilibrium state. External field of Bz=48 mT is applied to stabilize a skyrmion. (c) Skyrmion travel distance and (d) skyrmion dimater as a function of pulse-time. For skyrmion travel distance, initial skyrmion position was set to d=0, so the negative distance exhibits that skyrmion moved beyond its initial position. The sample pulse profile shown in Fig. 4 in main text is used for Va=1 V (blue), Va=2 V (black) and Va=5 V (red), respectively. Scale bars, 200 nm.

Supplementary Note 1. DMI measurement from the field-driven domain width variation
We measured the domain width from the full-field magnetic transmission X-ray microscopy (MTXM) images as the external magnetic field is changed. The domain width reflects the competition between the demagnetizing energy and the domain wall (DW) energy: the demagnetizing energy prefers DW generation whereas there is an accompanying energy cost for the generation of each DW. However, strong Dzyaloshinskii-Moriya interaction (DMI) can effectively reduce the DW energy cost by locally stabilizing Néel walls. In the presence of DMI, the DW energy is given as s DW = 4 AK u,eff -p D , where is the exchange stiffness, Ku,eff is the effective uniaxial anisotropy constant, and D is the DMI constant 1,2 . Therefore, by calculating the DW surface energy from domain widths, we can determine the DMI constant analytically. 3 Supplementary Fig. 1a Using material parameters measured from the VSM measurements and the relation between domain wall surface energy and DMI constant, s (1) and (2) yields the DMI constants of Supplementary Fig. 4 shows the result of the spin-Hall efficiency and DMI effective field measurements. As schematically shown in Supplementary Fig. 4a, we measured the AH voltage while sweeping the out-of-plane magnetic field in the presence of an in-plane magnetic field and in-plane dc-current. The AH measurements were conducted at various in-plane dc currents (Idc) and in-plane fields (Hx) to characterize magnetization switching as a function of Idc and Hx. The in-plane field was applied along the x-axis due to chiral Néel DWs in this geometry points toward either +x or -x direction. Representative normalized AH loops with Hx = 2500 Oe and Idc=±4 mA are shown in Supplementary Fig. 4b. The AH loops along the Hz axis are oppositely shifted for  [8,9].

Supplementary Note 5. Magnetic domain configuration after pulse applications
In Fig. 2 of the main text, we showed that the application of consecutive bipolar pulses could transform the labyrinth domains into multiple skyrmions. However, it is also important to show that the transformation is not from the current-induced sample property variation, which might be possible when the electric currents are large enough to cause significant Joule-heating.
Large Joule-heating could lead to structural changes that would alter magnetic properties even after the current pulse is turned off. To investigate the effect, we have swept an external field after the pulse application and obtained magnetic domain images. Supplementary Fig. 5 shows MTXM images after pulse-induced skyrmion generation ( Supplementary Fig. 5a), saturation field application ( Supplementary Fig. 5b) and turning-off the external field ( Supplementary Fig. 5c).
When a large external field, Hz=200 mT, was applied in Supplementary Fig. 5b, most of created skyrmions were annihilated, leading to a uniform magnetization state. We then turned off the external field and it drove the magnetization state to the labyrinth state as shown in Supplementary Fig. 5c, and this confirms that the magnetic property has not been changed due to bipolar current pulses. We believe this simple observation implies that the pulse-induced skyrmion generation is indeed from the strong topological fluctuation induced by oscillating spin currents.
Here we show experimentally observed skyrmion dynamics at the pulse amplitude of Va=1.5 V. In Fig. 3 in main text, we show skyrmion dynamics when the bipolar pulse amplitudes are Va=2 V and Va=2.5 V, where the pulses induce skyrmion excitation behaviours. However, when the pulse amplitude is relatively small, as shown in Supplementary Fig. 6, there is no observable shape-wise transformation. This indicates that the external current pulse amplitude should be larger than jth to induce the excitation bahaviors, and the current threshold for our sample is roughly j th =1´10 11 A m -2 .
Here we explain the skyrmion diameter determination procedure used to extract the actual diameter of the individual skyrmion from MTXM images. The diameter was determined by fitting four line-scans of the XMCD signal across the MTXM image as indicated in Supplementary Fig.   7. Each line-scan was fitted to a Gaussian, and the full-width at half maximum (FWHM) was used to determine the skyrmion diameter along the given axis. The diameter used in the main text was calculated by D skyrmion = (D 2 y=0 + D 2 x=0 + D 2 y=x + D 2 y=-x ) / 4 , and the diameter of the represented skyrmion in Supplementary Fig. 7 was measured to be ~117 nm using this formula. The skyrmion diameters and domain widths mentioned in the main text were calculated following this method.
In the main text, we first generated multiple magnetic skyrmions electrically, and then isolated a single skyrmion for dynamics measurement by applying external magnetic field.
Because one might think that the isolated skyrmion is a pinned skyrmion, in this note, we show how a skyrmion behaves in the presence of skyrmion pinning sites. In a previous study by Woo et al. 3 , it was shown that the pinned skyrmions annihilate rather easily by external magnetic field or electric current. Because a local variation in interface-induced DMI is likely responsible, they show that skyrmions pinned at a region with locally reduced DMI has a lower energy barrier for annihilation. Analogously, we believe that our studied skyrmion, which survived even at a high background magnetic field, has more ideal internal magnetic structure resembling an ideal skyrmion structure with the largest local DMI. To reveal the effect of skyrmion pinning on its dynamic behaviors, we have conducted additional micromagnetic simulations shown in Supplementary Fig. 8.
Supplementary Fig. 8 shows the effect of non-uniform DMI constant on skyrmion dynamics: i) displacement and ii) size variation. Supplementary Fig. 8a first shows the simulated distribution of DMI constant, which randomly varies between 1.5 mJ m -2 and 1.9 mJ m -2 across a simulation mesh. Note that the variation is only ~20 % with respect to the measured average DMI value, 1.68 mJ m -2 . We employed random DMI distribution, which is the likely case in a real sample. We first created a single skyrmion and the skyrmion found its stabilized position and size in the given potential landscape. To mimic the experimental studies shown in Fig. 4 of the main text, we applied bipolar current pulses (with the same profile shown in Fig. 4b of the main text) and examined the displacement and size variation of a skyrmion by varying the pulse amplitude from 1 V to 5 V. Supplementary Fig. 8c and d reveal that, regardless of pulse amplitude, the skyrmion behaves in a very random fashion in the presence of DMI pinning. More importantly, for both travel distance and size variation, the skyrmion never came back to its original state.
Note that the stroboscopic pump-probe technique of MTXM restricts the imaging to fully reproducible magnetic events by synchronizing the incoming X-ray photon flashes (probe) and injecting current pulses (pump). This analysis reveals that, if observed skyrmion was at or near DMI pinning sites, we could not observe its dynamical behavior using stroboscopic time-resolved X-ray measurement. Thus, we believe that the observed skyrmion in main text was positioning at a region where the interfacial DMI is quite uniform, where the variation is significantly lower than 20%. It also agrees well with previous report, revealing the low-pinning characteristic of the amorphous-CoFeB based ferromagnetic multilayers. 3