High-speed domain wall racetracks in a magnetic insulator

Recent reports of current-induced switching of ferrimagnetic oxides coupled to heavy metals have opened prospects for implementing magnetic insulators into electrically addressable devices. However, the configuration and dynamics of magnetic domain walls driven by electrical currents in insulating oxides remain unexplored. Here we investigate the internal structure of the domain walls in Tm3Fe5O12 (TmIG) and TmIG/Pt bilayers, and demonstrate their efficient manipulation by spin–orbit torques with velocities of up to 400 ms−1 and minimal current threshold for domain wall flow of 5 × 106 A cm−2. Domain wall racetracks are defined by Pt current lines on continuous TmIG films, which allows for patterning the magnetic landscape of TmIG in a fast and reversible way. Scanning nitrogen-vacancy magnetometry reveals that the domain walls of TmIG thin films grown on Gd3Sc2Ga3O12 exhibit left-handed Néel chirality, changing to an intermediate Néel–Bloch configuration upon Pt deposition. These results indicate the presence of interfacial Dzyaloshinskii–Moriya interaction in magnetic garnets, opening the possibility to stabilize chiral spin textures in centrosymmetric magnetic insulators.

plane SQUID measurements performed in the film before (blue) and after exposure of the surface to the Ar-plasma (black), which reproduces the exposure of the TmIG surface to the Ar-plasma in the TmIG(8.3 nm)/Pt(5.0 nm) sample during the etching of the Pt layer. For calculating / , we considered that the effective thickness of the TmIG layer has been reduced to 7.5 nm after exposure of the surface to the Ar-plasma due to both etching and surface passivation.

Saturation magnetization
The magnetization of TmIG is known to be sensitive to the film thickness as well as to oxygen content. Indeed, a significant reduction of 3 compared to bulk values (~110 kA m -1 , see Supplementary Ref. 3) has been reported to occur for TmIG films below ~10 nm thickness 4,5 , which can be due to either finite size effects 4 or a slight oxygen deficiency caused by low oxygen pressure during growth 2,6 . The SQUID measurements reported in Supplementary Figs. 3a and 4 show that our TmIG(8.3 nm)/Pt(5.0 nm) and TmIG(8.5 nm) films present a reduced Ms compared to the bulk. Importantly, both films exhibit perpendicular magnetic anisotropy, both before and after exposure of the films to Ar-plasma. For the TmIG(8.3 nm)/Pt(5.0 nm) sample, the Ar-plasma was employed to pattern the Pt layer into racetrack devices (see Methods). For the reference TmIG(8.5 nm) film, the surface was exposed to the Ar-plasma in order to reproduce the exposure time of the TmIG surface of the TmIG(8.3 nm)/Pt(5.0 nm) sample during the etching of the Pt layer. The exposure time was set according to the calibrated etching rate of Pt determined using Pt reference films.
For calculating 3 from the SQUID measurements, we assume that the effective TmIG thickness of the TmIG/Pt sample is reduced by about 1 nm to 7.3 nm after the etching of the Pt due to partial etching (as evidenced by AFM, see Supplementary Fig. 2) and likely passivation of the top surface of the TmIG layer, as suggested by the comparison of the SQUID data taken for the reference TmIG(8.5 nm) film before and after exposure to the Ar-plasma (see Supplementary Fig. 4), and between the measured 3 of the pristine reference TmIG film and the TmIG/Pt sample after etching. By assuming 1 nm reduction of the TmIG thickness, the SQUID measurements indicate that the saturation magnetization is 3 = (55 ± 2) kA m -1 and 3 = (52 ± 3) kA m -1 in the reference TmIG film before and after the Ar-plasma exposure ( Supplementary Fig. 4), respectively, and that 3 = (59 ± 2) kA m -1 in the TmIG/Pt sample after etching (red curve, Supplementary Fig. 3a). Note that some portion of the film surface is still covered with Pt after etching, which explains the slightly larger 3 measured for the Pt/YIG sample (see also the NV magnetometry data below).
The saturation magnetization in TmIG/Pt is larger than in TmIG (see Supplementary Fig. 3a).
From SQUID measurements, we find that in TmIG/Pt the saturation magnetization is 3 = (77 ± 2) kA m -1 , which corresponds to a difference in 3 of ~20 kA m -1 with respect to TmIG. This difference is likely to be due to a partial polarization of the Pt atoms in proximity with TmIG. By assuming that the first three atomic layers of Pt in contact with TmIG get polarized, we estimate that this difference is equivalent to a magnetic moment per Pt atom of about 0.4 7 .
The surface magnetization / obtained by NV magnetometry measurements compare well with the saturation magnetization measured by SQUID. By dividing the measured / of the TmIG/Pt sample after etching (see Fig. 2) by = 8.3 nm and = 7.3 nm for the TmIG/Pt and TmIG regions, respectively, we obtain 3 = (75 ± 2) kA m -1 and 3 = (50 ± 3) kA m -1 . Regarding the reference sample, the surface magnetization measured before the exposure of the surface to the Ar-plasma was / = (48.9 ± 3.2) 7 nm -2 , which corresponds to 3 = (53 ± 4) kA m -1 (see also Supplementary Note 7).

Coercive field
The coercive field measured by SQUID for the TmIG(8.3 nm/Pt(5.0 nm) sample changes from 9 ~ 13 to ~ 6 Oe after etching and patterning of the Pt film (see Supplementary Fig. 3a). A reduction of 9 from ∼ 19 to ~ 6 Oe, is also observed in the reference TmIG(8.5 nm) layer after exposure to the Ar-plasma (see Supplementary Fig. 4). Although the coercive field is reduced due to the etching process, the saturation field of TmIG(8.5 nm) is similar to the one measured before etching. However, the saturation field of TmIG/Pt increases substantially after patterning the Pt layer into Hall bar-like racetrack devices, which indicates that having a combination of etched TmIG and unetched TmIG/Pt regions at the surface of the film influences the magnetization reversal process.
Spatially-resolved wide-field MOKE measurements performed on the TmIG/Pt sample after patterning of the Pt layer show that the coercive field in the region underneath the Pt devices is usually much larger than in the area next to them. Supplementary Figures 3b,c show representative MOKE measurements taken on an area partially covered by Pt during field-driven magnetization reversal.
Starting from a fully magnetized state with / < 0, we observe that most of the area surrounding the device has already switched at / = +20 Oe (white contrast in Supplementary Fig. 3c, bottom image), whereas the area covered by Pt remains magnetized down (dark contrast). Further increase of the magnetic field results in a sharp switching of the whole area underneath the Pt-device at / ~+ 40 Oe (see violet curve in Supplementary Fig. 3b; note that the coercive field is similar to the one obtained by AHE-like measurements, see Fig. 1b). These measurements suggest that, besides changes of the magnetic anisotropy that may occur between the TmIG/Pt and TmIG regions, the edges of the Pt pattern act as pinning centres that prevent the free expansion of domains and domain walls during a magnetic field sweep, thus influencing the magnetization reversal dynamics. Note that different coercive fields were measured in different regions and devices across the film, which we attribute to the particular local distribution of defects.
These observations support the idea that the low-concentration of pinning centres present in TmIG is the most relevant ingredient for the square-like magnetization reversal observed in the pristine TmIG/Pt (blue dots in Supplementary Fig. 3a and Supplementary Fig. 4). The more progressive reversal of the magnetization measured on the same sample after etching of the Pt layer (red dots in Supplementary Fig. 3a), which starts at a lower applied magnetic field, is consistent with the presence of additional surface defects introduced by the etching process, which act as both domain nucleation and domain wall pinning centres, resulting in a more complex magnetization reversal process. The observed reduction in the coercive field of the TmIG reference film after Ar-plasma exposure, and the progressive approach to saturation upon magnetization reversal, with similar saturation field than the one measured before etching, is consistent with the interpretation that nucleation centres are likely introduced along the surface, which modify the magnetization reversal process, but without resulting in a noticeable modification of the magnetic anisotropy or saturation magnetization of the film. According to the theory of the spin Hall magnetoresistance (SMR), the first harmonic response of the magnetoresistance in TmIG/Pt can be described as 7,8 :

Supplementary Note 3. Electrical characterization of TmIG/Pt by spin
where and denote the polar and azimuthal angle of the normalized magnetization vector = ( , , )/ 3 collinear to the applied field (see Supplementary Fig. 5a), /2 = 0.1 is the width/length ratio of the measuring configuration of the Hall bar (i.e., 10/100, see Supplementary Fig.   5a), L is the longitudinal base resistance, Δ NOP the SMR amplitude, _^`, NOP the anomalous Halllike SMR amplitude, and d^`/ the ordinary Hall resistance. Supplementary Fig. 5b shows the normalized ( EE − L )/ L angular dependent magnetoresistance measurements performed in our sample with rotating along the three main planes of the sample. L is determined to be ~640 W.
The change in resistance follows the expected behaviour for SMR 7,9 : i) a sin U dependence for rotating in the plane of the film (green, = 90°), ii) a distorted sin U dependence for rotating in the -plane (blue, = 90°) due to the strong demagnetizing field, and iii) no significant change when rotates in the -plane (red, = 0° where N^ is the spin-Hall angle, Ž the spin diffusion length,

Supplementary Note 4. Factors influencing magnetization reversal beyond the Pt current line: DW depinning field, Joule heating and the Oersted field
As presented in the manuscript, a precise control of the magnetic moment underneath the Pt current line can be achieved in a continuous TmIG film by applying current pulses in the Pt line without altering the magnetic moments of the surrounding region (Fig. 1d). However, the extremely small depinning field of the DWs in TmIG (~ 1-2 Oe, see Supplementary Fig. 6) makes the current-induced dynamics extremely sensitive to the presence of out-of-plane magnetic fields. Supplementary Fig. 7 shows a sequence of differential MOKE images taken during forward switching in the presence of an out-of-plane field / ~ 2 Oe, showing that, in contrast to what is observed in Fig. 1d and Fig. 3b contraction. Within the experimental error, ¥¦ remains roughly constant although ˜ changes by a factor of ~4, which allows us to conclude that the DW speed is accurately evaluated upon changing ˜ and not influenced by DW inertia. We attribute the slight increase of ¥¦ at large ˜ to Joule heating.
For the measurements presented in Fig. 4 we reduced the influence of Joule heating by measuring ¥¦ at the lower edge of the parameter space ˜ at any given E , E combination. Joule heating (as well as the Oersted field, see Supplementary Note 4) is found to influence the DW dynamics and magnetization switching at current densities ≳ 1 × 10 -A cm -2 . The error bars in b and c indicate the uncertainty in estimating ¥¦ from the DW displacement obtained for a sequence of current pulses.  Fig. 2). •± = (55 ± 2°) is determined by sample fabrication. Analysis of the stray field •± allows us to determine that •± = (83 ± 3)°.

Determination of the stand-off distance :
The sample-to-sensor distance is inferred in situ from the change in the stray field •± at the TIG/Pt edge (see Fig. 2b) due to the different magnetic response of TmIG relative to TmIG/Pt (see Fig. 2c), which we mainly attribute to a proximity induced polarization of the Pt layer (see second dataset taken in a reference TmIG film). The change in magnetization gives rise to a stray field that is added to the field produced by the DW. In order to disentangle both fields we use a differential approach by shifting the images along the -axis and subtracting them from each other, see Supplementary Fig. 16. In this way we cancel the domain wall stray field and end up with a stray field showing only two Pt edges. The magnetic stray field emanating from the Pt edges, with the image orientated such that they are aligned with the -direction, can be described analytically as where L , " denote the edge positions and 3,µ• is the surface magnetization of Pt. By fitting this model to the experimental line scan we can extract a value for the stand-off distance and 3,µ• .
Further fit parameters are the edge positions and the azimuth angle of the NV vector orientation. To improve statistics and estimate the error, we fit several line scans across the stripe using the same starting parameters and extract the mean value and standard error. For the image shown in Fig. 2b and Supplementary Fig. 16, we obtain = 104 ± 3.3 nm. Further stand-off distance measurements on a separate calibration sample (Pt/Co/AlOx) before and after the domain wall measurement are in good agreement with this value. To compensate for the fact that we have not included the height profile of the stripe as well as the Dzyaloshinskii-Moriya interaction, we deliberately over-estimated the error in the stand-off distance to be larger than the fit errors and set it to 5 nm.

Fits of the domain wall magnetization profile:
We fit several line scans of the DW in TmIG and TmIG/Pt using the same starting fit parameters as The last term describes the uncertainty due to the error of the stand-off distance . Since the fitting algorithm assumes the stand-off distance to be fixed, it is not included in the fitting results directly. We estimate ÍÎ Ï Ð Í" Ï via finite differences by repeating the fitting procedure with the stand-off distance equal to the error boundaries ± = ̅ ± with ̅ = 104 nm.

Second dataset: reference TmIG film
We recorded a second dataset with a different scanning probe ( = 66 ± 6 nm) on an unprocessed TmIG film of thickness 8.5 nm. Analysis of this second dataset yielded a chiral angle of = (180 ± 0)°, which corresponds to a pure left-handed chiral Néel domain wall structure, a DW width of ∆ ¥¦ = (20 ± 4) nm, and an out-of-plane surface magnetization / = (48.9 ± 3.2) 7 nm -2 , which corresponds to 3 = (53 ± 4) kA m -1 . These values are consistent with the ones presented in Fig. 2 for TmIG(8.3 nm), supporting the finding of a stronger DMI in an all-oxide structure without the presence of a metallic heavy metal layer.