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# Current-driven dynamics and ratchet effect of skyrmion bubbles in a ferrimagnetic insulator

## Abstract

Magnetic skyrmions are compact chiral spin textures that exhibit a rich variety of topological phenomena and hold potential for the development of high-density memory devices and novel computing schemes driven by spin currents. Here, we demonstrate the room-temperature interfacial stabilization and current-driven control of skyrmion bubbles in the ferrimagnetic insulator Tm3Fe5O12 coupled to Pt, showing the current-induced motion of individual skyrmion bubbles. The ferrimagnetic order of the crystal together with the interplay of spin–orbit torques and pinning determine the skyrmion dynamics in Tm3Fe5O12 and result in a strong skyrmion Hall effect characterized by a negative deflection angle and hopping motion. Further, we show that the velocity and depinning threshold of the skyrmion bubbles can be modified by exchange coupling Tm3Fe5O12 to an in-plane magnetized Y3Fe5O12 layer, which distorts the spin texture of the skyrmions and leads to directional-dependent rectification of their dynamics. This effect, which is equivalent to a magnetic ratchet, is exploited to control the skyrmion flow in a racetrack-like device.

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## Data availability

The data that support the findings of this study have been deposited in the Research Collection database of the ETH Zurich and are available from https://doi.org/10.3929/ethz-b-000542503.

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## Acknowledgements

We acknowledge A. Thiaville, A. Hrabec and C. Moutafis for useful discussions and M. Müller for technical assistance with the MOKE set-up. This work was funded by the Swiss National Science Foundation (grant nos. 200020-200465 (P.G.), 200021-188414 (M.T.), 200021-178825 (M.F.), PZ00P2-179944 (B.J.J.) and 200020-175600 (C.L.D.)), the European Research Council (Advanced Grant 694955-INSEETO (M.F.)) and ETH Zürich (Career Seed Grant SEED-20 19-2 (S.V.)). S.R.-G. acknowledges support from the Spanish Ministry of Economy and Competitiveness (FPI fellowship and grant no. RTI2018-095303-B-C53). S.V. acknowledges financial support by the Ministry of Science, Innovation and Universities through the Maria de Maeztu Program for Units of Excellence in R&D (grant no. CEX2018-000805-M) and the Comunidad de Madrid through the Atracción de Talento program (grant no. 2020-T1/IND-20041).

## Author information

Authors

### Contributions

S.V. conceived the study and coordinated the experimental work. J.S., E.G. and M.T. grew and characterized the films. S.V. fabricated the devices. S.V. and S.R.-G. performed the transport and MOKE experiments and analysed the data. B.J.J. assisted with the time-resolved transport measurements. M.S.W. and P.W. performed the NV measurements with the help of S.V. S.V. and P.G. wrote the manuscript. P.G., M.T., C.L.D. and M.F. supervised the work. All authors contributed to the scientific discussion and manuscript revisions.

### Corresponding authors

Correspondence to Saül Vélez or Pietro Gambardella.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Nanotechnology thanks the anonymous reviewers for their contribution to the peer review of this work.

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## Extended data

### Extended Data Fig. 1 Skyrmion bubble radius.

a, Differential MOKE image of a representative Q = +1 skyrmion bubble for $$H_z = - 20$$ Oe. The white (dark) contrast indicates regions with m of TmIG pointing up (down). Scale bar, 1 μm. b, Line profile of the MOKE intensity taken along the red dashed line in a (red solid line) together with its fitting (light grey) assuming that the skyrmion is a square box function having an ellipsoidal shape convoluted by a Gaussian function with standard deviation ~300 nm, which represents the spatial resolution of the MOKE set up49. The domain wall width, which is $${{\Delta }}_{{{{\mathrm{DW}}}}}\sim 60$$ nm (Fig. 2), is neglected in the fitting procedure. The main diameters a and b of the skyrmion bubble are extracted by fitting the two orthogonal axes of the ellipsoid. From the fit in b we estimate $$a\sim 1.2$$ μm. c, Skyrmion bubble radius R as a function of $$H_z$$. The radius is estimated as $$R = (a + b)/4$$. Each data point corresponds to the average value obtained from fitting over 10 independent skyrmion bubbles with circular shape ($$b/a \gtrsim 0.9$$). The error bars represent the standard deviation of the measurements. See Supplementary Note 6 for discussion on the field dependence of the skyrmion bubble radius and bubble stabilization with $$H_z$$.

### Extended Data Fig. 2 Skyrmion ellipticity and orientation.

a, Statistical analysis of the skyrmion ellipticity b/a from fitting over 1000 skyrmion bubbles assuming an ellipsoidal shape (see schematic). The histograms are extracted from analyzing the MOKE images of the bubble trajectories presented in Fig. 4a. b, Analysis of the orientation of the skyrmion ellipsoids from the data in a. The angle β defines the orientation of the longest axis of the ellipsoid with respect to the current (see schematic).

### Extended Data Fig. 3 Jx−tp threshold conditions for skyrmion depinning (blue circles), heat dominated motion (red triangles), and random nucleation and annihilation of skyrmion bubbles in TmIG (black squares).

$$|H_z| = 20$$ Oe and the YIG layer is demagnetized. No difference was observed between $$Q = + 1$$ and $$- 1$$ skyrmion bubbles. Supplementary Note 9 presents the current threshold for skyrmion depinning in the presence of $${{{\mathbf{H}}}}_y$$, that is, with $${{{\mathbf{M}}}}_{{{{\mathrm{YIG}}}}}$$ controlled with an in-plane magnetic field. All measurements of the skyrmion dynamics presented in this work were performed for $$t_{{{\mathrm{p}}}},\left| {J_x} \right|$$ conditions comprised between the curves defined by the blue circles and the red triangles. Above the threshold defined by the red triangles, the mean displacements $$\overline {\Delta x} ,\overline {\Delta y}$$ abruptly drop, indicating that the skyrmion dynamics are dominated by Joule heating induced random skyrmion motion rather than by SOTs. We attribute this behavior to the exponential increase of the skyrmion diffusivity with temperature, which is expected in materials with low disorder and low damping such as TmIG9.

### Extended Data Fig. 4 Current-induced temperature increase.

a, Schematic of the experimental setup. The voltage output of the pulse generator is applied through the device and both the voltage drop at the device and the pulse are monitored with an Oscilloscope with an internal impedance of 50 Ω. From these measurements, we can precisely determine the evolution of the sample resistance during the current pulse. b, Increase of the sample resistance during the application of a current pulse $$t_{{{\mathrm{p}}}} = 100$$ ns (left axis). The pulse starts at time 0 ns. The colour indicates different set currents computed from the base resistance of the device $$R_0(295\;{{{\mathrm{K}}}}) = 1130$$ Ω. The right axis shows the increase of temperature calculated from calibration measurements. We estimate the threshold for heat dominated motion for temperature increases of about 20 K.

### Extended Data Fig. 5 Mean $$\overline {\Delta {{{\mathbf{x}}}}}$$ and $$\overline {\Delta {{{\mathbf{y}}}}}$$ displacements for YIG demagnetized.

a, b, Average bubble displacements per pulse $$\overline {\Delta x}$$ and $$\overline {\Delta y}$$ as a function of $$t_{{{\mathrm{p}}}}$$ computed considering all pulse events, that is, including those that did not lead to bubble displacements. $$\overline {\Delta x}$$ and $$\overline {\Delta y}$$ increase linearly with the pulse length, exhibiting a finite value as $$t_{{{\mathrm{p}}}} \to 0$$. The difference between $$\overline {\Delta x}$$,$$\overline {\Delta y}$$ and $$x_0,y_0$$ (Fig. 4c,d) arises from the decrease of the bubble depinning probability when decreasing $$t_{{{\mathrm{p}}}}$$. Different symbols indicate different current densities. $$H_z = - 20$$ Oe ($$Q = + 1$$). YIG is demagnetized.

### Extended Data Fig. 6 Pulse length dependence of $${{{\boldsymbol{x}}}}_0,{{{\boldsymbol{y}}}}_0$$ with $${{{\mathbf{M}}}}_{{{{\mathbf{YIG}}}}}$$ along $$- {{{\mathbf{y}}}}$$.

a, b, Mean displacement values $$x_0,y_0$$ extracted from the trajectory of several skyrmion bubbles with $${{{\mathbf{M}}}}_{{{{\mathrm{YIG}}}}}$$ along $$- {{{\mathbf{y}}}}$$ (see Fig. 4a,b for details regarding the analysis). Data taken for $$H_z = - 20$$ Oe ($$Q = + 1$$) and for both polarities of $${{{\mathbf{J}}}}_x$$ (indicated by an arrow). The sign of $$x_0,y_0$$ corresponds to the sign of $${{{\mathbf{J}}}}_x.$$ Different colours indicate the current density. The error bars are the standard errors of $$x_0$$, $$y_0$$ calculated from the variance of these magnitudes to the double Gaussian distribution of $$\delta x,\delta y$$. As for the case of YIG demagnetized (Fig. 4c,d), $$x_0$$ and $$y_0$$ tend to finite values when $$t_{{{\mathrm{p}}}} \to 0$$. Remarkably, the $$x_0,y_0(t_{{{\mathrm{p}}}} \to 0)$$ values are similar for both directions of $${{{\mathbf{J}}}}_{{{\mathrm{x}}}}$$ and similar to the ones measured for YIG demagnetized. As $$t_{{{\mathrm{p}}}}$$ increases, $$x_0$$ and $$y_0$$ start to increase from a pulse length threshold value that depends on the amplitude of the current. Larger (smaller) current densities are required for driving skyrmion bubbles with $${{{\mathbf{M}}}}_{{{{\mathrm{YIG}}}}}$$ pointing to $$- {{{\boldsymbol{y}}}}$$ and $$J_{{{\mathrm{x}}}} < 0$$ ($$J_{{{\mathrm{x}}}} > 0$$), which is in agreement with the ratchet effect reported in Figs. 5 and 6 and Supplementary Note 10. c, Velocity of the skyrmion bubbles computed as $$\left| {v_0} \right| = \sqrt {x_0^2 + y_0^2} /t_{{{\mathrm{p}}}}$$ from the data shown in a and b. The sign of the velocity is defined by the sign of $$x_0$$; the error bars are computed by error propagation. As observed for the mean bubble velocity $$\bar v_{{{{\mathrm{sk}}}}}$$ for YIG demagnetized (Fig. 4e), $$v_0$$ increase as $$t_{{{\mathrm{p}}}}$$ reduces (note that $$v_0(t_{{{\mathrm{p}}}})$$ exhibits a stepper increase than $$\bar v_{{{{\mathrm{sk}}}}}(t_{{{\mathrm{p}}}})$$ when reducing tp).

### Extended Data Fig. 7 Skyrmion trajectories with MYIG collinear to Jx.

a, Skyrmion trajectories with Q=−1 and YIG demagnetized (see inset’s schematic). Data taken in a different device from the same YIG/TmIG/Pt heterostructure. Hz=+20 Oe, $$J_x = 3.5 \times 10^{11}$$ A m−2, and tp=20 ns. The measurement protocol is the same employed in Fig. 4a. b, c, Skyrmion trajectories for MYIG pointing to +x and x, respectively. $$\left| {H_x} \right| = 10$$ Oe. In contrast to the difference observed between MYIG parallel to +y and −y (Figs. 5a and b), the skyrmion dynamics for MYIG collinear with the current is, within the error, independent on the direction of MYIG. No clear differences between $${{{\mathbf{M}}}}_{{{{\mathrm{YIG}}}}}\parallel \pm {{{\mathbf{x}}}}$$ (b,c) and the demagnetized case (a) can be identified either.

## Supplementary information

### Supplementary Information

Supplementary Notes 1–10, Figs. 1–11 and Table 1.

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Vélez, S., Ruiz-Gómez, S., Schaab, J. et al. Current-driven dynamics and ratchet effect of skyrmion bubbles in a ferrimagnetic insulator. Nat. Nanotechnol. 17, 834–841 (2022). https://doi.org/10.1038/s41565-022-01144-x

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