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Observation of fluctuation-mediated picosecond nucleation of a topological phase


Topological states of matter exhibit fascinating physics combined with an intrinsic stability. A key challenge is the fast creation of topological phases, which requires massive reorientation of charge or spin degrees of freedom. Here we report the picosecond emergence of an extended topological phase that comprises many magnetic skyrmions. The nucleation of this phase, followed in real time via single-shot soft X-ray scattering after infrared laser excitation, is mediated by a transient topological fluctuation state. This state is enabled by the presence of a time-reversal symmetry-breaking perpendicular magnetic field and exists for less than 300 ps. Atomistic simulations indicate that the fluctuation state largely reduces the topological energy barrier and thereby enables the observed rapid and homogeneous nucleation of the skyrmion phase. These observations provide fundamental insights into the nature of topological phase transitions, and suggest a path towards ultrafast topological switching in a wide variety of materials through intermediate fluctuating states.

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Fig. 1: Topological magnetic phase transition mediated by a transient fluctuation state.
Fig. 2: All-optical topological switching in Pt/CoFeB/MgO and Pt/Co.
Fig. 3: Switching threshold in Pt/CoFeB/MgO as a function of laser pulse number, fluence and duration.
Fig. 4: Time-resolved observation of the topological phase transition.
Fig. 5: Atomistic simulation of laser-induced skyrmion nucleation.

Data availability

The data represented in Fig. 2 are provided in Extended Data Figs. 24. The data represented in Figs. 35 are available at Raw data generated at the European XFEL large-scale facility are available at

Code availability

The data analysis code used in this study is available with identifiers The code for the atomistic simulations is available from the corresponding author upon reasonable request.


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M.B. and B.D. gratefully acknowledge computing time at the Mogon supercomputers. We acknowledge the European XFEL in Schenefeld for provision of XFEL beamtime at the SCS instrument and thank the instrument group and facility staff for their assistance. In particular, we thank M. Teichmann, J. T. Delitz, A. Reich, C. Broers, M. Bergemann, E. Kamil, T. Kluyver, H. Fanghor, J. Moore, J. Engelke, M. Kuster, S. Hauf, K. Hansen, P. Fischer, C. Fiorini, D. Boukhelef, J. Szuba and K. Wrona for providing the instrumentation and infrastructure that enabled our experiment at the European XFEL. We thank M. Wieland and M. Drescher, Universität Hamburg, for providing us with their mobile laser hutch for the experiments at DESY. Work at MIT was supported by the DARPA TEE programme. Devices were fabricated using equipment in the MIT Microsystems Technology Laboratory and the MIT Nanostructures Laboratory. The samples were further manufactured at the TU Berlin Nano-Werkbank, which was supported by EFRE under contract no. 20072013 2/22. B.P., L.-M.K., K.G. and S.E. acknowledge financial support from the Leibniz Association via grant no. K162/2018 (OptiSPIN). L.C. acknowledges financial support from the NSF Graduate Research Fellowship Program and from the GEM Consortium. M.B. and B.D. acknowledge financial support from the Alexander von Humboldt Foundation, the Graduate School Materials Science in Mainz and the Transregional Collaborative Research Center (SFB/TRR) 173 SPIN+X. T.R.H. acknowledges the support of a postdoctoral fellowship from the Alexander von Humboldt Foundation. J.H.M. acknowledges funding from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) by a VENI grant and the Shell-NWO/FOM initiative ‘Computational sciences for energy research’ of Shell and Chemical Sciences, Earth and Life Sciences, Physical Sciences, FOM and STW.

Author information




B.P., F.B., G.S.D.B. and S.E. conceived the study. F.B., C.M.G., M.S., D.E., A. Churikova, I.L. and M.H. fabricated the samples. B.P., F.B., M.S., C.M.G., P.H., C.K., A.W., K.G., L.-M.K., C.S., C.v.K.S., J.F., A.C., S.H., L.C., S.Z. and K.B. performed the experiments at DESY and F.B., B.P., M.S., G.M., C.K., K.G., L.-M.K., S.H., L.C., D.S., R.C., L.M., J. Schlappa, A.Y., L.L.G., N.G., A. Scherz, C.D., R.G., D.H., J.Z., M.T. and D.L. performed the experiments at XFEL. F.E., A. Castoldi, S.M., M.P. and A. Samartsev remotely supported the DSSC detector calibration and operation. J.H.G., M.M. and T.R.H. performed the LTEM experiments. F.B., B.P., M.S., K.G., P.H., C.K. and A.W. analysed the X-ray experiments. B.D. and M.B. performed the atomistic modelling with support from J.H.M. F.B., B.P., J.H.M. and B.D. interpreted the results. B.P., F.B., M.S., A.W., K.G. and B.D. prepared the figures and F.B. and J.H.M. wrote the manuscript with input from B.P., B.D., G.S.D.B. and S.E. Supervision was by C.R., J. Sinova, G.S.D.B. and S.E. All the authors commented on the manuscript.

Corresponding authors

Correspondence to Felix Büttner or Bastian Pfau.

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Extended data

Extended Data Fig. 1 Process of holographic image reconstruction.

a, Hologram recorded with positive helicity light. b, Hologram recorded with negative helicity light. c, Difference hologram (positive minus negative helicity hologram). d, Patterson map (Fourier transform of difference hologram) showing four reconstructions and their complex conjugates. e, Magnification of a selected reconstruction. f, Reconstruction propagated to the reference focus point43.

Extended Data Fig. 2 Scanning electron micrographs of the holography samples employed in this study.

ac, Pt/CoFeB/MgO samples with patterned tracks for current injection. The holographic field of view (FOV) is defined by an aperture in the Cr/Au mask on the opposite sample side and is visible as shadow behind the tracks. The reference pinholes (four pinholes in (a) and (b), one pinhole in (c)) have their smallest exit aperture also at the opposite sample side, that is, the mask side. The sample in (a) was used for Figs. 2a and 3, sample in (b) for Fig. 2b, and the sample in (c) for Supplementary Section 1. d, Pt/Co sample with continuous magnetic film. The FOV appears as a shadow approximately in the center of the image and is surrounded by four reference pinholes with their smallest exit on the Pt/Co film side. The sample was used for Fig. 2c.

Extended Data Fig. 3 Measurement of the skyrmion topology via the skyrmion Hall effect.

a, For Bz = 37 mT. b, For Bz = − 36 mT. The first image in each sequence was produced by a single >16 mJ/cm2 laser pulse from a saturated state. Between subsequent images, single current pulses of the indicated polarity and direction (4 ns duration and between 7 × 1011 A/m2 and 9 × 1011 A/m2 in amplitude) were applied. The size of all circles is 1.3 μm. c,d, Spin structures of a negative polarity (black in x-ray images) and positive polarity (white) skyrmion, respectively.

Extended Data Fig. 4 Lorentz transmission electron (L-TEM) micrographs of Pt/Co.

a, Transport of intensity reconstruction Fig. 2d of the main paper. The color shows in-plane orientation of magnetization, as indicated by the color wheel. b, Representative L-TEM image of a stripe domain state at zero field obtained by adiabatic field cycling. White circles highlight vertical Bloch lines (note that the signal-to-noise ratio is not sufficient in this case to perform the TIE analysis). Both images were recorded in overfocus conditions45. Scale bars, 1 μm.

Extended Data Fig. 5 Simulated and experimentally observed spatial distribution of nucleated skyrmions.

a, Simulated integrated skyrmion count of 1000 skyrmions (10 px diameter) distributed according to a homogeneous nucleation probability in a 100 px diameter field of view. b, 1000 skyrmions distributed with 100 % probability in the central pixel. c, Experimentally observed distribution of optically-nucleated skyrmions (reproduced from Fig. 3 in the main text). d, Experimentally observed distribution of spin–orbit torque nucleated skyrmions (reproduced from24). The horizontal diameters of the fields of view are 100 px in (a) and (b), 1490 nm in (c) and 900 nm in (d). See Supplementary Section 4 for details.

Extended Data Fig. 6 Small-angle x-ray scattering during a magnetic field sweep recorded with various attenuation levels of the x-ray beam.

The membrane sample is topographically homogeneous, which means that any scattering is due to non-uniformities in the magnetic landscape. Arrows indicate the saturation field Hs (the field at which the scattering signal becomes zero), the nucleation field Hn (the field at which the scattering signal starts to deviate from the background value) and the coercive field Hc (the field at which the average magnetization is zero). Light gray arrows indicate the field sweep direction. Spectra were recorded for variable x-ray fluence by varying the transmission in a gas attenuator. The legend states the maximum peak fluence values encountered, assuming a Gaussian beam profile with a width of 30 μm (FWHM). X-ray induced skyrmion nucleation and annihilation is evidenced by an increased domain nucleation field and a reduced saturation field, respectively.

Extended Data Fig. 7 Schematic of the experimental sequence.

a, Hysteresis loop of Pt/Co and illustration of the measurement cycle and static hysteresis loop of the magnetic multilayer. The measurements starts at ‘init’ by saturating the sample (263 mT) and reducing the field to the open hysteresis area (83 mT, point 1). The laser pulse then nucleates skyrmions (3) via a transient state (2). The inset shows the full hysteresis loop of our Pt/Co multilayer. b, Schematic of the time traces of magnetic field, x-ray pulses, and infrared laser pulses during three successive cycles. Ideally each cycle would start with a field sweep to saturate the same and then keep the sample at remanence at μ0Hz = 83 mT. The pump–probe sequence consisting of three x-ray pulses and one infrared laser pulse would be applied during this stable low field time. The second and third cycle illustrate possible deviations from this scheme. As shown in the second cycle, the intensity of x-ray pulses can vary wildly and in some cases one of the three x-ray pulse intensities is so low that no conclusion can be drawn from the data. Moreover, as illustrated in the third sequence, the magnetic field did not always respond to the set commands, in which case no skyrmions were nucleated. Both the second and the third type of trains were rejected from the analysis.

Extended Data Fig. 8 Scattering spectra at all measured time delays.

Orange curves show the azimuthally averaged time-dependent scattering data, which is almost constant as a function of q for small delays and localizes towards smaller q at later times. Blue and green lines show the corresponding initial and final state spectra, respectively. The low q cutoff is due to missing pixels of the detector around the central beam.

Extended Data Fig. 9 Fits of the peaks of the q-dependent intensity distributions with a local parabola.

Each panel shows the transient and final state spectra corresponding to the indicated delay. Solid lines are fits to the data. Data points considered for the fit are plotted in full contrast while all other data points are plotted with reduced contrast. The inverse of the position of the maximum of each fit, 2π/qpeak, is the correlation length, which is a measure of the average skyrmion distance.

Extended Data Fig. 10 Natural logarithm of the scattered intensity versus the squared scattering momentum q2.

The time delay is indicated in each panel. Each panel shows the background-corrected transient and final state spectra and the Guinier fits52 of the peak shoulders. The legend provides the radii of gyration extracted from the fits.

Supplementary information

Supplementary Information

Supplementary discussion and Figs. 1–11.

Supplementary Video 1

The video shows four panels. On top is a plot of the total topological charge and the bath temperature as a function of time. A black vertical line indicates the current time of the simulation. Below are three panels, showing the normalized out-of-plane magnetization, the local topological charge density and a low-pass filtered version of the local topological charge density, where the filter size of the low-pass filter in reciprocal unit cells is indicated in the filtered image.

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Büttner, F., Pfau, B., Böttcher, M. et al. Observation of fluctuation-mediated picosecond nucleation of a topological phase. Nat. Mater. 20, 30–37 (2021).

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