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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The data analysis code used in this study is available with identifiers https://doi.org/10.5281/zenodo.4017322. The code for the atomistic simulations is available from the corresponding author upon reasonable request.
Wall, S. et al. Ultrafast disordering of vanadium dimers in photoexcited VO2. Science 362, 572–576 (2018).
Vogelgesang, S. et al. Phase ordering of charge density waves traced by ultrafast low-energy electron diffraction. Nat. Phys. 14, 184–190 (2018).
Zong, A. et al. Evidence for topological defects in a photoinduced phase transition. Nat. Phys. 15, 27–31 (2019).
Stojchevska, L. et al. Ultrafast switching to a stable hidden quantum state in an electronic crystal. Science 344, 177–180 (2014).
Zurek, W. H. Cosmological experiments in condensed matter systems. Phys. Rep. 276, 177–221 (1996).
Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181–1203 (1973).
Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).
Sie, E. J. et al. An ultrafast symmetry switch in a Weyl semimetal. Nature 565, 61–66 (2019).
Yamasaki, Y. et al. Dynamical process of skyrmion–helical magnetic transformation of the chiral-lattice magnet FeGe probed by small-angle resonant soft X-ray scattering. Phys. Rev. B 92, 220421 (2015).
Zhao, X. et al. Direct imaging of magnetic field-driven transitions of skyrmion cluster states in FeGe nanodisks. Proc. Natl Acad. Sci. USA 113, 4918–4923 (2016).
Wild, J. et al. Entropy-limited topological protection of skyrmions. Sci. Adv. 3, e1701704 (2017).
Berruto, G. et al. Laser-induced skyrmion writing and erasing in an ultrafast cryo-Lorentz transmission electron microscope. Phys. Rev. Lett. 120, 117201 (2018).
Je, S.-G. et al. Creation of magnetic skyrmion bubble lattices by ultrafast laser in ultrathin films. Nano Lett. 18, 7362–7371 (2018).
Barman, A. et al. Ultrafast magnetization dynamics in high perpendicular anisotropy [Co/Pt]n multilayers. J. Appl. Phys. 101, 09D102 (2007).
Pfau, B. et al. Ultrafast optical demagnetization manipulates nanoscale spin structure in domain walls. Nat. Commun. 3, 1100 (2012).
Lambert, C.-H. et al. All-optical control of ferromagnetic thin films and nanostructures. Science 345, 1337–1340 (2014).
Cape, J. A. & Lehman, G. W. Magnetic domain structures in thin uniaxial plates with perpendicular easy axis. J. Appl. Phys. 42, 5732–5756 (1971).
Grundy, P. J. Magnetic bubbles and their observation in the electron microscope. Contemp. Phys. 18, 47–72 (1977).
Büttner, F. et al. Dynamics and inertia of skyrmionic spin structures. Nat. Phys. 11, 225–228 (2015).
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).
Montoya, S. A. et al. Tailoring magnetic energies to form dipole skyrmions and skyrmion lattices. Phys. Rev. B 95, 024415 (2017).
Pollard, S. D. et al. Observation of stable Néel skyrmions in cobalt/palladium multilayers with Lorentz transmission electron microscopy. Nat. Commun. 8, 14761 (2017).
Romming, N. et al. Writing and deleting single magnetic skyrmions. Science 341, 636–639 (2013).
Büttner, F. et al. Field-free deterministic ultrafast creation of magnetic skyrmions by spin–orbit torques. Nat. Nanotechnol. 12, 1040–1044 (2017).
Büttner, F., Lemesh, I. & Beach, G. S. D. Theory of isolated magnetic skyrmions: from fundamentals to room temperature applications. Sci. Rep. 8, 4464 (2018).
Bergeard, N. et al. Irreversible transformation of ferromagnetic ordered stripe domains in single-shot infrared-pump/resonant-X-ray-scattering-probe experiments. Phys. Rev. B 91, 054416 (2015).
Iacocca, E. et al. Spin–current-mediated rapid magnon localisation and coalescence after ultrafast optical pumping of ferrimagnetic alloys. Nat. Commun. 10, 1756 (2019).
Litzius, K. et al. Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy. Nat. Phys. 13, 170–175 (2017).
Jiang, W. et al. Direct observation of the skyrmion Hall effect. Nat. Phys. 13, 162–169 (2016).
Everschor-Sitte, K., Sitte, M., Valet, T., Abanov, A. & Sinova, J. Skyrmion production on demand by homogeneous DC currents. New J. Phys. 19, 092001 (2017).
Eggebrecht, T. et al. Light-induced metastable magnetic texture uncovered by in situ Lorentz microscopy. Phys. Rev. Lett. 118, 097203 (2017).
Lemesh, I. et al. Current-induced skyrmion generation through morphological thermal transitions in chiral ferromagnetic heterostructures. Adv. Mater. 30, 1805461 (2018).
Janoschek, M. et al. Fluctuation-induced first-order phase transition in Dzyaloshinskii–Moriya helimagnets. Phys. Rev. B 87, 134407 (2013).
Rózsa, L., Simon, E., Palotás, K., Udvardi, L. & Szunyogh, L. Complex magnetic phase diagram and skyrmion lifetime in an ultrathin film from atomistic simulations. Phys. Rev. B 93, 024417 (2016).
Böttcher, M., Heinze, S., Egorov, S., Sinova, J. & Dupé, B. B–T phase diagram of Pd/Fe/Ir(111) computed with parallel tempering Monte Carlo. New J. Phys. 20, 103014 (2018).
Koshibae, W. & Nagaosa, N. Creation of skyrmions and antiskyrmions by local heating. Nat. Commun. 5, 5148 (2014).
Kim, D.-H. et al. Bulk Dzyaloshinskii–Moriya interaction in amorphous ferrimagnetic alloys. Nat. Mater. 18, 685–690 (2019).
Graves, C. E. et al. Nanoscale spin reversal by non-local angular momentum transfer following ultrafast laser excitation in ferrimagnetic GdFeCo. Nat. Mater. 12, 293–298 (2013).
Kazantseva, N., Nowak, U., Chantrell, R. W., Hohlfeld, J. & Rebei, A. Slow recovery of the magnetisation after a sub-picosecond heat pulse. Europhys. Lett. 81, 27004 (2007).
Litzius, K. et al. The role of temperature and drive current in skyrmion dynamics. Nat. Electron. 3, 30–36 (2020).
Eisebitt, S. et al. Lensless imaging of magnetic nanostructures by X-ray spectro-holography. Nature 432, 885–888 (2004).
Büttner, F. in Holographic Materials and Optical Systems (eds Naydenova, I., Babeva, T. & Nazarova, D.) (InTech, 2017).
Geilhufe, J. et al. Achieving diffraction-limited resolution in soft-X-ray Fourier-transform holography. Ultramicroscopy 214, 113005 (2020).
Feist, A. et al. Ultrafast transmission electron microscopy using a laser-driven field emitter: femtosecond resolution with a high coherence electron beam. Ultramicroscopy 176, 63–73 (2017).
Schneider, M., Hoffmann, H. & Zweck, J. Lorentz microscopy of circular ferromagnetic permalloy nanodisks. Appl. Phys. Lett. 77, 2909–2911 (2000).
Koopmans, B. et al. Explaining the paradoxical diversity of ultrafast laser-induced demagnetization. Nat. Mater. 9, 259–265 (2010).
Krupin, O. et al. Temporal cross-correlation of X-ray free electron and optical lasers using soft X-ray pulse induced transient reflectivity. Opt. Express 20, 11396–11406 (2012).
Porro, M. et al. Development of the DEPFET sensor with signal compression: a large format X-ray imager with mega-frame readout capability for the European XFEL. IEEE Trans. Nucl. Sci. 59, 3339–3351 (2012).
Hansen, K. et al. Qualification and integration aspects of the DSSC mega-pixel X-ray imager. IEEE Trans. Nucl. Sci. 66, 1966–1975 (2019).
Erdinger, F. et al. The DSSC pixel readout ASIC with amplitude digitization and local storage for DEPFET sensor matrices at the European XFEL. In 2012 IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC) 591–596 (2012).
Fangohr, H. et al. Data analysis support in Karabo at European XFEL. In TUCPA01, International Conference on Accelerator and Large Experimental Control Systems 245–252 (JACOW, 2018).
Feigin, L. A. & Svergun, D. I. Structure Analysis by Small-Angle X-Ray and Neutron Scattering (ed. Taylor, G. W.) (Plenum, 1987).
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.
The authors declare no competing interests.
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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.
a–c, 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.
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.
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.
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.
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 discussion and Figs. 1–11.
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). https://doi.org/10.1038/s41563-020-00807-1
Nature Materials (2021)