Letter | Published:

Ultrafast nonthermal photo-magnetic recording in a transparent medium

Nature volume 542, pages 7174 (02 February 2017) | Download Citation

Abstract

Discovering ways to control the magnetic state of media with the lowest possible production of heat and at the fastest possible speeds is important in the study of fundamental magnetism1,2,3,4,5, with clear practical potential. In metals, it is possible to switch the magnetization between two stable states (and thus to record magnetic bits) using femtosecond circularly polarized laser pulses6,7,8. However, the switching mechanisms in these materials are directly related to laser-induced heating close to the Curie temperature9,10,11,12. Although several possible routes for achieving all-optical switching in magnetic dielectrics have been discussed13,14, no recording has hitherto been demonstrated. Here we describe ultrafast all-optical photo-magnetic recording in transparent films of the dielectric cobalt-substituted garnet. A single linearly polarized femtosecond laser pulse resonantly pumps specific dd transitions in the cobalt ions, breaking the degeneracy between metastable magnetic states. By changing the polarization of the laser pulse, we deterministically steer the net magnetization in the garnet, thus writing ‘0’ and ‘1’ magnetic bits at will. This mechanism outperforms existing alternatives in terms of the speed of the write–read magnetic recording event (less than 20 picoseconds) and the unprecedentedly low heat load (less than 6 joules per cubic centimetre).

Main

To stabilize magnetic states of a single bit of a recording medium at room temperature, a magnetic anisotropy energy barrier of 60kT ≈ 0.25 aJ (where k is the Boltzman constant and T is the absolute temperature) is taken as a sufficient value15. This value would then also correspond to the energy that is ideally required to switch the magnetic state. In practice, however, about eight orders of magnitude more energy is used16,17,18 and much of it is subsequently lost via dissipation. It would be greatly advantageous to realize optical rather than current-induced switching of magnetic states, as light can be transferred with minimum losses and effectively modifies the barrier through opto-magnetic and photo-magnetic interactions19,20.

Cobalt-substituted yttrium iron garnet (YIG:Co) is an optically transparent ferrimagnetic dielectric (see Methods and Extended Data Fig. 1) with a cubic lattice and two antiferromagnetically coupled spin sublattices of Fe3+ in both tetrahedral and octahedral sites21. The dopant Co2+ and Co3+ ions replace Fe3+ in both types of sites22. These Co ions are responsible for the strong magnetocrystalline21 and photo-induced magnetic anisotropy13,20 as well as for the very large Gilbert damping23 α = 0.2. In an unperturbed state at room temperature, the equilibrium orientation of the magnetization is defined by cubic (−8.4 × 103 erg cm−3) and uniaxial (−2.5 × 103 erg cm−3) anisotropy, which favour orientation of the magnetization along one of the body diagonals of the cubic cell (the <111> axes) and perpendicular to the [001] axis, respectively. It results in four easy magnetization axes which are slightly inclined from the body diagonals, as shown in Fig. 1. To distinguish between different magnetic domains, we used a garnet film with a miscut of about 4°. In Fig. 1, the large stripe-like domains have magnetizations along M(L)+ near the [1−11] axis and M(L)− near the [11−1] axis and the small labyrinth-like domains have magnetizations along M(S)+ near the [111] axis and along M(S)− near the [1−1−1] axis.

Figure 1: Magnetic states and domain structure of YIG:Co.
Figure 1

Orientations of the easy magnetization axes and the pattern of magnetic domains with the magnetization directions close to the [111], [1−11], [11−1] and [1−1−1] axes, measured at zero magnetic field with a magneto-optical polarizing microscope. Owing to a miscut of the gadolinium gallium garnet substrate by 4°, the degeneracy between the states is partly broken and different magnetic domains cover non-equivalent volumes at zero external magnetic field22. The pattern shown at top, with all four magnetization states (M(L)+, M(L)−, M(S)+, M(S)−), can be obtained as follows. First, the sample is brought into the M(L)+ state by an external magnetic field of μ0H = 80 mT applied along the [1−10] direction. Second, the field is removed and the sample turns into a state with M(L)+ and M(S)− domains. Third, a magnetic field μ0H = 2 mT applied for a short time along the [110] direction favours M(L)− domains and results in the final pattern. After the magnetic field is removed, the pattern stays unchanged for several days at least. Magnetization orientations in the domains and type of the domain structure have been identified following the procedure in ref. 22.

To investigate the feasibility of switching with linearly polarized light in YIG:Co, we employed the technique of femtosecond magneto-optical imaging using a pump laser pulse with duration of 50 fs (see Methods and Extended Data Fig. 2). The images of magnetic domains were taken before and after the excitation with a single pump laser pulse (see Fig. 2a). Taking the difference between the images emphasizes the photo-magnetic changes and is used for detailed analysis. Light can lift the degeneracy between the domains by generating photo-induced magnetic anisotropy24. In our case, pumping the initial pattern of magnetic domains with a single laser pulse polarized along the [100] axis (ϕ = 0°) turns large white domains (M(L)+) into large black ones (M(L)−). Simultaneously, small black domains (M(S)−) turn into small white ones (M(S)+) (see Fig. 2a). The domain pattern stays remarkably unperturbed; only the contrast reverses. The initial state can be restored by pumping with a single laser pulse polarized along the [010] axis (ϕ = 90°). The recorded domains are stable for several days owing to the non-zero coercivity of the garnet film at room temperature (see Fig. 2b). The initial domain pattern can be also restored by a brief application of an in-plane magnetic field of the order of 80 mT. The symmetry of the observed all-optical switching suggests that the point group of the crystal is 4 (see Methods). Although it is expected that the point group of the (001) garnet surface is 4 mm, the actual symmetry can be lowered either by the magnetization component along the [001] axis or simply by distortions during its growth25.

Figure 2: Single-pulse photo-magnetic recording.
Figure 2

The initial domain structure was prepared by applying an external magnetic field μ0H = 80 mT along the [1−10] axis for a few seconds. After removing this field a stable domain pattern was formed. The images are 200 μm × 200 μm. The pump beam with the wavelength of 1,300 nm was focused to a spot 130 μm in diameter and with maximum fluence of 150 mJ cm−2. ϕ is the angle between the pump pulse polarization and the [100] axis. a, From left to right, the domain pattern before the laser excitation, after excitation with a single laser pulse polarized along the [100] axis, and subsequent excitation with a similar laser pulse polarized along the [010] axis. b, Differential changes after each of the pulse excitations and schematic demonstration of the ultrafast photo-magnetic recording of ‘0’ and ‘1’ bits with the linearly polarized pulses. c, Schematic of the switching of the magnetization between the two magnetic states M(L)+ and M(L)−, corresponding to all-optical recording of magnetic bits ‘0’ and ‘1’.

The minimum pump fluence required for magnetic recording in YIG:Co is very sensitive to the wavelength of the pump pulse. The switched area estimated from the magneto-optical images is plotted as a function of the pump fluence for different pump wavelengths (see Fig. 3). The wavelength was varied within the range 1,150–1,450 nm (1.08−0.86 eV), where the light resonantly excites electronic dd transitions in Co ions26. In the studied YIG:Co film, a resonant pumping of the transitions in Co3+ and Co2+ ions at the tetrahedral sites at 1,305 nm (ħω = 0.95 eV)27 is accompanied by absorption a of about 12% of the light energy (Extended Data Fig. 1). The spectral dependence in Fig. 3 reveals a pronounced resonant behaviour around this energy. It can be seen that the minimum pump fluence required to form a domain is about Imin = 34 mJ cm−2. This means that the magnetic recording is a result of absorption of about aImin/ħω ≈ 3 × 1016 photons per cm2. Given that the film is d = 7.5 μm thick, the absorbed photons required for the switching of the magnetization in a given volume would be about 1019 cm−3, corresponding to depositing aImin/d ≈ 6 J cm−3 of heat. For instance, recording a bit with size 20 nm × 20 nm × 10 nm would be accompanied by dissipations of just 22 aJ (about 5,300 kT). To the best of our knowledge, this is much lower than for all-optical switching of metals (10 fJ)28, existing hard-disk drives (10−100 nJ)16, flash memory (10 nJ)17 or spin-transfer torque random-access memory (450 pJ−100 fJ)18.

Figure 3: Energy efficiency of the all-optical magnetic recording.
Figure 3

The normalized switched area, calculated as the ratio of the recorded domain area (the black large domain on the images) to the area of pump laser spot πr2 (where r is the pump spot radius), is plotted as a function of the pump fluence. The plots correspond to the cases when the central wavelengths of the pump are around 1,200 nm (blue dots) and 1,300 nm (black dots and images). Dashed lines are guides to the eye. (The dots show the mean values averaged from multiple switching events for each fluence value. The errors are no larger than the dot size, being all below 5% of the switched area.) The magnetization is switched between the M(L)+ and M(L)− states (large domains) as well as between the M(S)− and M(S)+ states (small domains) with the help of the laser pulse polarized along the [100] axis (top panel of the images). The size of the images is 160 μm × 150 μm. The inset shows the spectral dependence of the normalized switched area for a pump fluence of 83 mJ cm−2 (the red solid line was fitted by Gaussian function).

Finally, we studied ultrafast dynamics of the magnetization switching, employing time-resolved single-shot magneto-optical imaging (see Extended Data Fig. 2). The magnetic domains were recorded with a single pump pulse and imaged with a single 40-fs unfocused probe pulse with a central wavelength of 800 nm. After each write–read event the recorded domains were erased by application of an external magnetic field of 80 mT in the [1−10] direction. Similarly to static magneto-optical imaging, reference images were taken before each pumping (that is, at negative time delay). This image was subtracted from that obtained at a given pump–probe delay. Varying the time delay Δt, a series of the magneto-optical images were obtained (see top inset in Fig. 4). To quantify the dynamics of the laser-induced changes we took an integral over the pumped area, normalized the data and plotted the result as a function of time delay between the pump and probe pulses. It can be seen that the recorded domain emerges with a characteristic time τ of about 20 ps and stabilizes after about 60 ps. For the recording and reading out, we used just two femtosecond laser pulses; to the best of our knowledge this experiment is the fastest-ever write–read magnetic recording event9. Unlike all-optical magnetic switching in metals6,7,8,9,10,11, the recording in transparent dielectrics does not require any destruction of magnetic order and operates without ultrafast heating of the medium up to the Curie point.

Figure 4: Time-resolved all-optical magnetic switching as observed by femtosecond single-shot imaging.
Figure 4

Time-dependence of the normalized magnetization projection on the [001] axis Mz with respect to the saturation magnetization. The data points were calculated as the ratio of the magneto-optical signal (the average image contrast) in the switched area to the magneto-optical signal in the case when the magnetization is aligned along the [001] axis. (The dots show the mean values and the errors are no larger than the dot size, being all below 5%. However, the stronger signal noise is caused by the sensitivity of the single-shot imaging to even the slightest illumination drift, which is unavoidable due to the motion of the delay line.) The red solid line was fitted using the exponential increase (1 − exp[−Δt/τ]) with the characteristic time τ = 19.5 ± 1.6 ps. The top inset shows the images of domains obtained at different time delays after subtraction of the reference image obtained at negative Δt. The lower inset shows the schematics of the magnetization trajectory during the switching. The magnetization is switched between M(L)+ and M(L)− states with the help of the laser pulse polarized along the [100] axis. The pump fluence was 150 mJ cm−2 and the central wavelength of the pump was 1,250 nm. The size of the images is 240 μm × 260 μm.

The time of 60 ps taken for the switching is in very good agreement with a quarter-period of the laser-induced precession of magnetization in YIG:Co film (see Extended Data Fig. 3). Therefore it is reasonable to suggest that, unlike all-optical switching in metals9, the mechanism of the spin switching in garnets proceeds via the precession of the net magnetization. In this scenario, to switch the magnetization from the initial M(L)+/M(S)− state, optical excitation should induce magnetic anisotropy, which favours the M(L)− and M(S)+ states, respectively. This means that the magnetization will start precession around a direction somewhere in between these M(L)− and M(S)+ states. When started from M(L)+, after about 60 ps, that is, after the first quarter of the precession period equal to 250 ps (see Extended Data Fig. 3a), the magnetization vector will be closer to the M(L)− state. If, at this moment, owing to relaxation of the photo-excited electrons, the initial magnetic anisotropy is restored, the magnetization will start to precess around the M(L)− direction, eventually arriving at this metastable state on a timescale defined by the damping of the oscillations. In reality, in YIG:Co film, the lifetime of the photo-induced anisotropy at room temperature is also of the order of 60 ps (ref. 13) and the damping is indeed very large (see Extended Data Fig. 3a). As a result, the magnetization in large domains moves along a trajectory from the initial M(L)+ state to the new metastable state M(L)− (see inset in Fig. 4). The switching of small domains between M(S)+ and M(S)− occurs simultaneously and in the same fashion. From the orientation of the linear polarization of the pump light, which results in the recording, it can be concluded that the photo-induced anisotropy originates from optical excitation of Co ions at tetrahedral sites13. Note that the amplitude of the spin precession induced by light (see Extended Data Fig. 3b) is also at maximum when the linear polarization of light is along the [100] or the [010] axes, thus supporting the mechanism described above.

The mechanism operates at room temperature and outperforms existing write–read events, accompanied by an unprecedentedly low heat load. Even faster switching can be anticipated if the photo-induced magnetic anisotropy is enhanced when the temperature is decreased20 or when iron is substituted by ions more anisotropic than cobalt ions.

We anticipate that magnetization switching caused by this photo-magnetic phenomenon will open up many opportunities for the design and development of materials and methods in the field of opto-magnetic recording. For instance, using the photo-magnetic garnet as a recording medium has similarities to heat-assisted magnetic recording, but without the need for much heat or for an electromagnet. Furthermore, it is known that magnetic anisotropy in garnet films can also be controlled by electric fields29. Tuning the strengths of the magnetocrystalline, photo-magnetic and electrically induced anisotropies such that switching is possible only under simultaneous electric field and light seems to enable faster and less dissipative magnetic random access memory.

Methods

Materials

The magnetization switching results were obtained on Co-substituted yttrium iron garnet (YIG:Co) film d = 7.5 μm thick with composition Y2CaFe3.9Co0.1GeO12. The single-crystal YIG:Co garnet film was grown by liquid-phase epitaxy on gadolinium gallium garnet Gd3Ga5O12 (001)-oriented substrates with 4° miscut and thickness 400 μm. The saturation magnetization at room temperature was 4πMS = 90 G and the Néel temperature was 445 K. The Gilbert damping measured using the ferromagnetic resonance technique gives α = 0.2. At room temperature the sample has both cubic (−8.4 × 103 erg cm−3) and uniaxial (−2.5 × 103 erg cm−3) anisotropy, which were measured by means of both ferromagnetic resonance and torque magnetometry.

The cubic anisotropy term is dominant, yielding easy axes of magnetization along <111>-type directions. The uniaxial term modifies this by tilting the easy axes slightly towards the sample plane. Thus such a crystal has eight possible magnetization states in a zero applied field, directed close to the body diagonals of a cube. By symmetry, those magnetization states should be energetically equivalent, but owing to substrate miscut this degeneracy is lifted and some of them have slightly lower energy. This is why in the demagnetized state the sample shows an alternating stripe pattern of magnetic phases22. The measured absorption coefficient within the spectral range of 1,150–1,450 nm for the studied sample is shown in Extended Data Fig. 1.

Magneto-optical imaging under single pump pulse excitation

The design of the time-resolved pump–probe experimental set-up for investigations of all-optical magnetic recording is shown in Extended Data Fig. 2. The domain structure of the garnet films we studied was visualized using a magneto-optical polarizing microscope with a standard light-emitting diode (LED) source of polarized light as a probe. In this case, the central wavelength of pump pulses with duration of 50 fs was varied within the spectral range 1,150–1,450 nm. Relying on the fact that domains with different orientation of the magnetization will result in different angles of the Faraday rotation, the domains were visualized with the help of an analyser and a charge-coupled device (CCD) camera. The images were acquired about 10 ms after excitation with a single pump pulse.

Time-resolved femtosecond single-shot imaging

For the investigation of magnetization switching dynamics we used laser pulses with duration of 40 fs and with the central wavelength of 800 nm as a probe. The linearly polarized unfocused probe beam passing through the sample was collected by an objective and the magneto-optical contrast was gained with the help of an analyser (see Extended Data Fig. 2). The acquired magneto-optical image was digitized and recorded with the help of the CCD camera. A single-shot pumping was achieved by placing a mechanical shutter in the path of the pump beam. The actuation time of the shutter was set to the minimum possible value of 60 ms. To exclude any possibility of excitation by more than one pump pulse, the repetition rate of the amplifier was brought down to 10 Hz. To improve the signal-to-noise ratio in the detection of the probe pulses, the exposition time of the camera was set at 1 ms. The activation time of the camera and the mechanical shutter were controlled by an electrical delay generator synchronized with the laser. Adjustment of the electrical delays for the shutter and the camera allowed us to capture the magneto-optical image produced by a single pump pulse. The delay generator was set to the standby mode and was controlled by an external computer. The asynchronous trigger from the computer results in the generation of a single trigger signal synchronized with the laser; this signal activates the camera and the shutter. To erase a long-lived state with the switched magnetization and to reinitialize the magnetic state, a magnetic field was applied after each single-shot event. Repeating such a single pump and single probe measurement for various values of the delays between the pump and the probe pulses (see Extended Data Fig. 2), we acquired images of the domains at various time moments after the arrival of the pump pulse. The delay time Δt could be adjusted in the range from 50 fs to 1 ns.

Estimation of temperature increase under laser pump pulse

To estimate the temperature increase as a result of excitation by a single pump pulse in our experiment, we take into account the minimum intensity required for the switching Imin = 34 mJ cm−2, the heat capacity of the garnet C = 430 J mol−1 K−1 at room temperature21, the molar mass m = 706 g mol−1 and the density ρ = 7.12 g cm−3. The measured absorption of the pump at the wavelength of 1,300 nm is about 12% (see Extended Data Fig. 1). The temperature increase as a result of absorption is thus ΔT = aIminm/(Cdρ) = 1.25 K. Such a temperature increase is at least two orders of magnitude lower than the one required to reach the Néel temperature.

Laser-induced magnetization precession

To study laser-induced spin oscillations induced by femtosecond laser pulses in YIG:Co film, we also carried out conventional time-resolved measurements using a magneto-optical pump–probe method. Pump pulses with duration 50 fs arrived at the sample with a repetition rate of 500 Hz. The angle of incidence was set to 10° from the sample normal; that is, from the [001] crystallographic axis of the garnet film. Equally short probe pulses had repetition rates twice as high and arrived at normal incidence to the sample. The central wavelength of the pump was set to 1,200 nm. This wavelength corresponds to a large amplitude of the spin oscillations. The central wavelength of the probe was 800 nm. The pump, with fluence below 70 mJ cm−2, was focused to a spot about 130 μm in diameter. The delay time Δt between the pump and the probe pulses could be adjusted within the range from 50 fs to 1 ns. The polarization plane of the linearly polarized pump pulse was set at an angle ϕ with respect to the [100] axis. The polarization plane of the probe beam was along the [1−10] axis. Using a balanced photodetector we measured the Faraday rotation of the probe as a function of the delay time Δt between the pump and probe pulses (see Extended Data Fig. 2). The Faraday rotation is proportional to the out-of-plane component of the magnetization Mz. All measurements were done under zero applied magnetic field and at room temperature. The measurements were performed in a stroboscopic mode and thus reveal the pump-induced dynamics, which is reproducible from pulse to pulse.

The magnetization precession signals show a strong dependence on the pump polarization (see Extended Data Fig. 3a). Moving the pump spot across the boundary between large domains with M(L)+ and M(L)− also allows us to excite spin precession with opposite phases. It is also interesting to note that if the probing spot is placed exactly on the wall, the antiphase signals from each domain average to zero. This is only possible if the underlying dynamics is due to a coherent rotation of the magnetization and not due to domain wall motion. The characteristic rise time of the signal is about 20 ps. The time delay at which the signal is at maximum is about 60 ps (see Extended Data Fig. 3a). Orthogonal polarizations along <100>-type directions result in the highest amplitude of the spin precession (see Extended Data Fig. 3b). These polarizations correspond to the global symmetry axes of the tetrahedrons in our garnet film hosting the Co ions. The amplitude of the precession follows a cos(2ϕ) dependence, which is typical for photo-magnetic effects13,20,24. The amplitude of the magnetization precession increases linearly with the pump fluence owing to the stronger light-induced effective field (see Extended Data Fig. 3c). The period of the precession is nearly constant (about 250 ps) and follows the frequency of the ferromagnetic resonance mode23 in the field of magnetic anisotropy. Note that the central wavelength of the pump corresponding to the most efficient switching does not coincide with the wavelength corresponding to the most effective excitation of the oscillations. This is because the oscillations are detected in a stroboscopic mode, which gives the largest signal when no switching takes place.

The microscopic mechanism of the photo-induced anisotropy has been extensively discussed previously13,20,24. The charge transfer process redistributes electrons among Co ions in nonequivalent crystal sites, changing the valence states of the Co ions and consequently, their contribution to magnetic anisotropy. The latter can be explained in terms of the single ion anisotropy model30. The pump light is used to excite optical transitions in the YIG:Co film in the tetrahedral Co ions. This approach allows us to achieve a large amplitude of the effective field of the photo-induced anisotropy (hundreds of Oe). Another important feature is that even though the number of the excited Co ions does not reach 100%, the single-ion anisotropy from Co is very high, producing a large light-induced field. Thus the photo-magnetism in the YIG:Co film is very efficient.

Symmetry analysis of the all-optical switching

We choose the coordinate system in which the coordinate axes x, y and z are aligned along the crystallographic directions [100], [010] and [001], respectively. To explain the effect of light on the magnetic anisotropy, the energy of the light–matter interaction should contain terms χijklEiEj*MkMl, where χijkl is a polar fourth-rank tensor, Ei is the ith component of the electric field of light, Ej* is the complex conjugate of the j-component of the electric field of light and Mk is the kth component of the magnetization20. In our experiment, polarized light switches two domains with My > 0 to two domains with My < 0 and back; in all four states between which the light switches the magnetization Mx > 0. The terms for which k = l do not depend on the sign of the magnetization components and thus cannot be responsible for the sign change of My. We can also see that the switching does not depend on the sign of Mz, because the same pulse has opposite effects on Mz in large and small domains. Hence if light is polarized along the [100] or the [010] direction, the part of the energy of the photo-induced magnetic anisotropy that is responsible for the switching can be written as:This energy must be considered as a thermodynamic potential. Its minimization with respect to M allows us to find the potential minimum and define the equilibrium orientation of the magnetization.

The expected point group for the (001) surface of the garnet is 4 mm, for which31 χyyyx = χxxxy = χxxyx = χyyxy= 0. However, a non-zero magnetization along the [001] axis, that is, Mz, effectively lowers the symmetry down to 4. The symmetry of the as-grown (with defects) garnet films can also be lowered simply owing to distortions during growth25.

For point group 4 χyyyx = −χxxxy and χxxyx = −χyyxy (ref. 31). Assuming that A = χxxxy+χxxyx, equation (1) can be simplified to:Assume that A < 0. In this case, under illumination of the garnet with light linearly polarized along the [100] direction the thermodynamic potential will be minimized if My > 0. Hence, such an excitation will promote switching of large white domains (M(L)+) into large black ones (M(L)−). Simultaneously, small black domains (M(S)−) will be switched into small white ones (M(S)+). If the light is polarized along the [010] axis, the thermodynamic potential is minimized when My < 0 and it means that the photoexcitation will promote switching of the magnetization in the large and small domains back into the M(L)+ and M(S)− states, respectively.

Data availability

Source data accompanies Figs 3 and 4 online. The data supporting other findings of this study are available from the corresponding author (A.S.) upon reasonable request.

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Acknowledgements

We acknowledge support from the National Science Centre Poland (grant DEC-2013/09/B/ST3/02669), the European Research Council under the European Union’s Seventh Framework Program (FP7/2007-2013)/ERC Grant Agreement No. 257280 (Femtomagnetism) and the Foundation for Fundamental Research on Matter. We thank A. Chizhik and A. M. Kalashnikova for discussions, S. Semin for technical assistance as well as A. Maziewski and Th. Rasing for continuous support.

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Affiliations

  1. Laboratory of Magnetism, Faculty of Physics, University of Bialystok, 1L Ciolkowskiego, 15-245 Bialystok, Poland

    • A. Stupakiewicz
    •  & K. Szerenos
  2. Radboud University, Institute for Molecules and Materials, 135 Heyendaalseweg, 6525 AJ Nijmegen, The Netherlands

    • D. Afanasiev
    • , A. Kirilyuk
    •  & A. V. Kimel

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Contributions

A.S. conceived the project with contributions from A.K. and A.V.K. The imaging and time-resolved magnetization precession were performed by K.S. D.A. developed femtosecond single-shot imaging and performed time-resolved imaging together with K.S. A.S. and A.V.K. co-wrote the manuscript with contributions from A.K., K.S. and D.A. The project was coordinated by A.S.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to A. Stupakiewicz or A. V. Kimel.

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https://doi.org/10.1038/nature20807

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