Ultrafast optical excitation of magnetic skyrmions

Magnetic skyrmions in an insulating chiral magnet Cu2OSeO3 were studied by all-optical spin wave spectroscopy. The spins in the conical and skyrmion phases were excited by the impulsive magnetic field from the inverse-Faraday effect, and resultant spin dynamics were detected by using time-resolved magneto-optics. Clear dispersions of the helimagnon were observed, which is accompanied by a distinct transition into the skyrmion phase, by sweeping temperature and magnetic field. In addition to the collective excitations of skyrmions, i.e., rotation and breathing modes, several spin precession modes were identified, which would be specific to optical excitation. The ultrafast, nonthermal, and local excitation of the spin systems by photons would lead to the efficient manipulation of nano-magnetic structures.

experiments 17,18 . We also identified precession signals not observed in the previous reports, which would be explained by the strong impulsive excitation of the spin system.

Results and Discussion
The magnetic phase diagram of Cu 2 OSeO 3 and experimental setups are shown in Fig. 1 (see Methods for the detail). Figure 2 shows the representative spin precession spectra in the conical and SkX phases under the H ex E 110 ½ (normal to the photon k-vector) [ Fig. 1(b)]. In both phases, transient Faraday rotations with opposite initial phase (p-rad. shifted) were observed for right-and left-circular polarized pump excitations (RCP and LCP), respectively. The spin motion was negligible when excited with linearly-polarized pump pulses [ Fig. 2 (a)], therefore we can safely rule out thermal effects and opticallyinduced changes in the magnetic anisotropy 23 . We observed no pump-induced change in the probe transmittance (not shown). The spins in the Cu 2 OSeO 3 feel strong inverse-Faraday field (6H IF ) along the light k-vector of the pump pulse [ Fig. 2(a) bottom inset], which tilts the magnetic moment (M) in the plane normal to the k-vector within the pump duration, triggering the spin precession generally expressed as sin t ð Þe  shown in Fig. 2(b). The large Faraday rotation at time zero is omitted from the data in the following.
It is notable that the spin precessions cannot be expressed with a single sinusoidal wave with an exponential decay [a characteristic modulation, called beating below, is exemplified by an arrow in Fig. 2 (b)]. This is naturally expected because the conical spins exhibit two fundamental excitation modes in our experimental geometry, called 6Q helimagnons 24 , which have been detected in Cu 2 OSeO 3 with the microwave resonance spectroscopy 17,18 . We also found that the spin precession in the SkX phase cannot be expressed with a single frequency. Therefore, we fitted all the spectra with two sinusoidal functions, as shown in Fig. 3(a), which allowed us to avoid arbitrary determination of the phase boundaries. (In the lower panel of Fig. 3(a), the spectrum near the phase boundary with a clear shoulder structure is shown.) The fitting works reasonably well in both conical and SkX phases, yielding temperature-and field-dependent oscillation frequencies, amplitudes, and damping constants. The oscillation frequencies are plotted as a function of temperature in Fig. 3(b), showing a discontinuous transition from the conical phase into the SkX phase. By comparing to the previous reports 17, 18 , we can assign the observed spin dynamics to the 6Q helimagnons in the conical phase and rotation modes of the skyrmions [ Fig. 3(b) insets], as will be discussed in detail below. By rendering the oscillation frequencies (of the 2Q mode and the CCW rotation) in the phase diagram, we can nicely visualize the SkX phase [ Fig. 3(c)].
When the external magnetic field H ex is applied along the sample normal (jj [110], Fig. 4), only one collective spin mode is expected in the SkX phase (and no mode in the other phases) 9 . In this setup, the Faraday rotation of the probe light is smaller than that of the former setup, consistent with the previous report 18 . We found that the observed spin dynamics can be fitted with a single sinusoidal function [ Fig. 4(a)]. The deduced oscillation frequencies fell into those of the skyrmion breathing motion, which also nicely reproduce the phase diagram deduced from the magnetic susceptibility measurements [ Fig. 4(b)].
The oscillation frequencies of the helimagnons, and those of the rotation and the breathing modes in the SkX phases nicely match to the values found in the previous reports 17,18 . Judging from this fact and also from the phase maps in Figs. 3(c) and 4(b), it is concluded that we have successfully detected skyrmions from their opticallyexcited dynamics. We note that the CW rotation mode has been inferred only from the nonreciprocal directional dichroism 17 , due probably to the small spectral weight as expected from the numerical calculations 9 . In contrast, we clearly identified two spin precessions in the SkX phase as shown in Fig. 3. There, the high frequency mode (,1.5 GHz) is not due to the mixing of the conical phase, judging from the discontinuous transition from the conical phase to the SkX phase seen in Fig. 3(b).
To scrutinize the observed spin modes, we plot the magneticfield dependence of the spin precessions in Fig. 5 for the different magnetic-field orientations. For the H ex E 110 ½ [ Fig. 5(a)], the precession frequency decreases with increasing the H ex in the conical spin phase 24  Therefore, in addtion to the reasoning from its absolute frequency, the higher-lying mode in the SkX phase can be assigned to the CW rotation. The reentrant behavior of the conical phase by increasing the H ex , after experiencing a pocket of the SkX phase at 56.5 K [ Fig. 5(a)], also supports the identification of the SkX phase, since this pocket is well isolated from other spin phases. It is also expected that the damping increases in the SkX phase 25 , which is roughly captured in our data in Fig. 5(b). The long-  lasting spin precession at low temperatures [ Fig. 2(b)] indicate that the spin scattering is mainly from thermal agitations.
The optical excitation can be distinct from that exerted by the microwaves, because the pump light imposes a strong impulsive magnetic-field at localized region (,100 mmw in our case), possibly with spatial gradients, thereby enabling the coupling to the spin waves with a finite range of frequencies and wave numbers. The amplitude of the impulsive magnetic-field would reach to several thousand Oe 23 , much larger than the external H ex of the current experiment [see also the inset of Fig. 2(a)] and the ac field of the previous microwave resonance experiments 17,18 . In such a situation, multi-magnon processes and the parallel pumping of the magnons (for H ex jj[110]) are expected. The latter generates two magnons of opposite wavevectors (6k ? 0) by the ellipticity of the precession orbit 26 . We tentatively ascribe the precession mode for H ex . 220 Oe jj[110] [Fig. 5(c)] to these excitations. It will be necessary to consider the dispersion relation of the collective spin modes for the non-zero k, as has been discussed in the case of magnetic bubble lattices 27 , especially if the excitation light spot close to the skyrmion size is employed (not the case here). The spin precessions seen in the low H ex region can be ascribed to the multi-domain states, while those in the ferrimagnetic phase (the high H ex region E½ 110) to the ferromagnetic and exchange modes having similar frequencies near the transition temperature 28 . Since the spins in Cu 2 OSeO 3 are found to form a quantum triplet states within the Cu 4 tetrahedra 29,30 , these spin dynamics would be better described by incorporating the quantum fluctuations. We note that the optical excitation can also generate ''forbidden'' spin resonances by using site-dependent magnetooptical susceptibilities 31 .
There is one feature to be noted and explained; the spin precession seems excited in the intermediate phase, i.e., slightly above the mag-netic transition temperature [around 58.5 K and 300 Oe in Fig. 3(c)]. The intermediate phase has larger spin fluctuations 14 , expected to host isolated skyrmions or fragmented skyrmion domains, and to be susceptible to the magnetic history of the sample. The spin dynamics invoked in this region may indicate the existence of these fragmented domains 19,20 , or other induced spin excitation by the strong inverse-Faraday field.
In the metallic helimagnet Fe 0.8 Co 0.2 Si, which is also known to host skyrmions, the spin dynamics has been analyzed with timedependent Gilbert dampings 32 , since no beating features in the precession signals were detected by the optical spectroscopy. In the case of Cu 2 OSeO 3 here, the beating and shoulder structures in the spin signals revealed the distinct multiple precession dynamics.

Conclusions
To summarize, we have successfully detected the collective excitation modes of skyrmions in the insulating chiral magnet Cu 2 OSeO 3 by optical pump-probe techniques. The rotation and breathing modes are identified in the skyrmion phase, and several additional spin precession modes have also been detected. We discussed the difference between the inverse-Faraday and microwave excitations, which may explain the observed multi-mode spin excitations.

Methods
Single crystals of Cu 2 OSeO 3 were grown by the chemical vapor transport method, and were polished down to 300 mm in thickness to expose (110) planes. The conical spin and SkX phases were checked by the magnetic susceptibility measurements [ Fig. 1  (a)], in which some demagnetization effects make small deviations from sample to sample 18 . We studied the spin dynamics by the time-resolved magneto-optics with pulsed laser sources (,120 fs, 1 kHz) at near-normal incidence [ Fig. 1(b)]. The pump pulse (2 mW on ,100 mmw spot) excite the spin system at 0.95 eV (within the optical gap) by the inverse-Faraday effect, and the induced spin precession was  Note that the pump pulse at 0.83 eV induced qualitatively the same spin dynamics with slightly reduced efficiency (not shown). The external magnetic field (H ex ) was applied by a pair of permanent magnets, which limited the phase space studied in our experiment.