Excitation of magnon accumulation by laser clocking as a source of long-range spin waves in transparent magnetic films

Optical tools are of great promise for generation of spin waves due to the possibility to manipulate on ultrashort time scales and to provide local excitation. However, a single laser pulse can inject spin waves only with a broad frequency spectrum, resulting in a short propagation distance and low amplitude. Here we excite a magnetic garnet film by a train of fs-laser pulses with 1 GHz repetition rate so that pulse separation is smaller than decay time of the magnetic modes which allows to achieve collective photonic impact on magnetization. It establishes a quasi-stationary source of SWs, namely a coherent magnon accumulation ("magnon cloud"). This approach has several appealing features: (i) the source is tunable; (ii) the SW amplitude can be significantly enhanced; (iii) the spectrum of the generated SWs is quite narrow that provides longer propagation distance; (iv) the periodic pumping results in almost constant in time SW amplitude up to 100 um away from the source; and (v) the SW emission shows a pronounced directionality. These results expand the capabilities of ultrafast coherent optical control of magnetization and pave a way for applications in data processing, including the quantum regime. The quasi-stationary magnon accumulation might be also of interest for the problem of magnon Bose-Einstein condensate.


Recent research on spin waves (SW) is increasingly driven by their unique linear and non-linear
properties as well as anticipated applications in telecommunications, image processing and even quantum computations [1][2][3][4][5]. SWs are launched if in a magnetically ordered material the magnetization is pushed out of equilibrium. Usually, this is achieved by microwaves generated by an antenna in close vicinity of the sample [6]. However, particular applications require a strong locality of the excitation and a specific distribution of spins in time and space, created on time scales much shorter than any decay time. For example, quantum information processing necessitates addressing a qubit by a magnetic field with a submicron gradient [5]. This challenge might be solved if the magnetic system is disturbed by ultra-short laser pulses, that can be focused microscopically [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].
Then the instantaneous impact of the laser pulse on the magnetization occurs only within the illumination spot with potentially sub-wavelength resolution if plasmonic nanogeometries are used [26,27].
Among the various mechanisms for optical pumping of magnetization in ferromagnets, the inverse Faraday effect is of particular importance [8,[21][22][23][24]. Here circularly polarized light affects the medium magnetization, as if an effective magnetic field ~[ × * ] would act, where is the electric field of the light wave [28]. As a result, is directed along the light wave vector. In ferromagnets it originates from stimulated Raman scattering on magnons. The inverse Faraday effect was observed in pump-probe experiments [21][22][23][24], where the magnetization dynamics is triggered by a pump and subsequently monitored by a delayed probe pulse of low intensity. The authors of Refs. [8][9][10] managed to demonstrate magnetostatic SWs in iron garnets in that way.
Almost all pump-probe studies so far were conducted in the single pump pulse regime where the magnetization oscillations decay before the subsequent pulse arrives. Double-pump coherent magnetization control was demonstrated in Ref. [21]. Recently, the magnetization precession was excited by a sequence of picosecond acoustic pulses [29]. However, so far there were no studies of the impact of a virtually infinite sequence of pump pulses exciting the sample at high rate such that upon pulse arrival the magnetization still shows the coherent dynamics induced by the preceding pulse.
Here we excite transparent magnetic films with a train of fs-laser pulses hitting periodically the sample with a period of 1 ns. This pulse separation is comparable to or even shorter than the decay time of the magnetization modes. Being periodic in time, the excitation generates a ( ) in the illuminated area which represents a quasi-continuous source of SWs showing several appealing features, namely directionality of the SWs as well as enhanced amplitudes for specific SW frequencies, providing frequency selectivity.

MATERIALS AND METHODS
The experiments here are conducted on monocrystalline magnetic films of bismuth-substituted The magnetization precession is excited and detected using a pump-probe technique based on asynchronous optical sampling (ASOPS). Two independent laser oscillators for the circularly polarized pump and the linearly polarized probe beams emit 50 fs pulses with a center wavelength of  ≈ 800 nm at a rate of about 1 GHz (Fig. 1a).

Collective photonic impact on magnetization
The train of circularly polarized pump pulses excites a periodic magnetization dynamics ( Fig. 1b) due to the inverse Faraday effect as confirmed by the fact that switching the pump helicity from σ + to σchanges the precession phase by . Sweeping the external magnetic field modifies the amplitude 0 , phase and frequency of the oscillations. In the time interval of T = 1 ns between two consecutive laser pulses the oscillations can be approximately described by a decaying sine function: = 0 − ⁄ si n( + ) (Fig. 1c), where is the decay time. Small deviations of the measured data from the fit curves are caused by excitation of SWs. Strikingly, the precession amplitude shows resonances for particular magnetic fields, at which the oscillation frequency is a multiple of the laser repetition rate, corresponding to the relation:     The amplitude of mode-A behaves quite similar to the mode discussed above in Figs. 1 and 2.
However, the mode-B amplitude changes with magnetic field much more prominently (Fig. 3a). In resonance where its frequency is a multiple of the excitation rate the mode-B amplitude is 5 times above the noise level and comparable to the mode-A amplitude. Remarkably, in the single pulse excitation regime, i.e. when the sample is excited at much lower repetition rate (1/T = 80 MHz), the amplitude of mode-B is much smaller than that of mode-A and, therefore, cannot be resolved.

Analysis of the observed phenomena
Accordingly, the precession amplitude shows a resonance when the oscillations are synchronized with the laser pulses, i.e. at = 2 . At these resonances = 0, i.e. the oscillations start with = 0 at the moment of subsequent pulse arrival, which is in good agreement with the experiment (Fig. 1c).
The ratio of the maximal and minimal amplitudes is given by Therefore, the amplitude is increased most strongly for a magnetization mode of high quality factor Q

Observation of tunable spin waves
Let us now shift the probe beam with respect to the pump to trace the SWs. The oscillating signals observed for different pump-probe separations confirm propagation of the SWs in the direction along field H (Fig. 4a). SWs are detectable for spatial shifts up to 100 µm (open red circles in Fig. 4b).
Notably, this distance is twice larger than for SWs excited in a single pulse regime. On the contrary, in the orthogonal direction the SWs are only observable within 10 µm from the pump beam center (filled orange circles in Fig. 4b). One more remarkable point is that the SW decay rate diminishes with increasing pump-probe distance. For propagation distances larger than 10 µm the rate undercuts 0.3 ns -1 (Fig. 4b) so that the oscillations almost do not decay in time in between the pump pulses (Fig. 4a).
All these unique features of the periodic pumping of SWs are related again to the synchronization of oscillations and also involve the specific character of the SW dispersion. Since the Gilbert damping in iron-garnets is relatively small: ~10 −3 which corresponds to ~100 ns, the decay time is mainly determined by the spread of SW energy away from the excitation spot and the dephasing of SW modes of different frequency due to the SW dispersion. While the former is inevitable, the latter may be tailored as in our case by the periodic pumping, because the repeated application of the pump pulses narrows the spectrum of generated SWs. Indeed, a single pump pulse with spot radius r excites SWs with wave numbers < 1/ corresponding to frequencies in the range (1/ ) < < (0) (for the backward magnetostatic SWs excited in our experiments) (Fig. 4c). However, the train of pulses singles out frequencies that are multiples of the laser repetition rate (1/ ) from this range (see red dashed line for = 6 / ). Since the SW spectrum becomes narrower thereby, the dephasing decreases and the SWs propagate over longer distances.  As the SW spectrum is anisotropic with respect to H so that ( , 0) ≠ (0, ) (see Fig. 4c) the laser pulse train excites SWs along different directions with various efficiencies. For example, at H = 1200 Oe a multiple of the pulse repetition rate is within the frequency window of the excitable SWs along the x-axis (for = 0.6 < 1 /2 = 3, Fig. 2c) while there is no multiple in the SW frequency range along the y-axis (dashed curve in Fig. 2c). As a result, SWs can be traced along the xaxis over distances of about 100 µm, but they can hardly be observed along the y-axis even for small distances from the pumped spot. Therefore, the periodic pumping introduces an additional potentiality as it excites SWs along specific directions which may be altered by changing the pulse repetition rate and the external magnetic field (Fig. 4d).
Finally, the phenomenon of the vanishing time decay of SWs at sufficiently large distances from the pump beam can be qualitatively explained by the local balance of the energy arriving from the optically excited area and the energy carried away by the SWs. The latter depends on the SW dispersion. The experimental data on the oscillation amplitude and the decay rate as function of separation between pump and probe are in an excellent agreement with calculations based on the SW dispersion (solid curves in Fig. 2b, Supplementary).

CONCLUSIONS
Summarizing the experimental data and their analysis, we have demonstrated that a train of optical pump pulses can drive the magnetization within the illuminated area thus exciting magnons.
The magnons become spread by propagation from the excitation spot and their superposition is observable as SWs. Therefore, the excited area can be considered as a coherent magnon accumulation ("cloud") which serves as source of SWs with parameters controllable by the details of the experimental protocol such as the laser illumination or the magnetic field.
The magnon cloud has several outstanding properties. In particular, the amplitude of the oscillations in this cloud can be significantly increased if the magnetization oscillation frequency is tuned by the magnetic field of moderate strength such that it becomes synchronized with the laser pulses. The enhancement factor can be as large as 9.3 for a magnetic mode of high quality factor (~232). Such enhancement has allowed us to observe a magnetization mode that is generally obscured in experiment using single pulse excitation by other modes of lower quality factor. Our technique therefore can be applied as highly sensitive spectroscopy tool for resolving magnetization precession modes. Remarkably, the decay rate of the precession amplitude strongly depends on the distance from the optical pump. At some distance the rate becomes so small that the oscillation hardly undergoes a decay anymore. Moreover, the periodic pumping additionally brings two important features for SW propagation: it significantly increases their propagation distance and provides also the possibility to tune directionality of propagation.
Generally, optical excitation of magnetic oscillations represents a detailed control tool of the magnetization distribution at sub-terahertz time scales. In combination with focusing by plasmonic antennas, also the spatial distribution can be tailored on subwavelength scales which is of prime importance for quantum information processing based on SWs [4]. The tunable, quasi-stationary magnon cloud as spin wave source might significantly broaden the functionality of this approach. The next step forward will be implementation of plasmonic structures to further enhance the magnetization precession by concentrating the optical fields in a nanometer thick magnetic film with a spot size of less than 100 nm in diameter [26]. Indeed, while a huge plasmonics-mediated increase of the direct magneto-optical effects was demonstrated recently [32], the plasmonic boost of the inverse magnetooptical effects is still waiting for its practical implementation [16].