Optical excitation of propagating magnetostatic waves
in an epitaxial Galfenol film by an ultrafast magnetic anisotropy change
Using a time-resolved optically-pumped scanning optical microscopy technique we demonstrate the laser-driven excitation and propagation of spin waves in a 20-nm film of a ferromagnetic metallic alloy Galfenol epitaxially grown on a GaAs substrate. In contrast to previous all-optical studies of spin waves we employ laser-induced thermal changes of magnetocrystalline anisotropy as an excitation mechanism. A tightly focused 70-fs laser pulse excites packets of magnetostatic surface waves with a propagation length of 3.4 m, which is comparable with that of permalloy. As a result, laser-driven magnetostatic spin waves are clearly detectable at distances up to 10 m, which promotes epitaxial Galfenol films to the limited family of materials suitable for magnonic devices. A pronounced in-plane magnetocrystalline anisotropy of the Galfenol film offers an additional degree of freedom for manipulating the spin waves’ parameters. Reorientation of an in-plane external magnetic field relative to the crystallographic axes of the sample tunes the frequency, amplitude and propagation length of the excited waves.
In magnonics coherent spin waves (SWs) are employed for encoding, transferring, and processing information [1, 2, 3]. The use of SWs enables scaling of magnonic elements down to the nanometer range owing to short wavelengths, and the reduction of Joule heating associated with the charge transfer in conventional electronics. Moreover, an extended functionality of magnonic devices is provided by the possibility to manipulate the amplitudes, phases, and wavevectors of SWs. Progress in the field of magnonics relies on the development of approaches to generate and transfer SWs in a controllable manner. Efficient conversion mechanisms between electrical/optical pulses and collective magnetic excitations are required to couple magnonic elements to electronic and photonic units [4, 5, 6]. For rapid growth of the field of magnonics, it is essential to extend the range of materials and structures supporting long SWs propagation distances and enabling their control [7, 8, 9, 10, 11].
Optical radiation allows the magnetic parameters of materials to be altered reversibly at various timescales down to femtoseconds [12, 13]. This has lead to the emergence of a photo-magnonics [14, 15, 16, 17, 18, 19, 20], where laser pulses with durations down to femtoseconds are employed as a tool for both driving SWs and for manipulating their propagation. In particular, it has been demonstrated that femtosecond laser pulses enable excitation of SWs with controlled wavevectors and propagation directions [18, 21, 22, 23]. However, up to now the effects of short laser pulses employed to drive SWs have been limited to ultrafast opto-magnetic phenomena [22, 18, 23, 24, 22, 21, 25], ultrafast demagnetization [17, 26, 27, 28], and coherent energy transfer from elastic waves to the magnon subsystem [24, 29, 30]. These mechanisms place constraints on the properties of the media, the laser pulse parameters, and the excitation geometries, while the excitation of propagating SWs by other femtomagnetic phenomena  remains unexplored. Furthermore, the range of materials where the optical generation of SWs has been realized is also very limited and, in fact, coincides with the known suitable media for magnonics .
In this Letter we examine the feasibility and advantages of exciting propagating SWs in an anisotropic ferromagnetic film by ultrafast laser-induced thermal changes of the magnetocrystalline anisotropy. Using time-resolved optically pumped scanning optical microscopy (TROPSOM)  we reveal propagating magnetostatic surface waves (MSSWs) excited by a femtosecond laser pulse in a 20-nm thick film of a ferromagnetic metallic alloy, Galfenol (FeGa) epitaxially grown on a GaAs substrate. We demonstrate that the propagating MSSWs packets are launched via the laser-induced thermal decrease of the magnetic anisotropy occurring on a picosecond time scale and localized within the excitation spot. The characteristics of the excited MSSWs can be controlled by the orientation of an applied in-plane magnetic field with respect to the magnetocrystalline anisotropy axes of the film. We show that the 20-nm thick Galfenol film supports e-propagation length of MSSWs as large as 3.4 m, comparable to that of Permalloy – a model metallic material for magnonics [26, 3]. Our results promote epitaxial Galfenol to the limited family of materials for magnon-spintronics, reconfigurable magnonics, and ultrafast photo-magnonics. Furthermore, the ultrafast thermal changes of magnetic anisotropy as a driving mechanism for the excitation of propagating SWs can be applied to a broad range of materials without specific constrains imposed on their electronic and magnetic structures .
For our study, we chose a 20-nm thick film of FeGa epitaxially grown on a 350-m thick (001)-GaAs substrate by magnetron sputtering, as described elsewhere . The Galfenol film was capped with 3-nm thick Al and 120-nm thick SiO layers. The back-side of the substrate was polished to optical quality. X-ray diffractometry showed that the Galfenol film has a mosaic structure with grain sizes of 12 nm, and their crystallographic axes misorientation of 1.3 deg. It is well established that thin films of iron and iron-based alloys epitaxially grown on GaAs exhibit intrinsic cubic and substrate-induced in-plane uniaxial magnetic anisotropies [33, 34, 35, 36]. In particular, in Galfenol films on (001)-GaAs substrates the uniaxial anisotropy axis emerges along the  direction [32, 37]. The presence of in-plane anisotropy axes favors excitation of magnetization precession via laser-induced thermal anisotropy changes in a simple geometry with an in-plane external magnetic field [38, 39]. Furthermore, in-plane anisotropy extends the possibilities to tune the characteristics of SWs, as compared to isotropic metallic and dielectric films [40, 41].
Optically-excited SWs were studied using the TROPSOM setup [Fig. 1] which enables detection of the spatial-temporal evolution of the polar magneto-optical Kerr rotation proportional to the transient changes of the out-of-plane magnetization component [see Supplimentary Material for details . Here is the laboratory frame with the axis directed along the sample normal and the axis chosen to be along the direction of an external DC magnetic field H. Optical pulses with nominal duration of 70 fs, central wavelength of 1050 nm, and 70 MHz repetition rate generated by the Yb-doped solid-state oscillator laser system were split into pump and probe parts. The central wavelength of the pump pulses was converted to 525 nm using a -BaBO crystal. Two microscope objectives were used to focus the pump and probe pulses onto the Galfenol film from the cap and the substrate sides, respectively [Fig. 1]. The FWHM of the resulting pump and probe spots were m. The pump fluence was 3.5 mJ/cm, and the probe fluence was approximately 20 times lower. The microobjective for the probe pulses is fixed. The microobjective for the pump pulses was mounted on the piezoelectric stage, which moves in the plane and controls the relative spatial positions of the pump and probe pulses. The pump-probe temporal delay was controlled by a delay line in the pump pulse optical path. In the experiments the temporal dependencies were obtained at various pump-probe displacements , and at various azimuthal orientations of the sample defined by the angle between the crystallographic axis and the -axis. The external magnetic field strength was =100 mT. All the measurements were performed at room temperature.
Figure 2(a,b) shows the spatial-temporal evolution of obtained by scanning the pump-probe time delay when the pump and probe spots are shifted with respect to each other by m, , i.e. transversely to the direction of the applied magnetic field . Experimental data for two orientations and of the sample axes with respect to the external field are presented. The former geometry corresponds to the field applied along the sample hard axis . Two types of pump-induced signal can be distinguished depending on whether the pump and probe spots overlap spatially or not. We show this in more detail in Fig. 2(c), where the cross-sections of the spatial-temporal maps at various are presented. When the pump and probe spots overlap spatially (), decaying oscillations of are observed. Examination of the dependence of the oscillations frequency on the external field strength (Fig. S2 in Supplemental Material ) confirms that they originate from the laser-induced precession of the magnetization and the corresponding changes of . Outside the pump-probe spatial overlap, i.e. at , well-defined wave-packets are observed in the signal. The tilts of the signal maxima reveal a positive group velocity of the propagating waves. Therefore, these wave-packets can be confidently ascribed to laser-induced MSSWs packets propagating transversely to H.
Spatio-temporal maps obtained at have revealed the presence of fast-decaying backward volume magnetostatic waves (BVMSWs) (Fig. S3 in Supplemental Material ). Such a difference in the propagation characters of laser-driven MSSWs and BVMSWs appears to be typical for thin metallic films [28, 26, 27]. Below we focus our discussion on the excitation and propagation of the MSSWs.
As can be seen in Figs. 2(a,b), the parameters of the magnetization precession at and of the MSSWs at vary with . To quantify the azimuthal dependences of the precession and MSSWs’ parameters, we fitted temporal signals obtained at different and at different with either of the functions:
Here , , , are the amplitude, decay time, frequency, and initial phase of the precession at , respectively. , , , are the amplitude, width, center position, and group velocity of the Gaussian-shaped packet, respectively. Good agreement between the experimental data and the fitted curves is reached, apart from a small discrepancy at the tails of the precession and wavepackets, as shown in Fig. 2(c).
Figures 3 (a,b) show the azimuthal dependences of frequency and amplitude obtained at . has a pronounced 4-fold symmetry with a 2-fold distortion. It corresponds well to the intrinsic cubic magnetic anisotropy defined by the anisotropy parameter with easy axes along and and the substrate-induced in-plane uniaxial magnetic anisotropy defined by the parameter with an easy axis along expected for such films .
A pronounced azimuthal dependence of the amplitude of the laser-driven precession [Fig. 3(b)] allows us to identify the excitation mechanism as an ultrafast laser-induced thermal change of the magnetic anisotropy demonstrated earlier for a range of Galfenol films of various thicknesses [39, 43]. In brief, excitation of the precession stems from a rapid decrease of the anisotropy constants and [38, 44, 45] and of the saturation magnetization  in response to the laser-induced increase of electronic and lattice temperatures. In the considered experimental geometry, the amplitude of the excited precession is a measure of the abrupt reorientation of the total effective field in the sample plane due to the laser-induced changes of and . We also note that the ultrafast demagnetization  as a primary excitation mechanism  can be ruled out owing to the in-plane orientation of the initial film magnetization.
The azimuthal dependence of MSSWs’ amplitudes at m, i.e. close to the edge of the excitation spot, naturally resembles the one for . For the situation changes drastically, as the amplitudes of the MSSWs packets outside the excitation spot are defined not only by the efficiency of excitation at the specific field direction [Fig. 3(b)], but by the spatial decay as well. To single out the latter contribution, we plot in Fig. 3(c) the dependence of the normalized amplitudes of the MSSWs packets m). As can be seen the decay is the slowest at . Thus, the MSSWs packets propagate large distances along the hard axes, despite small initial amplitudes defined by the excitation mechanism. In contrast, no propagating MSSWs packets are observed, if H is directed almost along the easy axes (), and the small amplitude precession is excited. We note that the azimuthal dependence of the MSSWs’ frequency , in turn, does not differ from the one at [FIG. 3(a)]. Although inside and outside the laser-excited area the frequency is determined by the laser-modified and equilibrium anisotropy parameters and saturation magnetization, respectively, their changes appear to be not large enough to yield a shift of the frequency detectable in this experiment.
The change of the amplitudes of the MSSWs packets with [FIG. 3(c)] can be well fitted by a single exponential decay:
with being the propagation length. This is an important parameter of SWs, which, in particular, determines whether Galfenol is a suitable material for magnonic applications. As can be seen in Fig. 3(d), demonstrates a pronounced azimuthal dependence with two maxima corresponding to the geometries with the field applied along the hard axes. The largest m is observed if H is aligned along the hardest anisotropy axis . Importantly, this value is very close to the propagation length found for optically excited MSSWs in a 20-nm thick Permalloy film .
In order to account for the observed azimuthal dependence of and of other parameters of the precession and MSSWs, we have calculated the spatial-temporal MSSWs’ maps for different , following the procedure described in [18, 21, 24]. In the calculations, MSSWs propagate in the film described by its equilibrium magnetic parameters. The MSSWs’ dispersion relation introduced in  is adapted for the specific anisotropy of the studied film (see Sec. IV in Supplemental Material  for details). The isotropic Gilbert damping constant is used to achieve an agreement between the calculated and experimentally observed values of . The excitation of MSSWs via a laser-induced change of the total effective field is accounted for by an additional field with a step-like temporal profile and the spatial profile corresponding to that of the pump spot.
The equilibrium magnetic parameters of the non-heated film J/m and J/m required for the dispersion calculations and their changes within the laser-excited area, , , and , are obtained by joint analysis of the experimental azimuthal dependencies of and within the pump spot (see details in Supplemental Material ). The equilibrium saturation magnetization for the thin Galfenol film T is given elsewhere [49, 50]. The experimental dependencies and are well described by general ferromagnetic resonance formulae , and by the variation of the total effective field direction, respectively, with the following laser-induced changes: %, %, and % [see solid lines in Figs. 3(a,b)]. We note that shows rather good agreement with the one reported earlier for a 100-nm Galfenol film .
Having calculated the maps (see Fig. S4 in Supplemental Material ) with the help of the the derived magnetic parameters, we fitted cross-sections of the maps at various and using Eq. (2). The azimuthal dependence of obtained in this way captures the main features found in the experiment [solid line in Fig. 3(d)]. It confirms that the different propagation lengths for different sets of the field direction and MSSWs’ wavevector are dictated by the anisotropy of the film. We note that the pronounced anisotropy of the propagation of the laser-driven MSSWs packets is in agreement with the recently demonstrated enhancement of the propagation characteristics of MSSWs in cubic iron films . In both cases the largest propagation length is observed in the so-called ”hard-hard” configuration, where the equilibrium magnetization and the MSSWs’ wavevector are oriented along the two orthogonal hard axes. In contrast to the experiments with antennae , where the MSSWs’ propagation is one-dimensional, laser-induced MSSWs packets propagating along the axis are spreading slightly along the axis as well. Our results for show that this spreading does not suppress the main features of the propagation of MSSWs packets.
Finally, we discuss the deviation of the experimentally observed temporal shapes of the MSSWs packets from the Gaussian shape given by Eq. (2), evident in Fig. 2(c). The most prominent deviation is observed at large time delays , i.e. at the tails of wave-packets, as was noted by other groups as well [52, 26, 27]. Our calculations based on the MSSWs dispersion relation show that this deviation originates from dispersion of SWs generated by a sudden change of effective field. Indeed, the discrepancy between the tails of the calculated wave-packets and the Gaussian-shaped ones can be clearly seen in Fig. 2(d).
In conclusion, we have demonstrated laser-induced excitation and propagation of magnetostatic spin waves in a 20 nm thick epitaxial Galfenol film on a GaAs substrate characterized by pronounced in-plane magnetic anisotropy. We have shown that ultrafast thermal magnetic anisotropy changes induced by tightly focused femtosecond laser pulses excite propagating MSSWs. The strong in-plane anisotropy (10 J/m) of the film enables the laser-induced excitation of MSSWs in a simple geometry with an in-plane external magnetic field. The anisotropy of the film provides the possibility to tune the frequency, amplitude and propagation length of the excited waves by changing the in-plane field orientation. We find that the propagation length of the MSSWs in the studied film reaches 3.4 m, which, along with other recent results on spin dynamics in Galfenol films [37, 53, 43], confidently promotes epitaxial Galfenol to the limited family of metallic materials for magnonics. Furthermore, epitaxial Galfenol is also known for having a large magnetostriction constant  and so offers the prospect of controlling the SWs propagation via a voltage-induced strain when, for example, coupled to a piezoelectric substrate, as was earlier realized in YIG . It is important to note that the laser-induced thermal magnetocrystalline anisotropy change represents a novel fundamental process for the excitation of SWs, which can be applied to a broad range of materials without limitations on their electronic and magnetic structures. Finally, we note that introducing laser-induced ultrafast thermal changes of magnetic anisotropy as a tool to generate SWs can have even broader impact on magnonics. Since abrupt and local changes of the magnetic anisotropy by laser pulses yields strong local modifications of the SWs’ dispersion relation, it can be seen as a pathway to realize an ultrafast optically-reconfigurable magnonic medium for efficient steering and conversion of SWs [54, 16, 15, 55].
The authors thank L. V. Lutsev and I. V. Savochkin for valuable discussions. The setup construction and experiments were carried out under a support of RSF (project No. 16-12-10485); calculations were performed under a support of RFBR (project No. 18-02-00824-A).
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