4.2. STXM-FMR Imaging 55
Fig. 4.7: Overview of the OOMMF simulated spin-wave profiles and combined and normalized amplitude/phase data extracted from STXM-FMR measurements (a) along and (b) across the Py strip in easy orientation, and (c) along and (d) across the Py strip in hard orientation.
Spin-wave Overview
The amplitude and phase data were extracted from the measured data and processed as described in sections3.3.2 and3.3.3, building an overview of the combined and nor-malized amplitude/phase data comparable to the simulations. The resulting overview
4.2. STXM-FMR Imaging 56
plots of the STXM-FMR data along (a), (c) and across (b), (d) the strip in easy (a), (b) and in hard (c), (d) orientations, respectively, are shown in Fig.4.7 together with the corresponding simulations. The vertical gray dashed lines indicate the correlation be-tween the measurements and the simulations. For comparison the adjusted simulations discussed in the previous section were used with the damping parameterα = 0.008 for both orientations. This value of the damping parameter was used for the hard orien-tation of the strip in adjusted simulations (see Fig.4.5(b,d,f)) and gives a good match between the simulations and the STXM-FMR measurements in both orientations. The bigger damping parameter in adjusted simulations for the easy orientation (see section 4.1.2) was used to fit the measured FMR linewidth. Although, the linewidth in one of the orientations could be different due to angle-dependent inhomogeneous broadening at particular MW frequency and not due to the change in Gilbert damping [84]. In Fig.4.7 for better visible matching in the figure the simulations are plotted with the same field step size as used for the measurements, i.e. 1 mT in easy orientation and 2 mT in hard orientation.
In Fig.4.7 comparison of the main FMR signal positions (in both orientations) in the simulations to the combined and normalized amplitude/phase data extracted from STXM-FMR measurements, a field mismatch is observed. That can be a result of the field calibration error of the measuring setup, small difference in the frequencies (simulations - 9.4 GHz, measurements - 9.43 GHz) or/and a possible saturation mag-netization difference between the samples measured with FMR and STXM-FMR. In easy orientation the mismatch is approximately 5 mT and in the hard orientation it is 9 mT (see also Tab.4.1). The reason for the different mismatch value in two orien-tations is that there was a step of remounting of the sample and recalibration of the electromagnet, when the orientation of the sample was changed. Another evidence of the mismatch not being a result of the sample shape difference is the relative position of the resonances in each orientation. As it was shown for the initial versus adjusted simulations (see section 4.1.2), the change in the sample shape also changes the rela-tive positions of the resonances within one orientation. Here the field gaps between the resonances measured with STXM-FMR are the same as in the simulations, meaning that the shape and the thickness were simulated very close to the real sample. The correlation of the measured and simulated spin-wave overview plots gives the spin-wave resonance fields listed in Tab.4.1. Further these FMR modes will be referred to using the field values from the simulation. The overall comparison of the spin-wave develop-ment overviews in the range of fields in both orientations of the strip along and across the strip in Fig.4.7 reveals a very good agreement between the simulations and the STXM-FMR measurements.
Spin-wave Dynamics
Time resolved simulations and STXM-FMR scans of the spatial distribution of the out-of-plane dynamic magnetization componentmz(t)(see Eq. (2.27)) within the strip
4.2. STXM-FMR Imaging 57
Fig. 4.8: Simulated and STXM-FMR-measured time evolution of mz(t) over one period for (a) easy and (b) hard orientation.
in the easy and the hard orientations are shown in Figs.4.8(a) and (b), respectively, for the quasi-uniform and spin-wave modes listed in Tab.4.1 (n={3,5,7}). The series of images are stacked in rows. The STXM-FMR scans depict 7 measured points of one
4.2. STXM-FMR Imaging 58
Fig. 4.9: (a) Chemical contrast with indication of the field direction; (b) amplitude and (c) phase analysis of the resonances at 87.8 mT in the easy orientation and 103.6 mT in the hard orientation. The top rows in (b) and (c) show measured data and bottom rows show simulated data.
magnetization precession period, while the simulations represent 14 points of the same period. The simulated images fit very well the measured spin-wave configuration, dynamics over the entire precession period. Both, measurements and simulations, reveal surprisingly a nonstanding character of the spin waves at resonance. That can be concluded from tracking the position of the nodes of the waves, which in the images are the white borders between red and blue regions. For example, in the easy orientation at 87.8 mT (n = 3) one can see that the nodes’ positions change from the center of the strip to the sho Thter edges during half of a precession period. The same is true for the hard orientation at 103.6 mT (n = 3), but in the opposite direction, the nodes change their position from the shorter edges of the strip to the center within half a period. The observed non-standing character of the spin waves shown in Fig.4.8 is most probably a result of the inhomogeneity of the internal field, its gradual decrease closer to the edges of the strip.
The more detailed amplitude/phase analysis (introduced in section 3.3.3) of the spin waves gives further differences between the two orientations and a good agreement
4.2. STXM-FMR Imaging 59
Fig. 4.10: (a) Measured and (b) simulated amplitude profiles, and (c) measured and (d) simulated phase profiles along the middle part of the Py strip marked with the red rectangle in the insets above the plots for the quasi-uniform mode andn = 3 spin wave in easy orientation and n= 3 spin wave in hard orientation.
between the simulations and the measurements. An example of this analysis for the n = 3 spin waves is shown in Fig.4.9. An exact position of the strip according to the external magnetic field is shown in Fig.4.9(a). In (b) the results of the amplitude analysis are shown for the measured and simulated data at 87.8 mT in easy orientation and at 103.6 mT in hard orientation. In (b) the phase analysis of the same data is demonstrated. For the analysis the scans and simulated images were used that are shown in Fig.4.8at the specified fields. That means that 7 points in time were analyzed from measured data and 14 points in time from the simulated data. As was mentioned above overall the analysis reveals a very good agreement between the measurements and the simulations. When comparing the two orientations, in the amplitude plots one can see two peaks in the easy orientation and three peaks in the hard orientation.
There are three distinct anti-nodes visible in the phase plots for both orientations. That means that in both orientations the spin wave with similar wave length is excited, but in the easy orientation the central part of the strip is muted. That is why the amplitude
4.2. STXM-FMR Imaging 60
in the center is minimum. The reason for that is an overlap of the quasi-uniform mode and the n = 3 spin wave in easy orientation. This can be seen in the FMR spectrum plotted in Fig.4.6(a) together with the spin-wave profiles overview in (c). The n = 3 mode signal is overlapping with the main signal of the quasi-uniform mode, while in the hard orientation the modes are separated in field (see panels (b) and (d) in the figure and also Figs.D.1 and D.2). Additionally, in the central part of the strip there is a phase shift between the quasi-uniform and the n = 3 spin-wave modes in both orientations that is represented in Figs4.7(a) and (c) by the color change from blue to red forn = 1 and n = 3 modes. The different separation of the modes and the phase shift together give the difference between the easy and the hard orientations observed in Fig.4.10. Another way of analyzing that in more detail is by looking closer at the phase and amplitude profiles of those modes.
In Fig.4.10 the correlation between the amplitude and the phase profiles along the middle part of the strip marked with the red rectangle in the insets above the plots (see section3.3.3for more details) is shown for the quasi-uniform mode andn = 3spin wave in easy orientation andn = 3 spin wave in hard orientation. The plots in (a) and (c) show the data measured with STXM-FMR, and (b) and (d) show simulated data. Blue circles on the amplitude and phase profiles indicate positions along the strip, where the magnetization of the quasi-uniform mode precesses in phase with the magnetization at then = 3mode in easy orientation (the phase between the modes fits). The orange dots indicate “out of phase” positions of the modes (with the phase shift of 180° between the modes), respectively. For the n = 3 mode amplitude profile plots in (a) clearly demonstrate two bigger maximums and one much smaller maximum in easy orientation and three distinct maximums in hard orientation. The simulated data shown in (b) reveals two distinct amplitude maximums in easy orientation and two bigger and one smaller maximums in hard orientation. It is clear from the blue dots positions that in both, STXM-FMR data and simulations, the amplitude is maximum at the regions, where the spin-wave mode is in phase with the quasi-uniform mode. Furthermore, at the orange points positions and further towards the center of the strip, where the phase difference is close to 180°, the amplitude decreases. Thus, STXM-FMR measurements confirm that in the easy orientation then= 3 mode is influenced by the quasi-uniform mode, with which it is overlapping according to the FMR measurements (see Fig.4.6 and also Fig.D.1).
The difference between the measured and simulated amplitude profiles is most probably a result of a shape anisotropy discrepancy, which can be deduced from the quasi-uniform mode amplitude profile. In the simulated data the amplitude profile has an almost flat region from 1 till 4 micron position along the strip. In the measured data the amplitude has a peak at around 3 micron and decreases towards the shorter edges of the strip.
In both cases the internal field profile within the strip can be approximately derived from the amplitude distribution at the quasi-uniform mode (see Eqs. (2.37)-(2.41) and [20]), as the magnetization precession angle depends on the local effective field.
Another confirmation for that is the distribution of the amplitude of the spin-wave
4.2. STXM-FMR Imaging 61
mode in easy orientation, which is enclosed within the quasi-uniform mode amplitude profile in both (a) and (b).
STXM-FMR measurements show a very good agreement with adjusted simulations both, in the static wave analysis using overview plots and in the dynamic spin-wave behavior. A nonstanding character is revealed for the spin spin-waves at the spin-spin-wave FMR modes. It is demonstrated that the spin-wave behavior at the resonances that are overlapping with the quasi-uniform mode, gets affected by the latter. It is suggested that the STXM-FMR signal amplitude distribution at the quasi-uniform FMR mode can be used to evaluate the internal field distribution and its influence on the excited spin waves within the strip.
Transient Behavior
Additionally to the measurements of the steady state of the magnetization preces-sion, the transient behavior was measured within the Py microstrip using STXM-FMR. These measurements were carried out at BESSY, at excitation frequency of fMW = 9.323GHz, nominal external field of 95 mT corresponding to the spin-wave mode n= 5 and for a different sample, compared to the one discussed above, with sim-ilar nominal parameters (the same shape, size, material). Simulation parameters used to fit the measurements are: rounded lateral shape of the strip, a thickness of 30 nm, saturation magnetization Ms = 750kA/m, Gilbert damping parameter α= 0.008, ex-change stiffness constant Aex = 13×10−12J/m, excitation frequency fMW = 9.43GHz and external field H = 88mT. The results of the simulations and STXM-FMR mea-surements are shown in Fig.4.11(a), depicting the transient behavior of the simulated and measured spin-wave profiles over the time. The spin-wave profiles are extracted in the similar way to the overview profiles (see sections 3.3.1 and 3.3.3). The simulations are plotted with the same time step as was used for the measurements.
Transient behavior here means an evolution of the system starting from the moment of applying the excitation and till the steady state is settled. The comparison of the measurements in Fig.4.11(a) to the simulations shows a good agreement. Moreover, simulations reveal that the measurements allow to record a part of the spin-wave dy-namics transient response starting from the approximately 6th period of the MW field and over 25 further periods of it. In Figs.4.11(b) and (c) an evolution of the simulated spin-wave profile along the microstrip and integrated over the strip out-of-plane dy-namic magnetization componentmz(t)(see Eq. (2.27)) during the first 50 cycles of the MW excitation are shown, respectively. In order to see if the stable state was reached during the measurements, the measured range is marked with dashed vertical lines in the figures. The latter confirms that the stable state was not measured yet. Though it shows that it is in principle possible to investigate transient behavior of spin waves within the microstructures. One can see in Figs.4.11(b) that the applied MW field excites the whole area of the strip uniformly. Further, the n = 5 spin wave is formed over the time as a result of multiple reflections and interference of the formed spin-wave
4.2. STXM-FMR Imaging 62
Fig. 4.11: (a) Simulated and measured with STXM-FMR time evolution of spin-wave profiles along the Py microstrip over 25 periods of the MW excitation. (b) Simulated time evolution of spin-wave profiles along the Py microstrip and (c) time dependency of the out-of-plane dynamic magnetization componentmz(t) over the first 50 cycles of the MW excitation.
eigenmodes. Wherein, when the stable state is established, a nonstanding spin-wave behavior is observed manifested in tilted (non-vertical) blue and red lines.
Summarizing the chapter, it is possible to excite a quasi-uniform (FMR) mode and a wide variety of spin waves within a single Py microstrip using uniform MW excitation.
These excitations can be calculated using micromagnetic simulations, measured with
4.2. STXM-FMR Imaging 63
microantenna-based FMR and directly imaged with a high spatio-temporal resolution using STXM-FMR. The experimental results are in excellent agreement with micro-magnetic simulations. Unexpectedly, a nonstanding character of the spin waves was revealed both, at and off resonance detected with microantenna-based FMR. These findings are surprising, because only a uniform excitation field is applied to the speci-men during the measurespeci-ments and originally only standing spin-waves were expected [78]. More detailed analysis of the simulated data demonstrated that the spin-wave patterns are a result of the interference of several spin-wave eigenmodes in at least two directions in the plane of the sample, parallel and perpendicular to the external static magnetic field. When analyzing the spin-wave excitations within the confined microstructure, it should be taken into account that the eigenmodes’ dispersion and, thus, the resulting spin waves depend strongly on the internal field distribution [9, 20, 26]. Moreover, the internal field within the microstrip is highly inhomogeneous due to its confined size, especially in the direction parallel to the external static magnetic field (see section 2.1.1). This together can be the main reason for the nonstanding charac-ter of the observed spin waves, as they are a superposition of these eigenmodes. The influence of the internal field distribution on the spin-wave behaviors was investigated by means of an overall shape modification of the strip in series of micromagnetic sim-ulations (the lateral shape and the thickness were changed), because the internal field distribution depends on the overall shape of the strip. It was demonstrated that by changing the overall shape of the strip it is possible to shift the mutual arrangement of the spin waves in the field range at the same MW frequency. The latter allows to mod-ify, for example, spin configuration of some particular spin waves (see Fig.4.10). These findings allow very useful insight in understanding of the spin-dynamics in rectangular confined microstructures and a spin-wave evolution during magnetization precession period.
5
Spin-wave Excitations in Complex Microstructures
A detailed analysis of spin waves excited in Py T- and L-strips microsctructures using uniform excitation is given in this chapter. First, results of micromagnetic simulations and microresonator-based FMR measurements are presented in order to demonstrate the fit of the adjusted simulations to the measured data. Further, T-strips, L-strips and a single strip are compared to each other. In the following section results of the STXM-FMR measurements carried out at SLAC (SLAC-measurements) are discussed showing spin dynamics within the vertical strip of the T-strips compared to L-strips. Finally, the findings of the SLAC-measurements are confirmed by more detailed STXM-FMR measurements from BESSY (BESSY-measurements).
Part of the results of this chapter were already published in [22].
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