6.2.1 Measurements on Cr/Fe/GaAs
Based on a good understanding of the TRMOKE data for the samples with Gilbert damping it is now interesting to compare these results with those obtained using sam-ples which exhibited strong two-magnon relaxation in FMR. The 20Au/20Cr/16Fe/-GaAsn/GaAsn+(001) sample provides such a case. In Fig. 6.6 the data for this sam-ple were measured for four different bias fields directed along the [110]Fe direction.
Clearly, the relaxation appears to be much faster compared to the samples with intrin-sic damping. In Fig. 6.8 the relaxation corresponding to this series of measurements was put into context with the FMR measurements on the same sample (relaxations are represented by the effective damping parameter,αeffγ
ω∆H. The apparent damping
Figure 6.6: Four data sets showing the time evolution of the magnetization in the 20Au/20Cr/16Fe/GaAs sample withHB [110]Fe at four different bias fields (a) HB = 0 Oe (f = 6.1 GHz),(b) HB = 250 Oe (f = 8.6 GHz),(c) HB = 500 Oe (f = 9.4 GHz), and (d)HB = 750 Oe (f = 11.3 GHz). Note that the apparent damping in(d) is significantly reduced. The effective damping parameters determined from all fits are shown in Fig. 6.8.
in the TRMOKE measurements is always smaller than is obtained from the FMR re-sults. Under certain experimental conditions (bias field, focussing of the pump beam) the two-magnon contribution to the damping was reduced by approximately 80%, as shown in Figs. 6.6d and 6.8 (open star at 11.3 GHz), and as shown in Fig. 6.6b the measured oscillations suddenly changed their phase. To understand these two unex-pected features one has to consider the spatial and time dependence of the magnetic pulse field created by the Schottky diode switch.
6.2.2 Pump field inhomogeneity
µ
Figure 6.7: Cross-section of the excitation profile generated by the Schottky diode, where x is parallel toM.
Since the photo current flows perpendicular to the Fe/GaAsninterface, its corresponding magnetic field is oriented in the film plane with circular field lines centered around the spot of the pump beam, as illus-trated in Fig. 3.17a. On the circle all angles from 0 to 2πbetween pump field direction and the direction of M are realized. The direction of M was fixed by the bias field to be parallel with [110]Fe. This exci-tation field configuration is similar to that used in experiments at SLAC [182, 183] (see also appendix A). As illustrated in Fig. 3.17a at points, where the
pump field direction is perpendicular to the magnetization the exciting torque reaches a maximum, and in places where M is parallel or antiparallel to the pump field no excitation takes place. Since the pump beam and the corresponding photo current have a Gaussian profile, the field amplitude as a function of distancerfrom the pump spot center is given by [87]
h∼ 1
whereR is the radius of the pump spot. The magnetic excitation is sickle shaped on both sides of the pump spot and is antisymmetric. The spatially most inhomogeneous Fourier component of the excitation is parallel to M and can be reasonably well described by a k-vector corresponding to k∗ = 2π/(4R) with k∗ M, as shown in Fig. 6.7. This result can be used for the discussion of magnon scattering.
6.2.3 Scattering of inhomogeneous modes
In Fig. 6.9 the spin wave dispersion spectra for in-plane k-vectors were calculated for f = 6.1 and 11.3 GHz with magnetic parameters corresponding to the 16 ML Fe film. Based on this figure one can understand why the strength of the two magnon scattering critically depends on the bias field and the diameter of the laser pump beam focal spot. At f = 11.3 GHz the excited mode has a k-vector close to the minimum (bottom) of the spin wave band. In this case there are obviously fewer degenerate magnons available compared to the lower bias fields where the initial excitation can find many degenerate spin waves, as illustrated by the intersection of the horizontal
α
Figure 6.8: Effective damping parameter as a function of the frequency for the 20Au/20Cr/16Fe/GaAs sample.
( • )
data points were obtained using FMR [167] and (✩) are the results from the TRMOKE fits. In these experiments the applied field was[110]Fe. The () symbols correspond to FMR measurements in the perpendicular configuration and represent the Gilbert damping.dotted line with the spin wave manifold in Fig. 6.9. In addition the magnon group velocity (∂ω/∂k) is zero at the bottom of the spin wave band. These two effects explain the decreased relaxation which was observed in Figs. 6.6d and 6.8 [184].
The presence of out-of-phase oscillations in Fig. 6.6b might be a consequence of a mode-mode coupling phenomenon where a significant amount of the initial excitation scatters into a spin wave mode which is out-of-phase with the initial excitation at the probed position.
In Fig. 6.8 the relaxation corresponding to this series of measurements was put into context with the FMR measurements on the same sample [167] (the FMR linewidth was expressed by an effective damping parameter: αeff = ∆Hωγ). The effective damp-ing in the TRMOKE measurements is significantly smaller than that obtained from FMR at the same frequency (10 GHz). This is probably a consequence of the reduced number of available spin wave states for scattering in the TRMOKE experiment com-pared to the FMR experiment, as shown in Fig. 6.9.
Figure 6.9: Spin wave dispersion band (spin wave manifold) for a 16 ML Fe film calculated for HB = 0 (f = 6.1 GHz) and HB = 750 Oe (f = 11.3 GHz) corresponding to the measurements shown in Figs. 6.6a and 6.6d. The family of curves in the spin wave manifold is obtained using different anglesψqbetween the magnetization the spin wave (Mandq). The bottom of the spin wave band corresponds toqM. The dashed vertical line represents the k-vector of the initial excitation of the magnetization∼π/2Rin the TRMOKE experiment and the (•) symbols highlight the position of this excitation within the spin wave band. Note that at f = 6.1 GHz many degenerate spin waves are available for scattering (horizontal dotted line) while atf = 11.3 GHz their number is substantially reduced.
6.2.4 Magnetic frustration and coercive fields
The Cr cap layer not only causes increased relaxation due to two-magnon scattering, but it also increases the coercive field from 4 Oe (for 20Au/16Fe/GaAs) to 30 Oe (20Au/21Cr/16Fe/GaAs), and strongly changes the magnetic anisotropies. These phenomena are very likely a consequence of antiferromagetic step induced (roughness driven) frustration effects at the Fe/Cr interface [168, 169, 178].
The increase of the coercive field as a function of the Cr thickness was measured using static Kerr microscopy on a sample with a wedged Cr cap layer. One side of the wedge corresponded to 20Au/16Fe/GaAs(001), and the other side of the wedge corresponded to 20Au/20Cr/16Fe/GaAs(001), as illustrated in Fig. 6.10. The wedge from 0 to 20 ML Cr was as wide as the Kerr microscope’s field of view of ∼ 350 µm. This wedge was produced by a shadow mask inside the MBE chamber during
0 5 10 15 20
Figure 6.10: (a)Shows a series of domain images (200µm×350µm) for a wedged 20Au/0-20Cr/16Fe/GaAs(001) sample. The black and white arrows indicate the magnetic domains and the arrow on the right shows the direction of the applied field. (b)Sample reflectivity and the corresponding thickness of the Cr wedge across the vertical direction of the images.
(c)The coercive fields as a function of the Cr thickness deduced from the series of domain images in(a) along with a cartoon of the wedged sample.
the growth of the Cr layer. The Cr thickness as a function of the position was obtained from the changing sample reflectivity (assuming a linear relation between the reflectivity and the Cr thickness), as can be seen in Fig. 6.10b. A domain wall was injected from the 20Au/16Fe/GaAs(001) side into the wedge. 20Au/16Fe/GaAs(001) samples have small coercive fields and the domain walls can be easily controlled in the field of view of the Kerr microscope by means of an external magnetic field. The injected domain wall had a zig-zag configuration (head-on) because the slope of the wedge was parallel to the easy axis of the film ([110]Fe). This wall was driven into the Cr covered part of the sample and the position of the domain wall was measured as a function of the applied magnetic pressure. This procedure allowed one to infer the coercive field as a function of the Cr cap layer thickness (shown in Fig. 6.10c). From this experiment one can conclude that the increase of the coercive field due to the Cr cap layer saturates at a thickness of 7 ML of Cr.
6.2.5 Field dependent magnetic properties
The measurement of the resonance frequency as a function of the bias field, shown in Fig. 6.5, directly illustrates how profoundly the magnetic parameters of the 16Fe layer are affected by the Cr cap layer. Two samples are shown: 20Au/16Fe/GaAsn (•◦) and 20Au/20Cr/16Fe/GaAsn (✩). Both samples were grown on thesame substrate using a shadow mask inside the MBE chamber. One can therefore attribute the difference in magnetic properties directly to the different cap layers. In the case of the Cr cap, the g-factor that describes the data well has the unreasonable value:
g = 1.79, and is at variance with the FMR results obtained at higher frequencies [167], as shown in Fig. 6.5. This implies that the Cr cap layer gives rise to field or frequency dependent magnetic anisotropies.