RF Excited Magnetization Dynamics

In the following experiments, the micro-focus laser spot probes the magnetization dynamics at a location approximately 1 μm away from the point contact tip, as indicated by the arrow in Figure 5-22, showing a BLS tip connecting to a 200 nm point contact. To obtain an idea of the possible modes that can be excited, the device is electrically pumped with a 13 dBm RF AC current of varying frequency to check for resonances in the BLS intensity spectrum. BLS intensity spectra were recorded for various strengths of the external magnetic field that is applied in the plane of the magnetic layer, along the long axis of the magnetic element, which is to the right in Figure 5-22. In Figure 5-23, the frequency of the RF excitation source is swept between 3.0 GHz and 18.0 GHz (x-axis), while for every excitation frequency, a BLS intensity spectrum is recorded and mapped in color scale as a function of the BLS scan frequency (y-axis). From the information in these images, integrated BLS intensity spectra can be calculated as a function of external field, which are displayed in Figure 5-24.

Figure 5-22: Image of a BLS tip connecting to a point contact. The circle indicates the location where the laser spot is focused on the free magnetic layer to obtain the BLS intensity spectra (approximately 1 μm to the left of the point contact).

For zero applied field, the system is observed to display a resonance around 8 GHz, which is visible both in the intensity maps (resonance indicated by the red area in the left panel of Figure 5-23-d) and in the integrated BLS intensity spectrum (resonance peak in the purple line in Figure 5-27). With increasing field, the resonance peak observed at 8 GHz for zero field red-shifts towards lower frequencies, while an additional lower frequency peak initially around 3 GHz is observed to blue-shift towards higher frequencies. The integrated BLS spectrum for the largest applied field (18.5 mT - blue line) features a hybrid peak that is composed of contributions of the high frequency mode with both its second harmonic and the previously observed lower frequency mode. (see Figure 5-23-a). Although the higher order peak at 4.9 GHz and the red-shifting peak at 5.7 GHz partly overlap for the maximum field value, they remain distinguishable. The lowest frequency peak, whose frequency increases

H₀

with increasing external field, is assumed to be due to excitation of the uniform dynamic mode, while the higher order peak is suspected to represent a spin wave mode, possibly the MSBVW one, considering the field geometry and the location of measurement.

Figure 5-23: Logarithmic (left) and linear scale (right) BLS spectral intensity (y-axis) maps as a function of RF excitation frequency (x-(y-axis). The externally applied field is increased from bottom (d) to top (a). The corresponding integrated BLS intensity spectra are displayed in Figure 5-24.

a) 18.5 mT

b) 6.2 mT

c) 3.1 mT

d) 0 mT

a) 18.5 mT

b) 6.2 mT

c) 3.1 mT

d) 0 mT

Figure 5-24: Integrated BLS spectra as a function of RF excitation frequency for various external field values. The externally applied field is increased from bottom (0 mT - purple line) to top (18.5 mT - blue line).

For intermediate fields, the peaks overlap, resulting in the highest integrated intensity peak (dark green curve) for a pumping frequency around 4.9 GHz. For an appropriate field setting, both modes are pumped effectively at a common frequency. Note that in all integrated spectra, a smaller peak is observable around 6.5 GHz, which is not assumed to be related to any magnetic phenomenon, since it does not shift with varying external field. This small ripple is instead assumed to be caused by RF transmission effects in either the device or cabling. The spectral maps in Figure 5-23 also reveal a set of horizontal, equally spaced lines. These are an artifact of the multi-mode laser cavity resonances of the laser that probes the sample.

18.5 mT

9.3 mT

6.2 mT

4.7 mT

3.1 mT

1.6 mT

0 mT

BLS intensity (backscattered photon count)

Frequency of RF source (GHz)

The red-shifting behavior of the suspected MSBVW mode in the integrated BLS intensity spectra remains somewhat puzzling. Note that also in the case of the MSBVW mode, frequency is expected to increase with increasing field, equation (2-35), unless the external field is able to lift any other anisotropy present in the system, by which the total internal field, and thus the frequency of the MSBVW mode could decrease. Although the free layer may experience slight stray field induced anisotropy due to the bottom exchange pinned layer, this interaction is expected to be an order of magnitude smaller than the external 18 mT field (see for example the magnetoresistance curve in Figure 5-7). Furthermore, if indeed the internal field would be lowered by the application of the external field, also the uniform mode frequency should go down, which is not the case.

A cautious hypothesis is formulated here that the red-shift could be caused by the interplay between the Oersted field generated by the excitation current and the externally applied field, in such a manner that the net local field at the place of measurement changes its direction from vertical to horizontal. This generates a local transition from MSSW to MSBVW mode behavior, implying a decrease in frequency.

Using the formula for the Oersted field of an infinitely long current carrying wire, the maximal field amplitude obtained at 1 μm away from the point contact is of the order of 7 mT, which is in the range of the applied fields and strong enough to cause tilting of the net internal magnetic field. Note that this reasoning is slightly complicated by the simultaneous effect of increasing overall frequency for both modes due to increasing field. A full quantitative argument would require precise fitting of the peak frequencies and the calculation of hybrid MSSW and MSBVW mode dispersion relations for the various angles of propagation.

To gain more insight into the observed resonances, the measurement of the BLS intensity as a function of excitation frequency is repeated for the zero and maximum field settings of the previous measurements. In order to increase the BLS signal, especially for the higher frequency modes which are known to decay faster, the laser spot is positioned closer to the point contact. The resulting BLS frequency versus RF excitation frequency maps for 0 mT and 18.5 mT in-plane fields, Figure 5-25, reveal increased detail compared to the previous measurements. Up to five harmonic modes are now observable above the main excitation frequency, along with two modes with 0.5 and 1.5 times the excitation frequency. These non-integer factor modes are assumed to be associated with magnon splitting processes. Note that in the case of an applied field, the splitting process seem to be prohibited below a threshold excitation frequency close to 8 GHz, indicated by the abrupt onset of both the 0.5 and 1.5 line at this frequency. Apparently, the splitting process cannot produce spin waves with a frequency less than approximately 4 GHz. This threshold can be explained by looking at the magnetostatic mode dispersion curves displayed in Figure 5-26, which are

calculated for a 10 nm thick permalloy film and an in-plane bias field of 20 mT. In these figures, subsequent curves indicate the transition from MSSW (top) to MSBVW (bottom) behavior, or alternatively, the wave vector changing its direction from perpendicular to parallel to the external field. Clearly, neither the MSSW nor the MSBVW mode can exist below the uniform mode frequency (in principle, the MSBVW mode can exist below this frequency, but the dipolar contribution to the dispersion curve is very small for very thin films). Finally, note that for zero applied field, no magnon splitting is observed between 11 GHz and 14 GHz, which cannot be explained so far.

Figure 5-25: Logarithmic scale BLS spectral intensity (y-axis) maps as a function of RF excitation frequency (x-axis, RF power 13dBm) for an externally applied in-plane field of 0 mT (left) and 18.5 mT (right). For the 18.5 mT field, the magnon splitting process is prohibited to produce magnons below approximately 4 GHz (i.e.

excitation frequency 8 GHz).

Figure 5-26: Effect of the application of an external field on the dispersion relations. In each figure, the top curve corresponds to the MSBVW mode, while the bottom curve represents the MSSW mode. The dispersion curves in between are for 15, 30, 45, 60 and 75 degrees angles between the wave vector and external field.

Clearly, for a 200 Oe field the magnon splitting process is prohibited for generating magnons with a frequency below 4 GHz. Calculation provided by H. Schultheiß.

0 mT 18.5 mT