Direct Observation of Sub-100 nm Spin Wave Propagation in Magnonic Wave-Guides

In magnonics research, capabilities of data processing mediated by spin waves are of current interest for beyond-CMOS data processing technologies, promising non-Boolean computing algorithms or majority gates substituting several tens of CMOS transistors and making this an exciting candidate for next level computing [1–3]. Furthermore, due to the short wavelength of magnons at technological relevant radio frequencies, smaller structural elements and, thus, miniaturization of various devices will be possible [4]. However, for magnonic logic operations, reliable spin wave guides are indispensable. Here, we use scanning transmission x-ray microscopy (STXM, MAXYMUS@BESSY II) with magnetic contrast and a spatial and temporal resolution of 18 nm and 35 ps respectively to investigate such wave-guides. These were structured in 50 nm thin Py stripes with a width of 350, 700 or 1400 nm and a length of 11 μm. A coplanar waveguide (Cr/Cu/Al) was deposited on top to allow RF excitation of spin waves in the structures (cf.Fig. 1 for a schematic sketch and a microscopy image). After time-domain STXM acquisition of the magnetization movie under RF excitation, a temporal Fourier transformation is performed to gain the spatial distribution of the spin wave amplitude and phase. This is shown exemplary in Fig. 2(a) for a 1400 nm wide Py stripe under CW excitation at 4.6 GHz and in an external field of 15 mT applied parallel to the long axis of the wave-guide (BV configuration). One can clearly observe that highly directed spin waves emerge from the edges of the wave-guide [5]. Due to the emission from both edges, a standing wave forms along the Py stripe. To quantify the spinwave properties a spatial Fourier transformation was performed to derive the k-space distribution of the wave vectors, which is shown in Fig. 2(b). Here, two components stand out beside the DC peak in the center showing that these microstructures act as multimode wave-guide. The first spin-wave modes has a wave vector k 1 = 4.7 μm -1 , which corresponds to a wavelength of $\lambda _{1} \quad =210$ nm, and a second mode with a k-vector $\mathrm {k}_{2} \quad = 10.5 \mu \mathrm {m}^{-1}$ is visible. Thus, we are able to microscopically observe a spin-wave with a wavelength of $\lambda _{2} =95$ nm and experimentally break through the 100 nm limit. Furthermore, we have performed a systematic variation of excitation frequency and applied external field for the different wave-guide widths. By varying these parameters, the wavelength as well as the propagation direction are tuned, indicating also diagonal and curved propagating of spin-waves that resembles the propagation of light in a graded-index fiber. Additionally, we recreated a data transmission scenario by using a Burst excitation scheme, i.e. four periods of RF excitation followed by a free decay time. Thereby, simultaneously excited multiple modes are carried by the Py wave-guide. They are interleaving without disrupting each other, further confirming the multimode properties of the wave-guide. Surprisingly, these modes did not disperse in frequency during the decay time making this system an ideal candidate for data transmission. In summary, we have directly observed sub-100 nm spin waves in a Py wave-guide by time-resolved STXM. The simple wave-guides were found to be able to non-dispersively carry multiple modes simultaneously. Thus, they are ideal candidates for magnon based data transmission between logic elements and provide a promising basis for future technology developments.