Experimental Realization of a Passive GHz Frequency-Division Demultiplexer for Magnonic Logic Networks

The emerging field of magnonics employs spin waves and their quanta, magnons, to implement wave-based computing on the micro- and nanoscale. Multi-frequency magnon networks would allow for parallel data processing within single logic elements whereas this is not the case with conventional transistor-based electronic logic. However, a lack of experimentally proven solutions to efficiently combine and separate magnons of different frequencies has impeded the intensive use of this concept. In this Letter, the experimental realization of a spin-wave demultiplexer enabling frequency-dependent separation of magnonic signals in the GHz range is demonstrated. The device is based on two-dimensional magnon transport in the form of spin-wave beams in unpatterned magnetic films. The intrinsic frequency-dependence of the beam direction is exploited to realize a passive functioning obviating an external control and additional power consumption. This approach paves the way to magnonic multiplexing circuits enabling simultaneous information transport and processing.


Abstract text:
The emerging field of magnonics employs spin waves and their quanta, magnons, to implement wave-based computing on the micro-and nanoscale. Multi-frequency magnon networks would allow for parallel data processing within single logic elements whereas this is not the case with conventional transistor-based electronic logic. However, a lack of experimentally proven solutions to efficiently combine and separate magnons of different frequencies has impeded the intensive use of this concept. In this Letter, the experimental realization of a spin-wave demultiplexer enabling frequency-dependent separation of magnonic signals in the GHz range is demonstrated. The device is based on two-dimensional magnon transport in the form of spinwave beams in unpatterned magnetic films. The intrinsic frequency-dependence of the beam direction is exploited to realize a passive functioning obviating an external control and additional power consumption. This approach paves the way to magnonic multiplexing circuits enabling simultaneous information transport and processing.
Main text: The concept of parallel data processing in single elements is very promising since it can multiply the throughput of future logic networks significantly. [1] One important requirement, the wave-based processing of data, has already been demonstrated by utilizing spin waves [2] in micro-and nanostructures. [3,4] Furthermore, the likewise necessary technique of simultaneous information transport in separated frequency-channels, called frequency-division multiplexing, [5] has been used in various other wave-based applications such as in fiber-optic networks. However, its implementation into magnonic networks has only been studied theoretically [1,6] or discussed in preparatory works [7,8,9,10,11] since a device for the efficient combination and separation of spin-wave signals of different frequencies is missing until now. In this work, we present the experimental realization of this required device, which employs caustic-like spin-wave beams to create a so-called magnonic frequency-division demultiplexer. Hence, our results enable the realization of magnonic multi-frequency circuits [6] which allow for parallel data processing in single devices. [1] Spin waves offer many advantages for wave-based computing [12,13,14,15,16,17] due to their micro-to nanometer small wavelengths at GHz-frequencies, [18,19,20] their enormous tunability by various parameters [21] and the possibility of charge-less information transport.
One exceptional property utilized in the following work is the anisotropic propagation of spin waves in suitable magnetic media, which can lead to the creation of narrow spin-wave beams and caustics [6,22,23,24,25,26,27,28,29] (see Experimental Section). Their sub-wavelength transverse aperture [26] is an outstanding reason for their potential use in nanostructured networks, especially when considering the beam formation of high-wavevector magnons. [23] The caustic-like spin-wave beams can be radiated from point-like sources into unpatterned magnetic films [24,25,26,27] and they are formed due to the non-collinearity of the wavevector and the group velocity vector. Furthermore, their propagation direction can be versatilely controlled by, e.g., frequency [6,22,24,27,28,29], magnetic field strength [22] and direction of the local magnetization. [25,26] In this work, we experimentally demonstrate how these caustic-like spin-wave beams can be used to realize controllable information transport in two-dimensional magnetic films with thicknesses of a few tens of nanometers. The guidance of the signal is not achieved by geometrical structuring [3,2] or magnetically induced channels [30] but by the inherent anisotropy of the magnonic system. Utilizing this anisotropic signal propagation allows for the realization of passive elements without any additional energy consumption since the magnonic system inherently collimates and steers the energy transport. As just one of the many possible applications of this concept, we present the realization of a passive demultiplexer exploiting the frequency-dependence of the beam direction. By inverting the geometry, a multiplexer can be realized equally well. [31] The experimental realization of the frequency-division demultiplexer is based on a 30-nm-thin film of the magnetic alloy CoFeB. In contrast to magnetic insulators like yttrium iron garnet (YIG), [28] the metallic ferromagnet CoFeB is much more compatible with state-of-the-art fabrication techniques of silicon-based microchips. Furthermore, CoFeB exhibits a much higher saturation magnetization (see Experimental Section) which enables the creation of caustic-like spin-wave beams in a broad frequency range. Being based on our previous studies, [6] we have designed a demultiplexer prototype by micromagnetic modelling. Subsequently, the sample has been fabricated and studied by detecting the spin-wave intensity using micro-focused Brillouin light scattering spectroscopy (µBLS). [32] After investigating the frequency-dependence of the spin-wave beam directions and comparing it to theoretical calculations, we verify the full functionality of the demultiplexer by two-dimensional measurements of the spin-wave intensity. Figure 1a,b presents the simulated intensity distribution inside of the designed structure for spin waves of frequencies 1 = 11.2 GHz and 2 = 13.8 GHz. The dashed arrows mark the beam directions that are predicted by the developed theoretical model (see Figure 1c and Experimental Section). The functional part of the device comprises the unpatterned area in the center of the structure in which the two-dimensional energy transport takes place. Input and output waveguides, which can serve as interfaces to adjacent magnonic building blocks in larger magnonic networks, are connected to this area. To provide an input signal, magnon excitation is simulated by applying localized alternating magnetic fields hrf inside the input waveguide.
The field distribution is chosen in accordance with the experiment in which these fields are created by microwave currents flowing through a microstrip antenna placed across the waveguide. The spin waves propagate towards the unpatterned area and, in agreement with previous observations, [6,24,25,26] two symmetric spin-wave beams are emitted from the waveguide opening, which acts as a point-like source exhibiting a broad wavevector spectrum.
The anisotropy of the spin-wave dispersion leads to a strong focusing of the energy.
Furthermore, the initial width of the spin-wave beams is determined by the width of the waveguide opening, for which reason an abrupt transition into the unstructured film area without widening was chosen. The observed frequency dependence of the beam directions is utilized to realize the demultiplexing functionality by properly adding two output waveguides after a certain propagation distance. Their positions are asymmetric with respect to the input, leading to the following consequence: at frequency 1 = 11.2 GHz (Figure 1a show that the major fraction of the losses arise from the intrinsic spin-wave damping during their propagation and not due the demultiplexing mechanism based on beam formation and channeling (the splitting is suppressible [6]).
Finally, the scalability and advantages of the presented concept should be discussed. The employed spin-wave beams are created due to the anisotropy of the magnonic system and, for limited length scales, their width is primary determined by the size of the source. [26] In the presented case, the anisotropy is induced by the dipole-dipole-interaction, which is dominant in the low-wavevector range of the magnon spectrum. However, a beam formation is also possible for high-wavevector spin waves whose dispersion characteristics are mainly dominated by the exchange interaction. [23] Hence, the presented concept to guide two-dimensional energy transport by spin-wave beams, formed due to the intrinsic anisotropy of the system, can be scaled down to significantly smaller length scales. Furthermore, the passive character of the signal steering is an important advantage over other concepts requiring energy-consuming external control. This is the case, e.g., with the previously demonstrated spin-wave timedivision multiplexer, which relies on external charge currents. [33] In conclusion, we have developed and experimentally realized a passive frequency-division demultiplexer, which is based on intrinsically steered two-dimensional signal transport in which can now be implemented in an energy-efficient way building on the presented prototype.

Experimental Section
Micro-focused Brillouin light scattering (µBLS) measurements: The spin-wave intensity is experimentally measured by utilizing µBLS [32] with a spatial resolution of around 250 nm. In in which the occurring energy splitting into two spin-wave beams is considered by the factor 1/2. It should be mentioned that the splitting can be suppressed by changing the design of the demultiplexer as shown in ref. [6]. Furthermore, the factor 0.5 has to be introduced since the spin-wave intensity is measured instead of the amplitude.
The group velocity of the spin waves differs inside the waveguides ( w ) and in the unpatterned film area ( f ) and can be calculated according to ref. [36,37]. To determine f , the spin-wave wavevector relating to the occurring beam angle is used for the calculations.
Furthermore, w is the spin-wave propagation distance in the waveguides whereas f is the corresponding distance in the film area. Finally, the spin-wave lifetime results from the damping parameter α and is approximated by the value ( = 0) at ferromagnetic resonance. is considered as explained in the following. This is the main difference to a previous theoretical approach [22] and our results reveal, that the observed direction of maximum focusing is not always given by the caustic direction (According to ref. [22], caustics occur at the points of the isofrequency curve where its curvature is zero). Due to this reason, we refer to the observed beams resulting from the focused energy transport as (caustic-like) spin-wave beams instead of caustics.
The first step of the developed approach is to include the wavevector spectrum Ak of the beam source in the calculations. It can be assumed that the spin waves propagate through the input in the form of the first waveguide mode having a sinusoidal shape along the short axis of the waveguide and only one maximum in the centre. If the input waves reach the transition zone at the connection between the waveguide and the unstructured area, the waveguide mode acts as a one-dimensional source (with effective width weff, explanation above) for secondary spin waves propagating into the unpatterned film area and forming beams due to their anisotropic propagation. The confinement of the mode across the waveguide leads to a broad spectrum Ak of the respective wavevector component ky, which can be calculated to Ak(ky) = cos(ky weff/2)/( 2 /weff 2 -ky 2 ) by spatial Fourier-transformation of the mode profile. This spectrum is considered by using the following procedure. First, the angle θvg between the group velocity vector and the external field direction is calculated from the isofrequency curve as a function of the wavevector component ky. Second, the wavevector spectrum Ak(ky) is projected onto the curve θvg(ky) by a numerical integration to determine the amount of excited spin waves propagating into the direction θvg. The result of this procedure is the spin-wave amplitude SW initial ( g ), which reflects the angle distribution of the spin-wave flow under consideration of the initial wavevector spectrum Ak. Maxima of SW initial ( g ) reveal a wave focusing into the respective directions. Their occurrence can be explained by the fact that the anisotropy of the system leads to isofrequency curves with expanded regions where the group velocity direction θvg is (nearly) unchanged for a broad range of wavevectors ky. If the excited spectrum Ak has a significant magnitude in these ranges of ky, an amplitude concentration occurs into the respective directions θvg leading to the maxima of SW initial ( g ). Hence, these maxima indicate the beam creation.
However, a second step is necessary to precisely determine the beam directions. The beam source described above has a certain extent which leads to the fact that the overall spin-wave  The signal is guided from the input waveguide into output 1 by a spin-wave beam. b) Spin-wave distribution at 2 = 13.8 GHz. The signal is channelled into output 2 due to the changed direction of the spin-wave beams in the unstructured film area. c) Isofrequency curves of the studied system. The directions of the group velocity vectors, which are perpendicular to the curve, vary with spinwave carrier frequency. d) Fabricated sample according to the developed layout of the demultiplexer.

Figure 2.
Experimental realization of spin-wave demultiplexing using the developed prototype device. a) Frequency-dependence of the spin-wave intensity in the output waveguides measured by µBLS. Spin-wave signals are detected inside the two outputs within non-overlapping frequency ranges exhibiting signal maxima at the frequencies f1 and f2. b) The measured frequencydependence of the direction of the spin-wave beams is compared with the developed theoretical model. Shaded areas mark the angular intervals of signal acceptance of both outputs. The centres of the intervals are given by the optimal angles B,1 exp and B,2 exp .

Figure 3.
Experimental verification of the beam-based demultiplexing mechanism. µBLS measurements of the spin-wave intensity are performed to visualize the two-dimensional spinwave transport. The separation of spin-wave signals from one shared input waveguide by frequency-dependent channelling into spatially detached output waveguides occurs due to the intrinsically controlled beam formation. a) Spin wave guidance into output 1 at 1 = 11.2 GHz and ,b) into output 2 at 2 = 13.8 GHz.