geometry and the magnetization state of ASIs for desired functionalities. These results indicate that ASIs can have great potential for programmable magnonics.

Here, we design a writable magnonic device which consists of a chiral or pinwheel ASI on top of a soft ferromagnetic thin film [Fig. 1(a)]. Through micromagnetic simulations we demonstrate that nanocale channels of spin wave transmission can be produced in the thin film under zero bias magnetic field. These nanochannels are regulatable by tuning the magnetization configuration of the top pinwheel ASI. The reconfigurability and rewritability of the ASI 38-39 enables these nanochannels in the ferromagnetic film to be globally switchable and locally writable. Our conceptual demonstration of writable magnonics could pave a new way for designing programmable spin-wave-based logic devices and circuits.

Recently, ferromagnetic thin film was introduced as an underlayer for an ASI system to tune the latter's frustration 40 and spin wave modes 23 . Here, we demonstrate the possibility for realizing writable magnonics in an ASI-mediated magnetic film [Fig. 1(a)], by taking advantage of the reconfigurability and rewritability of the ASI to create and control nano-scale spin wave paths in the underlayer. For our simulations, we chose the newly developed pinwheel ASI pattern, conceived by rotating each nanobar magnet in a square lattice by 45 o around its center [41][42][43][44][45] as illustrated in Fig. 1(b). The pinwheel ASI manifests novel properties, such as emergent charility 41 and domain wall topology 43 . One of its unique features is the formation of reconfigurable parallel chains of magnetic charges 43, 45 , which has been used to design programmable superconducting electronic devices 45 . In our simulations, we use elliptical nanobar magnets with dimensions of length L = 300 nm, width W = 80 nm and thickness T = 20 nm [Fig. 1

The pinwheel ASI has four-fold degenerate ferromagnetic orders, which are easily tunable by applying an in-plane external magnetic field 43, 45 . The black arrows in Figs. 2(a) and 2(b) show two of its degenerate magnetic configurations. Since an ASI made of 20 nm thick nanomagnets is athermal, these ordered configurations are stable under zero bias magnetic field at room temperature. The corresponding magnetization distribution of the underlying ferromagnetic film for these two ordered ASI configurations, displays vertical [Fig. 2(a)] and horizontal [Fig. 2(b)] meandering stripes of domain and domain walls in the absence of an external field, respectively. The two states are obtained by polarizing the sample with horizontal (for vertical domain state) and vertical (for horizontal domain state) in-plane magnetic fields, respectively. Therefore, it is easy to switch between the two states by tuning the magnetic configuration of the ASI pinwheel pattern. Furthermore, due to the athermal nature of the ASI, the in-plane magnetic field can be removed once the nanomagnets are polarized, so that the device can work at zero bias magnetic field.

6. Previous investigations have shown that domain walls can serve as excellent magnonic waveguide channels for spin wave propagation 49 . This suggests that the reconfigurable domains and/or domain walls in the underlying magnetic film mediated by the pinwheel ASI could be considered as a perfect magnonic crystal for in-situ control of spin wave transmissions. To examine the spin wave dynamics in our continuous magnetic film, we calculate the mode spectra for the vertical and horizontal domain states, as shown in Fig. 2(c). The excitation of the external magnetic field pulse is along +x (horizontal) direction in the sample plane. The spectra are calculated for both the top pinwheel ASI pattern and the underlayer film with periodic boundary conditions in the x-y plane. Both spectra show prominent peaks (V1 for vertical domain state and H1 for horizontal domain state) of eigenmodes with amplitudes much larger than the other minor modes V2, H2 and H3 [Fig. 2(c)]. However, the spectra of the vertical and horizontal domain states are quite distinct, i.e., in both their mode frequencies and amplitudes. The prominent eigenmodes of the horizontal/vertical domain states are at 3.71/4.30 GHz while the amplitude of the horizontal horizontal domain state is nearly three times higher than that of the vertical domain state. which is perpendicular to the microwave pulse direction. Therefore, strong resonance of moment precession in the domain walls is produced. We also investigated the spin wave excitations along y and z directions (see Figs. S3 and S4 in the supplementary material).

The significantly different responses between vertical and horizontal domain states are indicative of a perfect reconfigurable magnonic crystal, in which the spin wave transmission can be conveniently switched on and/or off by tuning the magnetic configurations of the top ASIs. The spectra with in-plane microwave excitations can be conveniently realized by broadband ferromagnetic resonance (FMR) experiments by patterning samples on top of a coplanar waveguide (CPW) 24-27, 30 or mounting samples on a CPW chip with a flip-chip technique 29 . Thus, our findings could be directly realized in experiments.

To further demonstrate the reconfigurable propagation of spin waves, we simulate a larger area of the sample. We apply a continuous excitation field (a sinusoidal field at H1= 3.71GHz along the x direction) in a 10 nm wide center line, as shown in Figs. 3(a) and 3(c).

The detailed simulation protocol is described in the supplementary material. Video 1 and 2 show time-dependent magnetic moment mappings in the two magnetic states, respectively, directly revealing the spin wave propagations in each state. We extract the spatial maps of the spin wave amplitude in the underlayer film, as displayed in Figs. 3(b) and 3(d). It shows that the transmission of spin wave is limited to a narrow range near the center excitation line and cannot propagate over a long distance in the horizontal direction [Video 1 and Fig. 3(b)]. This is consistent with the weak spin wave mode in the vertical domain state under an excitation in the x direction [Fig. 2(d)]. In contrast, in the horizontal domain state with strong mode channels [Fig. 2(e)], the spin wave transmits over a much longer distance along the horizontal nanochannels [Video 2 and Fig. 3(d)]. These results directly demonstrate in-situ switchable spin wave propagation by reconfiguring the magnetization states of the top layer pinwheel ASI structure.

Recent state-of-the-art nanomagnetic writing techniques allow local control of magnetic configurations of the ASI using the tip of a magnetic force microscope 38-39 . This approach can be used to realize writable spin wave nanochannels in our ASI mediated magnetic film. To demonstrate this concept, we simulate the spin wave propagation in a composite magnetization state, in which the left/right sides of the excitation line is in the vertical/horizontal domain states, respectively [Fig. 4(a)]. The magnetic configurations of the composite state are shown in Fig. S5(a) in the supplemental material. Such a state is nearly impossible to achieve with a global magnetization process, but can be conveniently realized by the above mentioned magnetic writing techniques [38][39] . The spatially resolved mode of H1 = 3.71 GHz displays the expected feature, i.e., the mode nanochannels appear 10. In summary, we introduced a reconfigurable magnonic crystal comprised of a pinwheel ASI pattern imprinted onto a soft ferromagnetic underlayer film. Using micromagnetic simulations, we showed that vertical and/or horizontal meandering stripes of magnetic domains and domain walls in the underlayer film can be induced by tuning the magnetic configuration of the top pinwheel ASI structure. These magnetic domains and domain walls are stable at zero bias magnetic field. Furthermore, the domain walls can sustain spin waves with well-defined frequency, providing nanochannel waveguides that are switchable and writable. Our results demonstrate a convenient and flexible approach to effectively guide and manipulate spin waves, highlighting a new application of artificial spin ices for writable magnonics. This highly reconfigurable magnonic crystal would stimulate future magnonic applications, such as programmable spin wave circuits and logic devices for energy-efficient information and data processing. Fig. 1 | Design of a system with writable spin wave nanochannels. (a) Schematic showing a pinwheel artificial spin ice on top of an underlayer film. (b) Parameters of the top pinwheel artificial spin ice. Spin wave spectra with y-and z-direction excitations. The spin wave excitations are not only determined by the magnetic configurations of the sample system, but also significantly influenced by the direction of the driving microwaves. We also simulate the spin wave spectra driven by microwave pulses along y and z directions. The results can be found in spatial dependence [Figs. S3(b) and S3(c)] for the two domain states excited with a ydirection microwave pulse are simply reversed from the x-direction microwave pulse [Figs.

2(c)-2(e)]. In this case, the vertical domain shows clear nanochannels of magnonic mode, which are not observed in the horizontal domain state. The reversal in y-direction microwave excitations can be easily understood by analyzing the orientation of the moments in domain walls and that of the driving microwave pulse, the same analysis used for x-direction excitations. For the case of out-of-plane microwave excitation along the zdirection, which is perpendicular to the domain wall moments (in-plane) for both states, the spectra are exactly identical for both vertical and horizontal domain states, as shown in Fig. S4(a). The prominent modes for both states display continuous nanochannels (but with orthogonal directions for both states) under z direction microwave excitation [Fig. S4(b) and S4(c)]. However, the mode is much weaker than those from the in-plane microwave excitations. The spectra for vertical and horizontal domain states excited by a field pulse along the z direction (defined in Fig. 1a).

The axis scale is the same as that in Fig. 2 Video 1. Spin wave propagation in the vertical domain state in Fig. 3(a). Video 2. Spin wave propagation in the horizontal domain state in Fig. 3(c). Video 3. Spin wave propagation in the composite state in Fig. 4(a). Video 4. Spin wave propagation in the composite state in Fig. 4(b). Video 5. Spin wave propagation in the composite state in Fig. S6(a).