Introduction

The manipulation of spin-waves represents a promising alternative to conventional electronics for the development of energy-efficient computing platforms. In the last few years, many concepts of spin-wave based devices have been proposed1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19. However, the experimental realization of a nanoscale spin-wave circuitry for guiding, manipulating, and controlling the interference of magnons, which is the basis for realizing nanomagnonic devices, is still missing. A major challenge is the efficient channeling and steering of spin-waves, which so far has been achieved in micron sized elements using external fields20,21,22,23,24 or arrays of nanomagnets25. In the route toward nanomagnonics, the use of nanoscale spin-textures for controlling the propagation of spin-waves is highly appealing. Recently, the concept of spin-wave channeling within domain walls has been theoretically proposed26,27,28, and experimental evidence for spin-wave confinement at a domain wall has been provided on a straight wall stabilized via shape anisotropy29. However, so far, the difficulty of engineering the spin-texture at the nanoscale with conventional techniques has hindered the realization and investigation of magnonic circuits based on domain walls. In particular, the steering of spin-waves by means of curved domain walls and the use of complex spin-textures for controlling the interference of multiple modes propagating within a nanoscale spin-wave circuitry remain elusive. Furthermore, the direct observation and a detailed investigation of these confined spin-wave modes are still missing.

In this work, we demonstrate the fundamental building blocks of spin-waves circuitry, i.e., arbitrarily shaped magnonic nanowaveguides and a prototypic spin-wave circuit allowing for the tunable superposition of signals propagating in two converging waveguides, by patterning the spin-texture of a ferromagnetic thin film via thermally assisted magnetic scanning probe lithography (tam-SPL)30,31. The absence of a physical patterning and the reversibility of tam-SPL allows the realization of fully reconfigurable nanomagnonic structures based on spin-textures with engineered functionality. Through space and time-resolved scanning transmission X-ray microscopy (STXM), we provide direct evidence for the channeling and steering of localized spin-wave modes propagating along straight and curved domain wall-based waveguides, with no need for an applied bias magnetic field. Furthermore, we demonstrate the tunable spatial superposition and interference of confined spin-wave modes propagating within two converging nanoscale waveguides. The experimental realization of reconfigurable nanomagnonic circuits based on doman walls paves the way to the use of engineered spin-textures as building blocks of spin-wave based computing devices.

Results

Experimental protocol and sample structure

In Fig. 1, we report a sketch of the experiments. Different spin-textures were patterned in an exchange bias ferromagnet/antiferromagnet bilayer (Fig. 1a), by sweeping a heated scanning probe in an external magnetic field for setting the unidirectional magnetic anisotropy strength and direction in the ferromagnetic film. This allows for the nanopatterning of engineered spin-configurations, as in the case of the curved 180° Néel domain wall of Fig. 1a, which is stabilized by patterning two magnetic domains with antiparallel remanent magnetization. Straight and curved domain walls, as well as complex spin-textures comprising two converging domain walls, were obtained by controlling the geometry of the area scanned by the tip. Spin-waves were excited by injecting a radio frequency (RF) current in a microstrip antenna. Static and time-resolved images with magnetic contrast were acquired via STXM by measuring the transmitted X-ray intensity, so that the X-ray magnetic circular dichroism (XMCD) provides contrast to the in-plane component of the magnetization Mx (Fig. 1b) (Methods section).

The configuration of the spin-wave modes is shown in Fig. 1c. Spin-waves are confined in the transverse direction of the wall by the reduced local effective field arising from the inhomogeneous magnetization profile, and propagate freely along the wall26,29. Such modes, called Winter magnons26,32,33, are characterized by an elliptical precession of the spins along the wall, with the major axis lying in the film plane, associated to a propagating flexural motion of the wall profile, analogous to transverse elastic waves on a string.

Figure 2a, b shows the sample structure, consisting of an exchange bias Co40Fe40B20 20 nm/Ir22Mn78 10 nm/Ru 2 nm multilayer34, and the optical image of the sample. The white dashed line indicates the orientation of a patterned domain wall with respect to the antenna.

In Fig. 2c–e, the static STXM images of the spin-textures patterned via tam-SPL are reported, where the dark (bright) contrast corresponds to Mx > 0 (<0). The black region at the bottom of the figure shows the boundary of the microstrip. For the straight and parabolic domain walls of Fig. 2c, d, respectively, the images acquired at zero external field display sharp 180° Néel walls. The corresponding micromagnetic simulations (Fig. 2f, g) show a 180° spin rotation within the sample plane, with the central spins (white regions) defining the domain wall profile lying along the y-axis30,35.

Figure 2e shows the static image of a more complex spin-texture comprising two 180° Néel walls tilted by a 30° angle from each other, sharing a common apex. In this case, a static 1.5 mT magnetic field was applied in the x-direction in order to precisely control the distance between the two domain walls and the position of the apex (see discussion below). The image of the same structure acquired at remanence is shown in Supplementary Figure 1. The corresponding micromagnetic simulation (Fig. 2h) shows that the two domains walls merge at the intersection, where the magnetization orientation is determined by the spin configuration of the two walls. After the intersection, a narrow “transition” region is formed, where the magnetization rotates continuously until a uniform magnetization orientation is reached within the domain.

Spin-wave propagation along patterned domain walls

Spin-waves were imaged stroboscopically via time-resolved STXM (Methods). In Fig. 3, the results for straight and curved domain walls are reported. Figure 3a shows snapshots of the normalized Mx contrast for the straight wall, calculated as the magnetic deviation ΔMx(t) from the time-averaged state Mx(t), acquired at different times within a single period7,36. A Gaussian filtering was used for enhancing the contrast (see Supplementary Note 2, Supplementary Table 1 and Supplementary Movie 1, 2 for video and raw data video). The excitation frequency was 1.28 GHz and no static external magnetic field was applied. The normalized Mx contrast shows spin-waves confined at the domain wall and propagating away from the antenna located at the bottom of the panels.

The spatial map of the amplitude of the spin-wave excitation is reported in Fig. 3b. The map is obtained by fitting the time-trace of each acquired pixel (raw data) with a sinusoidal function, and plotting for each pixel the amplitude of the corresponding fit (see Supplementary Note 3 and Supplementary Figure 2). Both Fig. 3b and the horizontal profile extracted from it at x = 1.1 μm from the stripline (Fig. 3c) show that the mode is confined at the domain wall, with a lateral extension (FWHM) of 120 nm. In order to demonstrate the propagating character of the spin-waves, the time-traces (sinusoidal fitting) related to pixels located within the domain wall at different distances from the antenna are plotted as a function of time (Fig. 3d). The time delay observed when moving away from the antenna corresponds to a linear phase shift with distance (Fig. 3e), clearly confirming the propagating character of the mode and allowing to estimate its wave vector.

Spin-waves propagating along a curved path, at remanence, are shown in the snapshots of Fig. 3f, extracted from Supplementary Movie 3 (see Supplementary Movie 4 for the raw data and Supplementary Table 3, Supplementary Movie 13, 14 for the Mx(t)). The excitation frequency was 1.11 GHz. A Gaussian filtering was used for enhancing the contrast. The mode is confined at the wall and follows its profile, showing a lateral extension of 115 nm (Fig. 3g, h). Both the sinusoidal fits (of raw data) as a function of time (Fig. 3i) and the phase analysis of Fig. 3j confirm the propagating nature of the mode. Figure 3 shows spin-waves confined at the patterned walls detected up to 2 μm away from the antenna. Longer propagation distances are reported in Supplementary Movies 5, 6, where we show spin-waves propagating along a curved domain wall and clearly detectable up to 3.5 μm from the microstrip.

Micromagnetic simulations of the confined spin-wave modes are presented in Fig. 4 (see Methods and Supplementary Figure 3 for details). Figure 4a, b shows micromagnetic simulations for the straight (curved) wall, carried out at remanence, driven by a line source of sinusoidal magnetic field at 1.28 GHz (1.11 GHz), as in the experimental data of Fig. 3. The Mx and Mz components are reported in the left and right panels, respectively, while the magnetic deviation ΔMx(t) from the time averaged value 〈Mx(t)〉, which corresponds to the STXM signal reported in Fig. 3, is shown in the central panel. The flexural motion of the wall, associated with the spin precession within the wall, can be observed for both straight and curved geometries. In good agreement with the experimental results, these findings indicate that wall-bound Winter-like modes, propagating along the wall, can be excited in both the straight and curved geometries.

Figure 4c reports the dispersion relation simulated for spin-waves confined at a straight 180° Néel domain wall, together with the experimental one. The simulations were performed with the same geometry as in Fig. 4a, but using a sinc-shaped field pulse as excitation (Methods). The experimental values of the wave vector were extracted from the linear fitting of the phase shift vs. distance curves obtained from experiments performed at different excitation frequencies (see discussion for Fig. 3 and Supplementary Note 3).

In good agreement with the experimental results, the simulations confirm the propagating character of the excitations, showing a positive dispersion and the presence of a small bandgap below 0.3 GHz, which can be ascribed to the residual effective field within the domain wall due to exchange bias and uniaxial anisotropies26. The simulated (experimental) spin-wave group velocity vg = ∂ω/∂k, extracted at k→ 0, is vgSim = 2.30 ± 0.34 km s−1 (vgExp = 2.77 ± 1.4 km s−1). Noteworthy, the demonstration of the propagating character and of the positive dispersion confirms that such guided modes can be used for transporting information within integrated nanomagnonic circuits.

Waveguides for efficiently controlling and manipulating confined spin-wave modes constitute fundamental building blocks for the realization of nanomagnonic devices. In the following, we demonstrate a nanomagnonic circuit allowing for the tunable spatial superposition and interference of guided spin-wave modes propagating in two converging waveguides.

Tunable spatial superposition of confined modes

Figure 5a shows the STXM images of a spin-texture comprising two domain walls (see also Fig. 2e). By applying a small static magnetic field in the −x-direction, ranging from 2 mT to 1.68 mT, the distance between the two domain walls (dashed white lines) can be controlled. In the top panel, the two domain walls are spatially separate. By decreasing the field, the two walls are brought closer (central panel) and finally converge at the common apex (lower panel).

Figure 5b shows STXM snapshots from the three different configurations for a 1.28 GHz excitation frequency. The images were smoothed with a gaussian filter for increasing contrast (see Supplementary Note 2, Supplementary Table 2 and Supplementary Movie 712 for the videos and raw data). The normalized Mx contrast shows, in all three cases, two guided spin-wave modes propagating from the antenna with different relative phases. These two modes, which are spatially separate close to the antenna, approach as the domain walls converge, and partially overlap for low applied fields. In order to better visualize the progressive overlapping of the two modes, each pixel of the data of Fig. 5b was fitted with a sinusoidal function (see Supplementary Note 3 and the discussion of Fig. 3). Figure 5c shows the amplitude of the sinusoidal fit along the horizontal profiles of Fig. 5a (green dashed lines), in the three configurations. The two peaks, with full width at half maximum (FWHM) of around 200 nm, correspond to the two guided modes. For an applied magnetic field of 2 mT, the two modes are separated by 810 nm and do not overlap. By decreasing the field down to 1.68 mT, the two modes are brought closer and to partially overlap, with a peak-to-peak distance of 340 nm.

In the top panels of Fig. 5d the sinusoidal fits along the horizontal profiles of Fig. 5a (green dashed lines) are plotted as a function of time for the different applied fields. In the bottom panels, single sinusoidal profiles are extracted from the positions marked by the color-coded stars in the top panels. Blue and yellow curves show the magnetization dynamics in correspondence of the maximum amplitude of the two guided modes. As expected, their phase difference depends on the applied field, because of the modulation of the waveguide geometry and spin configuration.

The red curves show the dynamics in the region where the two modes overlap. For 2.00 mT (left panel), the two modes are spatially separate, therefore at y = 0 no excitation is measured (red dashed line). For lower fields (central and right panels), we observe a sizeable modulation of the excitation amplitude and phase in the overlap region, which arises from the tuning of the spatial superposition of the two guided modes. We anticipate that the control of the superposition, phase difference and amplitude of the guided modes via external stimuli such as fields or current, allows to envision the implementation of logic functions in spin-texture based devices, such as Mach-Zehnder-type spin-wave interferometers9.

Discussion

In this work, we experimentally realized the fundamental building blocks of a reconfigurable spin-wave circuitry based on patterned spin-textures, i.e. arbitrarily shaped magnonic nanowaveguides. We directly imaged and studied via space and time-resolved STXM the channeling and steering of spin-waves propagating within nanoscale straight and curved paths, without the need for external applied fields. Furthermore, we realized a prototypical nanomagnonic circuit allowing for the tunable spatial superposition of signals propagating in two converging waveguides. The experimental realization of a reconfigurable nanoscale circuitry allowing for the steering, manipulation and controlled interference of spin-waves has been a long-standing challenge. This work clearly demonstrates that engineered spin-textures represent a powerful, versatile tool for realizing such a circuitry, marking a fundamental step toward the development of integrated nanomagnonic computing devices.

Methods

Sample fabrication

Co40Fe40B20 20 nm/Ir22Mn78 10 nm/Ru 2 nm stacks were deposited on 200 nm thick Si3N4 membranes by DC magnetron sputtering using an AJA Orion8 system with a base pressure below 1 × 10−8 Torr. During the deposition, a 30 mT magnetic field was applied in the sample plane for setting the magnetocrystalline uniaxial anisotropy direction in the CoFeB layer and the exchange bias direction in the as-grown sample. Then, the samples underwent an annealing in vacuum at 250 °C for 5 min, in a 400 mT magnetic field oriented in the same direction as the field applied during the growth. The resulting exchange bias field was 2.5 mT.

Thermally assisted magnetic Scanning Probe Lithography (tam-SPL) was performed via NanoFrazor Explore (SwissLitho AG). Spin-textures were patterned by sweeping in a raster-scan fashion the scanning probe, heated above the blocking temperature of the exchange bias system TB ≈ 300 °C, in presence of an external magnetic field. Two rotatable permanent magnets were employed for generating a uniform external magnetic field applied in the sample plane during patterning.

2 μm × 30 μm microstrip antennas were then fabricated via optical lithography using a Heidelberg MLA100 Maskless Aligner and lift-off, after depositing a 50 nm thick SiO2 insulating layer via magnetron sputtering. A Cr 5 nm/Cu 200 nm bilayer was deposited by means of thermal evaporation.

Scanning trasmission X-ray microscopy

The time-dependent magnetic configuration of the samples was investigated with time-resolved scanning transmission X-ray microscopy at the PolLux (X07DA) endstation of the Swiss Light Source37. In this technique, monochromatic X-rays, tuned to the Co L3 absorption edge (photon energy of about 781 eV), are focused using an Au Fresnel zone plate with an outermost zone width of 25 nm onto a spot on the sample, and the transmitted photons are recorded using an avalanche photodiode as detector. To form an image, the sample is scanned using a piezoelectric stage, and the transmitted X-ray intensity is recorded for each pixel in the image. The typical images we employed for the investigation of the spin-wave propagation in our samples were acquired with a point resolution between 40 nm and 75 nm.

Magnetic contrast in the images is achieved through the X-ray magnetic circular dichroism (XMCD) effect, by illuminating the sample with circularly polarized X-rays. As the XMCD effect probes the component of the magnetization parallel to the wave vector of the circularly polarized X-rays, the samples were mounted to achieve a 30° orientation of the surface with respect to the X-ray beam, allowing us to probe the in-plane component of the magnetization.

The time-resolved images were acquired in a pump-probe scheme, using an RF magnetic field of amplitude around 1 mT, generated by injecting an RF current in a microstrip antenna as pumping signal and the X-ray flashes generated by the synchrotron light source as probing signal. The pumping signal was synchronized to the 500 MHz master clock of the synchrotron light source (i.e., to the X-ray flashes generated by the light source) through a field programmable gate array (FPGA) setup. Due to the specific requirements of the FPGA-based pump-probe setup installed at the PolLux endstation, RF frequencies of fexc = 500 × M/N [MHz], being N a prime number and M a positive integer, were accessible. For the measurements presented in this work, N was typically selected to be equal to 23, giving a phase resolution of about 15° in the time-resolved images. Depending on the RF frequency, the temporal resolution of the time-resolved images is given by 2/M [ns], with its lower limit given by the width of the X-ray pulses generated by the light source (i.e., about 70 ps FWHM).

Micromagnetic simulations

Micromagnetic simulations of the magnetization dynamics were carried out by solving the Landau–Lifshitz–Gilbert equation of motion, using the open-source, GPU-accelerated software MuMax3. The total simulated volume had dimensions of 20,480 × 2560 × 20 nm3 and of 10,240 × 5120 × 20 nm3 for the straight and the curved wall, respectively, and was discretized into cells having dimensions of 5 × 5 × 20 nm3. Periodic boundary conditions in the x-direction were used to reproduce an infinite domain wall. The following parameters for the CoFeB were used: saturation magnetization Ms = 800 kA m−1, in-plane uniaxial anisotropy constant Ku = 103 J m−3 with the easy direction parallel to the x-axis (see Fig. 4 in the main text) and exchange constant Aex = 2 × 10−11 J m−1. The Gilbert damping parameter was set to α = 0.02. The exchange bias field was modeled as an external magnetic field of 2.5 mT, applied along the x-axis in opposite direction inside and outside the patterned area. In order to simulate the transition between two domains with opposite exchange bias, a 250 nm wide transition region with zero exchange bias field was placed in correspondence of the domain wall.

To simulate the spatial profile of the spin-wave modes, for both the straight and the curved wall the magnetization dynamics was excited applying a time-varying sinusoidal magnetic field to one line of cells at the center of the rectangular region and parallel to the y-axis. The field amplitude was 30 mT. In the simulation of the dispersion relation of the straight wall, in order to excite spin-waves, we used a sinc-shaped field pulse $$b\left( t \right) = b_0\frac{{{\rm sin}\left( {2\pi f_0\left( {t - t_0} \right)} \right)}}{{2\pi f_0\left( {t - t_0} \right)}}$$ directed along the x-axis, with amplitude b0 = 30 mT and frequency f0 = 5 GHz. The dispersion relation was calculated by performing a Fourier-transform of the x-component of the magnetization both in space and time in the whole simulated area.