Interference-based magnonic devices – which exploit eigenmode transportation of ordered spins, i.e. spin waves – are potential candidates to overcome the increased power consumption and Joule heating of traditional information storage and transport devices. In this work, we present a custom-made time-resolved magneto-optical Kerr effect (TR-MOKE) microscope for visualizing locally and time-resolved the dynamic magnetization, i.e. propagating spin waves. Using femtosecond laser pulses synchronized to the phase of a microwave source, which is used to drive spin-wave dynamics, we demonstrate time-resolved 2D spin-wave images with a spatial resolution &lt; 500 nm. To investigate magnonic interference behaviors, we fabricate a diffraction grating in a 200 nm thick ferrimagnetic YIG film by argon ion-beam etching. A coplanar waveguide (CPW) located parallel to the grating, is used to coherently excite spin-waves which are imaged by TR-MOKE. Our results represent the experimental realization of a self-imaging phenomenon applied to spin-waves, well-known within the field of linear optics as the Talbot effect [1-3], where it finds several applications in optical measurement techniques. We investigate the spin-wave Talbot effect for different orientations of the external magnetic field with respect to the YIG plane and spin-wave propagation direction. Each geometry displays different interferometric behaviors, in agreement with recent theoretical predictions [2]. Furthermore, as depicted in Fig. 1, we demonstrate that the interference pattern can be tuned through careful selection of the external magnetic field strength. This work contributes to the understanding of spin-wave interference behaviors for enhancing the performance of future magnonic devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/1b2a2492a50567ffd239f789cdf02461.jpg)

Fig. 1: The top sketch indicates the sample with the ground line of the CPW (yellow stripe) and the diffraction grating (black squares). The lower images display the MOKE signal, which is indicated by the gray scale, at various external magnetic fields. It can be seen that the localization of the interference maxima can be shifted by changing the external magnetic field strength. Here, the magnetic field was applied along the Y-direction.

Experimental Observation of the Spin-Wave Talbot Effect

Classifying or predicting complex time-dependent signals (e.g. speech, financial data, the weather) is a challenging computational task. Reservoir computing (RC) is an efficient neuromorphic computing approach that is ideally suited to such tasks and is typically implemented in software using a recurrent neural network (RNN) with fixed synaptic weights (the reservoir) connected to a single, trainable readout layer. However, more efficient implementations of RC are possible if the software RNN reservoir is substituted with a physical system with the correct properties, such as non-linear response to input signals and inherent memory, leading to a readily deployable, hardware-based neuromorphic computing platform [1]. In this work, we propose a novel approach to RC where the dynamics of a single magnetic domain wall (DW) trapped between two defect sites in a nanostrip acts as a hardware-based reservoir. We demonstrate how such a device, with dimensions smaller than 1 µm, is capable of performing complex data analysis tasks, such as speech recognition. We have modelled a Ni nanowire with two anti-notches (shown in the inset of Fig. 1(a)) using both a simple 1D model[2] and micromagnetic simulations. Both models show the DW exhibit complex oscillatory dynamics similar to the Duffing oscillator, thus giving highly non-linear responses to applied magnetic fields (Fig. 1(a)). We exploit the DW dynamics for RC by using an applied field to inject time-multiplexed input signals into the reservoir and show how this approach allows the device to perform classification tasks. We have explored how the regime of applied fields affects the accuracy of sine and square wave classification, showing that the best recognition rate is obtained at the edge of a chaotic regime of oscillation (Fig. 1(b)). We have also demonstrated that the same approach can be used for more complex tasks, such as spoken digit recognition and handwritten digits recognition. Our work opens a new perspective for neuromorphic computing in nanomagnetic hardware.

**References:**

[1] M. Riou et al., Phys. Review Applied,2019 [2] A. Pivano et al., Phys Review B, 2016

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/947f0ad21dbe4e988fab9e7c037ab764.jpg)
Fig. 1: Simulations of Ni nanostrip at 500 MHz. Figure (a) shows a typical bifurcation diagram computed with 1D model at 500MHz and the inset of Fig. 1(a) illustrates the typical geometry of a Ni nano-strip with two anti-nothces separated by 350 nm. Figure (b) shows the recognition rate for the sine and square task computed with 1D model of a domain wall in a Ni nanostrip. The input field is oscillatory comprising two terms: H-the constant offset of the field and ΔH-the amplitude of the stimulus. The inset shows a sequence of inputs and its corresponding output calculated during the classification process using 1D model.

Razvan Ababei

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