Magnon Reservoir Computing – MARIN

The materials used in the MARIN project are ferrite garnets and Heusler alloys. These materials were chosen because of their low magnetic damping, which implies low thresholds for nonlinear excitation. Additionally, these materials have respectively insulating and semi-metallic properties, providing different integration possibilities for spintronic devices. Epitaxial growth of these materials was carried out and optimised to allow for lateral structuring of the samples as well as their optical response. The samples were nanostructured laterally to study linear and nonlinear processes in the dynamics of spin waves.

The samples produced were divided into two families: samples for studying propagative spin waves in both linear and nonlinear regimes, primarily based on Heusler Co2MnSi; and samples for studying the nonlinear processes involved in confined mode excitations, primarily based on ferrite BiYIG. These experimental studies relied on the use of three spectroscopy methods: (i) induction spin wave spectroscopy for propagative spin waves, (ii) MRFM (Microwave Radiation Force Microscopy) spin wave spectroscopy for confined spin waves, and (iii) Brillouin microfocused spectroscopy for studying both propagative and confined spin waves.

The analysis of these measurements was complemented by micromagnetic simulations and analytical models to interpret and explain the experimental results obtained.

Epitaxial growth and fabrication

Heusler materials were optimised to allow for the fabrication of laterally confined structures while preserving the intrinsic properties of the materials. Ferrite garnets, on the other hand, were optimised through fine-tuning of bismuth doping to control the magnetocrystalline anisotropy of the material and to increase the Faraday rotation of the material at the optical wavelengths used in Brillouin spectroscopy at 532 nm. The fabrication process thus enabled the realisation of nanostructures with lateral dimensions up to 300 nm. Devices dedicated to propagative spin waves were produced in the form of straight channels, while those dedicated to confined spin waves were produced in the form of disks and ellipses.

Propagative spin wave spectroscopy

Propagative spin waves were studied in both linear and nonlinear regimes, primarily in Heusler-based devices, using induction spectroscopy and Brillouin focused spectroscopy. Temperature-dependent ferromagnetic resonance studies revealed the influence of substrate-induced constraints and an increase in damping at low temperatures due to the electron-magnon interaction. Induction spin wave spectroscopy allowed for the determination of 100% spin polarisation, confirming the semi-metallic character after fabrication. Moreover, the non-adiabaticity parameter of the spin transfer coupling was determined due to the low damping, and this value is 40 times greater than the damping. Furthermore, Brillouin spectroscopy was used to study nonlinear processes in these same devices. A very low threshold of nonlinearity was measured, confirming the low damping of these materials. This threshold corresponds to an interaction between four spin waves, where two spin waves interact to produce two new spin waves.

Confined spin wave spectroscopy

The ferrite garnet devices were studied using MRFM and Brillouin focused spectroscopy. These studies showed that in these samples, a wide variety of nonlinear processes are present, whether the system is uniform or in a vortex state. As a result, the usual three-spin wave and four-spin wave processes have been observed at low excitation thresholds depending on the micromagnetic state. Moreover, these studies have also shown that other auto-oscillation and Floquet processes exist, as well as collaborative or competitive processes depending on the stabilised micromagnetic state, frequency, and power of excitation.

Despite the challenges associated with the growth and lateral structuring of epitaxially grown materials, we have taken advantage of their remarkable properties in terms of damping for specific spintronic wave devices. For example, in the case of Heusler materials, the low damping combined with 100% spin polarisation at the Fermi level and a non-adiabatic term of the spin transfer coupling may enable effective control of spin waves and specifically nonlinear thresholds. Moreover, a fine understanding of a wide variety of nonlinear processes in a unique ferrite garnet disk, such as self-modulation, three-magnon cascades, or Floquet bands, demonstrated by some members of the consortium within the framework of another European project, can envision the use of spin waves for non-Boolean information processing. The expertise acquired in terms of linear spin wave spectroscopy and sample growth/fabrication can be used in future projects, such as coupling spin waves to other degrees of freedom existing in solid state physics.

Whether it is on the surface of a lake, in colour patterns of halos and coronas in the atmosphere, or as fringes in optical or gravitational waves, wave interference is a phenomenon which plays an important role in our everyday life and allows us to address the most complex questions. But what about computation? Imagine a bucket of water into which a series of pebbles of different weights are dropped. By observing the resulting interference patterns, which contain information on past and present events, can we deduce the original sequence of these pebbles? The answer is yes! It is known that interference of water waves can be an efficient medium for a liquid state machine, an example of the neuro-inspired paradigm of reservoir computing. Here, the pebbles represent a complex temporal waveform, much like a voice signal; recognising such signals requires not only knowing the constituent frequencies, but also the order in which they arrive. Here, we propose that spin waves, which are elementary excitations of magnetic systems, can offer an efficient implementation of reservoir computing at the submicron scale. Because of their inherent nonlinearities and capacity to couple to transport phenomena, we envisage advanced pattern recognition tasks in magnonic devices at GHz frequencies.
With the MARIN project, we aim to realise experimentally such a magnonic reservoir computer. The MARIN project will investigate experimentally and theoretically the capacity of SWs in micro- and nanostructured thin films to satisfy the three basic requirements of reservoir computing, namely: (i) approximation – whether similar inputs result in similar outputs; (ii) separability – whether distinct input classes result in distinct output classes; and (iii) fading memory – how quickly inputs are forgotten over time. The basic control mechanism is the nonlinear coupling between SWs, which allows orthogonal eigenmodes of the equilibrium state to interact with each other as their amplitudes increase. Because such coupling also involves thresholding events, like for spiking neurons, we can achieve computational tasks with a cognitive nature like classification. This will be applied to demonstrate advanced signal recognition, e.g. on time-series, as a first step towards a proof-of-concept of efficient analogue non-Boolean operations.
Two media will be used: the well-established epitaxial YIG films and the epitaxial Heusler thin which both exhibit very low intrinsic magnetic damping mandatory to be able to efficiently excite non-linear spin-waves. The energy transfer from one non-linear spin-wave to another in a deterministic manner at the hearth of the reservoir computing scheme envisioned will be studied theoretically by micromagnetics simulations in the real and reciprocal space and experimentally by inductive spin wave spectroscopy, magnetic resonance force microscopy and microfocused Brillouin light scattering. Two different realisations of such time-series analysis are proposed as proof of concept devices: (i) a spectral analyser which performs an on-chip spin-wave Fourier transformation and (ii) a classifier of waves which as a first goal will be designed to sort sine from square waves in the GHz regime. This will allow for a new hardware implementation of reservoir computing that relies on the liquid state machine concept at GHz frequencies, which could be useful for processing telecommunications signals.