The 2024 magnonics roadmap.

Magnonicsis a research field that has gained an increasing interest in both the fundamental and applied sciences in recent years. This field aims to explore and functionalize collective spin excitations in magnetically ordered materials for modern information technologies, sensing applications and advanced computational schemes. Spin waves, also known as magnons, carry spin angular momenta that allow for the transmission, storage and processing of information without moving charges. In integrated circuits, magnons enable on-chip data processing at ultrahigh frequencies without the Joule heating, which currently limits clock frequencies in conventional data processors to a few GHz. Recent developments in the field indicate that functional magnonic building blocks for in-memory computation, neural networks and Ising machines are within reach. At the same time, the miniaturization of magnonic circuits advances continuously as the synergy of materials science, electrical engineering and nanotechnology allows for novel on-chip excitation and detection schemes. Such circuits can already enable magnon wavelengths of 50 nm at microwave frequencies in a 5G frequency band. Research into non-charge-based technologies is urgently needed in view of the rapid growth of machine learning and artificial intelligence applications, which consume substantial energy when implemented on conventional data processing units. In its first part, the 2024 Magnonics Roadmap provides an update on the recent developments and achievements in the field of nano-magnonics while defining its future avenues and challenges. In its second part, the Roadmap addresses the rapidly growing research endeavors on hybrid structures and magnonics-enabled quantum engineering. We anticipate that these directions will continue to attract researchers to the field and, in addition to showcasing intriguing science, will enable unprecedented functionalities that enhance the efficiency of alternative information technologies and computational schemes.

Collective Spin-Wave Dynamics in Gyroid Ferromagnetic Nanostructures.

Expanding upon the burgeoning discipline of magnonics, this research elucidates the intricate dynamics of spin waves (SWs) within three-dimensional nanoenvironments. It marks a shift from traditionally used planar systems to exploration of magnetization configurations and the resulting dynamics within 3D nanostructures. This study deploys micromagnetic simulations alongside ferromagnetic resonance measurements to scrutinize magnetic gyroids, periodic chiral configurations composed of chiral triple junctions with a period in nanoscale. Our findings uncover distinctive attributes intrinsic to the gyroid network, most notably the localization of collective SW excitations and the sensitivity of the gyroid's ferromagnetic response to the orientation of the static magnetic field, a correlation closely tied to the crystallographic alignment of the structure. Furthermore, we show that for the ferromagnetic resonance, multidomain gyroid films can be treated as a magnonic material with effective magnetization scaled by its filling factor. The implications of our research carry the potential for practical uses such as an effective, metamaterial-like substitute for ferromagnetic parts and lay the groundwork for radio frequency filters. The growing areas of 3D magnonics and spintronics present exciting opportunities to investigate and utilize gyroid nanostructures for signal processing purposes.

Impact of 3D Curvature on the Polarization Orientation in Non-Ising Domain Walls.

Ferroelectric domain boundaries are quasi-two-dimensional functional interfaces with high prospects for nanoelectronic applications. Despite their reduced dimensionality, they can exhibit complex non-Ising polarization configurations and unexpected physical properties. Here, the impact of the three-dimensional (3D) curvature on the polarization profile of nominally uncharged 180° domain walls in LiNbO3 is studied using second-harmonic generation microscopy and 3D polarimetry analysis. Correlations between the domain-wall curvature and the variation of its internal polarization unfold in the form of modulations of the Néel-like character, which we attribute to the flexoelectric effect. While the Néel-like character originates mainly from the tilting of the domain wall, the internal polarization adjusts its orientation due to the synergetic upshot of dipolar and monopolar bound charges and their variation with the 3D curvature. Our results show that curved interfaces in solid crystals may offer a rich playground for tailoring nanoscale polar states.

Non-Ising and chiral ferroelectric domain walls revealed by nonlinear optical microscopy.

The properties of ferroelectric domain walls can significantly differ from those of their parent material. Elucidating their internal structure is essential for the design of advanced devices exploiting nanoscale ferroicity and such localized functional properties. Here, we probe the internal structure of 180° ferroelectric domain walls in lead zirconate titanate (PZT) thin films and lithium tantalate bulk crystals by means of second-harmonic generation microscopy. In both systems, we detect a pronounced second-harmonic signal at the walls. Local polarimetry analysis of this signal combined with numerical modelling reveals the existence of a planar polarization within the walls, with Néel and Bloch-like configurations in PZT and lithium tantalate, respectively. Moreover, we find domain wall chirality reversal at line defects crossing lithium tantalate crystals. Our results demonstrate a clear deviation from the ideal Ising configuration that is traditionally expected in uniaxial ferroelectrics, corroborating recent theoretical predictions of a more complex, often chiral structure.

Curvature-Induced Asymmetric Spin-Wave Dispersion.

In magnonics, spin waves are conceived of as electron-charge-free information carriers. Their wave behavior has established them as the key elements to achieve low power consumption, fast operative rates, and good packaging in magnon-based computational technologies. Hence, knowing alternative ways that reveal certain properties of their undulatory motion is an important task. Here, we show using micromagnetic simulations and analytical calculations that spin-wave propagation in ferromagnetic nanotubes is fundamentally different than in thin films. The dispersion relation is asymmetric regarding the sign of the wave vector. It is a purely curvature-induced effect and its fundamental origin is identified to be the classical dipole-dipole interaction. The analytical expression of the dispersion relation has the same mathematical form as in thin films with the Dzyalonshiinsky-Moriya interaction. Therefore, this curvature-induced effect can be seen as a "dipole-induced Dzyalonshiinsky-Moriya-like" effect.

Interface Magnetoelectric Coupling in Co/Pb(Zr,Ti)O3.

Magnetoelectric coupling at multiferroic interfaces is a promising route toward the nonvolatile electric-field control of magnetization. Here, we use optical measurements to study the static and dynamic variations of the interface magnetization induced by an electric field in Co/PbZr0.2Ti0.8O3 (Co/PZT) bilayers at room temperature. The measurements allow us to identify different coupling mechanisms. We further investigate the local electronic and magnetic structure of the interface by means of transmission electron microscopy, soft X-ray magnetic circular dichroism, and density functional theory to corroborate the coupling mechanism. The measurements demonstrate a mixed linear and quadratic optical response to the electric field, which results from a magneto-electro-optical effect. We propose a decomposition method of the optical signal to discriminate between different components involved in the electric field-induced polarization rotation of the reflected light. This allows us to extract a signal that we can ascribe to interface magnetoelectric coupling. The associated surface magnetization exhibits a clear hysteretic variation of odd symmetry with respect to the electric field and nonzero remanence. The interface coupling is remarkably stable over a wide frequency range (1-50 kHz), and the application of a bias magnetic field is not necessary for the coupling to occur. These results show the potential of exploiting interface coupling with the prospect of optimizing the performance of magnetoelectric memory devices in terms of stability, as well as fast and dissipationless operation.

The magnetoelectrochemical switch.

In the field of spintronics, the archetype solid-state two-terminal device is the spin valve, where the resistance is controlled by the magnetization configuration. We show here how this concept of spin-dependent switch can be extended to magnetic electrodes in solution, by magnetic control of their chemical environment. Appropriate nanoscale design allows a huge enhancement of the magnetic force field experienced by paramagnetic molecular species in solutions, which changes between repulsive and attractive on changing the electrodes' magnetic orientations. Specifically, the field gradient force created within a sub-100-nm-sized nanogap separating two magnetic electrodes can be reversed by changing the orientation of the electrodes' magnetization relative to the current flowing between the electrodes. This can result in a breaking or making of an electric nanocontact, with a change of resistance by a factor of up to 10(3). The results reveal how an external field can impact chemical equilibrium in the vicinity of nanoscale magnetic circuits.

Spectral analysis of topological defects in an artificial spin-ice lattice.

Arrays of suitably patterned and arranged magnetic elements may display artificial spin-ice structures with topological defects in the magnetization, such as Dirac monopoles and Dirac strings. It is known that these defects strongly influence the quasistatic and equilibrium behavior of the spin-ice lattice. Here, we study the eigenmode dynamics of such defects in a square lattice consisting of stadiumlike thin film elements using micromagnetic simulations. We find that the topological defects display distinct signatures in the mode spectrum, providing a means to qualitatively and quantitatively analyze monopoles and strings that can be measured experimentally.

Element-specific magnetic hysteresis of individual 18 nm Fe nanocubes.

Correlating the electronic structure and magnetic response with the morphology and crystal structure of the same single ferromagnetic nanoparticle has been up to now an unresolved challenge. Here, we present measurements of the element-specific electronic structure and magnetic response as a function of magnetic field amplitude and orientation for chemically synthesized single Fe nanocubes with 18 nm edge length. Magnetic states and interactions of monomers, dimers, and trimers are analyzed by X-ray photoemission electron microscopy for different particle arrangements. The element-specific electronic structure can be probed and correlated with the changes of magnetic properties. This approach opens new possibilities for a deeper understanding of the collective response of magnetic nanohybrids in multifunctional materials and in nanomagnetic colloidal suspensions used in biomedical and engineering technologies.

Beating the walker limit with massless domain walls in cylindrical nanowires.

We present a micromagnetic study on the current-induced domain-wall motion in cylindrical Permalloy nanowires with diameters below 50 nm. The transverse domain walls forming in such thin, round wires are found to differ significantly from those known from flat nanostrips. In particular, we show that these domain walls are zero-mass micromagnetic objects. As a consequence, they display outstanding dynamic properties, most importantly the absence of a breakdown velocity generally known as the Walker limit. Our simulation data are confirmed by an analytic model which provides a detailed physical understanding. We further predict that a particular effect of the current-induced dynamics of these domain walls could be exploited to measure the nonadiabatic spin-transfer torque coefficient.

Exchange explosions: Magnetization dynamics during vortex-antivortex annihilation.

A magnetic vortex and an antivortex can annihilate, resulting in a homogeneous magnetization. A detailed description of the magnetization dynamics of such annihilation processes is obtained by micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. We show that, depending on the relative polarization of the vortex-antivortex pair, the annihilation process is either a continuous transformation of the magnetic structure or it involves the propagation of a micromagnetic singularity (Bloch point) causing a burstlike emission of spin waves. These results provide new insight into a fundamental micromagnetic process that has recently been proposed for a controlled generation of spin waves.

Domain-wall induced phase shifts in spin waves.

We study the interaction between two important features of ferromagnetic nanoparticles: magnetic domain walls and spin waves. Micromagnetic simulations reveal that magnetostatic spin waves change their phase as they pass through domain walls. Similar to an Aharonov-Bohm experiment, we suggest to probe this effect by splitting the waves on different branches of a ring. The interference of merging waves depends on the domain walls in the branches. A controlled manipulation of spin-wave phases could be the first step towards nanoscaled ferromagnetic devices performing logical operations based on spin-wave propagation.