Domain-wall induced phase shifts in spin waves

Distinct Transmission of Left- and Right-Handed Magnon Modes in Compensated Ferrimagnet/Antiferromagnet Structures

The chirality of magnons, exhibiting left- and right-handed polarizations analogous to the counterparts of spin-up and spin-down, has emerged as a promising paradigm for information processing. However, the potential of this paradigm is constrained by the controllable excitation and transmission of chiral magnons. Here, the magnon transmission is explored in the Gd3Fe5O12/NiO/Pt structures. It is demonstrated that both left- and right-handed magnon modes, thermally generated in the compensated ferrimagnet Gd3Fe5O12, can efficiently propagate through the antiferromagnetic NiO layer. Remarkably, these modes undergo distinct decay processes in NiO, manifested by different evolutions of the spin diffusion length with temperature. This behavior can be explained by an exchange model rooted in the spin-flop magnetic configuration between Gd3Fe5O12 and NiO, which establishes a chiral selection rule for magnon transmission. These findings offer significant fundamental insight into controlling chiral magnons, opening avenues for chirality-based magnonics.

Antiferromagnetic Spin Wave Amplification by Scattering in the Presence of Non-Uniform Dzyaloshinskii-Moriya Interaction

In this study, we suggest a method to amplify spin waves (SWs) in antiferromagnets (AFMs). By introducing a non-uniform Dzyaloshinskii-Moriya (DM) interaction, the potential barrier forms a resonant cavity. SWs with an opposite chirality undergo scattering and are resonantly amplified at a phase-matching condition. The calculation is performed in the insulating AFMs where the electric-field-induced DM interaction and pseudo-dipole anisotropy broaden the parabolic-like SW band for multiple resonant modes. Using a transfer matrix method, we also show numerically that scattering between SWs contributes significantly to the SW amplification. Since the electric field selectively amplifies the SWs with resonant frequencies, the proposed device works as an SW transistor and rectifier. This finding will contribute to insulating AFM-based magnon devices where Joule heating is, in principle, avoided.

Wave-driven phase wave patterns in a ring of FitzHugh-Nagumo oscillators

We explore a biomimetic model that simulates a cell, with the internal cytoplasm represented by a two-dimensional circular domain and the external cortex by a surrounding ring, both modeled using FitzHugh-Nagumo systems. The external ring is dynamically influenced by a pacemaker-driven wave originating from the internal domain, leading to the emergence of three distinct dynamical states based on the varying strengths of coupling. The range of dynamics observed includes phase patterning, the propagation of phase waves, and interactions between traveling and phase waves. A simplified linear model effectively explains the mechanisms behind the variety of phase patterns observed, providing insights into the complex interplay between a cell's internal and external environments.

Designed Spin-Texture-Lattice to Control Anisotropic Magnon Transport in Antiferromagnets

Spin waves in magnetic materials are promising information carriers for future computing technologies due to their ultra-low energy dissipation and long coherence length. Antiferromagnets are strong candidate materials due, in part, to their stability to external fields and larger group velocities. Multiferroic antiferromagnets, such as BiFeO3 (BFO), have an additional degree of freedom stemming from magnetoelectric coupling, allowing for control of the magnetic structure, and thus spin waves, with the electric field. Unfortunately, spin-wave propagation in BFO is not well understood due to the complexity of the magnetic structure. In this work, long-range spin transport is explored within an epitaxially engineered, electrically tunable, 1D magnonic crystal. A striking anisotropy is discovered in the spin transport parallel and perpendicular to the 1D crystal axis. Multiscale theory and simulation suggest that this preferential magnon conduction emerges from a combination of a population imbalance in its dispersion, as well as anisotropic structural scattering. This work provides a pathway to electrically reconfigurable magnonic crystals in antiferromagnets.

Heat current-driven topological spin texture transformations and helical q-vector switching

The use of magnetic states in memory devices has a history dating back decades, and the experimental discovery of magnetic skyrmions and subsequent demonstrations of their control via magnetic fields, heat, and electric/thermal currents have ushered in a new era for spintronics research and development. Recent studies have experimentally discovered the antiskyrmion, the skyrmion's antiparticle, and while several host materials have been identified, control via thermal current remains elusive. In this work, we use thermal current to drive the transformation between skyrmions, antiskyrmions and non-topological bubbles, as well as the switching of helical states in the antiskyrmion-hosting ferromagnet (Fe0.63Ni0.3Pd0.07)3P at room temperature. We discover that a temperature gradient [Formula: see text] drives a transformation from antiskyrmions to non-topological bubbles to skyrmions while under a magnetic field and observe the opposite, unidirectional transformation from skyrmions to antiskyrmions at zero-field, suggesting that the antiskyrmion, more so than the skyrmion, is robustly metastable at zero field.

A puzzling insensitivity of magnon spin diffusion to the presence of 180-degree domain walls

We present room-temperature measurements of magnon spin diffusion in epitaxial ferrimagnetic insulator MgAl_0.5Fe_1.5O₄ (MAFO) thin films near zero applied magnetic field where the sample forms a multi-domain state. Due to a weak uniaxial magnetic anisotropy, the domains are separated primarily by 180° domain walls. We find, surprisingly, that the presence of the domain walls has very little effect on the spin diffusion - nonlocal spin transport signals in the multi-domain state retain at least 95% of the maximum signal strength measured for the spatially-uniform magnetic state, over distances at least five times the typical domain size. This result is in conflict with simple models of interactions between magnons and static domain walls, which predict that the spin polarization carried by the magnons reverses upon passage through a 180° domain wall.

Influence of Dzyaloshinskii-Moriya interaction and perpendicular anisotropy on spin waves propagation in stripe domain patterns and spin spirals

Texture-based magnonics focuses on the utilization of spin waves in magnetization textures to process information. Using micromagnetic simulations, we study how (1) the dynamic magnetic susceptibility, (2) dispersion relations, and (3) the equilibrium magnetic configurations in periodic magnetization textures in a ultrathin ferromagnetic film in remanence depend on the values of the Dzyaloshinskii-Moriya interaction and the perpendicular magnetocrystalline anisotropy. We observe that for large Dzyaloshinskii-Moriya interaction values, spin spirals with periods of tens of nanometers are the preferred state; for small Dzyaloshinskii-Moriya interaction values and large anisotropies, stripe domain patterns with over a thousand times larger period are preferable. We observe and explain the selectivity of the excitation of resonant modes by a linearly polarized microwave field. We study the propagation of spin waves along and perpendicular to the direction of the periodicity. For propagation along the direction of the periodicity, we observe a bandgap that closes and reopens, which is accompanied by a swap in the order of the bands. For waves propagating in the perpendicular direction, some modes can be used for unidirectional channeling of spin waves. Overall, our findings are promising in sensing and signal processing applications and explain the fundamental properties of periodic magnetization textures.

Equilibrium and symmetries of altitudinal magnetic rotors on a circle

Macroscopic magnets can easily be manipulated and positioned so that interactions between themselves and with external fields induce interesting dynamics and equilibrium configurations. In this work, we use rotating magnets positioned in a line or at the vertices of a regular polygon. The rotation planes of the magnets can be modified at will. The rich structure of stable and unstable configurations is dictated by symmetry and the side of the polygon. We show that both symmetric solutions and their symmetry-breaking bifurcations can be explained with group theory. Our results suggest that the predicted magnetic textures should emerge at any length scale as long as the interaction is polar, and the system is endowed with the same symmetries.

Edge spin wave transmission through a vertex domain wall in triangular dots

Spin waves (SWs), being usually reflected by domain walls (DWs), could also be channeled along them. Edge SWs yield the interesting, and potentially applicable to real devices property of broadband spin wave confinement to the edges of the structure. Here, we investigate through numerical simulations the propagation of quasi one-dimensional spin waves in triangle-shaped amorphous YIG (Y3Fe5O12) micron sized ferromagnets as a function of the angle aperture. The edge spin waves (ESWs) have been propagated over the corner in triangles of 2 microns side with a fixed thickness of 85 nm. Parameters such as superior vertex angle (in the range of 40$$^\circ $$ ∘ –75$$^\circ $$ ∘ ) and applied magnetic field have been optimized in order to obtain a higher transmission coefficient of the ESWs over the triangle vertex. We observed that for a certain aperture angle for which dominated ESW frequency coincides with one of the localized DW modes, the transmission is maximized near one and the phase shift drops to $$\pi /2$$ π / 2 indicating resonant transmission of ESWs through the upper corner. We compare the obtained results with existing theoretical models. These results could contribute to the development of novel basic elements for spin wave computing.

Strain-Tuned Spin-Wave Interference in Micro- and Nanoscale Magnonic Interferometers

Here, we report on the experimental study of spin-wave propagation and interaction in the double-branched Mach–Zehnder interferometer (MZI) scheme. We show that the use of a piezoelectric plate (PP) with separated electrodes connected to each branch of the MZI leads to the tunable interference of the spin-wave signal at the output section. Using a finite element method, we carry out a physical investigation of the mechanisms of the impact of distributed deformations on the magnetic properties of YIG film. Micromagnetic simulations and finite-element modelling can explain the evolution of spin-wave interference patterns under strain induced via the application of an electric field to PP electrodes. We show how the multimode regime of spin-wave propagation is used in the interferometry scheme and how scaling to the nanometer size represents an important step towards a single-mode regime. Our findings provide a simple solution for the creation of tunable spin-wave interferometers for the magnonic logic paradigm.

Magnonic Metamaterials for Spin-Wave Control with Inhomogeneous Dzyaloshinskii-Moriya Interactions

A magnonic metamaterial in the presence of spatially modulated Dzyaloshinskii-Moriya interaction is theoretically proposed and demonstrated by micromagnetic simulations. By analogy to the fields of photonics, we first establish magnonic Snell's law for spin waves passing through an interface between two media with different dispersion relations due to different Dzyaloshinskii-Moriya interactions. Based on magnonic Snell's law, we find that spin waves can experience total internal reflection. The critical angle of total internal reflection is strongly dependent on the sign and strength of Dzyaloshinskii-Moriya interaction. Furthermore, spin-wave beam fiber and spin-wave lens are designed by utilizing the artificial magnonic metamaterials with inhomogeneous Dzyaloshinskii-Moriya interactions. Our findings open up a rich field of spin waves manipulation for prospective applications in magnonics.

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

Real-space observations of 60-nm skyrmion dynamics in an insulating magnet under low heat flow

Thermal-current induced electron and spin dynamics in solids –dubbed “caloritronics”– have generated widespread interest in both fundamental physics and spintronics applications. Here, we examine the dynamics of nanometric topological spin textures, skyrmions driven by a temperature gradient ∇T or heat flow, that are evaluated through in-situ real-space observations in an insulating helimagnet Cu₂OSeO₃. We observe increases of the skyrmion velocity and the Hall angle with increasing ∇T above a critical value of ~ 13 mK/mm, which is two orders of magnitude lower than the ∇T required to drive ferromagnetic domain walls. A comparable magnitude of ∇T is also observed to move the domain walls between a skyrmion domain and the non-topological conical-spin domain from cold to hot regions. Our results demonstrate the efficient manipulation of skyrmions by temperature gradients, a promising step towards energy-efficient “green” spintronics.

Skyrmions are a type of topological spin texture that great potential across a wide variety of technological applications. Here, Yu et al. study the thermally driven motion of Skyrmions and find a minimum temperature gradient for the motion of skyrmions two orders of magnitude smaller than for domain walls.

Effective phase noise considerations in magnon based parametric excitations

Magnon-phase is an important entity in the parametric processes involving magnons, yet the general qualitative and quantitative consequences of the phase-noise on nonlinear properties remain far from understood. In the current simulation-based theoretical study, we explore the direct impact the phase-noise has on non-linearity. We use analytical techniques usually employed in the study of hydrodynamics to explain the magnon-based nonlinear phenomena. The behavior of the threshold-field and growth rate of the magnons in the presence of Gaussian phase-noise is analytically predicted. These predictions are verified by micromagnetic simulations. Such results are of crucial importance in the design and engineering of both traditional and futuristic devices.

The interactions between spin wave and stacked domain walls

In this study, the interactions between spin wave (SW) and stacked domain walls in a magnetic nanostrip are investigated via micromagnetic simulation. It is found that under the excitation of SW, the metastable TWVW structure consisting of a transverse wall (TW) and a vortex wall (VW) may transform into a 360° wall or may completely annihilate depending on the frequency and amplitude of the SW. In contrast, stacked TWs (STWs) structure shows good robustness. Similar to a single TW, the STWs can be moved by SW and the inside TWs exhibit coherent motions. Notably, the frequency dependence of STWs' velocity demonstrates obvious emergence, shift and disappearance of the resonant peaks. Such changes are found to be in accordance with SW reflection, which thus agrees with the mechanism of linear momentum transfer torque (LMTT). In concern with the SW transmission through STWs, we show that by varying TWs number and SW frequency, a wide range of transmission efficiency η can be obtained. At certain frequencies, η may increase with TWs number and may go beyond 100%, which indicates a lowered attenuation by STWs. On the other hand, the phase shift of the transmitted SW always increases linearly with the TWs number and can be resonantly enhanced at frequencies same as that of TWs normal modes. Mapping of SW reveals that the phase shift is a result of fast propagation of SW through TWs. The fast propagation and the low attenuation of SW through STWs suggests that STWs may serve as an excellent SW channel. Meanwhile, the induced STWs motion and the controlled SW transmission and phase shift by STWs also promises great uses of STWs in future magnonic devices and domain wall devices.

Magnonic Bending, Phase Shifting and Interferometry in a 2D Reconfigurable Nanodisk Crystal

Strongly interacting nanomagnetic systems are pivotal across next-generation technologies including reconfigurable magnonics and neuromorphic computation. Controlling magnetization states and local coupling between neighboring nanoelements allows vast reconfigurability and a host of associated functionalities. However, existing designs typically suffer from an inability to tailor interelement coupling post-fabrication and nanoelements restricted to a pair of Ising-like magnetization states. Here, we propose a class of reconfigurable magnonic crystals incorporating nanodisks as the functional element. Ferromagnetic nanodisks are crucially bistable in macrospin and vortex states, allowing interelement coupling to be selectively activated (macrospin) or deactivated (vortex). Through microstate engineering, we leverage the distinct coupling behaviors and magnonic band structures of bistable nanodisks to achieve reprogrammable magnonic waveguiding, bending, gating, and phase-shifting across a 2D network. The potential of nanodisk-based magnonics for wave-based computation is demonstrated via an all-magnon interferometer exhibiting XNOR logic functionality. Local microstate control is achieved here via topological magnetic writing using a magnetic force microscope tip.

Nanoimaging of Ultrashort Magnon Emission by Ferromagnetic Grating Couplers at GHz Frequencies

On-chip signal processing at microwave frequencies is key for modern mobile communication. When one aims at small footprints, low power consumption, reprogrammable filters, and delay lines, magnons in low-damping ferrimagnets offer great promise. Ferromagnetic grating couplers have been reported to be specifically useful as microwave-to-magnon transducers. However, their interconversion efficiency is unknown and real-space measurements of the emitted magnon wavelengths have not yet been accomplished. Here, we image with subwavelength spatial resolution the magnon emission process into ferrimagnetic yttrium iron garnet (YIG) at frequencies up to 8 GHz. We evidence propagating magnons of a wavelength of 98.7 nm underneath the gratings, which enter the YIG without a phase jump. Counterintuitively, the magnons exhibit an even increased amplitude in YIG, which is unexpected and due to a further wavelength conversion process. Our results are of key importance for magnonic components, which efficiently control microwave signals on the nanoscale.

Voltage control of magnetic domain wall injection into strain-mediated multiferroic heterostructures

Effective control of domain wall (DW) injection into magnetic nanowires is of great importance for future novel device applications in spintronics, and currently relies on magnetization switching by the local external magnetic field obtained from metal contact lines or a spin-transfer torque (STT) effect from spin-polarized current. However, the external field is an obstacle for realizing practical spintronic devices with all-electric operation, and high current density can occasionally damage the devices. In this work, voltage controlled in-plane magnetic DW injection into a magnetic nanowire in the strain-mediated multiferroic heterostructures is studied by means of fully coupled micromagnetic-mechanical Finite Element Method (FEM) simulations. We propose an engineered shaped nano-magnet on a piezoelectric thin film in which a 180° magnetization rotation in the DW injection region is accomplished with in-plane piezostrain and magnetic shape anisotropy, thereby, leading to a DW injection into the nanowire. In this architecture, we computationally demonstrate repeated creation of DWs by voltage-induced strains without using any magnetic fields. Our FEM simulation results demonstrated an ultralow area energy consumption per injection (∼52.48 mJ m^-2), which is drastically lower than the traditional magnetic field and STT driven magnetization switching. A fast-overall injection time within ∼3.4 ns under continuous injection is also demonstrated. Further reduction of energy consumption and injection time can be achieved by optimization of the structure and material selections. The present design and computational analyses can provide an additional efficient method to realize low-power and high-speed spintronic and magnonic devices.

Mutual control of coherent spin waves and magnetic domain walls in a magnonic device

The successful implementation of spin-wave devices requires efficient modulation of spin-wave propagation. Using cobalt/nickel multilayer films, we experimentally demonstrate that nanometer-wide magnetic domain walls can be applied to manipulate the phase and magnitude of coherent spin waves in a nonvolatile manner. We further show that a spin wave can, in turn, be used to change the position of magnetic domain walls by means of the spin-transfer torque effect generated from magnon spin current. This mutual interaction between spin waves and magnetic domain walls opens up the possibility of realizing all-magnon spintronic devices, in which one spin-wave signal can be used to control others by reconfiguring magnetic domain structures.

Spin-Wave Phase Inverter upon a Single Nanodefect

Local modification of magnetic properties of nanoelements is a key to design future-generation magnonic devices in which information is carried and processed via spin waves. One of the biggest challenges here is to fabricate simple and miniature phase-controlling elements with broad tunability. Here, we successfully realize such spin-wave phase shifters upon a single nanogroove milled by a focused ion beam in a Co-Fe microsized magnonic waveguide. By varying the groove depth and the in-plane bias magnetic field, we continuously tune the spin-wave phase and experimentally evidence a complete phase inversion. The microscopic mechanism of the phase shift is based on the combined action of the nanogroove as a geometrical defect and the lower spin-wave group velocity in the waveguide under the groove where the magnetization is reduced due to the incorporation of Ga ions during the ion-beam milling. The proposed phase shifter can easily be on-chip integrated with spin-wave logic gates and other magnonic devices. Our findings are crucial for designing nanomagnonic circuits and for the development of spin-wave nano-optics.

Control of spin-wave transmission by a programmable domain wall

Active manipulation of spin waves is essential for the development of magnon-based technologies. Here, we demonstrate programmable spin-wave filtering by resetting the spin structure of pinned 90° Néel domain walls in a continuous CoFeB film with abrupt rotations of uniaxial magnetic anisotropy. Using micro-focused Brillouin light scattering and micromagnetic simulations, we show that broad 90° head-to-head or tail-to-tail magnetic domain walls are transparent to spin waves over a broad frequency range. In contrast, magnetic switching to a 90° head-to-tail configuration produces much narrower and strongly reflecting domain walls at the same pinning locations. Based on these results, we propose a magnetic spin-wave valve with two parallel domain walls. Switching the spin-wave valve from an open to a closed state changes the transmission of spin waves from nearly 100 to 0%. Active control over spin-wave transport through programmable domain walls could be utilized in magnonic logic devices or non-volatile memory elements.

Magnon-based spintronic devices crucially rely on the capability of spin wave manipulation. Here the authors achieve active control of spin wave transmission by programming a pinned 90 degree Néel domain wall in a continuous CoFeB/BaTiO₃ film with abrupt rotations of uniaxial magnetic anisotropy.

Ferromagnetic domain walls as spin wave filters and the interplay between domain walls and spin waves

Spin waves (SW) are low energy excitations of magnetization in magnetic materials. In the promising field of magnonics, fundamental SW modes, magnons, are accessible in magnetic nanostructure waveguides and carry information. The SW propagates in both metals and insulators via magnetization dynamics. Energy dissipation through damping can be low compared to the Joule heating in conventional circuits. We performed simulations in a quasi-one-dimensional ferromagnetic strip and found that the transmission of the propagating SW across the domain wall (DW) depends strongly on the tilt angle of the magnetization at low frequencies. When the SW amplitude is large, the magnetization tilt angle inside the DW changes due to the effective fields. The SW transmission, the DW motion, and the magnetization tilt angle couple to each other, which results in complex DW motion and SW transmission. Both SW filtering and DW motions are key ingredients in magnonics.

Antiferromagnetic domain wall as spin wave polarizer and retarder

As a collective quasiparticle excitation of the magnetic order in magnetic materials, spin wave, or magnon when quantized, can propagate in both conducting and insulating materials. Like the manipulation of its optical counterpart, the ability to manipulate spin wave polarization is not only important but also fundamental for magnonics. With only one type of magnetic lattice, ferromagnets can only accommodate the right-handed circularly polarized spin wave modes, which leaves no freedom for polarization manipulation. In contrast, antiferromagnets, with two opposite magnetic sublattices, have both left and right-circular polarizations, and all linear and elliptical polarizations. Here we demonstrate theoretically and confirm by micromagnetic simulations that, in the presence of Dzyaloshinskii-Moriya interaction, an antiferromagnetic domain wall acts naturally as a spin wave polarizer or a spin wave retarder (waveplate). Our findings provide extremely simple yet flexible routes toward magnonic information processing by harnessing the polarization degree of freedom of spin wave.

Spin waves are promising candidates as carriers for energy-efficient information processing, but they have not yet been fully explored application wise. Here the authors theoretically demonstrate that antiferromagnetic domain walls are naturally spin wave polarizers and retarders, two key components of magnonic devices.

Ultrafast domain wall dynamics in magnetic nanotubes and nanowires

The dynamic properties of magnetic domain walls in nanotubes and in cylindrical nanowires can be significantly different from the well known domain wall dynamics in thin films and in flat thin strips. The main differences are the occurrence of chiral symmetry breaking and, perhaps more importantly, the possibility to obtain magnetic domain walls that are stable against the usual Walker breakdown. This stability enables the magnetic field-driven propagation of the domain walls in nanotubes and nanocylinders at constant velocities which are significantly higher than the usual propagation speeds of the domain walls. Simulations predict that the ultrafast motion of magnetic domain walls at velocities in a range above 1000 m s^-1 can lead to the spontaneous excitation of spin waves in a process that is the magnetic analog of the Cherenkov effect. In the case of solid cylindrical wires, the domain wall can contain a micromagnetic point singularity. We discuss the current knowledge on the ultrafast dynamics of such Bloch points, which remains still largely unexplored.

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.

A novel method for the injection and manipulation of magnetic charge states in nanostructures

Realising the promise of next-generation magnetic nanotechnologies is contingent on the development of novel methods for controlling magnetic states at the nanoscale. There is currently demand for simple and flexible techniques to access exotic magnetisation states without convoluted fabrication and application processes. 360° domain walls (metastable twists in magnetisation separating two domains with parallel magnetisation) are one such state, which is currently of great interest in data storage and magnonics. Here, we demonstrate a straightforward and powerful process whereby a moving magnetic charge, provided experimentally by a magnetic force microscope tip, can write and manipulate magnetic charge states in ferromagnetic nanowires. The method is applicable to a wide range of nanowire architectures with considerable benefits over existing techniques. We confirm the method’s efficacy via the injection and spatial manipulation of 360° domain walls in Py and Co nanowires. Experimental results are supported by micromagnetic simulations of the tip-nanowire interaction.

Magnetic domain walls as reconfigurable spin-wave nanochannels

In the research field of magnonics, it is envisaged that spin waves will be used as information carriers, promoting operation based on their wave properties. However, the field still faces major challenges. To become fully competitive, novel schemes for energy-efficient control of spin-wave propagation in two dimensions have to be realized on much smaller length scales than used before. In this Letter, we address these challenges with the experimental realization of a novel approach to guide spin waves in reconfigurable, nano-sized magnonic waveguides. For this purpose, we make use of two inherent characteristics of magnetism: the non-volatility of magnetic remanence states and the nanometre dimensions of domain walls formed within these magnetic configurations. We present the experimental observation and micromagnetic simulations of spin-wave propagation inside nano-sized domain walls and realize a first step towards a reconfigurable domain-wall-based magnonic nanocircuitry.

Chirality-Dependent Transmission of Spin Waves through Domain Walls

Spin-wave technology (magnonics) has the potential to further reduce the size and energy consumption of information-processing devices. In the submicrometer regime (exchange spin waves), topological defects such as domain walls may constitute active elements to manipulate spin waves and perform logic operations. We predict that spin waves that pass through a domain wall in an ultrathin perpendicular-anisotropy film experience a phase shift that depends on the orientation of the domain wall (chirality). The effect, which is absent in bulk materials, originates from the interfacial Dzyaloshinskii-Moriya interaction and can be interpreted as a geometric phase. We demonstrate analytically and by means of micromagnetic simulations that the phase shift is strong enough to switch between constructive and destructive interference. The two chirality states of the domain wall may serve as a memory bit or spin-wave switch in magnonic devices.

The magnetic monopole and the separation between fast and slow magnetic degrees of freedom

The Landau-Lifshitz-Gilbert (LLG) equation that describes the dynamics of a macroscopic magnetic moment finds its limit of validity at very short times. The reason for this limit is well understood in terms of separation of the characteristic time scales between slow degrees of freedom (the magnetization) and fast degrees of freedom. The fast degrees of freedom are introduced as the variation of the angular momentum responsible for the inertia. In order to study the effect of the fast degrees of freedom on the precession, we calculate the geometric phase of the magnetization (i.e. the Hannay angle) and the corresponding magnetic monopole. In the case of the pure precession (the slow manifold), a simple expression of the magnetic monopole is given as a function of the slowness parameter, i.e. as a function of the ratio of the slow over the fast characteristic times.

Microwave excitation of spin wave beams in thin ferromagnetic films

An inherent element of research and applications in photonics is a beam of light. In magnonics, which is the magnetic counterpart of photonics, where spin waves are used instead of electromagnetic waves to transmit and process information, the lack of a beam source limits exploration. Here, we present an approach enabling generation of narrow spin wave beams in thin homogeneous nanosized ferromagnetic films by microwave current. We show that the desired beam-type behavior can be achieved with the aid of a properly designed coplanar waveguide transducer generating a nonuniform microwave magnetic field. We test this idea using micromagnetic simulations, confirming numerically that the resulting spin wave beams propagate over distances of several micrometers. The proposed approach requires neither inhomogeneity of the ferromagnetic film nor nonuniformity of the biasing magnetic field. It can be generalized to different magnetization configurations and yield multiple spin wave beams of different width at the same frequency.

Direct observation of isolated Damon-Eshbach and backward volume spin-wave packets in ferromagnetic microstripes

The analysis of isolated spin-wave packets is crucial for the understanding of magnetic transport phenomena and is particularly interesting for applications in spintronic and magnonic devices, where isolated spin-wave packets implement an information processing scheme with negligible residual heat loss. We have captured microscale magnetization dynamics of single spin-wave packets in metallic ferromagnets in space and time. Using an optically driven high-current picosecond pulse source in combination with time-resolved scanning Kerr microscopy probed by femtosecond laser pulses, we demonstrate phase-sensitive real-space observation of spin-wave packets in confined permalloy (Ni80Fe20) microstripes. Impulsive excitation permits extraction of the dynamical parameters, i.e. phase- and group velocities, frequencies and wave vectors. In addition to well-established Damon-Eshbach modes our study reveals waves with counterpropagating group- and phase-velocities. Such unusual spin-wave motion is expected for backward volume modes where the phase fronts approach the excitation volume rather than emerging out of it due to the negative slope of the dispersion relation. These modes are difficult to excite and observe directly but feature analogies to negative refractive index materials, thus enabling model studies of wave propagation inside metamaterials.

Deterministic Control of Magnetization Dynamics in Reconfigurable Nanomagnetic Networks for Logic Applications

Information processing based on nanomagnetic networks is an emerging area of spintronics, as the energy consumption and integration density of the current semiconductor technology are reaching their fundamental limits. Nanomagnet-based devices rely on manipulating the magnetic ground states for device operations. While the static behavior of nanomagnets has been explored, little information is available on their dynamic behavior. Here, we demonstrate an additional functionality based on their collective dynamic response and explore the concept utilizing networks of bistable rhomboid nanomagnets. The control of the magnetic ground states of the networks was achieved by the geometrical design of the nanomagnets instead of the conventional interelement dipolar coupling. Dynamic responses of both the ferromagnetic and antiferromagnetic ground states were monitored using broadband ferromagnetic resonance spectroscopy, the Brillouin light scattering technique, and direct magnetic force microscopy. Micromagnetic simulations and numerical calculations validate our experimental observations. This method would have potential implications for low-power magnonic devices based on reconfigurable microwave properties.

All-optical investigation of tunable picosecond magnetization dynamics in ferromagnetic nanostripes with a width down to 50 nm

Ferromagnetic nanostripes are important elements for a number of interesting technologies including magnetic racetrack memory, spin logic and magnonics. Understanding and controlling magnetization dynamics in such nanostripes are hence important problems in nanoscience and technology. Here we present an all-optical excitation and detection of ultrafast magnetization dynamics, including spin waves, in 5 μm long Ni80Fe20 nanostripes with varying stripe widths from 200 nm down to 50 nm. We observed a strong width dependent variation in the frequency, anisotropy and the spatial nature of spin waves in these systems. The effect of inter-stripe interaction is also studied and the 50 nm wide stripe is found to be nearly magnetostatically isolated, allowing us to detect the dynamics of a 50 nm wide individual stripe using an all-optical measurement technique. The tunability in magnetization dynamics with stripe widths is important for their applications in various spin based technologies.

Photodrive of magnetic bubbles via magnetoelastic waves

Precise control of magnetic domain walls continues to be a central topic in the field of spintronics to boost infotech, logic, and memory applications. One way is to drive the domain wall by current in metals. In insulators, the incoherent flow of phonons and magnons induced by the temperature gradient can carry the spins, i.e., spin Seebeck effect, but the spatial and time dependence is difficult to control. Here, we report that coherent phonons hybridized with spin waves, magnetoelastic waves, can drive magnetic bubble domains, or curved domain walls, in an iron garnet, which are excited by ultrafast laser pulses at a nonabsorbing photon energy. These magnetoelastic waves were imaged by time-resolved Faraday microscopy, and the resultant spin transfer force was evaluated to be larger for domain walls with steeper curvature. This will pave a path for the rapid spatiotemporal control of magnetic textures in insulating magnets.

Narrow Magnonic Waveguides Based on Domain Walls

The channeling of spin waves with domain walls in ultrathin ferromagnetic films is demonstrated theoretically and through micromagnetics simulations. It is shown that propagating excitations localized to the wall, which appear in the frequency gap of bulk spin wave modes, can be guided in curved geometries and propagate in close proximity to other channels. For Néel-type walls arising from a Dzyaloshinskii-Moriya interaction, the channeling is strongly nonreciprocal and group velocities can exceed 1  km/s in the long wavelength limit for certain propagation directions. The channeled modes represent an unusual analogy of whispering gallery waves that are one dimensional and nonreciprocal with this interaction. Moreover, a sufficiently strong Dzyaloshinskii-Moriya interaction can create a degeneracy of channeled and propagating modes at a critical wave vector.

Magneto-Plasmonics and Resonant Interaction of Light with Dynamic Magnetisation in Metallic and All-Magneto-Dielectric Nanostructures

A significant interest in combining plasmonics and magnetism at the nanoscale gains momentum in both photonics and magnetism sectors that are concerned with the resonant enhancement of light-magnetic-matter interaction in nanostructures. These efforts result in a considerable amount of literature, which is difficult to collect and digest in limited time. Furthermore, there is insufficient exchange of results between the two research sectors. Consequently, the goal of this review paper is to bridge this gap by presenting an overview of recent progress in the field of magneto-plasmonics from two different points of view: magneto-plasmonics, and magnonics and magnetisation dynamics. It is expected that this presentation style will make this review paper of particular interest to both general physical audience and specialists conducting research on photonics, plasmonics, Brillouin light scattering spectroscopy of magnetic nanostructures and magneto-optical Kerr effect magnetometry, as well as ultrafast all-optical and THz-wave excitation of spin waves. Moreover, readers interested in a new, rapidly emerging field of all-dielectric nanophotonics will find a section about all-magneto-dielectric nanostructures.

Magnon-driven domain-wall motion with the Dzyaloshinskii-Moriya interaction

We study domain-wall (DW) motion induced by spin waves (magnons) in the presence of the Dzyaloshinskii-Moriya interaction (DMI). The DMI exerts a torque on the DW when spin waves pass through the DW, and this torque represents a linear momentum exchange between the spin wave and the DW. Unlike angular momentum exchange between the DW and spin waves, linear momentum exchange leads to a rotation of the DW plane rather than a linear motion. In the presence of an effective easy plane anisotropy, this DMI induced linear momentum transfer mechanism is significantly more efficient than angular momentum transfer in moving the DW.

Spin waves and domain wall modes in curved magnetic nanowires

The confinement of spin waves in inhomogeneous fields and spin wave interaction with domain walls has attracted interest due to possible applications in magnonics. We investigate spin waves in curved ferromagnetic nanowires. The field dispersion and localization of spin waves is revealed by comparison to known modes in stripes and taking into account the specific field reversal of the curved wire. In small wires we find a strongly altered mode spectrum in a certain field regime. Micromagnetic simulations show an extended domain wall within the wire in this field region. The domain wall shows several dynamic modes and changes the remaining spin wave modes. We find mode suppression as well as newly arising modes due to the strong inhomogenous internal field of the wall.

Spin-torque building blocks

The discovery of the spin-torque effect has made magnetic nanodevices realistic candidates for active elements of memory devices and applications. Magnetoresistive effects allow the read-out of increasingly small magnetic bits, and the spin torque provides an efficient tool to manipulate - precisely, rapidly and at low energy cost - the magnetic state, which is in turn the central information medium of spintronic devices. By keeping the same magnetic stack, but by tuning a device's shape and bias conditions, the spin torque can be engineered to build a variety of advanced magnetic nanodevices. Here we show that by assembling these nanodevices as building blocks with different functionalities, novel types of computing architecture can be envisaged. We focus in particular on recent concepts such as magnonics and spintronic neural networks.

Spin wave nonreciprocity for logic device applications

The utilization of spin waves as eigenmodes of the magnetization dynamics for information processing and communication has been widely explored recently due to its high operational speed with low power consumption and possible applications for quantum computations. Previous proposals of spin wave Mach-Zehnder devices were based on the spin wave phase, a delicate entity which can be easily disrupted. Here, we propose a complete logic system based on the spin wave amplitude utilizing the nonreciprocal spin wave behavior excited by microstrip antennas. The experimental data reveal that the nonreciprocity of magnetostatic surface spin wave can be tuned by the bias magnetic field. Furthermore, engineering of the device structure could result in a high nonreciprocity factor for spin wave logic applications.

How do spin waves pass through a bend?

Spin-wave devices hold great promise to be used in future information processing. Manipulation of spin-wave propagation inside the submicrometer waveguides is at the core of promoting the practical application of these devices. Just as in today's silicon-based chips, bending of the building blocks cannot be avoided in real spin-wave circuits. Here, we examine spin-wave transport in bended magnonic waveguides at the submicron scale using micromagnetic simulations. It is seen that the impact of the bend is relevant to the frequency of the passing spin wave. At the lowest frequencies, the spin wave continuously follows the waveguide in the propagation process. At the higher frequencies, however the bend acts as a mode converter for the passing spin wave, causing zigzag-like propagation path formed in the waveguide behind the bend. Additionally, we demonstrate a logic-NOT gate based on such a waveguide, which could be combined to perform logic-NAND operation.

Artificial ferroic systems: novel functionality from structure, interactions and dynamics

Lithographic processing and film growth technologies are continuing to advance, so that it is now possible to create patterned ferroic materials consisting of arrays of sub-1 μm elements with high definition. Some of the most fascinating behaviour of these arrays can be realised by exploiting interactions between the individual elements to create new functionality. The properties of these artificial ferroic systems differ strikingly from those of their constituent components, with novel emergent behaviour arising from the collective dynamics of the interacting elements, which are arranged in specific designs and can be activated by applying magnetic or electric fields. We first focus on artificial spin systems consisting of arrays of dipolar-coupled nanomagnets and, in particular, review the field of artificial spin ice, which demonstrates a wide range of fascinating phenomena arising from the frustration inherent in particular arrangements of nanomagnets, including emergent magnetic monopoles, domains of ordered macrospins, and novel avalanche behaviour. We outline how demagnetisation protocols have been employed as an effective thermal anneal in an attempt to reach the ground state, comment on phenomena that arise in thermally activated systems and discuss strategies for selectively generating specific configurations using applied magnetic fields. We then move on from slow field and temperature driven dynamics to high frequency phenomena, discussing spinwave excitations in the context of magnonic crystals constructed from arrays of patterned magnetic elements. At high frequencies, these arrays are studied in terms of potential applications including magnetic logic, linear and non-linear microwave optics, and fast, efficient switching, and we consider the possibility to create tunable magnonic crystals with artificial spin ice. Finally, we discuss how functional ferroic composites can be incorporated to realise magnetoelectric effects. Specifically, we discuss artificial multiferroics (or multiferroic composites), which hold promise for new applications that involve electric field control of magnetism, or electric and magnetic field responsive devices for high frequency integrated circuit design in microwave and terahertz signal processing. We close with comments on how enhanced functionality can be realised through engineering of nanostructures with interacting ferroic components, creating opportunities for novel spin electronic devices that, for example, make use of the transport of magnetic charges, thermally activated elements, and reprogrammable nanomagnet systems.

Wave modes of collective vortex gyration in dipolar-coupled-dot-array magnonic crystals

Lattice vibration modes are collective excitations in periodic arrays of atoms or molecules. These modes determine novel transport properties in solid crystals. Analogously, in periodical arrangements of magnetic vortex-state disks, collective vortex motions have been predicted. Here, we experimentally observe wave modes of collective vortex gyration in one-dimensional (1D) periodic arrays of magnetic disks using time-resolved scanning transmission x-ray microscopy. The observed modes are interpreted based on micromagnetic simulation and numerical calculation of coupled Thiele equations. Dispersion of the modes is found to be strongly affected by both vortex polarization and chirality ordering, as revealed by the explicit analytical form of 1D infinite arrays. A thorough understanding thereof is fundamental both for lattice vibrations and vortex dynamics, which we demonstrate for 1D magnonic crystals. Such magnetic disk arrays with vortex-state ordering, referred to as magnetic metastructure, offer potential implementation into information processing devices.

Magnonic domain wall heat conductance in ferromagnetic wires

We present a theoretical study of magnon-mediated heat transport in electrically insulating ferromagnetic wires containing a domain wall (DW). In the regime of validity of continuum micromagnetism, a DW is found to have no effect on the heat conductance. However, spin waves are found to be reflected by DWs with widths of a few lattice spacings, which is associated with emergence of an additional spin wave bound state. The resulting DW heat conductance should be significant for thin films of yttrium iron garnet with sharply defined magnetic domains.

Enhanced transmission through squeezed modes in a self-cladding magnonic waveguide

We study spin-wave propagation in 360-nm wide Ni(80)Fe(20) nanowires using all-electrical spin-wave spectroscopy. Creating a zigzag-like magnetization state, we find enhanced spin-wave transmission compared to the states of more homogeneous magnetization. Micromagnetic simulations show that the spin waves propagate in narrow channels, which in particular, are remotely positioned from the edges. The internal channels reflect field-controlled self-cladding. Interestingly, rotation of the magnetic field at a specific value is found to vary the propagation velocity without changing the eigenfrequency. This opens the perspective of the velocity modulation transistor following a concept known from semiconductor electronics.

Enhanced functionality in magnonics by domain walls and inhomogeneous spin configurations

This paper discusses nanomagnetic structures enabling the manipulation of propagating spin waves. We address in particular how domain walls, or more generally speaking inhomogeneous spin configurations, enhance the control of spin-wave transmission and thereby the functionality of magnonic devices. Three different microscopic mechanisms are outlined, considering an interference device, a spin-wave bus and a magnonic crystal. Inhomogeneous spin configurations are argued to shift the spin-wave phase, guide spin waves in nanochannels and allow for reprogrammable spin-wave band structures in periodic nanostructures, respectively. Such devices and functionalities are relevant for further developments in magnonics.

All-magnonic spin-transfer torque and domain wall propagation

The spin-wave transportation through a transverse magnetic domain wall (DW) in a magnetic nanowire is studied. It is found that the spin wave passes through a DW without reflection. A magnon, the quantum of the spin wave, carries opposite spins on the two sides of the DW. As a result, there is a spin angular momentum transfer from the propagating magnons to the DW. This magnonic spin-transfer torque can efficiently drive a DW to propagate in the opposite direction to that of the spin wave.