Skyrmion-Based Dynamic Magnonic Crystal

Electronic properties, skyrmions and bimerons in Janus CrXY (X, Y = S, Se, Te, Cl, Br, I, and X ≠ Y) monolayers

Using first-principles calculations, we systematically investigate the electronic properties, chiral skyrmions and bimerons in two-dimensional (2D) Janus CrXY (X, Y = S, Se, Te, Cl, Br, I, and X ≠ Y) monolayers. We found that the categories of nonmagnetic atoms (X and Y in CrXY) determine whether CrXY is a ferromagnetic metal or a semiconductor. Unexpectedly, the CrBrS monolayer of these CrXY materials is a room temperature ferromagnetic semiconductor with a Curie temperature of 303 K, and it possesses an off-plane magnetic anisotropy energy of 0.06 meV. Besides, a strong Dzyaloshinskii-Moriya interaction (DMI) of 3.10 meV is found in CrTeI and is mainly induced by the strong spin-orbit coupling of the nonmagnetic atoms Te(I) rather than that of the magnetic Cr atoms. Furthermore, using micromagnetic simulations, skyrmions can be stabilized in CrSeBr without external magnetic fields. More importantly, the bimerons in CrSeCl with in-plane magnetic anisotropy can be transformed into skyrmions or a ferromagnetic state by controlling the direction of external magnetic fields. Our work investigates fourteen kinds of Janus monolayers, serving as guidelines for materials research on DMI, skyrmions and bimerons.

Skyrmion-Excited Spin-Wave Fractal Networks

Magnetic skyrmions exhibit unique, technologically relevant pseudo-particle behaviors which arise from their topological protection, including well-defined, 3D dynamic modes that occur at microwave frequencies. During dynamic excitation, spin waves are ejected into the interstitial regions between skyrmions, creating the magnetic equivalent of a turbulent sea. However, since the spin waves in these systems have a well-defined length scale, and the skyrmions are on an ordered lattice, ordered structures from spin-wave interference can precipitate from the chaos. This work uses small-angle neutron scattering (SANS) to capture the dynamics in hybrid skyrmions and investigate the spin-wave structure. Performing simultaneous ferromagnetic resonance and SANS, the diffraction pattern shows a large increase in low-angle scattering intensity, which is present only in the resonance condition. This scattering pattern is best fit using a mass fractal model, which suggests the spin waves form a long-range fractal network. The fractal structure is constructed of fundamental units with a size that encodes the spin-wave emissions and are constrained by the skyrmion lattice. These results offer critical insights into the nanoscale dynamics of skyrmions, identify a new dynamic spin-wave fractal structure, and demonstrate SANS as a unique tool to probe high-speed dynamics.

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.

Theoretical Investigation of Skyrmion Dynamics in Pt/Co/MgO Nanodots

In this article, we present a numerical study on stabilization and eigenmodes of the so-called skyrmion chiral spin texture in nanometric dots. The first aim of this study is to identify the appropriate multilayer in a set of Pt/Co/MgO structures with different Co thicknesses that have been previously experimentally characterized. Stabilization occurs if the energy favoring skyrmions is greater than the geometric mean of the exchange and anisotropy energies. Both the energy favoring skyrmions and the anisotropy contribution depend on the Co thickness. The appropriate multilayer is obtained for a specific Co thickness. MuMax simulations are used to calculate the precise static magnetization configuration for the experimental parameters, allowing us select the appropriate structure. Moreover, in view of experimental study of skyrmion dynamics by means of Brillouin light scattering, the eigenfrequency, eigenmode profile, and spectral density are calculated for different dot sizes. Finally, the optimal dot size that allows for a feasible experiment is obtained.

Skyrmion Echo in a System of Interacting Skyrmions

We consider helical rotation of skyrmions confined in the potentials formed by nanodisks. Based on numerical and analytical calculations we propose the skyrmion echo phenomenon. The physical mechanism of the skyrmion echo formation is also proposed. Because of the distortion of the lattice, impurities, or pinning effect, confined skyrmions experience slightly different local fields, which leads to dephasing of the initial signal. The interaction between skyrmions also can contribute to the dephasing process. However, switching the magnetization direction in the nanodiscs (e.g., by spin transfer torque) also switches the helical rotation of the skyrmions from clockwise to anticlockwise (or vice versa), and this restores the initial signal (which is the essence of skyrmion echo).

Applications of nanomagnets as dynamical systems: I

When magnets are fashioned into nanoscale elements, they exhibit a wide variety of phenomena replete with rich physics and the lure of tantalizing applications. In this topical review, we discuss some of these phenomena, especially those that have come to light recently, and highlight their potential applications. We emphasize what drives a phenomenon, what undergirds the dynamics of the system that exhibits the phenomenon, how the dynamics can be manipulated, and what specific features can be harnessed for technological advances. For the sake of balance, we point out both advantages and shortcomings of nanomagnet based devices and systems predicated on the phenomena we discuss. Where possible, we chart out paths for future investigations that can shed new light on an intriguing phenomenon and/or facilitate both traditional and non-traditional applications.

Magnetic Topological Insulator Heterostructures: A Review

Topological insulators (TIs) provide intriguing prospects for the future of spintronics due to their large spin-orbit coupling and dissipationless, counter-propagating conduction channels in the surface state. The combination of topological properties and magnetic order can lead to new quantum states including the quantum anomalous Hall effect that was first experimentally realized in Cr-doped (Bi,Sb)₂ Te₃ films. Since magnetic doping can introduce detrimental effects, requiring very low operational temperatures, alternative approaches are explored. Proximity coupling to magnetically ordered systems is an obvious option, with the prospect to raise the temperature for observing the various quantum effects. Here, an overview of proximity coupling and interfacial effects in TI heterostructures is presented, which provides a versatile materials platform for tuning the magnetic and topological properties of these exciting materials. An introduction is first given to the heterostructure growth by molecular beam epitaxy and suitable structural, electronic, and magnetic characterization techniques. Going beyond transition-metal-doped and undoped TI heterostructures, examples of heterostructures are discussed, including rare-earth-doped TIs, magnetic insulators, and antiferromagnets, which lead to exotic phenomena such as skyrmions and exchange bias. Finally, an outlook on novel heterostructures such as intrinsic magnetic TIs and systems including 2D materials is given.

Skyrmion Formation in Nanodisks Using Magnetic Force Microscopy Tip

We demonstrated numerically the skyrmion formation in ultrathin nanodisks using a magnetic force microscopy tip. We found that the local magnetic field generated by the magnetic tip significantly affects the magnetization state of the nanodisks and leads to the formation of skyrmions. Experimentally, we confirmed the influence of the local field on the magnetization states of the disks. Micromagnetic simulations explain the evolution of the magnetic state during magnetic force microscopy scanning and confirm the possibility of skyrmion formation. The formation of the horseshoe magnetic domain is a key transition from random labyrinth domain states into the skyrmion state. We showed that the formation of skyrmions by the magnetic probe is a reliable and repetitive procedure. Our findings provide a simple solution for skyrmion formation in nanodisks.

Geometrically Constrained Skyrmions

Skyrmions are chiral swirling magnetization structures with nanoscale size. These structures have attracted considerable attention due to their topological stability and promising applicability in nanodevices, since they can be displaced with spin-polarized currents. However, for the comprehensive implementation of skyrmions in devices, it is imperative to also attain control over their geometrical position. Here we show that, through thickness modulations introduced in the host material, it is possible to constrain three-dimensional skyrmions to desired regions. We investigate skyrmion structures in rectangular FeGe platelets with micromagnetic finite element simulations. First, we establish a phase diagram of the minimum-energy magnetic state as a function of the external magnetic field strength and the film thickness. Using this understanding, we generate preferential sites for skyrmions in the material by introducing dot-like “pockets” of reduced film thickness. We show that these pockets can serve as pinning centers for the skyrmions, thus making it possible to obtain a geometric control of the skyrmion position. This control allows for stabilization of skyrmions at positions and in configurations that they would otherwise not attain. Our findings may have implications for technological applications in which skyrmions are used as units of information that are displaced along racetrack-type shift register devices.

Real-Space Observation of Magnon Interaction with Driven Space-Time Crystals

The concept of space-time crystals (STC), i.e., translational symmetry breaking in time and space, was recently proposed and experimentally demonstrated for quantum systems. Here, we transfer this concept to magnons and experimentally demonstrate a driven STC at room temperature. The STC is realized by strong homogeneous microwave pumping of a micron-sized permalloy (Py) stripe and is directly imaged by scanning transmission x-ray microscopy (STXM). For a fundamental understanding of the formation of the STC, micromagnetic simulations are carefully adapted to model the experimental findings. Beyond the mere generation of a STC, we observe the formation of a magnonic band structure due to back folding of modes at the STC's Brillouin zone boundaries. We show interactions of magnons with the STC that appear as lattice scattering, which results in the generation of ultrashort spin waves (SW) down to 100-nm wavelengths that cannot be described by classical dispersion relations for linear SW excitation. We expect that room-temperature STCs will be useful to investigate nonlinear wave physics, as they can be easily generated and manipulated to control their spatial and temporal band structures.

Magnetic Direct-Write Skyrmion Nanolithography

Magnetic skyrmions are stable spin textures with quasi-particle behavior and attract significant interest in fundamental and applied physics. The metastability of magnetic skyrmions at zero magnetic field is particularly important to enable, for instance, a skyrmion racetrack memory. Here, the results of the nucleation of stable skyrmions and formation of ordered skyrmion lattices by magnetic force microscopy in (Pt/CoFeSiB/W)_n multilayers, exploiting the additive effect of the interfacial Dzyaloshinskii-Moriya interaction, are presented. The appropriate conditions under which skyrmion lattices are confined with a dense two-dimensional liquid phase are identified. A crucial parameter to control the skyrmion lattice characteristics and the number of scans resulting in the complete formation of a skyrmion lattice is the distance between two adjacent scanning lines of a magnetic force microscopy probe. The creation of skyrmion patterns with complex geometry is demonstrated, and the physical mechanism of direct magnetic writing of skyrmions is comprehended by micromagnetic simulations. This study shows a potential of a direct-write (maskless) skyrmion (topological) nanolithography with sub-100 nm resolution, where each skyrmion acts as a pixel in the final topological image.

Kerr effect anomaly in magnetic topological insulator superlattices

We report the magneto-optical Kerr effect (MOKE) study of magnetic topological insulator superlattice films with alternating transition-metal and rare-earth doping. We observe an unexpected hump in the MOKE hysteresis loops upon magnetization reversal at low temperatures, reminiscent of the topological Hall effect (THE) reported in transport measurements. The THE is commonly associated with the existence of magnetic skyrmions, i.e. chiral spin textures originating from topological defects in real space. Here, the observation of the effect is tied to ferromagnetic ordering in the rare-earth-doped layers of the superlattice. Our study may provide a new approach for the non-invasive optical investigation of skyrmions in magnetic films, complementary to electrical transport measurements, where the topological Hall signal is often the only hint of non-trivial magnetization patterns.

Electron Beam Lithography of Magnetic Skyrmions

The emergence of magnetic skyrmions, topological spin textures, has aroused tremendous interest in studying the rich physics related to their topology. While skyrmions promise high-density and energy-efficient magnetic memory devices for information technology, the manifestation of their nontrivial topology through single skyrmions and ordered and disordered skyrmion lattices could also give rise to many fascinating physical phenomena, such as chiral magnon and skyrmion glass states. Therefore, generating skyrmions at designated locations on a large scale, while controlling the skyrmion patterns, is the key to advancing topological magnetism. Here, a new, yet general, approach to the "printing" of skyrmions with zero-field stability in arbitrary patterns on a massive scale in exchange-biased magnetic multilayers is presented. By exploiting the fact that the antiferromagnetic order can be reconfigured by local thermal excitations, a focused electron beam with a graphic pattern generator to "print" skyrmions is used, which is referred to as skyrmion lithography. This work provides a route to design arbitrary skyrmion patterns, thereby establishing the foundation for further exploration of topological magnetism.

Demonstration of k-vector selective microscopy for nanoscale mapping of higher order spin wave modes

As a potential route towards beyond CMOS computing magnonic waveguides show outstanding properties regarding fundamental wave physics and data transmission. Here, we use time resolved scanning transmission X-ray microscopy to directly observe spin waves in magnonic permalloy waveguides with nanoscale resolution. Additionally, we demonstrate an approach for k-vector selective imaging to deconvolute overlapping modes in real space measurements. Thereby, we observe efficient excitation of symmetric and antisymmetric modes. The profiles of higher order modes that arise from sub-micron confinement are precisely mapped out and compared to analytical models. Thus, we lay a basis for the design of multimode spin wave transmission systems and demonstrate a general technique for k-specific microscopy that can also be used beyond the field of magnonics.

Magnonic crystals: towards terahertz frequencies

This topical review presents an overview of the recent experimental and theoretical attempts on designing magnonic crystals for operation at different frequencies. The focus is put on the microscopic physical mechanisms involved in the formation of the magnonic band structure, allowed as well as forbidden magnon states in various systems, including ultrathin films, multilayers and artificial magnetic structures. The essential criteria for the formation of magnonic bandgaps in different frequency regimes are explained in connection with the magnon dynamics in such structures. The possibility of designing small-size magnonic crystals for operation at ultrahigh frequencies (terahertz and sub-terahertz regime) is discussed. Recently discovered magnonic crystals based on topological defects and using periodic Dzyaloshinskii-Moriya interaction, are outlined. Different types of magnonic crystals, capable of operation at different frequency regimes, are put within a rather unified picture.

Emergent Dynamics of Artificial Spin-Ice Lattice Based on an Ultrathin Ferromagnet

We present high-frequency dynamics of magnetic nanostructure lattices, fabricated in the form of "artificial spin-ice", that possess magnetically frustrated states. Dynamics of such structures feature multiple resonance excitation that reveals rich and intriguing microwave characteristics, which are highly dependent on field-cycle history. Geometrical parameters such as dimensions and ferromagnetic layer thickness, which control the interplay of different demagnetizing factors, are found to play a pivotal role in governing the dynamics. Our findings are highlighted by the evolution of unique excitations pertaining to magnetic frustration, which are well supported by static magnetometry studies and micromagnetic simulations.

A nontrivial crossover in topological Hall effect regimes

We propose a new theory of the topological Hall effect (THE) in systems with non-collinear magnetization textures such as magnetic skyrmions. We solve the problem of electron scattering on a magnetic skyrmion exactly, for an arbitrary strength of exchange interaction and the skyrmion size. We report the existence of different regimes of THE and resolve the apparent contradiction between the adiabatic Berry phase theoretical approach and the perturbation theory for THE. We traced how the topological charge Hall effect transforms into the spin Hall effect upon varying the exchange interaction strength or the skyrmion size. This transformation has a nontrivial character: it is accompanied by an oscillating behavior of both charge and spin Hall currents. This hallmark of THE allows one to identify the chirality driven contribution to Hall response in the experiments.

Room-Temperature Current-Induced Generation and Motion of sub-100 nm Skyrmions

Magnetic skyrmions are nanoscale windings of the spin configuration that hold great promise for technology due to their topology-related properties and extremely reduced sizes. After the recent observation at room temperature of sub-100 nm skyrmions stabilized by interfacial chiral interaction in magnetic multilayers, several pending questions remain to be solved, notably about the means to nucleate individual compact skyrmions or the exact nature of their motion. In this study, a method leading to the formation of magnetic skyrmions in a micrometer-sized track using homogeneous current injection is evidenced. Spin-transfer-induced motion of these small electrical-current-generated skyrmions is then demonstrated and the role of the out-of-plane magnetic field in the stabilization of the moving skyrmions is also analyzed. The results of these experimental observations of spin torque induced motion are compared to micromagnetic simulations reproducing a granular type, nonuniform magnetic multilayer in order to address the particularly important role of the magnetic inhomogeneities on the current-induced motion of sub-100 nm skyrmions for which the material grains size is comparable to the skyrmion diameter.

Coupled gyration modes in one-dimensional skyrmion arrays in thin-film nanostrips as new type of information carrier

We report on a micromagnetic numerical simulation study of dynamic coupling between neighboring skyrmions periodically arranged in narrow-width nanostrips. We explored the coupled gyration modes and their characteristic dispersions in terms of the interdistance between the neighboring skyrmions. The application of perpendicular magnetic fields allows for the control and modification of the dispersion of the coupled gyration modes. The coupled gyration modes of individual skyrmions might provide a new type of information carrier in narrow-width straight and curved nanostrips, as driven by magnetic interactions in such continuous thin films.

Brillouin light scattering studies of 2D magnonic crystals

Magnonic crystals, materials with periodic modulation of their magnetic properties, represent the magnetic counterpart of photonic, phononic and plasmonic crystals, and have been largely investigated in recent years because of the possibility of using spin waves as a new means for carrying and processing information over a very large frequency bandwidth. Here, we review recent Brillouin light scattering studies of 2D magnonic crystals consisting of single- and bi-component arrays of interacting magnetic dots or antidot lattices. In particular, we discuss the principal properties of the magnonic band diagram of such systems, with emphasis given to its dependence on both magnetic and the geometrical parameters. Thanks to the possibility of tailoring their band structure by means of several degrees of freedom, planar magnonic crystals offer a good opportunity to design an innovative class of nanoscale microwave devices.

Electron Scattering on a Magnetic Skyrmion in the Nonadiabatic Approximation

We present a theory of electron scattering on a magnetic Skyrmion for the case when the exchange interaction is moderate so that the adiabatic approximation and the Berry phase approach are not applicable. The theory explains the appearance of a topological Hall current in the systems with magnetic Skyrmions, the special importance of which is its applicability to dilute magnetic semiconductors with a weak exchange interaction.

Dynamical magnetoelectric phenomena of multiferroic skyrmions

Magnetic skyrmions, vortex-like swirling spin textures characterized by a quantized topological invariant, realized in chiral-lattice magnets are currently attracting intense research interest. In particular, their dynamics under external fields is an issue of vital importance both for fundamental science and for technical application. Whereas observations of magnetic skyrmions has been limited to metallic magnets so far, their realization was also discovered in a chiral-lattice insulating magnet Cu2OSeO3 in 2012. Skyrmions in the insulator turned out to exhibit multiferroic nature with spin-induced ferroelectricity. Strong magnetoelectric coupling between noncollinear skyrmion spins and electric polarizations mediated by relativistic spin-orbit interaction enables us to drive motion and oscillation of magnetic skyrmions by application of electric fields instead of injection of electric currents. Insulating materials also provide an environment suitable for detection of pure spin dynamics through spectroscopic measurements owing to the absence of appreciable charge excitations. In this article, we review recent theoretical and experimental studies on multiferroic properties and dynamical magnetoelectric phenomena of magnetic skyrmions in insulators. We argue that multiferroic skyrmions show unique coupled oscillation modes of magnetizations and polarizations, so-called electromagnon excitations, which are both magnetically and electrically active, and interference between the electric and magnetic activation processes leads to peculiar magnetoelectric effects in a microwave frequency regime.