Isolated zero field sub-10 nm skyrmions in ultrathin Co films

Engineering skyrmion from spin spiral in transition metal multilayers

Skyrmions having topologically protected field configurations with particle-like properties play an important role in various fields of science. Our present study focus on the generation of skyrmion from spin spiral in the magnetic multilayers of 4d/Fe/Ir(111) with 4d = Y, Zr, Nb, Mo, Ru, Rh. Here we investigate the impact of 4d transition metals on the isotropic Heisenberg exchanges and anti-symmetric Dzyaloshinskii-Moriya interactions originating from the broken inversion symmetry at the interface of 4d/Fe/Ir(111) multilayers. We find a strong exchange frustration due to the hybridization of the Fe-3d layer with both 4d and Ir-5d layers which modifies due to band filling effects of the 4d transition metals. We strengthen the analysis of exchange frustration by shedding light on the orbital decomposition of isotropic exchange interactions of Fe-3d orbitals. Our spin dynamics and Monte Carlo simulations indicate that the magnetic ground state of 4d/Fe/Ir(111) transition multilayers is a spin spiral in theab-plane with a period of 1 to 2.5 nm generated by magnetic moments of Fe atoms and propagating along thea-direction. The spiral wavelengths in Y/Fe/Ir(111) are much larger compared to Rh/Fe/Ir(111). In order to manipulate the skyrmion phase in 4d/Fe/Ir(111), we investigate the magnetic ground state of 4d/Fe/Ir(111) transition multilayers with different external magnetic field. An increasing external magnetic field of ∼12 T is responsible for deforming the spin spiral into a isolated skyrmion which flips into skyrmion lattice phase around ∼18 T in Rh/Fe/Ir(111). Our study predict that the stability of magnetic skyrmion phase in Rh/Fe/Ir(111) against thermal fluctuations is upto temperatureT⩽90 K.

Magnetic domain wall and skyrmion manipulation by static and dynamic strain profiles

Magnetic domain walls and skyrmions in thin film micro- and nanostructures have been of interest to a growing number of researchers since the turn of the millennium, motivated by the rich interplay of materials, interface and spin physics as well as by the potential for applications in data storage, sensing and computing. This review focuses on the manipulation of magnetic domain walls and skyrmions by piezoelectric strain, which has received increasing attention recently. Static strain profiles generated, for example, by voltage applied to a piezoelectric-ferromagnetic heterostructure, and dynamic strain profiles produced by surface acoustic waves, are reviewed here. As demonstrated by the success of magnetic random access memory, thin magnetic films have been successfully incorporated into complementary metal-oxide-semiconductor back-end of line device fabrication. The purpose of this review is therefore not only to highlight promising piezoelectric and magnetic materials and their properties when combined, but also to galvanise interest in the spin textures in these heterostructures for a variety of spin- and straintronic devices.

Kagomerization of transition metal monolayers induced by two-dimensional hexagonal boron nitride

The kagome lattice is an exciting solid state physics platform for the emergence of nontrivial quantum states driven by electronic correlations: topological effects, unconventional superconductivity, charge and spin density waves, and unusual magnetic states such as quantum spin liquids. While kagome lattices have been realized in complex multi-atomic bulk compounds, here we demonstrate from first-principles a process that we dub kagomerization, in which we fabricate a two-dimensional kagome lattice in monolayers of transition metals utilizing an hexagonal boron nitride (h-BN) overlayer. Surprisingly, h-BN induces a large rearrangement of the transition metal atoms supported on a fcc(111) heavy-metal surface. This reconstruction is found to be rather generic for this type of heterostructures and has a profound impact on the underlying magnetic properties, ultimately stabilizing various topological magnetic solitons such as skyrmions and bimerons. Our findings call for a reconsideration of h-BN as merely a passive capping layer, showing its potential for not only reconstructing the atomic structure of the underlying material, e.g. through the kagomerization of magnetic films, but also enabling electronic and magnetic phases that are highly sought for the next generation of device technologies.

Quantification of Hybrid Topological Spin Textures and Their Nanoscale Fluctuations in Ferrimagnets

Noncolinear spin textures, including chiral stripes and skyrmions, have shown great potential in spintronics. Basic configurations of spin textures are either Bloch or Néel types, and the intermediate hybrid type has rarely been reported. A major challenge in identifying hybrid spin textures is to quantitatively determine the hybrid angle, especially in ferrimagnets with weak net magnetization. Here, we develop an approach to quantify magnetic parameters, including chirality, saturation magnetization, domain wall width, and hybrid angle with sub-5 nm spatial resolution, based on Lorentz four-dimensional scanning transmission electron microscopy (Lorentz 4D-STEM). We find strong nanometer-scale variations in the hybrid angle and domain wall width within structurally and chemically homogeneous FeGd ferrimagnetic films. These variations fluctuate during different magnetization circles, revealing intrinsic local magnetization inhomogeneities. Furthermore, hybrid skyrmions can also be nucleated in FeGd films. These analyses demonstrate that the Lorentz 4D-STEM is a quantitative tool for exploring complex spin textures.

Role of isotropic and anisotropic Dzyaloshinskii-Moriya interaction on skyrmions, merons and antiskyrmions in theCnvsymmetric system

The lattice Hamiltonian with the presence of a chiral magnetic isotropic Dzyaloshinskii-Moriya interaction (DMI) in a square and hexagonal lattice is numerically solved to give the full phase diagram consisting of skyrmions and merons in different parameter planes. The phase diagram provides the actual regions of analytically unresolved asymmetric skyrmions and merons, and it is found that these regions are substantially larger than those of symmetric skyrmions and merons. With magnetic field, a change from meron or spin spiral (SS) to skyrmion is seen. The complete phase diagram for theCnvsymmetric system with anisotropic DMI is drawn and it is shown that this DMI helps to change the SS propagation direction. Finally, the well-defined region of a thermodynamically stable antiskyrmion phase in theCnvsymmetric system is shown.

Experimental demonstration of a skyrmion-enhanced strain-mediated physical reservoir computing system

Physical reservoirs holding intrinsic nonlinearity, high dimensionality, and memory effects have attracted considerable interest regarding solving complex tasks efficiently. Particularly, spintronic and strain-mediated electronic physical reservoirs are appealing due to their high speed, multi-parameter fusion and low power consumption. Here, we experimentally realize a skyrmion-enhanced strain-mediated physical reservoir in a multiferroic heterostructure of Pt/Co/Gd multilayers on (001)-oriented 0.7PbMg1/3Nb2/3O3-0.3PbTiO3 (PMN-PT). The enhancement is coming from the fusion of magnetic skyrmions and electro resistivity tuned by strain simultaneously. The functionality of the strain-mediated RC system is successfully achieved via a sequential waveform classification task with the recognition rate of 99.3% for the last waveform, and a Mackey-Glass time series prediction task with normalized root mean square error (NRMSE) of 0.2 for a 20-step prediction. Our work lays the foundations for low-power neuromorphic computing systems with magneto-electro-ferroelastic tunability, representing a further step towards developing future strain-mediated spintronic applications.

Controlled Surface Modification to Revive Shallow NV- Centers

Near-surface negatively charged nitrogen vacancy (NV) centers hold excellent promise for nanoscale magnetic imaging and quantum sensing. However, they often experience charge-state instabilities, leading to strongly reduced fluorescence and NV coherence time, which negatively impact magnetic imaging sensitivity. This occurs even more severely at 4 K and ultrahigh vacuum (UHV, p = 2 × 10^-10 mbar). We demonstrate that in situ adsorption of H₂O on the diamond surface allows the partial recovery of the shallow NV sensors. Combining these with band-bending calculations, we conclude that controlled surface treatments are essential for implementing NV-based quantum sensing protocols under cryogenic UHV conditions.

Chiral Magnetic Interactions in Small Fe Clusters Triggered by Symmetry-Breaking Adatoms

The chirality of the interaction between the local magnetic moments in small transition-metal alloy clusters is investigated in the framework of density-functional theory. The Dzyaloshinskii–Moriya (DM) coupling vectors Dij between the Fe atoms in Fe2X and Fe3X with X = Cu, Pd, Pt, and Ir are derived from independent ground-state energy calculations for different noncollinear orientations of the local magnetic moments. The local-environment dependence of Dij and the resulting relative stability of different chiral magnetic orders are analyzed by contrasting the results for different adatoms X and by systematically varying the distance between the adatom X and the Fe clusters. One observes that the adatoms trigger most significant DM couplings in Fe2X, often in the range of 10–30 meV. Thus, the consequences of breaking the inversion symmetry of the Fe dimer are quantified. Comparison between the symmetric and antisymmetric Fe-Fe couplings shows that the DM couplings are about two orders of magnitude weaker than the isotropic Heisenberg interactions. However, they are in general stronger than the anisotropy of the symmetric couplings. In Fe3X, alloying induces interesting changes in both the direction and strength of the DM couplings, which are the consequence of breaking the reflection symmetry of the Fe trimer and which depend significantly on the adatom-trimer distance. A local analysis of the chirality of the electronic energy shows that the DM interactions are dominated by the spin-orbit coupling at the adatoms and that the contribution of the Fe atoms is small but not negligible.

Micromagnetic Design of Skyrmionic Materials and Chiral Magnetic Configurations in Patterned Nanostructures for Neuromorphic and Qubit Applications

Our study addresses the problematics of magnetic skyrmions, nanometer-size vortex-like swirling topological defects, broadly studied today for applications in classic, neuromorphic and quantum information technologies. We tackle some challenging issues of material properties versus skyrmion stability and manipulation within a multiple-scale modeling framework, involving complementary ab-initio and micromagnetic frameworks. Ab-initio calculations provide insight into the anatomy of the magnetic anisotropy, the Dzyaloshinskii-Moriya asymmetric exchange interaction (DMI) and their response to a gating electric field. Various multi-layered heterostructures were specially designed to provide electric field tunable perpendicular magnetization and sizeable DMI, which are required for skyrmion occurrence. Landau-Lifshitz-Gilbert micromagnetic calculations in nanometric disks allowed the extraction of material parameter phase diagrams in which magnetic textures were classified according to their topological charge. We identified suitable ranges of magnetic anisotropy, DMI and saturation magnetization for stabilizing skyrmionic ground states or writing/manipulating them using either a spin-transfer torque of a perpendicular current or the electric field. From analyzing the different contributions to the total magnetic free energy, we point out some critical properties influencing the skyrmions' stability. Finally, we discuss some experimental issues related to the choice of materials or the design of novel magnetic materials compatible with skyrmionic applications.

Strain-Driven Zero-Field Near-10 nm Skyrmions in Two-Dimensional van der Waals Heterostructures

Magnetic skyrmions─localized chiral spin structures─show great promise for spintronic applications. The recent discovery of two-dimensional (2D) magnets opened new opportunities for topological spin structures in atomically thin van der Waals (vdW) materials. Despite recent progress in stabilizing metastable skyrmions in 2D magnets, their lifetime, essential for applications, has not been explored yet. Here, using first-principles calculations and atomistic spin simulations, we predict that compressive strain leads to stabilizing zero-field skyrmions with diameters close to 10 nm in a Fe₃GeTe₂/germanene vdW heterostructure. The origin of these unique skyrmions is attributed to the high tunability of Dzyaloshinskii-Moriya interaction and magnetocrystalline anisotropy energy by strain, which generally holds for Fe₃GeTe₂ heterostructures with buckled substrates. Furthermore, we calculate the energy barriers protecting skyrmions against annihilation and their lifetimes using transition-state theory. We show that nanoscale skyrmions in strained Fe₃GeTe₂/germanene can be stable for hours at temperatures up to 20 K.

Spin-orbit enabled all-electrical readout of chiral spin-textures

Chirality and topology are intimately related fundamental concepts, which are heavily explored to establish spin-textures as potential magnetic bits in information technology. However, this ambition is inhibited since the electrical reading of chiral attributes is highly non-trivial with conventional current perpendicular-to-plane (CPP) sensing devices. Here we demonstrate from extensive first-principles simulations and multiple scattering expansion the emergence of the chiral spin-mixing magnetoresistance (C-XMR) enabling highly efficient all-electrical readout of the chirality and helicity of respectively one- and two-dimensional magnetic states of matter. It is linear with spin-orbit coupling in contrast to the quadratic dependence associated with the unveiled non-local spin-mixing anisotropic MR (X-AMR). Such transport effects are systematized on various non-collinear magnetic states – spin-spirals and skyrmions – and compared to the uncovered spin-orbit-independent multi-site magnetoresistances. Owing to their simple implementation in readily available reading devices, the proposed magnetoresistances offer exciting and decisive ingredients to explore with all-electrical means the rich physics of topological and chiral magnetic objects.

One challenge for encoding information in chiral spin textures is how to read the information electrically. Here, Lima Fernandes et al. show that chiral spin textures exhibit a magnetoresistance signature which could allow for efficient electric readout of the chirality and helicity.

Skyrmions at vanishingly small Dzyaloshinskii-Moriya interaction or zero magnetic field

By introducing biquadratic together with usual bilinear ferromagnetic nearest neighbor exchange interaction in a square lattice, we find that the energy of the spin-wave mode is minimized at a finite wavevector for a vanishingly small Dzyaloshinskii-Moriya interaction (DMI), supporting a ground state with spin-spiral structure whose pitch length is unusually short as found in some of the experiments. Apart from reproducing the magnetic structures that can be obtained in a canonical model with nearest neighbor exchange interaction only, a numerical simulation of this model with further introduction of magnetic anisotropy and magnetic field predicts many other magnetic structures some of which are already observed in the experiments. Among many observed structures, nanoscale skyrmion even at vanishingly small DMI is found for the first time in a model. The model provides the nanoscale skyrmions of unit topological charge at zero magnetic field as well. We obtain phase diagrams for all the magnetic structures predicted in the model.

Magnetic skyrmions for unconventional computing

Improvements in computing performance have significantly slowed down over the past few years owing to the intrinsic limitations of computing hardware. However, the demand for data computing has increased exponentially. To solve this problem, tremendous attention has been focused on the continuous scaling of Moore's law as well as the advanced non-von Neumann computing architecture. A rich variety of unconventional computing paradigms has been devised with the rapid development of nanoscale devices. Magnetic skyrmions, spin swirling quasiparticles, have been endowed with great expectations for unconventional computing due to their potential as the smallest information carriers by exploiting their physics and dynamics. In this paper, we provide an overview of the recent progress of skyrmion-based unconventional computing from a joint device-application perspective. This paper aims to build up a panoramic picture, analyze the remaining challenges, and most importantly to shed light on the outlook of skyrmion based unconventional computing for interdisciplinary researchers.

Controlling bimerons as skyrmion analogues by ferroelectric polarization in 2D van der Waals multiferroic heterostructures

Atom-thick van der Waals heterostructures with nontrivial physical properties tunable via the magnetoelectric coupling effect are highly desirable for the future advance of multiferroic devices. In this work on LaCl/In₂Se₃ heterostructure consisting of a 2D ferromagnetic layer and a 2D ferroelectric layer, reversible switch of the easy axis and the Curie temperature of the magnetic LaCl layer has been enabled by switching of ferroelectric polarization in In₂Se₃. More importantly, magnetic skyrmions in the bimerons form have been discovered in the LaCl/In₂Se₃ heterostructure and can be driven by an electric current. The creation and annihilation of bimerons in LaCl magnetic nanodisks were achieved by polarization switching. It thus proves to be a feasible approach to achieve purely electric control of skyrmions in 2D van der Waals heterostructures. Such nonvolatile and tunable magnetic skyrmions are promising candidates for information carriers in future data storage and logic devices operated under small electrical currents.

Spin waves in skyrmionic structures with various topological charges

Equilibrium properties and localized magnon excitations are investigated in topologically distinct skyrmionic textures. The observed shape of the structures and their orientation on the lattice is explained based on their vorticities and the symmetry of the crystal. The transformation between different textures and their annihilation as a function of magnetic field is understood based on the energy differences between them. The angular momentum spin-wave eigenmodes characteristic of cylindrically symmetric structures are combined in the distorted spin configurations, leading to avoided crossings in the magnon spectrum. The susceptibility of the skyrmionic textures to homogeneous external fields is calculated, revealing that a high number of modes become detectable due to the hybridization between the angular momentum eigenmodes. These findings should contribute to the observation of spin waves in distorted skyrmionic structures via experiments and numerical simulations, widening the range of their possible applications in magnonic devices.

Role of higher-order exchange interactions for skyrmion stability

Transition-metal interfaces and multilayers are a promising class of systems to realize nanometer-sized, stable magnetic skyrmions for future spintronic devices. For room temperature applications, it is crucial to understand the interactions which control the stability of isolated skyrmions. Typically, skyrmion properties are explained by the interplay of pair-wise exchange interactions, the Dzyaloshinskii-Moriya interaction and the magnetocrystalline anisotropy energy. Here, we demonstrate that higher-order exchange interactions - which have so far been neglected - can play a key role for the stability of skyrmions. We use an atomistic spin model parametrized from first-principles and compare three different ultrathin film systems. We consider all fourth-order exchange interactions and show that, in particular, the four-site four spin interaction has a large effect on the energy barrier preventing skyrmion and antiskyrmion collapse into the ferromagnetic state. Our work opens perspectives to stabilize topological spin structures even in the absence of Dzyaloshinskii-Moriya interaction.

Sub-nanoscale atom-by-atom crafting of skyrmion-defect interaction profiles

Magnetic skyrmions are prime candidates as information carriers for spintronic devices due to their topological nature and nanometric size. However, unavoidable inhomogeneities inherent to any material leads to pinning or repulsion of skyrmions that, in analogy to biology concepts, define the phenotype of the skyrmion-defect interaction, generating complexity in their motion and challenging their application as future bits of information. Here, we demonstrate that atom-by-atom manufacturing of multi-atomic defects, being antiferromagnetic or ferromagnetic, permits the breeding of their energy profiles, for which we build schematically a Punnet-square. As established from first-principles for skyrmions generated in PdFe bilayer on Ir(111) surface, the resulting interaction phenotype is rich. It can be opposite to the original one and eventually be of dual pinning-repulsive nature yielding energy landscapes hosting multi-domains. This is dictated by the stacking site, geometry, size and chemical nature of the adsorbed defects, which control the involved magnetic interactions. This work provides new insights towards the development of disruptive device architectures incorporating defects into their design aiming to control and guide skyrmions.

Magnetic Skyrmions in a Hall Balance with Interfacial Canted Magnetizations

Magnetic skyrmions are attracting interest as efficient information-storage devices with low energy consumption, and have been experimentally and theoretically investigated in multilayers including ferromagnets, ferrimagnets, and antiferromagnets. The 3D spin texture of skyrmions demonstrated in ferromagnetic multilayers provides a powerful pathway for understanding the stabilization of ferromagnetic skyrmions. However, the manipulation mechanism of skyrmions in antiferromagnets is still lacking. A Hall balance with a ferromagnet/insulating spacer/ferromagnet structure is considered to be a promising candidate to study skyrmions in synthetic antiferromagnets. Here, high-density Néel-type skyrmions are experimentally observed at zero field and room temperature by Lorentz transmission electron microscopy in a Hall balance (core structure [Co/Pt]_n /NiO/[Co/Pt]_n ) with interfacial canted magnetizations because of interlayer ferromagnetic/antiferromagnetic coupling between top and bottom [Co/Pt]_n multilayers, where the Co layers in [Co/Pt]_n are always ferromagnetically coupled. Micromagnetic simulations show that the generation and density of skyrmions are strongly dependent on interlayer exchange coupling (IEC) and easy-axis orientation. Direct experimental evidence of skyrmions in synthetic antiferromagnets is provided, suggesting that the proposed approach offers a promising alternative mechanism for room-temperature spintronics.

Theory of an electron asymmetric scattering on skyrmion textures in two-dimensional systems

We discuss in detail the electron scattering pattern on skyrmion-like magnetic textures in two-dimensional geometry. The special attention is focused on analyzing the scattering asymmetry, which is a precursor of the topological Hall effect. We present analytical results valid in the limiting regimes of strong and weak coupling, we analyze analytically the conditions when the transverse response acquires a quantized character determined by the topological charge of a magnetic texture, we also derive the numerical scheme that gives access to the exact solution of the scattering problem. We describe how the electron scattering asymmetry is modified due to an additional short-range impurity located inside a magnetic skyrmion. Based on the numerical computations we investigate the properties of the asymmetric scattering for an arbitrary magnitude of the interaction strength and the topology of a magnetic texture, we also account for the presence or absence of a scalar impurity.

Atomistic Perspective of Long Lifetimes of Small Skyrmions at Room Temperature

The current development to employ magnetic skyrmions in novel spintronic device designs has led to a demand for room-temperature-stable skyrmions of ever smaller size. We present extensive studies on skyrmion stability in atomistic magnetic systems in two- and three-dimensional geometries. We show that for materials described by the same micromagnetic parameters, the variation of the atomistic exchange between different neighbors, the stacking order, and the number of layers of the atomic lattice can significantly influence the rate of the thermally activated decay of a skyrmion. These factors alone are important considerations, but we show that their combination can open up novel avenues of materials design in the search for sub-10 nm skyrmions, as their lifetime can be extended by several orders of magnitude.

Electrical Detection of Domain Walls and Skyrmions in Co Films Using Noncollinear Magnetoresistance

A large noncollinear magnetoresistance (NCMR) is observed for Rh/Co atomic bilayers on Ir(111) using scanning tunneling microscopy and spectroscopy. The effect is 20% at the Fermi energy and large in a broad energy range. The NCMR can be used to electrically detect nanometer-scale domain walls and skyrmions directly in the tunnel current without the need for a differential measurement. The NCMR results from changes in the density of states of noncollinear spin textures with respect to the ferromagnetic state. Density functional theory calculations reveal that they originate from spin mixing between majority d_{xz} and minority p_{z} states.