Skyrmion Lattice Research Articles

Skyrmion Lattice Phases in Thin Film Multilayer

AbstractPhases of matter are ubiquitous with everyday examples including solids and liquids. In reduced dimensions, particular phases, such as the 2D hexatic phase and corresponding phase transitions occur. A particularly exciting example of 2D ordered systems are skyrmion lattices, where in contrast to previously studied 2D colloid systems, the skyrmion size and density can be tuned by temperature and magnetic fields. This allows for the system to be driven from a liquid phase to the onset of a hexatic phase as deduced from the analysis of the hexagonal order. Using coarse‐grained molecular dynamics simulations of soft disks, the skyrmion interaction potentials are determined, and it is found that the simulations are able to reproduce the phase behavior. This shows that not only the static behavior of skyrmions is qualitatively well described in terms of a simple 2D model system but skyrmion lattices are versatile and tunable 2D model systems that allow for studying phases and phase transitions in reduced dimensions.

Stability of Néel-type skyrmion lattice against oblique magnetic fields in GaV4S8 and GaV4Se8

The orientation of N\'eel-type skyrmions in the lacunar spinels GaV$_4$S$_8$ and GaV$_4$Se$_8$ is tied to the polar axes of their underlying crystal structure through the Dzyaloshinskii-Moriya interaction. In these crystals, the skyrmion lattice phase exists for externally applied magnetic fields parallel to these axes and withstands oblique magnetic fields up to some critical angle. Here, we map out the stability of the skyrmion lattice phase in both crystals as a function of field angle and magnitude using dynamic cantilever magnetometry. The measured phase diagrams reproduce the major features predicted by a recent theoretical model, including a reentrant cycloidal phase in GaV$_4$Se$_8$. Nonetheless, we observe a greater robustness of the skyrmion phase to oblique fields, suggesting possible refinements to the model. Besides identifying transitions between the cycloidal, skyrmion lattice, and ferromagnetic states in the bulk, we measure additional anomalies in GaV$_4$Se$_8$ and assign them to magnetic states confined to polar structural domain walls.

Neutron sub-micrometre tomography from scattering data.

Neutrons are valuable probes for various material samples across many areas of research. Neutron imaging typically has a spatial resolution of larger than 20 µm, whereas neutron scattering is sensitive to smaller features but does not provide a real-space image of the sample. A computed-tomography technique is demonstrated that uses neutron-scattering data to generate an image of a periodic sample with a spatial resolution of ∼300 nm. The achieved resolution is over an order of magnitude smaller than the resolution of other forms of neutron tomography. This method consists of measuring neutron diffraction using a double-crystal diffractometer as a function of sample rotation and then using a phase-retrieval algorithm followed by tomographic reconstruction to generate a map of the sample's scattering-length density. Topological features found in the reconstructions are confirmed with scanning electron micrographs. This technique should be applicable to any sample that generates clear neutron-diffraction patterns, including nanofabricated samples, biological membranes and magnetic materials, such as skyrmion lattices.

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.

Topological Nernst Effect of the Two-Dimensional Skyrmion Lattice

The topological Hall effect (THE) and its thermoelectric counterpart, the topological Nernst effect (TNE), are hallmarks of the skyrmion lattice phase (SkL). We observed the giant TNE of the SkL in centrosymmetric Gd_{2}PdSi_{3}, comparable in magnitude to the largest anomalous Nernst signals in ferromagnets. Significant enhancement (suppression) of the THE occurs when doping electrons (holes) to Gd_{2}PdSi_{3}. On the electron-doped side, the topological Hall conductivity approaches the characteristic threshold ∼1000 (Ω cm)^{-1} for the intrinsic regime. We use the filling-controlled samples to confirm Mott's relation between TNE and THE and discuss the importance of Gd-5d orbitals for transport in this compound.

Metastable skyrmion lattices governed by magnetic disorder and anisotropy in β -Mn-type chiral magnets

Magnetic skyrmions are vortex-like topological spin textures often observed in structurally chiral magnets with Dzyaloshinskii-Moriya interaction. Among them, Co-Zn-Mn alloys with a $\beta$-Mn-type chiral structure host skyrmions above room temperature. In this system, it has recently been found that skyrmions persist over a wide temperature and magnetic field region as a long-lived metastable state, and that the skyrmion lattice transforms from a triangular lattice to a square one. To obtain perspective on chiral magnetism in Co-Zn-Mn alloys and clarify how various properties related to the skyrmion vary with the composition, we performed systematic studies on Co$_{10}$Zn$_{10}$, Co$_9$Zn$_9$Mn$_2$, Co$_8$Zn$_8$Mn$_4$ and Co$_7$Zn$_7$Mn$_6$ in terms of magnetic susceptibility and small-angle neutron scattering measurements. The robust metastable skyrmions with extremely long lifetime are commonly observed in all the compounds. On the other hand, preferred orientation of a helimagnetic propagation vector and its temperature dependence dramatically change upon varying the Mn concentration. The robustness of the metastable skyrmions in these materials is attributed to topological nature of the skyrmions as affected by structural and magnetic disorder. Magnetocrystalline anisotropy as well as magnetic disorder due to the frustrated Mn spins play crucial roles in giving rise to the observed change in helical states and corresponding skyrmion lattice form.

Dynamically reconfigurable magnonic crystal composed of artificial magnetic skyrmion lattice

Skyrmion-based magnonic crystal (MC) provides the dynamic tunability of manipulating magnonic band structure, and this brings obvious advantages over geometry or material-modulated MCs with a static band. But the existence of stable skyrmion usually requires strong Dzyaloshinskii–Moriya interaction (DMI) in combination with an external magnetic field under specific strength, and all these features limit the experimental realization and practical designing of the skyrmion-based MC. Here, we introduce the concept of artificial magnetic skyrmion-based MC. The artificial skyrmion lattice is realized by patterning an array of magnetic nanodisks on a thin film. The coupling between nanodisks and thin film generates an array of skyrmions possessing the same period as the nanodisk array. Via applying the pulsed magnetic field, one can turn on and off the skyrmion lattice, which allows switching between two very different magnonic band structures. Furthermore, via a honeycomb lattice, we extend this design to the dynamic on and off for chiral magnon edge state. The on and off switching is fast and in the range of nanoseconds. Considering that the coupling from nanodisks can greatly enhance the stability of skyrmions, no matter whether the DMI or magnetic field exists or not, our design points to a simple realization of dynamic skyrmion MC and topological magnonic devices.

Anomalous magnetoresistance in centrosymmetric skyrmion-lattice magnet Gd2PdSi3

We performed a systematic study of the temperature- and field-dependence of magnetization and resistivity of Gd2PdSi3, which is a centrosymmetric skyrmion crystal. We show that a phase diagram can be constructed based on the anomalous magnetoresistance with one-to-one correspondence among all the feature, while the DC magnetization behavior is consistent with the reported phase diagram based on AC susceptibility. In addition, the crossover boundary from a paramagnetic state into the field-induced ferromagnetic state is also identified. Our results suggest that the ferromagnetic spin fluctuations above the Néel temperature play a key role in the high sensitivity of the resistivity anomalies to magnetic field, pointing to the rich interplay of different magnetic correlations at zero and finite wave vectors underlying the skyrmion lattice in this frustrated itinerant magnet.

N\xe9el-type skyrmion in WTe2/Fe3GeTe2 van der Waals heterostructure

The promise of high-density and low-energy-consumption devices motivates the search for layered structures that stabilize chiral spin textures such as topologically protected skyrmions. At the same time, recently discovered long-range intrinsic magnetic orders in the two-dimensional van der Waals materials provide a new platform for the discovery of novel physics and effects. Here we demonstrate the Dzyaloshinskii–Moriya interaction and Néel-type skyrmions are induced at the WTe2/Fe3GeTe2 interface. Transport measurements show the topological Hall effect in this heterostructure for temperatures below 100 K. Furthermore, Lorentz transmission electron microscopy is used to directly image Néel-type skyrmion lattice and the stripe-like magnetic domain structures as well. The interfacial coupling induced Dzyaloshinskii–Moriya interaction is estimated to have a large energy of 1.0 mJ m−2. This work paves a path towards the skyrmionic devices based on van der Waals layered heterostructures.

Theoretical investigation of antiferromagnetic skyrmions in a triangular monolayer

The chiral spin textures of a two-dimensional (2D) triangular system, where both antiferromagnetic (AF) Heisenberg exchange and chiral Dzyaloshinsky–Moriya interactions co-exist, are investigated numerically with an optimized quantum Monte Carlo method based on mean-field theory. We find that: helical, skyrmionic and vortical AF crystals can be formed when an external magnetic field is applied perpendicular to the 2D monolayer; the sizes of these skyrmions and vortices change abruptly at several critical points of the external magnetic field; each of these AF crystals can be decomposed into three periodical ferromagnetic sublattices. The quantum ingredient implemented into the theoretical framework helps to track the existence of AF skyrmion lattices down to low temperatures.

Metastable solitonic states in the strained itinerant helimagnet FeGe

The tensile strain is a promising tool for creation and manipulation of magnetic solitonic textures in the chiral helimagnets via tunable control of magnetic anisotropy and Dzyaloshinskii-Moriya interaction. Here, by using the in-situ resonant small-angle x-ray scattering we demonstrate that the skyrmion and chiral soliton lattices can be achieved as metastable states in FeGe lamella as distinct states or even simultaneously by combining the tensile strain and magnetic fields in various orientations with respect to the deformation. The small-angle scattering data are discussed in the frame of the analytical model which is sufficient to describe the experimental results for soliton lattice. By using the experimental results and analytical theory, unwinding of the metastable skyrmions in the perpendicular magnetic field as seen by small-angle scattering experiment was analyzed by the micromagnetic simulation.

Macroscopic manifestation of domain-wall magnetism and magnetoelectric effect in a N\xe9el-type skyrmion host

We report a magnetic state in GaV4Se8 which emerges exclusively in samples with mesoscale polar domains and not in polar mono-domain crystals. It is manifested by a sharp anomaly in the magnetic susceptibility and the magnetic torque, distinct from other anomalies observed also in polar mono-domain samples upon transitions between the cycloidal, the Néel-type skyrmion lattice and the ferromagnetic states. We ascribe this additional transition to the transformation of distinct magnetic textures, confined to polar domain walls (DW), to the ferromagnetic (FM) state. The emergence of these DW-confined magnetic states is likely driven by the mismatch of different spin spirals, hosted by the adjacent domains. A clear anomaly in the magneto-current indicates that the DW-confined magnetic states also have strong contributions to the magnetoelectric response. We expect polar DWs to commonly host such confined magnetic edge states and, thus, offer a fertile ground to explore novel forms of magnetism.

Magnetism and Néel skyrmion dynamics in GaV4S8−ySey

We present an investigation of the influence of low-levels of chemical substitution on the magnetic ground state and N{\' e}el skyrmion lattice (SkL) state in GaV$_4$S$_{8-y}$Se$_y$, where $y =0, 0.1, 7.9$, and $8$. Muon-spin spectroscopy ($\mu$SR) measurements on $y=0$ and 0.1 materials reveal the magnetic ground state consists of microscopically coexisting incommensurate cycloidal and ferromagnetic environments, while chemical substitution leads to the growth of localized regions of increased spin density. $\mu$SR measurements of emergent low-frequency skyrmion dynamics show that the SkL exists under low-levels of substitution at both ends of the series. Skyrmionic excitations persist to temperatures below the equilibrium SkL in substituted samples, suggesting the presence of skyrmion precursors over a wide range of temperatures.

Melting of a skyrmion lattice to a skyrmion liquid via a hexatic phase.

The phase transition most commonly observed is probably melting, a transition from ordered crystalline solids to disordered isotropic liquids. In three dimensions, melting is a single, first-order phase transition. In two-dimensional systems, however, theory predicts a general scenario of two continuous phase transitions separated by an intermediate, oriented liquid state, the so-called hexatic phase with short-range translational and quasi-long-range orientational orders. Such hexatic phases occur in colloidal systems, Wigner solids and liquid crystals, all composed of real-matter particles. In contrast, skyrmions are countable soliton configurations with non-trivial topology and these quasi-particles can form two-dimensional lattices. Here we show, by direct imaging with cryo-Lorentz transmission electron microscopy, that magnetic field variations can tune the phase of the skyrmion ensembles in Cu2OSeO3 from a two-dimensional solid through the long-speculated skyrmion hexatic phase to a liquid. The local spin order persists throughout the process. Remarkably, our quantitative analysis demonstrates that the aforementioned topological-defect-induced crystal melting scenario well describes the observed phase transitions.

Room-temperature skyrmions in strain-engineered FeGe thin films

Skyrmions hold great promise for low-energy consumption and stable high-density information storage, and stabilization of the skyrmion lattice (SkX) phase at or above room temperature is greatly desired for practical use. The topological Hall effect can be used to identify candidate systems above room temperature, a challenging regime for direct observation by Lorentz electron microscopy. Atomically ordered FeGe thin films are grown epitaxially on Ge(111) substrates with $\ensuremath{\sim}4%$ tensile strain. Magnetic characterization reveals enhancement of the Curie temperature to 350 K due to strain, well above the bulk value of 278 K. A strong topological Hall effect was observed between 10 and 330 K, with a significant increase in magnitude observed at 330 K. The increase in magnitude occurs just below the Curie temperature, similar to the onset of the SkX phase in bulk FeGe. The results suggest that strained FeGe films may host a SkX phase above room temperature when significant tensile strain is applied.

Quantum hydrodynamics approach for the research of magnetic skyrmions

We propose a new approach of many-particle quantum hydrodynamics to describe a system of interacting magnetic skyrmions in the external fields. The model is based on the description of skyrmions as a fluid of point-like particles. The equations of many-particle quantum hydrodynamics are obtained for a system of skyrmions with induced dipole moments and charges. The dipole–dipole interaction between dipoles and the Coulomb interaction between charges are taken into account. The influence of quantum effects in the form of the Bohm quantum potential is obtained. The contribution of Magnus effect to the dynamics of dipoles current density is predicted. The electron–skyrmion interactions are considered, based on a two-fluid model of quantum hydrodynamics with separate description of spin-up and spin-down electrons on the background of skyrmion lattice. The proposed model can be further used to study the dynamical effects in a system of skyrmions in the external fields.

High-field depinned phase and planar Hall effect in the skyrmion host Gd2PdSi3

For the skyrmion-hosting intermetallic Gd$_2$PdSi$_3$ with centrosymmetric hexagonal lattice and triangular net of rare earth sites, we report a thorough investigation of the magnetic phase diagram. Our work reveals a new magnetic phase with isotropic value of the critical field for all orientations, where the magnetic ordering vector $\mathbf{q}$ is depinned from its preferred directions in the basal plane. This is in contrast to the highly anisotropic behavior of the low field phases, such as the skyrmion lattice (SkL), which are easily destroyed by in-plane magnetic field. The bulk nature of the SkL and of other magnetic phases was evidenced by specific-heat measurements. Resistivity anisotropy, likely originating from partial gapping of the density of states along $\mathbf{q}$ in this RKKY magnet, is picked up via the planar Hall effect (PHE). The PHE confirms the single-$\mathbf{q}$ nature of the magnetic order when the field is in the hexagonal plane, and allows to detect the preferred directions of $\mathbf{q}$. For field aligned perpendicular to the basal plane, several scenarios for the depinned phase (DP), such as tilted conical order, are discussed on the basis of the data.

Chiral Magnonics: Reprogrammable Nanoscale Spin Wave Networks Based on Chiral Domain Walls.

SummarySpin waves offer promising perspectives as information carriers for future computational architectures beyond conventional complementary metal-oxide-semiconductor (CMOS) technology, owing to their benefits for device minimizations and low-ohmic losses. Although plenty of magnonic devices have been proposed previously, scalable nanoscale networks based on spin waves are still missing. Here, we demonstrate a reprogrammable two-dimensional spin wave network by combining the chiral exchange spin waves and chiral domain walls. The spin-wave network can be extended to two dimensions and offers unprecedented control of exchange spin waves. Each cell in the network can excite, transmit, and detect spin waves independently in the chiral domain wall, and spin-wave logics are also demonstrated. Our results open up perspectives for integrating spin waves into future logic and computing circuits and networks.

Skyrmion fluctuations at a first-order phase transition boundary

Magnetic skyrmions are topologically protected spin textures with promising prospects for applications in data storage. They can form a lattice state due to competing magnetic interactions and are commonly found in a small region of the temperature—magnetic field phase diagram. Recent work has demonstrated that these magnetic quasi-particles fluctuate at the μeV energy scale. Here, we use a coherent x-ray correlation method at an x-ray free-electron laser to investigate these fluctuations in a magnetic phase coexistence region near a first-order transition boundary where fluctuations are not expected to play a major role. Surprisingly, we find that the relaxation of the intermediate scattering function at this transition differs significantly compared to that deep in the skyrmion lattice phase. The observation of a compressed exponential behavior suggests solid-like dynamics, often associated with jamming. We assign this behavior to disorder and the phase coexistence observed in a narrow field-window near the transition, which can cause fluctuations that lead to glassy behavior.

Spin current pumped by confined breathing skyrmion

Spin pumping is a widely recognized method to generate the spin current in the spintronics, which can be found in varieties of magnetic materials and is acknowledged as a fundamentally dynamic process equivalent to the spin-transfer torque. In this work, we theoretically verified the oscillating spin current mixed by AC and DC components can be pumped from the microwave-motivated breathing skyrmion. The spin current can be pumped within a relatively low-frequency microwave compared with the in-plane ferromagnetic resonance (FMR). Although the amplitude of spin current density for a single confined skyrmion is several times lower than the FMR spin pumping, the pumped current would be improved to be the same order as the FMR through a tight skyrmion lattice. Based on the spin pumping of breathing skyrmion, we designed a high reading-speed racetrack memory model whose reading speed is much higher than the SOT (spin–orbit torque)/STT (spin-transfer torque) skyrmion racetrack. Our work focuses on the spin pumping phenomenon inside the breathing skyrmion, and it may contribute to the applications of the skyrmion-based device.