Skyrmion Density Research Articles

Voltage control of skyrmions: Creation, annihilation, and zero-magnetic field stabilization

Voltage manipulation of skyrmions is a promising path toward low-energy spintronic devices. Here, voltage effects on skyrmions in a GdOx/Gd/Co/Pt heterostructure are observed experimentally. The results show that the skyrmion density can be both enhanced and depleted by the application of an electric field, along with the ability, at certain magnetic fields to completely switch the skyrmion state on and off. Further, a zero magnetic field skyrmion state can be stabilized at a negative bias voltage using a defined voltage and magnetic field sequence. The voltage effects measured here occur on a few-second timescale, suggesting an origin in voltage-controlled magnetic anisotropy rather than ionic effects. By investigating the skyrmion nucleation rate as a function of temperature, we extract the energy barrier to skyrmion nucleation in our sample. Further, micromagnetic simulations are used to explore the effect of changing the anisotropy and Dzyaloshinskii–Moriya interaction on skyrmion density. Our work demonstrates the control of skyrmions by voltages, showing functionalities desirable for commercial devices.

Antiferromagnetic skyrmions and skyrmion density wave in a Rashba-coupled Hund insulator

We discover magnetic phases hosting highly elusive and technologically important antiferromagnetic skyrmion quasiparticles in a model for a Rashba-coupled Hund insulator. The results are based on unbiased simulations of a classical superexchange model derived, in this work, from a realistic microscopic electronic Hamiltonian. We also discover a skyrmion density wave ground state characterized by a $(Q,Q)$ modulation in the local skyrmion density map. A unique inhomogeneous state characterized by a circular pattern in the spin structure factor and filamentary real-space textures is identified as the parent of sparse antiferromagnetic skyrmions. We predict that the magnetic states reported here can be realized in thin films of multiorbital systems involving $4d$ or $5d$ transition metals.

Direct observation of topological Hall effect in Co/Pt nanostructured films

A method consisting of simultaneous measurements of a Hall effect and a magneto-optic Kerr effect is used to study a topological Hall effect in thin ferromagnetic films. The method is based on the idea that the values of the topological effects are different at dc and optical frequencies. The topological Hall effect in the artificial lattices of magnetic bubbles in nanostructured Co/Pt multilayers with perpendicular magnetic anisotropy is investigated using this method. The Lorentz transmission electron microscopy measurements demonstrate skyrmionic topology of the magnetic bubbles. The measured topological Hall effect is proportional to the skyrmion density in the system.

Fractal Analysis of Skyrmions Generated by Field-Assisted Fine-tuning of Magnetic Anisotropy

Magnetic skyrmions are topologically protected whirling spin textures nucleated from other ferromagnetic states that have great potential applications for nanoscale devices. To realize this potential, it is important to find useful methods to generate skyrmions in a controlled fashion and to identify tools to quantitatively describe their formation. Here we generate skyrmions in perpendicularly magnetized $\mathrm{Mg}\mathrm{O}/{\mathrm{Mn}}_{2}\mathrm{Co}\mathrm{Al}/\mathrm{Pd}$ ultrathin films and investigate their formation by fractal analysis. Using an in-plane field, we modify the effective magnetic anisotropy of the films to control the nucleation of skyrmions from two distinct domain states in the films: labyrinth domains typically found in perpendicular materials and a featureless monodomain ferromagnetic phase. By using fractal analysis, we obtain a magnetic phase diagram related to the fractal dimension of the domains that can describe the evolution of the magnetic states and can be used to categorize the formation of skyrmions. Moreover, we find that the skyrmion density is determined not only by the critical material parameter $\ensuremath{\kappa}$ but also by a repulsive skyrmion-skyrmion interaction at high in-plane magnetic fields. We thus establish a reliable and powerful method to generate skyrmions and a way to analyze the evolution of skyrmions.

Operando control of skyrmion density in a Lorentz transmission electron microscope with current pulses

Magnetic skyrmions hold promise for spintronic devices. To explore the dynamical properties of skyrmions in devices, a nanoscale method to image spin textures in response to a stimulus is essential. Here, we apply a technique for operando electrical current pulsing of chiral magnetic devices in a Lorentz transmission electron microscope. In ferromagnetic multilayers with interfacial Dzyaloshinskii–Moriya interaction, we study the creation and annihilation of skyrmions localized by point-like pinning sites due to defects. Using a combination of experimental and micromagnetic techniques, we establish a thermal contribution for the creation and annihilation of skyrmions in our study. Our work reveals a mechanism for controlling skyrmion density, which enables an examination of skyrmion magnetic field stability as a function of density. We find that high-density skyrmion states are more stable than low-density states or isolated skyrmions resisting annihilation over a magnetic field range that increases monotonically with density.

Fast and robust algorithm for energy minimization of spin systems applied in an analysis of high temperature spin configurations in terms of skyrmion density

An algorithm for the minimization of the energy of magnetic systems is presented and applied to the analysis of thermal configurations of a ferromagnet to identify inherent structures, i.e. the nearest local energy minima, as a function of temperature. Over a rather narrow temperature interval, skyrmions appear and reach a high temperature limit for the skyrmion density. In addition, the performance of the algorithm is further demonstrated in a self-consistent field calculation of a skyrmion in an itinerant magnet. The algorithm is based on a geometric approach in which the curvature of the spherical domain is taken into account and as a result the length of the magnetic moments is preserved in every iteration. In the limit of infinitesimal rotations, the minimization path coincides with that obtained using damped spin dynamics while the use of limited-memory quasi-newton minimization algorithms, such as the limited-memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) algorithm, significantly accelerates the convergence.

Skyrmion generation from irreversible fission of stripes in chiral multilayer films

Competing interactions produce finite-size textures in myriad condensed matter systems, typically forming elongated stripe or round bubble domains. Transitions between stripe and bubble phases, driven by field or temperature, are expected to be reversible in nature. Here we report on the distinct character of the analogous transition for nanoscale spin textures in chiral Co/Pt-based multilayer films, known to host N\'{e}el skyrmions, using microscopy, magnetometry, and micromagnetic simulations. Upon increasing field, individual stripes fission into multiple skyrmions, and this transition exhibits a macroscopic signature of irreversibility. Crucially, upon field reversal, the skyrmions do not fuse back into stripes, with many skyrmions retaining their morphology down to zero field. Both the macroscopic irreversibility and the microscopic zero-field skyrmion density are governed by the thermodynamic material parameter determining chiral domain stability. These results establish the thermodynamic and microscopic framework underlying ambient skyrmion generation and stability in chiral multilayer films and provide immediate directions for their functionalization in devices.

Electrical Control of Skyrmion Density via Skyrmion-Stripe Transformation

A comprehensive understanding of numerous electrical current-induced magnetic texture transformations is necessary to ensure the reliability of skyrmionic devices during operation. Here, we present an experimental study of unipolar current-induced skyrmion-stripe transformation in a $\mathrm{Pt}/\mathrm{Co}/\mathrm{Fe}/\mathrm{Ir}$ magnetic bilayer. High current density pulses induce a densely packed skyrmion state, as commonly reported in many other studies, and skyrmion nucleation is expected to lessen with diminishing current density. However, at a lower current density where pinning effects become significant, a regime where current-induced skyrmion annihilation and skyrmion-to-stripe transformation is observed. Kerr imaging reveals that, under a low current pulse, the rapidly expanding stripes crowd out and annihilate the skyrmions before quickly decaying and leaving behind a sparse skyrmion population. Our findings establish an additional requirement of a minimum operating current density in the design of skyrmionic devices to avoid unintended skyrmion deletion. On the other hand, this skyrmion annihilation can also be strategically employed as a technique for skyrmion density control using solely current modulation in future skyrmionic devices.

Strain-tunable ferromagnetism and chiral spin textures in two-dimensional Janus chromium dichalcogenides

Using first-principles calculations and micromagnetic simulations, we systematically investigate the magnetic properties of two-dimensional Janus chromium dichalcogenides ($\mathrm{Cr}X\mathrm{Te}, X=\mathrm{S}$, Se) under strain. We find that the CrSTe monolayer has high Curie temperature (${T}_{c}$) of 295 K and an out-of-plane magnetic anisotropy. The CrSeTe monolayer has large Dzyaloshinskii-Moriya interaction (DMI) which can host chiral N\'eel domain wall (DW), and under an external magnetic field, the skyrmion states can be induced. As tensile strain increases, ferromagnetic exchange coupling and perpendicular magnetic anisotropy of Janus $\mathrm{Cr}X\mathrm{Te}$ monolayers both increase significantly, and the magnitude of DMI is reduced, which results in the giant ferromagnetism enhancement. Interestingly, for CrSeTe monolayer, distinct spin textures from chiral DW to uniform ferromagnetic states are induced under tensile strain. Moreover, the diameter and density of skyrmions in CrSeTe can be tuned by the amplitude of external magnetic field and strain. These findings highlight that the Janus $\mathrm{Cr}X\mathrm{Te}$ monolayers as good candidates for spintronic nanodevices.

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.

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.

Enhancement of zero-field skyrmion density in [Pt/Co/Fe/Ir]2 multilayers at room temperature by the first-order reversal curve

Magnetic skyrmions are novel topological spin textures on the nanoscale, and significant efforts have been taken to improve their zero-field density at room temperature (RT). In this work, we reported an approach of improving zero-field skyrmion density in [Pt/Co/Fe/Ir]2 multilayers at RT by using the first-order reversal curve (FORC) technique to obtain information on the irreversible or reversible behaviors in the magnetization switching process. It was found from the FORC diagram that the magnetization reversal mechanism can be characterized into three stages: (1) reversible labyrinth stripe domains expanding or shrinking stage; (2) irreversible stripe domains fracturing stage; and (3) irreversible skyrmion annihilation stage. Furthermore, the zero-field skyrmion density can be highly improved by choosing reversal fields from the irreversible stripe domains fracturing stage. The highest skyrmion density was approached according to the maximum FORC distribution ρ. Our results have established the FORC measurement as a valuable tool for investigating magnetic multilayers of high skyrmion densities.

Onset of a skyrmion phase by chemical substitution in MnGe-based chiral magnets

We study the evolution of the magnetic phase diagram of Mn$_{1-x}$Fe$_{x}$Ge alloys with concentration $x$ ($0 \leq x \leq 0.3$) by small-angle neutron scattering. We unambiguously observe the absence of a skyrmion lattice (or A-phase) in bulk MnGe and its onset under a small Mn/Fe substitution. The A-phase is there endowed with an exceptional skyrmion density, and is stabilized within a very large temperature region and a field range which scales with the Fe concentration. Our findings highlight the possibility to fine-tune properties of skyrmion lattices by means of chemical doping.

Shear banding, intermittency, jamming, and dynamic phases for skyrmions in inhomogeneous pinning arrays

We examine driven skyrmion dynamics in systems with inhomogeneous pinning where a strip of strong pinning coexists with a region containing no pinning. For driving parallel to the strip, we find that the initial skyrmion motion is confined to the unpinned region and the skyrmion Hall angle is zero. At larger drives, a transition occurs to a phase in which motion also appears within the pinned region, creating a shear band in the skyrmion velocity, while the skyrmion Hall angle is still zero. As the drive increases further, the flow becomes disordered and the skyrmion Hall angle increases with drive until saturating at the highest drives when the system transitions into a moving crystal phase. The different dynamic phases are associated with velocity and density gradients across the pinning boundaries. We map out the dynamic phases as a function of pinning strength, skyrmion density, and Magnus force strength, and correlate the phase boundaries with features in the velocity-force curves and changes in the local and global ordering of the skyrmion structure. For large Magnus forces, the shear banding instability is replaced by large scale intermittent flow in the pinned region accompanied by simultaneous motion perpendicular to the direction of the drive, which appears as oscillations in the transport curves. We also examine the case of a drive applied perpendicular to the strip, where we find a jamming effect in which the skyrmion flow is blocked by skyrmion-skyrmion interactions until the drive is large enough to induce plastic flow.

Reentrant pinning, dynamic row reduction, and skyrmion accumulation for driven skyrmions in inhomogeneous pinning arrays

We examine the dynamics of skyrmions in systems with a region of strong pinning coexisting with a pin-free region, where the equilibrium state has a uniform skyrmion density. Under an applied drive, skyrmions accumulate in the pin-free region along the edge of the pinned region due to the skyrmion Hall effect. As the drive increases, a series of dynamical structural transitions occur in the flowing skyrmion lattice similar to those observed in the compression dynamics of crystals. These transitions correspond to reductions in the number of flowing rows of skyrmions due to the collective motion of the skyrmions into the pinned region, and they are accompanied by a series of steps in the velocity force curves leading to a negative differential conductivity. When the number of pinning sites is sufficiently large, a drive-induced pinning effect can occur in which the skyrmion Hall effect forces all of the skyrmions to enter the strongly pinned region. This reentrant pinning effect becomes more pronounced for increasing intrinsic skyrmion Hall angle and larger pinning sites.

Skyrmion phase and competing magnetic orders on a breathing kagom\xe9 lattice

Magnetic skyrmion textures are realized mainly in non-centrosymmetric, e.g. chiral or polar, magnets. Extending the field to centrosymmetric bulk materials is a rewarding challenge, where the released helicity/vorticity degree of freedom and higher skyrmion density result in intriguing new properties and enhanced functionality. We report here on the experimental observation of a skyrmion lattice (SkL) phase with large topological Hall effect and an incommensurate helical pitch as small as 2.8 nm in metallic Gd3Ru4Al12, which materializes a breathing kagomé lattice of Gadolinium moments. The magnetic structure of several ordered phases, including the SkL, is determined by resonant x-ray diffraction as well as small angle neutron scattering. The SkL and helical phases are also observed directly using Lorentz-transmission electron microscopy. Among several competing phases, the SkL is promoted over a low-temperature transverse conical state by thermal fluctuations in an intermediate range of magnetic fields.

Skyrmion Crystals in Frustrated Shastry–Sutherland Magnets

The phase diagrams of the frustrated classical spin model with the Dzyaloshinskii–Moriya (DM) interaction on the Shastry–Sutherland lattice are studied by means of Monte Carlo simulations. For ferromagnetic next‐nearest‐neighboring (J2) interactions, the introduced exchange frustration enhances the effect of the DM interaction, which enlarges the magnetic field‐range with the skyrmion lattice phase and increases the skyrmion density. For antiferromagnetic J2 interactions, the so‐called 2q phase (two‐sublattice skyrmion crystal) and the spin‐flop phase are observed, and their stabilizations are closely dependent on the DM interaction and J2 interaction, respectively. The simulated results are qualitatively explained from the energy competitions among these couplings, which provide an important guidance for finding skyrmion crystals in frustrated magnets.

Weak coupling theory of topological Hall effect

Topological Hall effect (THE) caused by a noncoplanar spin texture characterized by a scalar spin chirality is often described by the Berry phase, or the associated effective magnetic field. This picture is appropriate when the coupling, $M$, of conduction electrons to the spin texture is strong (strong-coupling regime) and the adiabatic condition is satisfied. However, in the weak-coupling regime, where the coupling $M$ is smaller than the electrons' scattering rate, the adiabatic condition is not satisfied and the Berry phase picture does not hold. In such a regime, the relation of the effective magnetic field to the spin texture can be "nonlocal", in contrast to the "local" relation in the strong coupling case. Focusing on the case of continuous but general spin texture, we investigate the THE in various characteristic regions in the weak-coupling regime, namely, (1) diffusive and local, (2) diffusive and nonlocal, and (3) ballistic. In the presence of spin relaxation, there arise two more regions in the "weakest-coupling" regime: (1') diffusive and local, and (2') diffusive and nonlocal. We derived the analytic expression of the topological Hall conductivity (THC) for each region, and found that the condition for the locality of the effective field is governed by transverse spin diffusion of electrons. In region 1, where the spin relaxation is negligible and the effective field is local, the THC is found to be proportional to $M$, instead of $M^3$ of the weakest-coupling regime. In the diffusive, nonlocal regions (2 and 2'), the effective field is given by a spin chirality formed by "effective spins" that the electrons see during their diffusive motion. Applying the results to a skyrmion lattice, we found the THC decreses as the skyrmion density is increased in region 2', reflecting the nonlocality of the effective field, and shows a maximum at the boundary to the "local" region.

Nonlinear transport, dynamic ordering, and clustering for driven skyrmions on random pinning

Using numerical simulations, we examine the nonlinear dynamics of skyrmions driven over random pinning. For weak pinning, the skyrmions depin elastically, retaining sixfold ordering; however, at the onset of motion there is a dip in the magnitude of the structure factor peaks due to a decrease in positional ordering, indicating that the depinning transition can be detected using the structure factor even within the elastic depinning regime. At higher drives the moving skyrmion lattice regains full ordering. For increasing pinning strength, we find a transition from elastic to plastic depinning that is accompanied by a sharp increase in the depinning threshold due to the proliferation of topological defects, similar to the peak effect found at the elastic to plastic depinning transition in superconducting vortex systems. For strong pinning and strong Magnus force, the skyrmions in the moving phase can form a strongly clustered or phase separated state with highly modulated skyrmion density, similar to that recently observed in continuum-based simulations for strong disorder. As the Magnus force is decreased, the density phase separated state crosses over to a dynamically phase separated state with uniform density but with flow localized in bands of motion, while in the strongly damped limit, both types of phase separated states are lost. In the strong pinning limit, we find highly nonlinear velocity-force curves in the transverse and longitudinal directions, along with distinct regions of negative differential conductivity in the plastic flow regime. The negative differential conductivity is absent in the overdamped limit. The Magnus force is responsible for both the negative differential conductivity and the clustering effects, since it causes faster moving skyrmions to partially rotate around slower moving or pinned skyrmions.

The evolution of skyrmions in Ir/Fe/Co/Pt multilayers and their topological Hall signature

The topological Hall effect (THE) is the Hall response to an emergent magnetic field, a manifestation of the skyrmion Berry-phase. As the magnitude of THE in magnetic multilayers is an open question, it is imperative to develop comprehensive understanding of skyrmions and other chiral textures, and their electrical fingerprint. Here, using Hall-transport and magnetic-imaging in a technologically viable multilayer film, we show that topological-Hall resistivity scales with the isolated-skyrmion density over a wide range of temperature and magnetic-field, confirming the impact of the skyrmion Berry-phase on electronic transport. While we establish qualitative agreement between the topological-Hall resistivity and the topological-charge density, our quantitative analysis shows much larger topological-Hall resistivity than the prevailing theory predicts for the observed skyrmion density. Our results are fundamental for the skyrmion-THE in multilayers, where interfacial interactions, multiband transport and non-adiabatic effects play an important role, and for skyrmion applications relying on THE.