Skyrmion Lattice Research Articles

Polyhexatic and polycrystalline states of skyrmion lattices

Abstract We report Monte Carlo studies of lattices of up to $10^{5}$ skyrmions treated as particles with negative core energy and repulsive interaction obtained from a microscopic spin model. Temperature dependence of translational and orientational correlations has been investigated for different experimental protocols and initial conditions. Cooling the skyrmion liquid from fully disordered high-temperature state results in the formation of a skyrmion polycrystal. A perfect skyrmion lattice prepared at $T=0$, on raising temperature undergoes a first-order melting transition into a polyhexatic state that consists of large orientationally ordered domains of fluctuating shape. On the further increasing temperature, these domains decrease in size, leading to a fully disordered liquid of skyrmions.

Monte Carlo studies of noncollinear magnetic phases in multiferroic Cu2OSeO3

Monte Carlo simulations based on a first-principles-derived Hamiltonian are conducted to study the finite-temperature properties of chiral-lattice multiferroic insulator ${\mathrm{Cu}}_{2}{\mathrm{OSeO}}_{3}$. The use of this numerical technique (i) reveals basic features of the phase diagram as a function of temperature and external magnetic field, including the long-range helical phase at low temperature and zero magnetic field and the skyrmion lattice phase, in which skyrmions are arranged in a two-dimensional hexagonal lattice, and (ii) leads to the discovery of an overlooked vortex lattice phase in a narrow pocket of the phase diagram near the fluctuations' disordered-helical phase transition. The scheme also provides strong numerical evidence that the transition to a helical state in ${\mathrm{Cu}}_{2}{\mathrm{OSeO}}_{3}$ is of first order driven by critical fluctuations.

Spontaneous Biskyrmion Lattice in a Centrosymmetric Rhombohedral Rare-Earth Magnet with Easy-Plane Anisotropy.

Magnetic skyrmion and its derivatives have demonstrated fascinating topological behaviors with potential applications in future spintronic devices. Despite the recent progress, the spontaneous skyrmion lattice and successive topological transition in the magnets with easy-plane magnetic anisotropy are still elusive especially at room temperature. Here, in a centrosymmetric rhombohedral Nd2Co17 magnet with easy-plane magnetic anisotropy, spontaneous biskyrmions are observed over a wide temperature range across room temperature, and then evolve into enclosed in-plane domains with nanometric size due to the enhancement of the planar magnetic anisotropy. The spontaneous generation of the biskyrmion lattice and its evolution along different crystal orientations demonstrate the crucial role of intrinsic bi-anisotropy and demagnetization effects. This discovery provides a fundamental insight into the nature of topological magnetic textures in easy-plane anisotropy materials and suggests an arena to explore the topological states in rare-earth magnets as well as their applications in spintronics.

Precursor skyrmion states near the ordering temperatures of chiral magnets.

In noncentrosymmetric magnets, chiral Dzyaloshinskii-Moriya interactions (DMI) provide a distinctive mechanism for the stabilization of localized skyrmion states in two and three dimensions with a fixed sense of rotation. Near the ordering transition, the skyrmion strings develop attractive skyrmion-skyrmion interactions and ultimately become confined in extended clusters or textures [A. O. Leonov and U. K. Rößler, Nanomaterials, 2023, 13, 891], which is a consequence of the coupling between the magnitude and the angular part of the order parameter. Multi-skyrmionic states built from isolated skyrmions (IS) can form multiple modulated magnetic phases that may underlie the exotic magnetic phenomena of "partial order" or the field-driven "A-phase" observed in MnSi and other cubic helimagnets. Based on the standard phenomenological Dzyaloshinskii model, we obtain numerically exact solutions for skyrmion lattices (SkL), formulate their basic properties, and elucidate physical mechanisms of their formation and stability. Our detailed numerical studies show that the bound skyrmion states arise as hexagonal lattices of ±π-skyrmions (with the magnetization in the center along or opposite to the magnetic field) or square staggered lattices of π/2-skyrmions, which contain defect lines with zero modulus value and thus may form thermodynamically stable states only near the ordering temperature. In the simplest case of a two-dimensional (2D) skyrmionic texture, the structure is homogeneous in the third dimension (3D). The skyrmions preserve an ideal axisymmetric "double twist" core in condensed phases, while continuation into a space-filling texture is frustrated. The evolution of skyrmion lattices in an increasing magnetic field leads to a succession of phase transitions of first or second kind between diverse textures and finally ends due to the formation of isolated skyrmion-filaments with fixed radius and shape embedded in a homogeneously magnetized matrix. In the framework of the phenomenological model including only isotropic interactions (exchange, Zeeman, and DM energy contributions), the considered skyrmion lattices are only metastable states as the competing conical one-dimensional spiral forms the equilibrium state. But due to the weak couplings between skyrmions, secondary effects like anisotropies can stabilize skyrmionic textures as compared to simple helices. Also the topological nature of skyrmion condensates makes the magnetization processes in chiral magnets history-dependent and hysteretic.

Strain-induced magnetic phase transition, magnetic anisotropy switching and bilayer antiferromagnetic skyrmions in van der Waals magnet CrTe2.

In recent years, considerable attention has been paid to the research of peculiar magnetism in two-dimensional (2D) van der Waals (vdW) layered materials. Here, we unveil the major features and deep physical mechanisms of a magnetic phase transition and magnetic anisotropy switching in monolayer CrTe2 and antiferromagnetic (AFM) skyrmions in bilayer CrTe2via first-principles calculations and micromagnetic simulations. We find that a magnetic phase transition from stripy-type AFM to ferromagnetic (FM) order can be induced by applying a tensile strain of 3%. More interestingly, the magnetic easy axis can be switched between in-plane and off-plane via adjusting the magnitude of strain. Besides, the topologically protected bilayer AFM skyrmion is stabilized by a large Dzyaloshinskii-Moriya interaction (DMI) of 1.43 meV and a skyrmion lattice can be induced by a magnetic field of 6.9 T at 100 K. Different from the monolayer magnetic skyrmion, the bilayer AFM skyrmion is more promising in spintronic nanodevices owing to the suppressed skyrmion Hall effect. Our findings clarify the underlying mechanisms of the strain-tunable magnetic phase transition, magnetic anisotropy switching and bilayer AFM skyrmions in vdW magnet CrTe2, and also highlight the promising applications of CrTe2 in next-generation information storage devices.

Instability of skyrmion lattice under microwave magnetic field due to single-q helimagnetic excitation mode

Composed of the three spiral magnetic vectors, the structure of skyrmion lattice (SkL) can be destructed by spin excitations in possibly two ways: one is to make decoherence of all the helices through the phase change of a certain spiral magnetic vector, and the other is to inhibit one or two spiral components while enhancing the others so that it becomes a magnetic structure of single or double magnetic vectors. Here, we present a micromagnetic study on the spin excitations of a two-dimensional SkL under the in-plane microwave magnetic field. By calculating the parameters describing the in-plane spin excitations mode, we find that the spin configuration tends to be an enhanced single-vector spiral magnetic structure due to the excitation modes under some specific frequencies so that the SkL will collapse to the topologically trivial state. Our results help to form a deeper understanding of the spin excitation in SkL under an ac magnetic field.

Skyrmion and meron ordering in quasi-two-dimensional chiral magnets

We revisit the well-known theoretical phase diagram for a two-dimensional chiral magnet with an easy-axis uniaxial anisotropy and an applied magnetic field. A particular emphasis is given to merons---quanta of the phase transition between the cycloid and the hexagonal skyrmion lattice, which possess fractional topological charges $\ifmmode\pm\else\textpm\fi{}1/2$. A localized state of two coupled merons with opposite topological charges exhibits the nonreciprocal current-driven dynamics: it experiences no skyrmion Hall effect, but due to the asymmetry of the attracting intermeron potential gives rise to asymmetric current-velocity characteristics. We also address the problem of skyrmion ordering into hexagonal and square skyrmion crystals. In an entire field range, the square lattice turns out a saddle point state between differently oriented hexagonal lattices. Merons separating elongated skyrmions were also shown to form a local energy minimum by forming a hexagonal lattice shadowing the ordinary lattice of skyrmions. In addition, we focus on the anisotropy-driven transformations of modulated phases and their isolated counterparts, which exist as detached branches of solutions on both sides from the critical anisotropy value. Moreover, a family of isolated skyrmions with both rotational senses can be found near this anisotropy value. Our results are useful from both the fundamental point of view, since they complement previous findings, and from the point of view of applications, since they provide guidelines for developing meron-based spintronic devices.

Topological Nernst effect emerging from real-space gauge field and thermal fluctuations in a magnetic skyrmion lattice

Recent studies on quantum transport in metals have revealed that a gauge field acting on the electron wavefunction yields a peculiar Hall or Nernst effect. When topologically nontrivial spin textures are present, a gauge field appears in real space and affects the electron transport. However, the understanding of the Nernst effect emerging from a real-space gauge field (topological Nernst effect) remains qualitative, and moreover, the influence of thermal fluctuations has been elusive. Here, we report a pronounced temperature-dependent topological Nernst effect in the metastable skyrmion lattice in MnSi. Our density functional theory, assuming a temperature-independent gauge field, is successful in an order-of-magnitude estimate of the Nernst signal, whereas the experimental values decrease more significantly with increasing temperature. A similar tendency is observed for the topological Hall effect, thus indicating that pronounced suppression of the real-space gauge field is crucial for the quantitative understanding of the quantum transport induced by topological spin textures at finite temperatures.

Topological electrostatics

We present a theory of optimal topological textures in nonlinear sigma-models with degrees of freedom living in the Grassmannian manifold. These textures describe skyrmion lattices of N-component fermions in a quantising magnetic field, relevant to the physics of graphene, bilayer and other multicomponent quantum Hall systems near integer filling factors ν > 1. We derive analytically the optimality condition, minimizing topological charge density fluctuations, for a general Grassmannian sigma model on a sphere and a torus, together with counting arguments which show that for any filling factor and number of components there is a critical value of topological charge above which there are no optimal textures. Below a solution of the optimality condition on a torus is unique, while in the case of a sphere one has, in general, a continuum of solutions corresponding to new non-Goldstone zero modes, whose degeneracy is not lifted (via a order from disorder mechanism) by any fermion interactions depending only on the distance on a sphere. We supplement our general theoretical considerations with the exact analytical results for the case of , appropriate for recent experiments in graphene.

Optimization strategies and artifacts of time-involved small-angle neutron scattering experiments.

Kinetic small-angle neutron scattering provides access to the microscopic properties of mesoscale systems under slow, periodic perturbations. By interlocking the phases of neutron pulse, sample modulation and detector signal, time-involved small-angle neutron scattering experiments (TISANE) allow one to exploit the neutron velocity spread and record data without major sacrifice in intensity at timescales down to microseconds. This article reviews the optimization strategies of TISANE that arise from specific aspects of the process of data acquisition and data analysis starting from the basic principles of operation. Typical artifacts of data recorded in TISANE due to the choice of time binning and neutron chopper pulse width are illustrated by virtue of the response of the skyrmion lattice in MnSi under periodic changes of the direction of the stabilizing magnetic field.

Magnetic Skyrmion Lattices in a Novel 2D‐Twisted Bilayer Magnet

AbstractMagnetic skyrmions are topologically protected spin swirling vertices, which are promising in device applications due to their particle‐like nature and excellent controlability. Magnetic skyrmions are extensively studied in a variety of materials and proposed to exist in the extreme 2D limit, i.e., in twisted bilayer CrI3 (TBCI). Unfortunately, the magnetic states of TBCIs with small twist angles are disorderly distributed ferromagnetic and antiferromagnetic (AFM) domains in recent experiments, and thus the method to get rid of disorders in TBCIs is highly desirable. Here, intralayer exchange interactions up to the third nearest neighbors without empirical parameters and very accurate interlayer exchange interactions are used to study the magnetic states of TBCIs. The functions of interlayer exchange interactions obtained using first‐principles calculations and stored in symmetry‐adapted artificial neural networks are proposed. Based on these, the subsequent Landau–Lifshitz–Gillbert equation calculations explain the disorderly distributed FM‐AFM domains in TBCIs with small twist angles and predict the orderly distributed skyrmions in TBCIs with large twist angles. This novel twisted 2D bilayer magnet can be used to design memory devices, monochromatic spin wave generators and many kinds of skyrmion lattices.

Transport properties of dipole skyrmions in amorphous Fe/Gd multilayers

Chiral magnets are known to possess interesting electromagnetic properties that result from the coupling of electrons with nontrivial magnetic phases, such as particle-like magnetic spin textures termed skyrmions. So far, it is unclear how the local and global chirality of magnetic spin textures contributes to the electromagnetic transport responses that have so far been observed. In this work, we focus on unraveling the contributions in the field-dependent longitudinal resistivity response that arises from magnetic spin textures in a centrosymmetric Fe/Gd multilayer that exhibits an array of magnetic phases ranging from stripe, mixed stripe-skyrmion, skyrmion lattice, and disordered skyrmion. Using a combination of transport measurements and micromagnetic simulations, we demonstrate a domain wall chirality reconfiguration occurs as the domain morphology transitions from disordered stripe to skyrmion lattice phase under applied fields that is responsible for the interesting transport responses noted in the field-dependent longitudinal resistivity.

Quantum skyrmion lattices in Heisenberg ferromagnets

Skyrmions are topological magnetic textures that can arise in non-centrosymmetric ferromagnetic materials. In most systems experimentally investigated to date, skyrmions emerge as classical objects. However, the discovery of skyrmions with nanometer length scales has sparked interest in their quantum properties. Here, we simulate the ground states of two-dimensional spin-$1/2$ Heisenberg lattices with Dzyaloshinskii-Moriya interactions and discover a broad region in the zero-temperature phase diagram which hosts quantum skyrmion lattices. We argue that the quantum skyrmion lattice phase can be detected experimentally in the magnetization profile via local magnetic polarization measurements as well as in the spin structure factor measurable via neutron scattering experiments. Finally, we explore the resulting quantum skyrmion state, analyze its real-space polarization profile and show that it is a non-classical state featuring entanglement between quasiparticle and environment mainly localized near the boundary spins of the skyrmion.

Topological thermal Hall effect of magnons in magnetic skyrmion lattice

Topological transports of fermions are governed by the Chern numbers of the energy bands lying below the Fermi energy. For bosons, e.g. phonons and magnons in a crystal, topological transport is dominated by the Chern number of the lowest energy band when the band gap is comparable to the thermal energy. Here, we demonstrate the presence of topological transport by bosonic magnons in a lattice of magnetic skyrmions - topological defects formed by a vortex-like texture of spins. We find a distinct thermal Hall signal in the magnetic skyrmion phase of an insulating polar magnet GaV4Se8, identified as the topological thermal Hall effect of magnons governed by the Chern number of the lowest energy band of the magnons in a triangular lattice of magnetic skyrmions. Our findings lay a foundation for studying topological phenomena of other bosonic excitations through thermal Hall probe.

Tuning of topological properties in the strongly correlated antiferromagnet Mn3Sn via Fe doping

Magnetic topological materials, in which strong correlations between magnetic and electronic properties of matter, give rise to various exotic phenomena such as anomalous Hall effect (AHE), topological Hall effect (THE), and skyrmion lattice. Here, we report on the electronic, magnetic, and topological properties of Mn$_{3-\it{x}}$Fe$_{\it{x}}$Sn single crystals ($\it{x}$=0, 0.25, and 0.35). Low temperature magnetic properties have been significantly changed with Fe doping. Most importantly, we observe that large uniaxial magnetocrystalline anisotropy that is induced by the Fe doping in combination with competing magnetic interactions at low temperature produce nontrivial spin-texture, leading to large topological Hall effect in the doped systems at low temperatures. Our studies further show that the topological properties of Mn$_{3-\it{x}}$Fe$_{\it{x}}$Sn are very sensitive to the Fe doping.

Vortex, stripe, Skyrmion lattice, and localized states in a spin–orbit coupled dipolar condensate

We investigate a spin-1/2 system containing both dipolar and non-dipolar components in a 52Cr Bose–Einstein condensate with spin–orbit coupling. Combined with energy analysis, phase diagram between contact interaction and Rashba spin–orbit coupling reveals four distinctive ground-state phases: vortex state phase, stripe phase, Skyrmion lattice phase, and localized Skyrmion phase. We adopt the condensate order parameter to characterize the supersolidity and topological charges of the quantum states of matter. In particular, we predict the emergence of a Skyrmion lattice phase with supersolidity which is justified by calculating the crystalline order. Moreover, we find that the critical value of the spin–orbit coupling from stripe to Skyrmion lattice increases with decreasing relative strength of the dipolar and contact interactions. Our results demonstrate the possibility for physicists to realize a wealth of controllable topological configurations in dipolar condensates, including Skyrmion lattices with both supersolidity and different topological charges adjusted by changing the strength of spin–orbit coupling. The topological phases we predict in this work can be realized by using state-of-the-art techniques in ultracold atomic experiments, such as using pulsed magnetic fields to induce and adjust spin–orbit couplings on atom chips of chromium, erbium, or dysprosium condensates.

Critical Temperature of a Superconductor/Ferromagnet Nanostructure near a Magnetic Skyrmion

Contact between a superconductor and a chiral ferromagnet containing complex magnetic structures (helical or conical texture, skyrmion, and chiral float) has been considered. The case of a single skyrmion has been studied more thoroughly. The influence of these magnetic inhomogeneities on the critical temperature becomes significant only for nanoscale spin structures (about 100 nm or smaller). Skyrmion lattices and single skyrmions of such sizes have recently been observed in experiments with thin magnetic layers. Within the proximity effect theory in the dirty limit, an approximate approach has been proposed to calculate the critical temperature in these systems. Great influence of nanoscale spin vortices on the critical temperature, in combination with topological stability and a low current density that is necessary for their motion, makes it possible to use these systems as efficient superconducting spin valves.

Magnetic ordering in GdAuAl[formula omitted]Ge[formula omitted] and TbAuAl[formula omitted]Ge[formula omitted]: Layered compounds with triangular lanthanide nets

We report the synthesis and magnetic properties of GdAuAl4Ge2 and TbAuAl4Ge2, where temperature and magnetic field dependent magnetization, heat capacity, and electrical resistivity measurements reveal that both compounds exhibit several magnetically ordered states at low temperatures, with evidence for magnetic fluctuations extending into the paramagnetic temperature region. For magnetic fields applied in the ab-plane there is particularly rich behavior, with several ordered state regions that are separated by metamagnetic phase transitions. Despite Gd being an isotropic S-state ion and Tb having an anisotropic J-state, there are similarities in the phase diagrams for the two compounds, suggesting that factors such as the symmetry of the crystalline lattice, which features well separated triangular planes of lanthanide ions, or the Ruderman–Kittel–Kasuya–Yosida interaction control the magnetism. We also point out similarities to other centrosymmetric compounds that host skyrmion lattices such as Gd2PdSi3, and propose that the LnAuAl4Ge2 family of compounds are of interest as reservoirs for complex magnetism and electronic behaviors.

Adaptive cognition implemented with a context-aware and flexible neuron for next-generation artificial intelligence.

Neuromorphic computing mimics the organizational principles of the brain in its quest to replicate the brain's intellectual abilities. An impressive ability of the brain is its adaptive intelligence, which allows the brain to regulate its functions "on the fly" to cope with myriad and ever-changing situations. In particular, the brain displays three adaptive and advanced intelligence abilities of context-awareness, cross frequency coupling, and feature binding. To mimic these adaptive cognitive abilities, we design and simulate a novel, hardware-based adaptive oscillatory neuron using a lattice of magnetic skyrmions. Charge current fed to the neuron reconfigures the skyrmion lattice, thereby modulating the neuron's state, its dynamics and its transfer function "on the fly." This adaptive neuron is used to demonstrate the three cognitive abilities, of which context-awareness and cross-frequency coupling have not been previously realized in hardware neurons. Additionally, the neuron is used to construct an adaptive artificial neural network (ANN) and perform context-aware diagnosis of breast cancer. Simulations show that the adaptive ANN diagnoses cancer with higher accuracy while learning faster and using a more compact and energy-efficient network than a nonadaptive ANN. The work further describes how hardware-based adaptive neurons can mitigate several critical challenges facing contemporary ANNs. Modern ANNs require large amounts of training data, energy, and chip area, and are highly task-specific; conversely, hardware-based ANNs built with adaptive neurons show faster learning, compact architectures, energy-efficiency, fault-tolerance, and can lead to the realization of broader artificial intelligence.

Skyrmion alignment and pinning effects in the disordered multiphase skyrmion material Co8Zn8Mn4

Underlying disorder in skyrmion materials may both inhibit and facilitate skyrmion reorientations and changes in topology. The identification of these disorder-induced topologically active regimes is critical to realizing robust skyrmion spintronic implementations, yet few studies exist for disordered bulk samples. Here, we employ small-angle neutron scattering (SANS) and micromagnetic simulations to examine the influence of skyrmion order on skyrmion lattice formation, transition, and reorientation dynamics across the phase space of a disordered polycrystalline Co$_{8}$Zn$_{8}$Mn$_{4}$ bulk sample. Our measurements reveal a new disordered-to-ordered skyrmion square lattice transition pathway characterized by the novel promotion of four-fold order in SANS and accompanied by a change in topology of the system, reinforced through micromagnetic simulations. Pinning responses are observed to dominate skyrmion dynamics in the metastable triangular lattice phase, enhancing skyrmion stabilization through a remarkable and previously undetected skyrmion memory effect which reproduces previous ordering processes and persists in zero field. These results uncover the cooperative interplay of anisotropy and disorder in skyrmion formation and restructuring dynamics, establishing new tunable pathways for skyrmion manipulation.