Skyrmion Crystal Research Articles

Coupling characteristics of optical skyrmions based on localized spoof plasmons (LSP)

In this work, we theoretically investigate the coupling characteristics of optical skyrmions based on localized spoof plasmons (LSPs). First, the single LSP optical skyrmion is realized and resonance modes attributed to different topological features are analyzed. Second, the coupling effect is observed through decreasing the distance between the adjacent LSP optical skyrmions. The coupling LSP optical skyrmions can preserve the topological behaviors, and particularly, three coupling modes (mode-a, mode-b, and mode-c) can be observed. Mode-a presents uniform magnetic field distributions, while mode-b and mode-c can be observed with asymmetric magnetic field distributions. Finally, the ten-coupling LSP optical skyrmions supported by space-coiling cylinders and square structures are realized and the robust topological features are discussed. The results may contribute to the future investigation on designing optical skyrmion crystals and advanced optical devices.

Quadruple-Q Skyrmion Crystal in Centrosymmetric Body-Centered Tetragonal Magnets

We conduct a numerical investigation into the stability of a quadruple-Q skyrmion crystal, a structure generated by the superposition of four spin density waves traveling in distinct directions within three-dimensional space, hosted on a centrosymmetric body-centered tetragonal lattice. Using simulated annealing applied to an effective spin model that includes momentum-resolved bilinear and biquadratic interactions, we construct a magnetic phase diagram spanning a broad range of model parameters. Our study finds that a quadruple-Q skyrmion crystal does not emerge within the phase diagram when varying the biquadratic interaction and external magnetic field. Instead, three distinct quadruple-Q states with topologically trivial spin textures are stabilized. However, we demonstrate that the quadruple-Q skyrmion crystal can become the ground state when an additional high-harmonic wave–vector interaction is considered. Depending on the magnitude of this interaction, we obtain two types of quadruple-Q skyrmion crystals exhibiting the skyrmion numbers of one and two. These findings highlight the emergence of diverse three-dimensional multiple-Q spin states in centrosymmetric body-centered tetragonal magnets.

Dipolar wavevector interference induces a polar skyrmion lattice in strained BiFeO3 films.

Skyrmions can form regular arrangements, so-called skyrmion crystals (SkXs). A mode with multiple wavevectors q then describes the arrangement. While magnetic SkXs, which can emerge in the presence of Dzyaloshinskii-Moriya interaction, are well established, polar skyrmion lattices are still elusive. Here we report the observation of polar SkXs with a well-defined double-q state in ultrathin BiFeO3 films on LaAlO3. The compressive strain induced by the LaAlO3 substrate yields a dipolar topological texture with a periodic arrangement of skyrmions. The square-like superstructure with a lattice constant of 2.68 nm features a periodic modulation of polarization fields and topological charge density. The film furthermore exhibits an enhanced electromechanical response with an increased converse piezoelectric coefficient (d33) compared with SkX-free films. Transmission electron microscopy experiments in combination with phase-field simulations indicate that the dipole skyrmion texture results from the interference of two orthogonal single-q dipole patterns. We anticipate that the interference of multiple wavevectors may lead to a diversity of topological crystals with a variety of symmetries and lattice constants.

Exploring topological spin order by inverse Hamiltonian design: A stabilization mechanism for square skyrmion crystals

Exploring topological spin order by inverse Hamiltonian design: A stabilization mechanism for square skyrmion crystals

A $C^\ast$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals

Understanding the interaction of real- and reciprocal space topology in skyrmion crystals is an open problem. We approach it from the viewpoint of C^\astC*-algebras and calculate all admissible Chern numbers of a strongly coupled tight-binding skyrmion system on a triangular lattice as a function of Fermi energy and texture parameters. Our analysis reveals the topological complexity of electronic states coupled to spin textures, and the failure of the adiabatic picture to account for it in terms of emergent electromagnetism. On the contrary, we explain the discontinuous jumps in the real-space winding number in terms of collective evolution in real-, reciprocal, and mixed space Chern numbers. Our work sets the stage for further research on topological dynamics in complex dynamic spin textures coupled to external fields.

Low-lying magnon frequency comb in skyrmion crystals

Low-lying magnon frequency comb in skyrmion crystals

Multipolar Skyrmion Crystals in Non-Kramers Doublet Systems.

We study the Kondo lattice model of multipolar magnetic moments interacting with conduction electrons on a triangular lattice. Bond-dependent electron hoppings induce a compasslike anisotropy in the effective Ruderman-Kittel-Kasuya-Yosida interaction between multipolar moments. This unique anisotropy stabilizes multipolar skyrmion crystals at zero magnetic field. In a unit cell, the skyrmion fractionalizes into meron composites subject to the conservation of total topological charge. Diverse multipolar phases in the phase diagram give rise to novel spontaneous Hall response of conduction electrons.

Stability of Noncentrosymmetric Square Skyrmion Crystals with Easy-Axis and Easy-Plane Magnetic Anisotropy

We investigate the stability tendency of a magnetic skyrmion crystal in noncentrosymmetric tetragonal systems with the Dzyaloshinskii–Moriya interaction. We show that the stability region of the square skyrmion crystal on a square lattice depends on the Ising-type magnetic anisotropic interaction by performing the simulated annealing for the spin model. The easy-axis anisotropic interaction tends to narrow the region where the square skyrmion crystal is stabilized when the magnetic field is applied in the out-of-plane direction. In contrast, the easy-plane anisotropic interaction tends to enlarge the stability region. Meanwhile, the square skyrmion crystal induced by the easy-axis anisotropic interaction is robust compared with that induced by the easy-plane anisotropic interaction when the magnetic field is tilted from the out-of-plane to the in-plane direction. The results indicate that the instability toward the square skyrmion crystal in noncentrosymmetric crystals is sensitive to both magnetic anisotropy and magnetic fields.

Short-Period Skyrmion Crystals in Itinerant Body-Centered Tetragonal Magnets

In this study, we investigate the stability of a magnetic skyrmion crystal with short-period magnetic modulations in a centrosymmetric body-centered tetragonal system. By performing the simulated annealing for the spin model, incorporating the effects of the biquadratic interaction and high-harmonic wave–vector interaction in momentum space, we find that the double-Q square skyrmion crystal consisting of two spin density waves is stabilized in an external magnetic field. We also show that double-Q states appear in both low- and high-field regions; the low-field spin configuration is characterized by an anisotropic double-Q modulation consisting of a superposition of the spiral wave and sinusoidal wave, while the high-field spin configuration is characterized by an isotropic double-Q modulation consisting of a superposition of two sinusoidal waves. Furthermore, we show that the obtained multiple-Q instabilities can be realized for various ordering wave vectors. The results provide the possibility of realizing the short-period skyrmion crystals under the body-centered tetragonal lattice structure.

Breakdown of Volterra's Elasticity Theory of Dislocations in Polar Skyrmion Lattices.

Emerging polar skyrmion crystals (SkX) have raised much interest for technological applications owing to their nontrivial topologies of electric dipoles, quasiparticle-like behaviors, and unique electrical responses. Understanding SkX defects, especially dislocations, is crucial for their unique lattice dynamics and responses; however, it still remains elusive. Here, we have not only demonstrated that a SkX dislocation exhibits an anomalously deformed core structure with over 50% elongation of skyrmions but also discovered that Volterra's elasticity theory of dislocation is broken down in SkX. Our phase-field simulation reveals that these distinct features of SkX dislocation arise from a rigid to soft quasiparticle transition of skyrmions depending on the electric field and temperature. In SkX, there exist inherent mechanics that mitigate the mismatch by both migration and deformation of skyrmions. This work provides novel insights into a new class of lattice mechanics and related functionality arising from the unique properties of quasi-particle SkX.

Antiferro skyrmion crystals consisting of skyrmions and anti-skyrmions on a bilayer square lattice

An antiferro-type skyrmion crystal consisting of skyrmions with a negative topological charge and antiskyrmions with a positive topological charge manifests itself in its peculiar topological magnetism. We theoretically investigate the emergence of such an antiferro-type skyrmion crystal, where the topological charge exists in each sublattice but vanishes in the whole system. By performing the simulated annealing for an effective spin model with competing exchange interactions and staggered Dzyaloshinskii-Moriya interaction in momentum space on a bilayer square lattice, we find that the synergy between the antiferromagnetic interlayer exchange interaction and high-harmonic wave-vector interaction in addition to the staggered Dzyaloshinskii-Moriya interaction results in the antiferro-type skyrmion crystal in an external magnetic field. We show that the antiferro-type skyrmion crystal turns into the ferro-type skyrmion crystal with the same topological charge for both layers when the magnitude of the external magnetic field is varied. We also demonstrate that the competing interactions between ordering wave-vector channels and their high-harmonic wave-vector channels are essential in stabilizing the antiferro-type skyrmion crystal. Our results provide important ingredients to realize the antiferro-type skyrmion crystal by the external magnetic field, which can be utilized for low-power and high-speed spintronic devices based on antiferromagnetic materials.

Stability and deformation of a vacancy defect in skyrmion crystal under external magnetic and temperature fields

Skyrmion, a local bubble-like topological magnetization structure, can collectively emergent in magnets in a lattice form skyrmion crystal (SkX). SkX has great application potential in functional devices because it can manipulate material properties via coupling with atomic lattices. The lattice defects such as vacancy widely exist in the SkX as well, and they have rich dynamic behaviors and have great implications for the host material. However, although the nature of ideal SkX is well studied, the characteristics of SkX defects are relatively underdeveloped. Here, we deeply studied the structural properties of a vacancy defect in the SkX by a thermodynamic phase-field simulation. We found that the higher external magnetic and temperature fields favor rigid skyrmions (crystal), in which the SkX vacancy is less deformed, while the lower fields favor softer skyrmions where the SkX vacancy structure is considerably deformed. Such unique deformation and stability of the SkX vacancy are mainly the results of the competition between free energies in the view of thermodynamics. Our study demonstrated that the external field-controlled static properties of SkX vacancy highly depend on the quasiparticle nature of skyrmions. This indicates the properties of SkX defects can be controlled by the SkX features under different fields, which should open an avenue for the study and design of smart materials and advanced devices by engineering skyrmion crystals.

Sliding Dynamics of Current-Driven Skyrmion Crystal and Helix in Chiral Magnets.

The skyrmion crystal (SkX) and helix (HL) phases, present in typical chiral magnets, can each be considered as forms of density waves but with distinct topologies. The SkX exhibits gyrodynamics analogous to electrons under a magnetic field, while the HL state resembles topological trivial spin density waves. However, unlike the charge density waves, the theoretical analysis of the sliding motion of SkX and HL remains unclear, especially regarding the similarities and differences in sliding dynamics between these two spin density waves. In this Letter, we systematically explore the sliding dynamics of SkX and HL in chiral magnets in the limit of large current density. We demonstrate that the sliding dynamics of both SkX and HL can be unified within the same theoretical framework as density waves, despite their distinct microscopic orders. Furthermore, we highlight the significant role of gyrotropic sliding induced by impurity effects in the SkX state, underscoring the impact of nontrivial topology on the sliding motion of density waves. Our theoretical analysis shows that the effect of impurity pinning is much stronger in HL compared with SkX, i.e., χ^{SkX}/χ^{HL}∼α^{2} (χ^{SkX}, χ^{HL}: susceptibility to the impurity potential, α (≪1) is the Gilbert damping). Moreover, the velocity correction is mostly in the transverse direction to the current in SkX. These results are further substantiated by realistic Landau-Lifshitz-Gilbert simulations.

Dynamical generation of skyrmion and bimeron crystals by a circularly polarized electric field in frustrated magnets

Dynamical generation of skyrmion and bimeron crystals by a circularly polarized electric field in frustrated magnets

Skyrmion crystal formation and temperature–magnetic-field phase diagram of the frustrated triangular lattice Heisenberg magnet with easy-axis magnetic anisotropy

Skyrmion crystal formation and temperature–magnetic-field phase diagram of the frustrated triangular lattice Heisenberg magnet with easy-axis magnetic anisotropy

Baby skyrmion crystals stabilized by vector mesons

In this letter we study soliton crystals in the (2+1)-dimensional analogue model of the (3+1)-dimensional Adkins–Nappi model of nuclear physics. The baby ω-Skyrme model studied here is an O(3) nonlinear σ model coupled to a massive vector meson, the ω-meson. Using recently developed methods in the (3+1)-dimensional ω-Skyrme model we are able to construct soliton crystals in this (2+1)-dimensional baby ω-Skyrme model. The resulting crystals form a hexagonal lattice structure and are qualitatively and quantitatively similar to crystals observed in the standard baby Skyrme model.

Skyrmion crystals stabilized by ω-mesons

We investigate the ground state crystalline structure of nuclear matter in the ω-meson variant of the Skyrme model. After minimizing energy with respect to variations of both the Skyrme field and the period lattice, we find four distinct periodic solutions which are similar to those found in the standard Skyrme model. We use these crystals to calculate coefficients in the Bethe-Weizsäcker semi-empirical mass formula and the compression modulus of infinite nuclear matter, and find a significant improvement as compared with other variants of the Skyrme model.

Topological magnons in a non-coplanar magnetic order on the triangular lattice

The bond-dependent Kitaev interaction K is familiar in the effective spin model of transition metal compounds with octahedral ligands. In this work, we find a peculiar non-coplanar magnetic order can be formed with the help of K and next-nearest neighbor Heisenberg coupling J 2 on the triangular lattice. It can be seen as a miniature version of skyrmion crystal, since it has nine spins and an integer topological number in a magnetic unit cell. The magnon excitations in such an order are studied by the linear spin-wave theory. Of note is that the change in the relative size of J 2 and K produces topological magnon phase transitions although the topological number remains unchanged. We also calculated the experimentally observable thermal Hall conductivity, and found that the signs of thermal Hall conductivity will change with topological phase transitions or temperature changes in certain regions.

Field-induced transformation between triangular and square skyrmion crystals in a tetragonal polar magnet

Field-induced transformation between triangular and square skyrmion crystals in a tetragonal polar magnet

Skyrmion lattice in centrosymmetric magnets with local Dzyaloshinsky–Moriya interaction

It is common for the local inversion symmetry to break in crystals, even though the whole crystal has global inversion symmetry. This local inversion symmetry breaking allows for a local Dzyaloshinsky–Moriya interaction (DMI) in magnetic crystals. Here we show that the local DMI can stabilize a skyrmion as a metastable excitation or as a skyrmion crystal in equilibrium. We consider the crystal structure with layered structure as an example, where local inversion is violated in each layer but a global inversion center exists in the middle of the two layers. These skyrmions come in pairs that are related by inversion symmetry. The two skyrmions with opposite helicity in a pair form a bound state. We study the properties of a skyrmion pair in the ferromagnetic background and determine the equilibrium phase diagram, where a robust lattice of skyrmion pairs is stabilized. Our results point to a new direction to search for the skyrmion lattice in centrosymmetric magnets.