Stabilization mechanisms of magnetic skyrmion crystal and multiple-$Q$ states based on momentum-resolved spin interactions

Abstract

Multiple-$Q$ states as represented by a magnetic skyrmion crystal and hedgehog crystal have been extensively studied in recent years owing to their unconventional physical properties. The materials hosting multiple-$Q$ states have been so far observed in a variety of lattice structures and chemical compositions, which indicates rich stabilization mechanisms inducing the multiple-$Q$ states. We review recent developments in the research of the stabilization mechanisms of such multiple-$Q$ states with an emphasis on the microscopic spin interactions in momentum space. We show that an effective momentum-resolved spin model is a canonical model for not only understanding the microscopic origin of various multiple-$Q$ states but also exploring further exotic multiple-$Q$ states with topological properties. We introduce several key ingredients to realize the magnetic skyrmion crystal with the skyrmion numbers of one and two, hedgehog crystal, meron-antimeron crystal, bubble crystal, and other multiple-$Q$ states. We also review that the effective spin model can be used to reproduce the magnetic phase diagram in experiments efficiently.

arXiv comment103 pages, 22 figures, 3 tables; To appear in Materials Today Quantum

References in corpus (240)

• Berry Phase Effects on Electronic Properties
• Skyrmion Lattice in a Chiral Magnet
• Anomalous Hall effect
• Advances in the Physics of Magnetic Skyrmions and Perspective for Technology
• Spin current and magneto-electric effect in non-collinear magnets
• Spontaneous Skyrmion Ground States in Magnetic Metals
• Topological Hall effect in the A-phase of MnSi
• Blowing Magnetic Skyrmion Bubbles
• Ferroelectricity in spiral magnets
• Role of the Dzyaloshinskii-Moriya interaction in multiferroic perovskites
• Spin Transfer Torques in MnSi at Ultra-low Current Densities
• Direct Observation of the Skyrmion Hall Effect
• Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions
• Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet
• Discovery of Magnetic Antiskyrmions Beyond Room Temperature in Tetragonal Heusler Materials
• Skyrmion Lattice in a Doped Semiconductor
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles
• Spin Anisotropy and Quantum Hall Effect in the Kagome Lattice - Chiral Spin State based on a Ferromagnet-
• Multiple-q states and skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields
• Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet
• Berry Phase Theory of Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites
• A new class of chiral materials hosting magnetic skyrmions beyond room temperature
• Long wavelength helimagnetic order and skyrmion lattice phase in Cu2OSeO3
• Spin-Wave Modes and Their Intense Excitation Effects in Skyrmion Crystals
• Skyrmion phase and competing magnetic orders on a breathing kagome lattice
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Skyrmions and Anomalous Hall Effect in a Dzyloshinskii-Moriya Spiral Magnet
• Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet
• Observation of magnetic excitations of skyrmion crystal in a helimagnetic insulator
• Current-induced skyrmion generation and dynamics in symmetric bilayers
• Orbital ferromagnetism and anomalous Hall effect in antiferromagnets on distorted fcc lattice
• Field-free deterministic ultra fast creation of skyrmions by spin orbit torques
• Ginzburg-Landau theory for skyrmions in inversion-symmetric magnets with competing interactions
• Robust metastable skyrmions and their triangular-square lattice-structural transition in a high-temperature chiral magnet
• Stabilization of Skyrmion textures by uniaxial distortions in noncentrosymmetric cubic helimagnets
• Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy
• Control and manipulation of a magnetic skyrmionium in nanostructures
• Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets
• Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnets
• Chirality driven anomalous Hall effect in weak coupling regime
• Chiral skyrmions in cubic helimagnet films: the role of uniaxial anisotropy
• Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi
• Magnetic phase diagram of MnSi inferred from magnetization and ac susceptibility
• Spontaneous skyrmionic lattice from anisotropic symmetric exchange in a Ni-halide monolayer
• Creation and confirmation of Hopfions in magnetic multilayer systems
• Real-space observation of short-period cubic lattice of skyrmions in MnGe
• Formation and rotation of skyrmion crystal in the chiral-lattice insulator Cu2OSeO3
• Fractional antiferromagnetic skyrmion lattice induced by anisotropic couplings
• Electronic Orbital Currents and Polarization in Mott Insulators
• Quantized Anomalous Hall Effects in Skyrmion Crystal
• Compact Skyrmions, Merons and Bimerons in Thin Chiral Magnetic Films
• Bubble and Skyrmion Crystals in Frustrated Magnets with Easy-Axis Anisotropy
• Néel-type skyrmion lattice in tetragonal polar magnet VOSe${}_2$O${}_5$
• Topological Magnetic Phase in the Candidate Weyl Semimetal CeAlGe
• Hidden Multiple-spin Interactions as an Origin of Spin Scalar Chiral Order in Frustrated Kondo Lattice Models
• Antiferromagnetic skyrmion crystals: generation, topological Hall and topological spin Hall effect
• Versatile helimagnetic phases under magnetic fields in cubic perovskite SrFeO3
• Topological-chiral magnetic interactions driven by emergent orbital magnetism
• Enhanced Stability of Skyrmions in Two-Dimensional Chiral Magnets with Rashba Spin-Orbit Coupling
• Honeycomb-lattice Heisenberg-Kitaev model in a magnetic field: Spin canting, metamagnetism, and vortex crystals
• Specific heat of the skyrmion lattice phase and field-induced tricritical point in MnSi
• Topological Magnons and Edge States in Antiferromagnetic Skyrmion Crystals
• Long-range crystalline nature of the skyrmion lattice in MnSi
• Skyrmion knots in frustrated magnets
• Binding a Hopfion in Chiral Magnet Nanodisk
• Giant Skyrmions Stabilized by Dipole-Dipole Interactions in Thin Ferromagnetic Films
• Hopfions in chiral magnets
• Robust Zero-Field Skyrmion Formation in FeGe Epitaxial Thin Films
• Magnetic anisotropy, first-order-like metamagnetic transitions and large negative magnetoresistance in the single crystal of Gd${}_2$PdSi${}_3$
• Spiral spin-liquid and the emergence of a vortex-like state in MnSc${}_2$S${}_4$
• Meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets
• Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures
• Possible chiral phase transition in two-dimensional solid ${}^3$He
• Three-sublattice Skyrmion crystal in the antiferromagnetic triangular lattice
• Topological Nernst effect of the two-dimensional skyrmion lattice
• Skyrmion Logic System for Large-Scale Reversible Computation
• Theory of helical spin crystals: phases, textures and properties
• Imaging the coupling between itinerant electrons and localised moments in the centrosymmetric skyrmion magnet GdRu2Si2
• Unique Helical Magnetic Order and Field-Induced Phase in Trillium Lattice Antiferromagnet EuPtSi
• Square skyrmion crystal in centrosymmetric itinerant magnets
• Vortex Crystals with Chiral Stripes in Itinerant Magnets
• Spin-orbit physics of j=1/2 Mott insulators on the triangular lattice
• Emergent topological spin structures in a centrosymmetric cubic perovskite
• Chiral CP^2 skyrmions in three-band superconductors
• Stability of spontaneous quantum Hall state in the Triangular Kondo-lattice model
• Multiple-Q Instability by (d-2)-dimensional Connections of Fermi Surfaces
• Nanometric skyrmion lattice from anisotropic exchange interactions in a centrosymmetric host
• Towards a Microscopic Model of Magnetoelectric Interactions in Ni3V2O8
• Thermodynamically stable skyrmion lattice in tetragonal frustrated antiferromagnet with dipolar interaction
• Role of higher-order exchange interactions for skyrmion stability
• Systematic derivation of realistic spin-models for beyond-Heisenberg solids
• Three-dimensional dynamics of magnetic hopfion driven by spin transfer torque
• Néel- and Bloch-Type Magnetic Vortices in Rashba Metals
• Skyrmions in Chiral Magnets with Rashba and Dresselhaus Spin-Orbit Coupling
• Anomalous Hall resistivity and possible topological Hall effect in the EuAl${}_4$ antiferromagnet
• Noncoplanar multiple-$Q$ spin textures by itinerant frustration: Effects of single-ion anisotropy and bond-dependent anisotropy
• Zoology of multiple-Q spin textures in a centrosymmetric tetragonal magnet with itinerant electrons
• Magnetic hedgehog lattices in noncentrosymmetric metals
• Effect of magnetic anisotropy on Skyrmions with a high topological number in itinerant magnets
• Z_2-vortex lattice in the ground state of the triangular Kitaev-Heisenberg model
• Theory of Topological Spin Hall Effect in Antiferromagnetic Skyrmion: Impact on Current-induced Motion
• Uniaxial pressure dependence of magnetic order in MnSi
• Formation mechanism of helical Q structure in Gd-based skyrmion materials
• Fractional quantum-Hall liquid spontaneously generated by strongly correlated t_2g electrons
• Efficient Langevin Simulation of Coupled Classical Fields and Fermions
• Stability of skyrmion lattices and symmetries of quasi-two-dimensional chiral magnets
• Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates
• Asymmetric isolated skyrmions in polar magnets with easy-plane anisotropy
• Multiple skyrmion crystal phases by itinerant frustration in centrosymmetric tetragonal magnets
• Vortices, skyrmions, and chirality waves in frustrated Mott insulators with a quenched periodic array of impurities
• Field-Direction Sensitive Skyrmion Crystals in Cubic Chiral Systems: Implication to $4f$-Electron Compound EuPtSi
• Novel magnetic orderings in the kagome Kondo-lattice model
• Frustration-induced insulating chiral spin state in itinerant triangular-lattice magnets
• Zero-temperature phases for chiral magnets in three dimensions
• Multi-step topological transitions among meron and skyrmion crystals in a centrosymmetric magnet
• Controllable chirality-induced geometrical Hall effect in a frustrated highly-correlated metal
• Degeneracy Lifting of Néel, Bloch, and Anti-Skyrmion Crystals in Centrosymmetric Tetragonal Systems
• Helical magnetic structure and the anomalous and topological Hall effects in epitaxial B20 Fe${}_{1-y}$Co${}_y$Ge films
• The chiral biquadratic pair interaction
• Charge-Density-Wave Order and Multiple Magnetic Transitions in Divalent Europium Compound EuAl${}_4$
• Magnetic vortex crystals in frustrated Mott insulator
• Discovery of magnetic single- and triple-Q states in Mn/Re(0001)
• Chirality waves in two-dimensional magnets
• Extension of the standard Heisenberg Hamiltonian to multispin exchange interactions
• Effective spin model in momentum space: Toward a systematic understanding of multiple-$Q$ instability by momentum-resolved anisotropic exchange interactions
• Noncoplanar magnetic ordering driven by itinerant electrons on the pyrochlore lattice
• The Double-$Q$ Ground State with Topological Charge Stripes in the Skyrmion Candidate ${\text{GdRu}}_{\text{2}}{\text{Si}}_{\text{2}}$
• Magnetoelastic Coupling and Phases in the Skyrmion Lattice Magnet Gd2PdSi3 Discovered by High-resolution Dilatometry
• Triangular antiferromagnet with nonmagnetic impurities
• Magnetic and transport anomalies in R2RhSi3 (R= Gd, Tb, and Dy), resembling those of an exotic magnetic skyrmion Gd2PdSi3
• Topological Hall signatures of magnetic hopfions
• Magnetic structure of monatomic Fe chains on Re(0001): emergence of chiral multi-spin interactions
• Face centered cubic and hexagonal close packed skyrmion crystals in centro-symmetric magnets
• Switchable Quantum Anomalous Hall state in a strongly frustrated lattice magnet
• Skyrmion crystal and spiral phases in centrosymmetric bilayer magnets with staggered Dzyaloshinskii-Moriya interaction
• Controlling the helicity of magnetic skyrmions in a $\beta$-Mn-type high-temperature chiral magnet
• Spin order and fluctuations in the EuAl${}_4$ and EuGa${}_4$ topological antiferromagnets: A $\mu$SR study
• Mean-field approach for skyrmion lattice in hexagonal frustrated antiferromagnets
• Cubic and non-cubic multiple-q states in the Heisenberg antiferromagnet on the pyrochlore lattice
• Probing the topology of the quantum analog of a classical skyrmion
• Kitaev-Heisenberg model in a magnetic field: order-by-disorder and commensurate-incommensurate transitions
• Helicity locking of square skyrmion crystal in a centrosymmetric lattice system without vertical mirror symmetry
• Spin-flux phase in the Kondo lattice model with classical localized spins
• Nonlinear nonreciprocal transport in antiferromagnets free from spin-orbit coupling
• Multi-Q mesoscale magnetism in CeAuSb${}_2$
• Rectangular and square skyrmion crystals on a centrosymmetric square lattice with easy-axis anisotropy
• Antiferromagnetism in EuNiGe3
• Prospecting chiral multi-site interactions in prototypical magnetic systems
• Hedgehog-lattice spin texture in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice
• Locking of skyrmion cores on a centrosymmetric discrete lattice: onsite versus offsite
• Semiclassical dynamics of spin density waves
• Engineered Chiral Skyrmion and Skyrmionium States by the Gradient of Curvature
• Spin excitation spectra in helimagnetic states: proper-screw, cycloid, vortex crystal, and hedgehog lattice
• Rhombic skyrmion lattice coupled with orthorhombic structural distortion in EuAl${}_4$
• Quantum oscillations in a centrosymmetric skyrmion-hosting magnet GdRu2Si2
• Fractional impurity moments in two-dimensional non-collinear magnets
• Insight into the electronic structure of the centrosymmetric skyrmion magnet GdRu${}_2$Si${}_2$
• Symmetry Analysis of Spin-Dependent Electric Dipole and Its Application to Magnetoelectric Effects
• Skyrmion crystal in the RKKY system on the two-dimensional triangular lattice
• Controlled Creation of Quantum Skyrmions
• First-principles Dzyaloshinskii-Moriya interaction in a non-collinear framework
• Three-Dimensional Crystallization of Vortex Strings in Frustrated Quantum Magnets
• Multifarious skyrmion phases on a trilayer triangular lattice
• Positron spectroscopy of point defects in the skyrmion-lattice compound MnSi
• Formation of a Topological Monopole Lattice and its Dynamics in Three-dimensional Chiral Magnets
• The dynamics of local magnetic moments induced by itinerant Weyl electrons
• 3D Dirac Electrons on a Cubic Lattice with Noncoplanar Multiple-Q Order
• Quantum Skyrmion Lattices in Heisenberg Ferromagnets
• Vacancy-induced spin textures and their interactions in a classical spin liquid
• Anisotropy driven response of skyrmion lattice in MnSc${}_2$S${}_4$ to applied magnetic fields
• Phase transitions between helices, vortices, and hedgehogs driven by spatial anisotropy in chiral magnets
• Short period magnetization texture of B20-MnGe explained by thermally fluctuating local moments
• Widely-sweeping magnetic field-temperature phase diagrams for skyrmion-hosting centrosymmetric tetragonal magnets
• Composite Spin Crystal Phase in Antiferromagnetic Chiral Magnets
• Kinetic small angle neutron scattering of the Skyrmion lattice in MnSi
• Emergent SU(3) magnons and thermal Hall effect in the antiferromagnetic skyrmion lattice
• Magnetic field-temperature phase diagrams for multiple-$Q$ magnetic orderings: Exact steepest descent approach to long-range interacting spin systems
• Exploring metamagnetism of single crystalline \eun\ by neutron scattering
• Chiral spin density wave order on frustrated honeycomb and bilayer triangle lattice Hubbard model at half-filling
• Multi-$Q$ hexagonal spin density waves and dynamically generated spin-orbit coupling: time-reversal invariant analog of the chiral spin density wave
• Engineering chiral density waves and topological band structures by multiple-$Q$ superpositions of collinear up-up-down-down orders
• Quantum solitons with emergent interactions in a model of cold atoms on the triangular lattice
• Multiple-scattering approach for multi-spin chiral magnetic interactions: Application to the one- and two-dimensional Rashba electron gas
• Broken discrete symmetries in a frustrated honeycomb antiferromagnet
• Itinerancy-dependent non-collinear spin textures in SrFeO3, CaFeO3, and CaFeO3/SrFeO3 heterostructures probed via resonant x-ray scattering
• Ab initio exploration of short-pitch skyrmion materials: Role of orbital frustration
• Distorted triangular skyrmion lattice in a noncentrosymmetric tetragonal magnet
• Magnon condensation with finite degeneracy on the triangular lattice
• Isolated Skyrmions in the $C{P}^2$ nonlinear $\sigma$-model with a Dzyaloshinskii-Moriya type interaction
• Dynamical Switching of Magnetic Topology in Microwave-Driven Itinerant Magnet
• Skyrmion crystals in centrosymmetric triangular magnets under hexagonal and trigonal single-ion anisotropy
• Skyrmion and Tetarton Lattices in Twisted Bilayer Graphene
• Topological phase transition driven by magnetic field and topological Hall effect in an antiferromagnetic skyrmion lattice
• Temperature-driven transition from skyrmion to bubble crystals in centrosymmetric itinerant magnets
• $\mathbb{C}{P}^2$ Skyrmion Crystals in an SU(3) Magnet with a Generalized Dzyaloshinskii-Moriya Interaction
• CP${}^2$ Skyrmions and Skyrmion Crystals in Realistic Quantum Magnets
• Topological semimetal-to-insulator phase transition between noncollinear and noncoplanar multiple-Q states on a square-to-triangular lattice
• Engineering Dzyaloshinskii-Moriya interaction in B20 thin film chiral magnets
• Single helicity of the triple-$q$ triangular skyrmion lattice state in cubic chiral helimagnet EuPtSi
• Antiferromagnetic Skyrmions and Skyrmion Density Wave in Rashba Hund's Insulator
• Square skyrmion crystal in centrosymmetric systems with locally inversion-asymmetric layers
• Creation of nanometric magnetic skyrmions by global application of circularly polarized microwave magnetic field
• Shape of magnetic domain walls formed by coupling to mobile charges
• Multiple-$Q$ magnetic orders in Rashba-Dresselhaus metals
• Theoretical investigation of antiferromagnetic skyrmions in a triangular monolayer
• Triple-$q$ quadrupole-octupole order scenario for PrV${}_2$Al${}_{20}$
• Skyrmion lattice in centrosymmetric magnets with local Dzyaloshinsky-Moriya interaction
• Engineering antiferromagnetic skyrmions and antiskyrmions at metallic interfaces
• Triple-$\mathcal{Q}$ partial magnetic orders induced by quadrupolar interactions: Triforce order scenario for UNi${}_4$B
• Skyrmion and vortex crystals in the Hubbard model
• Noncollinear magnetic ordering in a frustrated magnet: Metallic regime and the role of frustration
• Dimension transcendence and anomalous charge transport in magnets with moving multiple-$Q$ spin textures
• Symmetry analysis of light-induced magnetic interactions via Floquet engineering
• Highly Efficient Induction of Spin Polarization by Circularly-Polarized Electromagnetic Waves in the Rashba Spin-Orbit Systems
• Hedgehog lattice and field-induced chirality in breathing-pyrochlore Heisenberg antiferromagnets
• Machine learning assisted derivation of effective low energy models for metallic magnets
• Ferrochiral, antiferrochiral, and ferrichiral skyrmion crystals in an itinerant honeycomb magnet
• SP-STM study of the multi-Q phases in GdRu2Si2
• Stability of Skyrmion Crystal Phase in Centrosymmetric Distorted Triangular-Lattice Antiferromagnets
• Anisotropic spin model and multiple-$Q$ states in cubic systems
• Skyrmion crystal under $D_{3h}$ point group: Role of out-of-plane Dzyaloshinskii-Moriya interaction
• Hidden Topological Transitions in Emergent Magnetic Monopole Lattices
• Skyrmion crystal with integer and fractional skyrmion numbers in a nonsymmorphic lattice structure with the screw axis
• Multipolar Skyrmion Crystals in Non-Kramers Doublet Systems
• Charge Order with a Noncoplanar Triple-Q Magnetic Order on a Cubic Lattice
• Multiple-$q$ dipole-quadrupole instability in spin-1 triangular-lattice systems
• Antiferro skyrmion crystal phases in a synthetic bilayer antiferromagnet under an in-plane magnetic field
• Magnetic bubble crystal in tetragonal magnets
• Hybrid skyrmion and anti-skyrmion phases in polar $C_{4v}$ systems
• Checkerboard bubble lattice formed by octuple-period quadruple-$Q$ spin density waves
• Theory of collective excitations in the quadruple-$Q$ magnetic hedgehog lattices
• Anisotropic skyrmion crystal on a centrosymmetric square lattice under an in-plane magnetic field
• Scalar spin chirality induced by a circularly polarized electric field in a classical kagome magnet
• Chern insulating state with double-$Q$ ordering wave vectors at the Brillouin zone boundary
• Engineering a skyrmion crystal in ferromagnetic/antiferromagnetic bilayers free from the DM interaction
• Three-sublattice antiferro-type and ferri-type skyrmion crystals in centrosymmetric magnets
• Field-direction-dependent skyrmion crystals in noncentrosymmetric cubic magnets: A comparison between point groups $(O,T)$ and $T_{\mathrm{d}}$
• Field-induced transformation between triangular and square skyrmion crystals in a tetragonal polar magnet
• Tuning skyrmions in B20 compounds by 4d and 5d doping

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