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.

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

References in corpus (136)

• 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
• Role of the Dzyaloshinskii-Moriya interaction in multiferroic perovskites
• Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions
• Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles
• A new class of chiral materials hosting magnetic skyrmions beyond room temperature
• Long wavelength helimagnetic order and skyrmion lattice phase in Cu2OSeO3
• 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
• Skyrmion fractionalization and merons in chiral magnets with easy-plane 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
• 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
• Néel-type skyrmion lattice in tetragonal polar magnet VOSe${}_2$O${}_5$
• Compact Skyrmions, Merons and Bimerons in Thin Chiral Magnetic Films
• Topological Magnetic Phase in the Candidate Weyl Semimetal CeAlGe
• Antiferromagnetic skyrmion crystals: generation, topological Hall and topological spin Hall effect
• Honeycomb-lattice Heisenberg-Kitaev model in a magnetic field: Spin canting, metamagnetism, and vortex crystals
• Topological Magnons and Edge States in Antiferromagnetic Skyrmion Crystals
• Skyrmion knots in frustrated magnets
• Giant Skyrmions Stabilized by Dipole-Dipole Interactions in Thin Ferromagnetic Films
• Meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets
• Theory of helical spin crystals: phases, textures and properties
• Imaging the coupling between itinerant electrons and localised moments in the centrosymmetric skyrmion magnet GdRu2Si2
• Square skyrmion crystal in centrosymmetric itinerant magnets
• Spin-orbit physics of j=1/2 Mott insulators on the triangular lattice
• Chiral CP^2 skyrmions in three-band superconductors
• Multiple-Q Instability by (d-2)-dimensional Connections of Fermi Surfaces
• Nanometric skyrmion lattice from anisotropic exchange interactions in a centrosymmetric host
• Thermodynamically stable skyrmion lattice in tetragonal frustrated antiferromagnet with dipolar interaction
• Noncoplanar multiple-$Q$ spin textures by itinerant frustration: Effects of single-ion anisotropy and bond-dependent anisotropy
• Anomalous Hall resistivity and possible topological Hall effect in the EuAl${}_4$ antiferromagnet
• Zoology of multiple-Q spin textures in a centrosymmetric tetragonal magnet with itinerant electrons
• Formation mechanism of helical Q structure in Gd-based skyrmion materials
• Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates
• Vortices, skyrmions, and chirality waves in frustrated Mott insulators with a quenched periodic array of impurities
• Multiple skyrmion crystal phases by itinerant frustration in centrosymmetric tetragonal magnets
• Novel magnetic orderings in the kagome Kondo-lattice model
• Frustration-induced insulating chiral spin state in itinerant triangular-lattice magnets
• Field-Direction Sensitive Skyrmion Crystals in Cubic Chiral Systems: Implication to $4f$-Electron Compound EuPtSi
• Multi-step topological transitions among meron and skyrmion crystals in a centrosymmetric magnet
• Degeneracy Lifting of Néel, Bloch, and Anti-Skyrmion Crystals in Centrosymmetric Tetragonal Systems
• Controllable chirality-induced geometrical Hall effect in a frustrated highly-correlated metal
• Charge-Density-Wave Order and Multiple Magnetic Transitions in Divalent Europium Compound EuAl${}_4$
• Discovery of magnetic single- and triple-Q states in Mn/Re(0001)
• 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
• Magnetoelastic Coupling and Phases in the Skyrmion Lattice Magnet Gd2PdSi3 Discovered by High-resolution Dilatometry
• The Double-$Q$ Ground State with Topological Charge Stripes in the Skyrmion Candidate ${\text{GdRu}}_{\text{2}}{\text{Si}}_{\text{2}}$
• 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
• Skyrmion crystal and spiral phases in centrosymmetric bilayer magnets with staggered Dzyaloshinskii-Moriya interaction
• Mean-field approach for skyrmion lattice in hexagonal frustrated antiferromagnets
• Spin order and fluctuations in the EuAl${}_4$ and EuGa${}_4$ topological antiferromagnets: A $\mu$SR study
• Probing the topology of the quantum analog of a classical skyrmion
• Helicity locking of square skyrmion crystal in a centrosymmetric lattice system without vertical mirror symmetry
• Nonlinear nonreciprocal transport in antiferromagnets free from spin-orbit coupling
• Rectangular and square skyrmion crystals on a centrosymmetric square lattice with easy-axis anisotropy
• Hedgehog-lattice spin texture in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice
• Prospecting chiral multi-site interactions in prototypical magnetic systems
• Semiclassical dynamics of spin density waves
• Locking of skyrmion cores on a centrosymmetric discrete lattice: onsite versus offsite
• 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
• Insight into the electronic structure of the centrosymmetric skyrmion magnet GdRu${}_2$Si${}_2$
• Skyrmion crystal in the RKKY system on the two-dimensional triangular lattice
• Symmetry Analysis of Spin-Dependent Electric Dipole and Its Application to Magnetoelectric Effects
• Controlled Creation of Quantum Skyrmions
• First-principles Dzyaloshinskii-Moriya interaction in a non-collinear framework
• Multifarious skyrmion phases on a trilayer triangular lattice
• Positron spectroscopy of point defects in the skyrmion-lattice compound MnSi
• Quantum Skyrmion Lattices in Heisenberg Ferromagnets
• The dynamics of local magnetic moments induced by itinerant Weyl electrons
• Anisotropy driven response of skyrmion lattice in MnSc${}_2$S${}_4$ to applied magnetic fields
• Short period magnetization texture of B20-MnGe explained by thermally fluctuating local moments
• Phase transitions between helices, vortices, and hedgehogs driven by spatial anisotropy in chiral magnets
• Widely-sweeping magnetic field-temperature phase diagrams for skyrmion-hosting centrosymmetric tetragonal 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
• Chiral spin density wave order on frustrated honeycomb and bilayer triangle lattice Hubbard model at half-filling
• Multiple-scattering approach for multi-spin chiral magnetic interactions: Application to the one- and two-dimensional Rashba electron gas
• Ab initio exploration of short-pitch skyrmion materials: Role of orbital frustration
• Distorted triangular skyrmion lattice in a noncentrosymmetric tetragonal magnet
• Dynamical Switching of Magnetic Topology in Microwave-Driven Itinerant Magnet
• Isolated Skyrmions in the $C{P}^2$ nonlinear $\sigma$-model with a Dzyaloshinskii-Moriya type interaction
• Skyrmion crystals in centrosymmetric triangular magnets under hexagonal and trigonal single-ion anisotropy
• CP${}^2$ Skyrmions and Skyrmion Crystals in Realistic Quantum Magnets
• Skyrmion and Tetarton Lattices in Twisted Bilayer Graphene
• $\mathbb{C}{P}^2$ Skyrmion Crystals in an SU(3) Magnet with a Generalized Dzyaloshinskii-Moriya Interaction
• Temperature-driven transition from skyrmion to bubble crystals in centrosymmetric itinerant magnets
• Topological phase transition driven by magnetic field and topological Hall effect in an antiferromagnetic skyrmion lattice
• Topological semimetal-to-insulator phase transition between noncollinear and noncoplanar multiple-Q states on a square-to-triangular lattice
• 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
• Engineering antiferromagnetic skyrmions and antiskyrmions at metallic interfaces
• 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
• 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
• Symmetry analysis of light-induced magnetic interactions via Floquet engineering
• Machine learning assisted derivation of effective low energy models for metallic magnets
• Hedgehog lattice and field-induced chirality in breathing-pyrochlore Heisenberg antiferromagnets
• SP-STM study of the multi-Q phases in GdRu2Si2
• Ferrochiral, antiferrochiral, and ferrichiral skyrmion crystals in an itinerant honeycomb magnet
• 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
• Multiple-$q$ dipole-quadrupole instability in spin-1 triangular-lattice systems
• Multipolar Skyrmion Crystals in Non-Kramers Doublet Systems
• Skyrmion crystal with integer and fractional skyrmion numbers in a nonsymmorphic lattice structure with the screw axis
• Hybrid skyrmion and anti-skyrmion phases in polar $C_{4v}$ systems
• Antiferro skyrmion crystal phases in a synthetic bilayer antiferromagnet under an in-plane magnetic field
• Magnetic bubble crystal in tetragonal magnets
• Checkerboard bubble lattice formed by octuple-period quadruple-$Q$ spin density waves
• Anisotropic skyrmion crystal on a centrosymmetric square lattice under an in-plane magnetic field
• Theory of collective excitations in the quadruple-$Q$ magnetic hedgehog lattices
• 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
• 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
• Three-sublattice antiferro-type and ferri-type skyrmion crystals in centrosymmetric magnets
• Tuning skyrmions in B20 compounds by 4d and 5d doping

Cited by in corpus (14)

• On the multi-$\mathbf{q}$ characteristics of magnetic ground states of honeycomb cobalt oxides
• Chirality/Axiality-Induced Axiality/Chirality via Surface Polarization
• Origin of multiple skyrmion phases in EuAl4
• Bimeron Crystals by a Linearly Polarized AC Electric Field in Frustrated Magnets
• Cascade of Spin Moiré Superlattices with In-Plane Field in Triangle Lattice Semimetal EuAg${}_4$Sb${}_2$
• Four-Spin Interactions as a Route to Multiple-Q Topological Magnetic Order
• Square skyrmion lattice in multiorbital $f$-electron systems
• Single-$q$ Cycloid and Double-$q$ Vortex Lattices in Layered Magnetic Semimetal EuAg${}_4$Sb${}_2$
• Topological phase transitions by time-dependent electromagnetic fields in frustrated magnets: Role of dynamical and static magnetic fields
• Effects of crystal field and momentum-based frustrated exchange interactions on multiorbital square skyrmion lattice
• Finite-temperature stability of skyrmion crystals in frustrated magnets: Role of sixfold anisotropy and uniform spin mode in momentum space
• Skyrmion generation via Laguerre-Gaussian beam irradiation in frustrated magnets
• Field-tunable quadruple-$Q$ states driven by momentum-space frustration
• Symmetry Rules on Multipole Interactions under Crystallographic Point Groups and Application to Multiple-$Q$ Multipole States