Helicity locking of square skyrmion crystal in a centrosymmetric lattice system without vertical mirror symmetry

Abstract

We theoretically investigate the stability of a square skyrmion crystal (SkX) in a centrosymmetric tetragonal lattice structure with the emphasis on the role of the magnetic anisotropy arising from the absence of vertical mirror symmetry. Our analysis is based on an effective bilinear and biquadratic model in momentum space, which is a canonical model for itinerant magnets in a weak-coupling regime. By performing the simulated annealing for the model on the two-dimensional square lattice, we find that the off-diagonal spin component in the interaction, which becomes nonzero when the vertical mirror symmetry is broken, gives rise to the square SkX with a definite helicity in an external magnetic field. We show that the helicity of the centrosymmetric SkXs is determined by the competition between the off-diagonal and diagonal anisotropic interactions, the latter of which appears in the discrete fourfold-rotational lattice structure. Furthermore, we discuss helicity-dependent physical phenomena by introducing odd-parity multipoles, where electric (magnetic) and electric (magnetic) toroidal multipoles are sources of an antisymmetric spin polarization and an Edelstein effect (a magnetoelectric effect). We also discuss the stability of the SkXs with different helicities in a magnetic field rotation. Our results provide a way of engineering the helicity-locked SkXs by the symmetric anisotropic interaction in centrosymmetric magnets, which is distinct from that by the antisymmetric Dzyaloshinskii-Moriya interaction in noncentrosymmetric magnets.

arXiv comment15 pages, 12 figures, 2 tables

References in corpus (97)

• Berry Phase Effects on Electronic Properties
• Skyrmion Lattice in a Chiral Magnet
• Anomalous Hall effect
• Antiferromagnetic spintronics
• Spontaneous Skyrmion Ground States in Magnetic Metals
• Topological Hall effect in the A-phase of MnSi
• Emergent electrodynamics of skyrmions in a chiral magnet
• Current-induced skyrmion dynamics in constricted geometries
• 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
• Static and Dynamical Properties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature
• 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
• A new class of chiral materials hosting magnetic skyrmions beyond room temperature
• Long wavelength helimagnetic order and skyrmion lattice phase in Cu2OSeO3
• Antiferromagnetic Skyrmion: Stability, Creation and Manipulation
• Skyrmion-electronics: Writing, deleting, reading and processing magnetic skyrmions toward spintronic applications
• Skyrmion phase and competing magnetic orders on a breathing kagome lattice
• Skyrmions and Anomalous Hall Effect in a Dzyloshinskii-Moriya Spiral Magnet
• Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet
• Cluster multipole theory for anomalous Hall effect in antiferromagnets
• Bottom-up design of spin-split and reshaped electronic band structures in spin-orbit-coupling free antiferromagnets: Procedure on the basis of augmented multipoles
• 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
• Prediction of low-Z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling
• Classification of atomic-scale multipoles under crystallographic point groups and application to linear response tensors
• Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets
• Spontaneous skyrmionic lattice from anisotropic symmetric exchange in a Ni-halide monolayer
• Skyrmion dynamics in a frustrated ferromagnetic film and current-induced helicity locking-unlocking transition
• Skyrmion Qubits: A New Class of Quantum Logic Elements Based on Nanoscale Magnetization
• Formation and rotation of skyrmion crystal in the chiral-lattice insulator Cu2OSeO3
• Quantized Anomalous Hall Effects in Skyrmion Crystal
• Néel-type skyrmion lattice in tetragonal polar magnet VOSe${}_2$O${}_5$
• Bubble and Skyrmion Crystals in Frustrated Magnets with Easy-Axis Anisotropy
• Hidden Multiple-spin Interactions as an Origin of Spin Scalar Chiral Order in Frustrated Kondo Lattice Models
• Electric-field control of the skyrmion lattice in Cu2OSeO3
• Three-dimensional skyrmion states in thin films of cubic helimagnets
• Nonreciprocal spin wave propagation in chiral-lattice ferromagnets
• Toroidal order in metals without local inversion symmetry
• Group-theoretical classification of multipole order: emergent responses and candidate materials
• Magnetic anisotropy, first-order-like metamagnetic transitions and large negative magnetoresistance in the single crystal of Gd${}_2$PdSi${}_3$
• Meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets
• Spontaneous Antisymmetric Spin Splitting in Noncollinear Antiferromagnets without Spin-Orbit Coupling
• Topological Nernst effect of the two-dimensional skyrmion lattice
• Skyrmion Crystal from RKKY Interaction Mediated by 2D Electron Gas
• Propagating spin excitations along skyrmion strings
• Imaging the coupling between itinerant electrons and localised moments in the centrosymmetric skyrmion magnet GdRu2Si2
• Square skyrmion crystal in centrosymmetric itinerant magnets
• Multipole classification in 122 magnetic point groups for unified understanding of multiferroic responses and transport phenomena
• Vortex Crystals with Chiral Stripes in Itinerant Magnets
• Multiple-Q Instability by (d-2)-dimensional Connections of Fermi Surfaces
• Multipole expansion for magnetic structures: A generation scheme for symmetry-adapted orthonormal basis set in crystallographic point group
• Nanometric skyrmion lattice from anisotropic exchange interactions in a centrosymmetric host
• Thermodynamically stable skyrmion lattice in tetragonal frustrated antiferromagnet with dipolar interaction
• Néel- and Bloch-Type Magnetic Vortices in Rashba Metals
• 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
• Magnetic hedgehog lattices in noncentrosymmetric metals
• Effect of magnetic anisotropy on Skyrmions with a high topological number in itinerant magnets
• First-principles theory of magnetic multipoles in condensed matter systems
• Magnetoelectric Resonances and Predicted Microwave Diode Effect of Skyrmion Crystal in Multiferroic Chiral-Lattice Magnet
• Magnetic hexadecapole order and magnetopiezoelectric metal in Ba${}_{1-x}$K${}_x$Mn${}_2$As${}_2$
• Unconventional Topological Hall Effect in Skyrmion Crystals Caused by the Topology of the Lattice
• Dynamical magnetoelectric phenomena of multiferroic skyrmions
• Electric Toroidal Quadrupoles in Spin-Orbit Coupled Metal Cd${}_2$Re${}_2$O${}_7$
• Multiple skyrmion crystal phases by itinerant frustration in centrosymmetric tetragonal magnets
• Field-Direction Sensitive Skyrmion Crystals in Cubic Chiral Systems: Implication to $4f$-Electron Compound EuPtSi
• Degeneracy Lifting of Néel, Bloch, and Anti-Skyrmion Crystals in Centrosymmetric Tetragonal Systems
• Theory of Orbital Magnetic Quadrupole Moment and Nonlinear Anomalous Thermoelectric Transport
• Charge-Density-Wave Order and Multiple Magnetic Transitions in Divalent Europium Compound EuAl${}_4$
• Pyrochlore Oxide Superconductor Cd2Re2O7 Revisited
• Magnetoelectric multipoles in metals
• Face centered cubic and hexagonal close packed skyrmion crystals in centro-symmetric magnets
• Skyrmion crystal and spiral phases in centrosymmetric bilayer magnets with staggered Dzyaloshinskii-Moriya interaction
• Theory of orbital magnetic quadrupole moment and magnetoelectric susceptibility
• 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
• Theory of magnetic skyrmion glass
• Magnetoelectric effect and orbital magnetization in skyrmion crystals: Detection and characterization of skyrmions
• 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
• The nature of the tensor order in Cd2Re2O7
• Skyrmion crystal in the RKKY system on the two-dimensional triangular lattice
• Mechanism of antisymmetric spin polarization in centrosymmetric multiple-$Q$ magnets based on bilinear and biquadratic spin cross products
• Odd-Parity Multipoles by Staggered Magnetic Dipole and Electric Quadrupole Orderings in CeCoSi
• Current-induced motion of twisted skyrmions
• Unravelling incommensurate magnetism and its emergence in iron-based superconductors
• Giant magnetoresistance and topological Hall effect in the EuGa4 antiferromagnet
• Double-$Q$ Chiral Stripe in the $d$-$p$ Model with Strong Spin-Charge Coupling
• Dynamical Switching of Magnetic Topology in Microwave-Driven Itinerant Magnet
• Skyrmion crystals in centrosymmetric triangular magnets under hexagonal and trigonal single-ion anisotropy
• Temperature-driven transition from skyrmion to bubble crystals in centrosymmetric itinerant magnets
• Spin-orbital-momentum locking under odd-parity magnetic quadrupole ordering
• Dimension transcendence and anomalous charge transport in magnets with moving multiple-$Q$ spin textures
• Revealing hidden magneto-electric multipoles using Compton scattering

Cited by in corpus (22)

• Unified description of electronic orderings and cross correlations by complete multipole representation
• Effective spin model in momentum space: Toward a systematic understanding of multiple-$Q$ instability by momentum-resolved anisotropic exchange interactions
• Rectangular and square skyrmion crystals on a centrosymmetric square lattice with easy-axis anisotropy
• Stabilization mechanisms of magnetic skyrmion crystal and multiple-$Q$ states based on momentum-resolved spin interactions
• Multifarious skyrmion phases on a trilayer triangular lattice
• Widely-sweeping magnetic field-temperature phase diagrams for skyrmion-hosting centrosymmetric tetragonal magnets
• Cluster Toroidal Multipoles Formed by Electric-Quadrupole and Magnetic-Octupole Trimers: A Possible Scenario for Hidden Orders in Ca${}_5$Ir${}_3$O${}_{12}$
• Nonreciprocal Transport in Noncoplanar Magnetic Systems without Spin-Orbit Coupling, Net Scalar Chirality, or Magnetization
• Square skyrmion crystal in centrosymmetric systems with locally inversion-asymmetric layers
• Ferroaxial moment induced by vortex spin texture
• Magnetic Toroidal Moment under Partial Magnetic Order in Hexagonal Zigzag-Chain Compound Ce${}_3$TiBi${}_5$
• Stability of Skyrmion Crystal Phase in Centrosymmetric Distorted Triangular-Lattice Antiferromagnets
• Skyrmion crystal under $D_{3h}$ point group: Role of out-of-plane Dzyaloshinskii-Moriya interaction
• Skyrmion crystal with integer and fractional skyrmion numbers in a nonsymmorphic lattice structure with the screw axis
• Checkerboard bubble lattice formed by octuple-period quadruple-$Q$ spin density waves
• Antiferro skyrmion crystal phases in a synthetic bilayer antiferromagnet under an in-plane magnetic field
• Hybrid skyrmion and anti-skyrmion phases in polar $C_{4v}$ systems
• Engineering a skyrmion crystal in ferromagnetic/antiferromagnetic bilayers free from the DM interaction
• Chern insulating state with double-$Q$ ordering wave vectors at the Brillouin zone boundary
• Magnetic instability under ferroaxial moment
• Field-tunable quadruple-$Q$ states driven by momentum-space frustration
• Skyrmion generation via Laguerre-Gaussian beam irradiation in frustrated magnets