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.

15 pages, 12 figures, 2 tables

References in corpus (50)

• Spontaneous Skyrmion Ground States in Magnetic Metals
• Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions
• A new class of chiral materials hosting magnetic skyrmions beyond room temperature
• Long wavelength helimagnetic order and skyrmion lattice phase in Cu2OSeO3
• 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
• Prediction of low-Z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling
• 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
• Néel-type skyrmion lattice in tetragonal polar magnet VOSe${}_2$O${}_5$
• Three-dimensional skyrmion states in thin films of cubic helimagnets
• Toroidal order in metals without local inversion symmetry
• Meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets
• 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
• 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
• 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
• Magnetoelectric Resonances and Predicted Microwave Diode Effect of Skyrmion Crystal in Multiferroic Chiral-Lattice Magnet
• Unconventional Topological Hall Effect in Skyrmion Crystals Caused by the Topology of the Lattice
• 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
• Charge-Density-Wave Order and Multiple Magnetic Transitions in Divalent Europium Compound EuAl${}_4$
• Pyrochlore Oxide Superconductor Cd2Re2O7 Revisited
• Skyrmion crystal and spiral phases in centrosymmetric bilayer magnets with staggered Dzyaloshinskii-Moriya interaction
• 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
• 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
• 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
• Revealing hidden magneto-electric multipoles using Compton scattering

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• 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
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• 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