Phase degree of freedom and topology in multiple- spin textures
arXiv:2201.03290 · doi:10.1103/PhysRevB.105.224405
Abstract
A periodic array of topological spin textures, such as skyrmions and hedgehogs, is called the multiple- spin texture, as it is represented by a superposition of multiple spin density waves. Depending on the way of superposition, not only the magnetic but also the topological properties are modified, leading to a variety of quantum transport and optical phenomena caused by the emergent electromagnetic fields through the Berry phase. Among others, the phase degree of freedom of the superposed waves is potentially important for such modifications, but its effect has not been fully elucidated thus far. Here we perform systematic theoretical analyses of magnetic and topological properties of the multiple- spin textures with the phase degree of freedom. By introducing a hyperspace with an additional dimension corresponding to the phase degree of freedom, we establish a generic framework to deal with the phase shift in the multiple- spin textures. Applying the framework to the two-dimensional 3 spin textures, we clarify the complete topological phase diagram while changing the phase and magnetization, which depends on the types of the superposed waves. We also study the three-dimensional 4 spin textures and clarify even richer topological phase diagrams. In particular, we find novel topological phase transitions associated with the previously unidentified Dirac strings on which the hedgehogs and antihedgehogs cause pair creation and fusion. Moreover, we demonstrate that phase shifts are caused by an external magnetic field in both 3 and 4 cases by analyzing the numerical data in the previous studies. Our results illuminate the topological aspects of the skyrmion and hedgehog lattices with the phase degree of freedom, which would be extended to other multiple- textures and useful for the exploration of topologically nontrivial magnetic phases and exotic quantum phenomena.
References in corpus (62)
- Topological Insulators
- Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
- Topological Order and the Quantum Spin Hall Effect
- Berry Phase Effects on Electronic Properties
- Skyrmion Lattice in a Chiral Magnet
- Topological Insulators in Three Dimensions
- Topological Insulators with Inversion Symmetry
- Topological invariants of time-reversal-invariant band structures
- Spontaneous Skyrmion Ground States in Magnetic Metals
- Topological Insulator Materials
- Emergent electrodynamics of skyrmions in a chiral magnet
- Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
- Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet
- Skyrmion Lattice in a Doped Semiconductor
- Berry Phase Theory of Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites
- Topological Hall effect and Berry phase in magnetic nanostructures
- Long wavelength helimagnetic order and skyrmion lattice phase in Cu2OSeO3
- Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets
- Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi
- Real-space observation of short-period cubic lattice of skyrmions in MnGe
- Skyrmion dynamics in a frustrated ferromagnetic film and current-induced helicity locking-unlocking transition
- Skyrmion Lattice in Two-Dimensional Chiral Magnet
- The skyrmion lattice phase in three dimensional chiral magnets from Monte Carlo simulations
- Hidden Multiple-spin Interactions as an Origin of Spin Scalar Chiral Order in Frustrated Kondo Lattice Models
- Topological-chiral magnetic interactions driven by emergent orbital magnetism
- Emergent electromagnetism in solids
- Anomalous Hall Effect and Skyrmion Number in Real- and Momentum-space
- Current induced rotational torques in the skyrmion lattice phase of chiral magnets
- Formation of a topological non-Fermi liquid in MnSi
- Topological Nernst effect of the two-dimensional skyrmion lattice
- Theory of helical spin crystals: phases, textures and properties
- Vortex Crystals with Chiral Stripes in Itinerant Magnets
- Emergent topological spin structures in a centrosymmetric cubic perovskite
- Topological magneto-optical effects and their quantization in noncoplanar antiferromagnets
- Chirality induced anomalous-Hall effect in helical spin crystals
- Néel- and Bloch-Type Magnetic Vortices in Rashba Metals
- Effective gauge field theory of spintronics
- Magnetic hedgehog lattices in noncentrosymmetric metals
- Phase Shift in Skyrmion Crystals
- Efficient Langevin Simulation of Coupled Classical Fields and Fermions
- Zero-temperature phases for chiral magnets in three dimensions
- Dynamics and energetics of emergent magnetic monopoles in chiral magnets
- Emergent electromagnetic induction beyond room temperature
- Emergent electromagnetism induced by topological defects created during magnetization reversal in nanowires
- Large Anomalous Nernst Effect in a Skyrmion Crystal
- 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
- Electromagnetic response in spiral magnets and emergent inductance
- Spin excitation spectra in helimagnetic states: proper-screw, cycloid, vortex crystal, and hedgehog lattice
- Intrinsic and extrinsic tunability of Rashba spin-orbit coupled emergent inductors
- Spin moiré engineering of topological magnetism and emergent electromagnetic fields
- Electric transport in three-dimensional Skyrmion/monopole crystal
- Formation of a Topological Monopole Lattice and its Dynamics in Three-dimensional Chiral Magnets
- Phase transitions between helices, vortices, and hedgehogs driven by spatial anisotropy in chiral magnets
- Magnetic field-temperature phase diagrams for multiple- magnetic orderings: Exact steepest descent approach to long-range interacting spin systems
- Weak coupling theory of topological Hall effect
- Topological Hall effect from strong to weak coupling
- Tuneable terahertz oscillation arising from Bloch-point dynamics in chiral magnets
- Multiple- magnetic orders in Rashba-Dresselhaus metals
- Shape of magnetic domain walls formed by coupling to mobile charges
- Ultrasonic elastic responses in monopole lattice
- Phase shift, ellipticity, angle, and topological number in skyrmion lattices
Cited by in corpus (15)
- Effective spin model in momentum space: Toward a systematic understanding of multiple- instability by momentum-resolved anisotropic exchange interactions
- Single helicity of the triple- triangular skyrmion lattice state in cubic chiral helimagnet EuPtSi
- Magnetic Hedgehog Lattice in a Centrosymmetric Cubic Metal
- Triple- partial magnetic orders induced by quadrupolar interactions: Triforce order scenario for UNiB
- Skyrmion and vortex crystals in the Hubbard model
- Unconventional Surface State Pairs in a High-Symmetry Lattice with Anti-ferromagnetic Band-folding
- Hidden Topological Transitions in Emergent Magnetic Monopole Lattices
- Phase shifts, band geometry and responses in triple-Q charge and spin density waves
- Current-induced motion of nanoscale magnetic torons over the wide range of the Hall angle
- Theory of collective excitations in the quadruple- magnetic hedgehog lattices
- 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 and
- Single- Cycloid and Double- Vortex Lattices in Layered Magnetic Semimetal EuAgSb
- A -algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals
- Stacking-dependent nonreciprocal transport in magnetic skyrmions