Isolated Skyrmions in the $C{P}^2$ nonlinear $\sigma$-model with a Dzyaloshinskii-Moriya type interaction

Abstract

We study two dimensional soliton solutions in the $C{P}^2$ nonlinear $\sigma$-model with a Dzyaloshinskii-Moriya type interaction. First, we derive such a model as a continuous limit of the $SU(3)$ tilted ferromagnetic Heisenberg model on a square lattice. Then, introducing an additional potential term to the derived Hamiltonian, we obtain exact soliton solutions for particular sets of parameters of the model. The vacuum of the exact solution can be interpreted as a spin nematic state. For a wider range of coupling constants, we construct numerical solutions, which possess the same type of asymptotic decay as the exact analytical solution, both decaying into a spin nematic state.

19 pages, 4 figures; v2: minor corrections, references added

References in corpus (6)

• Chiral CP^2 skyrmions in three-band superconductors
• Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• Pairing of Solitons in Two-Dimensional S=1 Magnets
• Spin-orbit coupling and electronic charge effects in Mott insulators
• On the role of Lifshitz invariants in liquid crystals

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• Domain Wall Skyrmions in Chiral Magnets
• Semi-classical simulation of spin-1 magnets
• CP${}^2$ Skyrmions and Skyrmion Crystals in Realistic Quantum Magnets
• $\mathbb{C}{P}^2$ Skyrmion Crystals in an SU(3) Magnet with a Generalized Dzyaloshinskii-Moriya Interaction
• Quantum nucleation of topological solitons
• Chiral Magnets from String Theory
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Demonstration of $\mathbb{C}{P}^2$ skyrmions in three-band superconductors by self-consistent solutions to a Bogoliubov-de Gennes model
• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Gravitational wave analogues in spin nematics and cold atoms
• Multiple-$q$ dipole-quadrupole instability in spin-1 triangular-lattice systems
• Orbital moiré and quadrupolar triple-q physics in a triangular lattice
• Symmetry Rules on Multipole Interactions under Crystallographic Point Groups and Application to Multiple-$Q$ Multipole States