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.

• Received 2 February 2021
• Accepted 10 February 2021

DOI:https://doi.org/10.1103/PhysRevD.103.065008

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Published by the American Physical Society