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The search for Kitaev spin liquid states has recently broadened to include anumber of honeycomb materials with integer spin moments. The qualitativedifference with their spin-1/2 counterparts is the presence of single-ionanisotropy (SIA). This motivates our investigation of the effects of SIA on theground state of the spin-$1$ Kitaev-Heisenberg (KH) model using thedensity-matrix renormalization group which allows construction of detailedphase diagrams around the Kitaev points. We demonstrate that positiveout-of-plane SIA induces an in-plane vortex state without the need foroff-diagonal interactions. Conversely, negative SIA facilitates the emergenceof a ferromagnetic state in presence of antiferromagnetic Heisenberginteractions, while a N\`eel state can emerge for ferromagnetic Heisenbergcoupling. These findings, pertinent even for weak SIA, not only enhance ourtheoretical understanding of the spin-1 KH model but also propose experimentalprospects for observing these novel magnetic states in material realizations.

Emergence of vortex state in the $S=1$ Kitaev-Heisenberg model with single-ion anisotropy