Recent theoretical and experimental advances have identified cobaltates with a high-spin $d^7$ electronic configuration as promising hosts for spin-orbit entangled $J_{\mathrm{eff}}=1/2$ magnetism that can support bond-dependent exchange interactions. In two-dimensional triangular lattices, the coexistence of such exchange frustration along with usual geometric frustration gives rise to a rich landscape of competing magnetic phases, establishing monolayer triangular $d^7$ cobaltates as a compelling platform for frustrated magnetism. Here we investigate a representative triangular-lattice monolayer cobaltate ${\mathrm{CoBr}}_2$, where first-principles density functional theory (DFT) calculations reveal a dominant nearest-neighbor $t_{2g}–e_g$ hopping channel that enhances the ferromagnetic Kitaev-type exchange interactions. In contrast, the nearest-neighbor Heisenberg term is highly sensitive to a direct $t_{2g}–t_{2g}$ hopping path and electronic correlations. The magnetic exchange parameters are evaluated using the hopping amplitudes obtained from DFT calculations within an exact diagonalization framework. We construct the first (${\mathrm{J}}_1$) and third (${\mathrm{J}}_3$) nearest neighbor Heisenberg exchange dependent $J_1–J_3$ magnetic phase diagram in the physically relevant regime and identify multiple competing ground states, including ferromagnetic, stripy, incommensurate, and ${120}^{\circ }$ antiferromagnetic orders. The Luttinger-Tisza analysis further predicts a ${\mathrm{Z}}_2$ vortex crystal phase, while exact diagonalization reveals a bond-nematic phase promoted by quantum fluctuations. Going beyond the conventional bond-independent XXZ picture typically applied to ${\mathrm{Co}}^{2+}$ systems, our results on monolayer ${\mathrm{CoBr}}_2$ establish ${\mathit{d}}^7$ cobalt dihalides as a promising platform to explore the interplay of long-range Heisenberg and bond-dependent exchange interactions that can stabilize diverse magnetic ground states on a triangular lattice.

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• Electronic structure
• Magnetism
• Magnetic insulators
• Magnetic systems