Spin-orbit driven $J_{eff} = 1/2$ magnetism in a d$^7$ triangular-lattice monolayer cobaltate

Abstract

Recent theoretical and experimental advances have identified cobaltates with a high-spin $d^7$ electronic configuration as promising hosts for spin-orbit entangled $J_{eff} = 1/2$ magnetism that can support bond-dependent exchange interactions. In two-dimensional triangular lattices, the coexistence of such exchange frustration along with 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 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 and third 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, spiral, and $120^{\circ}$ antiferromagnetic orders. The Luttinger-Tisza analysis further predicts a Z$_2$ vortex crystal phase, while exact diagonalization reveals a bond-nematic phase stabilized by the longer-range couplings. Going beyond the conventional bond-independent XXZ picture typically applied to Co$^{2+}$ systems, our results on monolayer CoBr$_2$ establish 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.