Spontaneous Chiral-Spin Ordering in Spin-Orbit Coupled Honeycomb Magnets*

Frustrated magnets with highly degenerate ground states are at the heart of hunting exotic states of matter. Recent studies in spin-orbit coupled honeycomb magnets have generated immense interest in bond-dependent interactions, appreciating a symmetric off-diagonal Γ interaction which exhibits a macroscopic degeneracy in the classical limit. Here, we study a generic spin model and discover a novel chiral-spin ordering with spontaneous broken time-reversal symmetry near the dominant Γ region. Furthermore, gapless excitations revealed by a vanishing energy gap and a finite central charge on cylinders are presented. A putative chiral spin liquid (CSL) via melting of classical large-unit-cell magnetic orders is proposed. Guided by ab-initio calculations, we suggest a practical route towards a sizeable Γ region in α-RuCl₃, paving the way for a future search of CSL in real materials.