Complex orders and chirality in the classical Kitaev-Γ model

It is well recognized that the low-energy physics of many Kitaev materials is governed by two dominant energy scales, the Ising-Type Kitaev coupling K and the symmetric off-diagonal Γ coupling. An understanding of the interplay between these two scales is therefore the natural starting point toward a quantitative description that includes subdominant perturbations that are inevitably present in real materials. This study focuses on the classical K-Γ model on the honeycomb lattice, with a specific emphasis on the region K<0 and Γ>0, which is the most relevant for the available materials and which remains enigmatic in both quantum and classical limits, despite much effort. We employ large-scale Monte Carlo simulations on specially designed finite-size clusters and unravel the presence of a complex multisublattice magnetic order in a wide region of the phase diagram, whose structure is characterized in detail. We show that this order can be quantified in terms of a coarse-grained scalar-chirality order, featuring a counterrotating modulation on the two spin sublattices. We also provide a comparison to previous studies and discuss the impact of quantum fluctuations on the phase diagram.