Effect of biaxial strain and carrier doping on intrinsic valley polarization in 2H-RuCl2 Monolayer

We perform a comprehensive first-principles investigation of the electronic, magnetic, and topological properties of monolayer (ML) 2H-RuCl${}_2$ under biaxial strain and carrier doping. At equilibrium, the material exhibits a ferromagnetic (FM) ground state with a significantly enhanced magnetic anisotropy energy (MAE) of 1.87 meV/Ru and a Curie temperature (T${}_c$) of approximately 280 K, positioning it near the threshold of room-temperature operation. Upon application of biaxial tensile strain, we observe a distinct spin reorientation from out-of-plane to in-plane magnetic anisotropy at 3.7%, explained via an orbital-resolved projected density of states (PDOS) analysis which reveals a shift in the unoccupied density from $d_{z^2}$ to in-plane orbitals $d_{xy}$ and $d_{x^2-y^2}$. The system also hosts two half-valley-metal (HVM) phases HVM1 and HVM2 at tensile strains 1.7% and 3.2%, respectively. Unlike previous reports, we find that the out-of-plane anisotropy is retained throughout the entire HVM1–HVM2 regime (1.7%–3.2% strain), enhancing the stability of the valley-polarized and topological states. Notably, we identify a correlation between the minimum of the exchange energy ($E_{ex}=E_{AFM}-E_{FM}$) and the emergence of the quantum anomalous Hall (QAH) phase, both occurring near 2.4% strain. Finally, we examine the influence of carrier doping and find that both electron and hole doping modify the magnitude of MAE and valley polarization, offering an external control mechanism without altering the easy axis orientation. These results highlight 2H-RuCl${}_2$ as a versatile 2D material platform with tunable magnetic and topological features suitable for next-generation spintronic and valleytronic applications.