and finite temperature properties*

We study the magnetic interactions in the Kitaev spin-liquid candidate α-RuCl₃ using ab initio, exact diagonalization, and thermal pure quantum state methods. First we derive a new effective Hamiltonian, using an ab initio downfolding scheme based on a density functional theory calculation for the monoclinic crystal structure (space group C2/m). The calculation includes local crystal field splitting, and local and non-local spin-orbit coupling. Both local and nonlocal Coulomb interactions are computed using the constrained RPA method, and the interaction parameters for the effective spin Hamiltonian are determined using second order perturbation theory. We report both zero and finite temperature properties for this and previously proposed models, including dynamical spin structure factors and the specific heat. Our results highlight the importance of further range anisotropic spin-spin interactions, both for producing the zigzag magnetic order and for predictions beyond static properties at zero temperature.