Anisotropic interactions opposing magnetocrystalline anisotropy in Sr${}_3$NiIrO${}_6$

We report our investigation of the electronic and magnetic excitations of Sr${}_3$NiIrO${}_6$ by resonant inelastic x-ray scattering at the Ir L${}_3$ edge. The intra-$t_{2g}$ electronic transitions are analyzed using an atomic model, including spin-orbit coupling and trigonal distortion of the IrO${}_6$ octahedron, confronted to {\it ab initio} quantum chemistry calculations. The Ir spin-orbital entanglement is quantified and its implication on the magnetic properties, in particular in inducing highly anisotropic magnetic interactions, is highlighted. These are included in the spin-wave model proposed to account for the dispersionless magnetic excitation that we observe at 90 meV. By counterbalancing the strong Ni${}^{2+}$ easy-plane anisotropy that manifests itself at high temperature, the anisotropy of the interactions finally leads to the remarkable easy-axis magnetism reported in this material at low temperature.