Generalization of de Gennes factor for the strong spin-orbit coupled systems.

The magnetic exchange interaction parameters of magnetic systems can be obtained from the consideration of energetics within density functional theory (DFT)-based approaches. Spin Hamiltonians, such as the Heisenberg model, are mainly used to fit the various total energies of magnetic configurations obtained from DFT band calculations, which can be directly compared to the experimental findings including spin-wave dispersions. However, for the strong spin-orbit coupled systems, these approaches often fail and predict wrong energy scales compared to the experimental values due to the entanglement of spin and orbital moments. By including the generalized de Gennes factor, which connects the spin and orbital moments to the total moment, we have found that the better description of exchange interaction parameters can be obtained for the strong spin-orbit coupled systems.