Estimation ofsp-dexchange constants revisited

We present a new computational method for estimating thesp-dexchange constant,Jeffsp-d, applicable to transition metal doped diluted magnetic semiconductors, transition metal oxides, and 2D- and 3D- dichalcogenides. The proposed method is based on results describing the variation of the magnetic features of a doped system with the variation of its magnetization density (M). The results forJeffsp-d(M)obtained with the proposed method are compared with the corresponding results,Jeffsp-d(ΔEVBM), obtained from estimations of the spin electron orbital splitting, ΔE^VBM, at the valence band maximum (VBM). The latter is estimated in two ways; either directly from plots of the band structure calculations or by calculating the energy difference between the band-centers of the spin-up and spin-down electron density of states of the doped systems. Despite the inherent drawbacks in these two estimation methods for ΔE^VBM, they lead to equivalent results and the correspondingJeffsp-d(ΔEVBM)are in good agreement with theJeffsp-d(M)ones.Ab initioresults obtained for the 2D-MoS₂doped with 3d-series transition metals are presented to demonstrate the validity and applicability of the proposed computational schemes for obtainingJeffsp-d. The proposed methods can be utilized as useful tools in the search of new materials for spintronics and valleytronics applications.