Estimation of sp-d exchange constants revisited

We present a new computational method for estimating the sp-d exchange constant, J(eff)(sp-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 for J(eff)(sp-d) (M) obtained with the proposed method are compared with the corresponding results, J(eff)(sp-d) (Delta E-VBM), obtained from estimations of the spin electron orbital splitting,.EVBM, 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 Delta E-VBM, they lead to equivalent results and the corresponding J(eff)(sp-d) (Delta E-VBM) are in good agreement with the J(eff)(sp-d) (M) ones. Ab initio results obtained for the 2D-MoS2 doped with 3d-series transition metals are presented to demonstrate the validity and applicability of the proposed computational schemes for obtaining J(eff)(sp-d). The proposed methods can be utilized as useful tools in the search of new materials for spintronics and valleytronics applications.