Machine-learned model Hamiltonian and strength of spin-orbit interaction in strained Mg2X (X = Si, Ge, Sn, Pb)

Abstract

We have developed multi-orbital tight-binding (MOTB) Hamiltonian models to describe the electronic characteristics of intermetallic compounds Mg2Si, Mg2Ge, Mg2Sn, and Mg2Pb subject to strain. We have incorporated spin-orbital mediated interactions and calibrated the MOTB models to the band structures of density functional theory (DFT) by a massively parallelized multi-dimensional Monte-Carlo search algorithm. The results show that a five-band tight-binding (TB) model reproduces the key aspects of the band structures in the entire Brillouin zone. The five-band TB model reveals that the compressive strain localizes the contribution of the 3s orbital of Mg to the conduction bands and the outer shell p orbitals of X to the valence bands. The tensile strain, in contrast, has a reversed effect and weakens the contribution of the 3s orbital of Mg and the outer shell p orbitals of X to the conduction bands and valence bands, respectively. We have found that the π bonding in the Mg2X compounds is negligible compared to the σ bondings, follow the hierarchy |σsp| > |σpp| > |σss|, and the largest variation against strain belongs to σpp. Moreover, the five-band TB model allowed for estimating the strength of SOC in Mg2X and obtaining its functionality with respect to the atomic number of X and strain. Additionally, the calculations find significant band gap tuning and band splitting due to strain. It is shown that a compressive strain of −10% can open a band gap at the Γ point in metallic Mg2Pb whereas a tensile strain of +10% closes the semiconducting band gap of Mg2Si. Also, +5% of tensile strain can remove the three-fold degeneracy of valence bands at the Γ point in semiconducting Mg2Ge. Our results and model approach can be useful in designing devices made of Mg2X more accurately.