Strain engineering of spin and Rashba splitting in Group-III monochalcogenide MX (M = Ga, In and X = S, Se, Te) monolayer

•The results show SOC decreases the bandgap and is more effective for heavy materials.•Spin-splitting increases in the conduction and valence band with increasing strain.•Rashba momentum and energy decrease with the strain but its coefficient is constant.•Heavier compounds (GaTe and InTe) show a higher Rashba coefficient close to 0.5 eVÅ.•Rashba coefficient shows correlation with the mass difference between M and X atoms. In this paper, spin properties of monolayer MX (M = Ga, In and X = S, Se, Te) in the presence of strain are studied. Density functional theory is used to investigate spin properties. The effect of spin-orbit coupling on the band gap is investigated, the results indicate the spin-orbit coupling has a higher effect in the compressive regime. Also, spin splitting in the conduction and valence bands respect to strain are compared for six materials. The location of conduction band minimum (CBM) imposed different type of spin splitting. These materials with mirror symmetry can display the Rashba effect while M valley is located at CBM. Strain tunes the conduction band minimum in three valleys (K, M and Γ valleys) and determines which spin effect (spin splitting, Rashba splitting or no spin splitting) has occurred in each strain for every material. Lastly, the relation between the Rashba parameter and the atomic mass is explored and it is observed that there is a linear correlation between atomic mass and Rashba coefficient.