Electronic structure, magnetic properties, spin orientation, and doping effect in Mn3Si2Te6

The layered material ${\mathrm{Mn}}_{3}{\mathrm{Si}}_{2}{\mathrm{Te}}_{6}$, with alternating stacking honeycomb and triangular layers, is attracting considerable attention due to its rich physical properties. Here, using density functional theory and classical Monte Carlo (MC) methods, we systematically study this system with the $3{d}^{5}$ electronic configuration. Near the Fermi level, the states are mainly contributed by Te $5p$ orbitals hybridized with Mn $3d$ orbitals, resembling a charge-transfer system. Furthermore, the spin orientations of the ferrimagnetic (FiM) ground state display different conductive behaviors when along the $ab$ plane or out-of-plane directions: insulating vs metallic states. The energy difference between the FiM [110] insulating and FiM [001] metallic phases is very small $(\ensuremath{\sim}0.71 \mathrm{meV}/\mathrm{Mn})$. Changing the angle $\ensuremath{\theta}$ of spin orientation from in-plane to out-of-plane directions, the band gaps of this system are gradually reduced, leading to an insulator-metal transition, resulting in an enhanced electrical conductivity, related to the colossal angular magnetoresistance (MR) effect. Although the three main magnetic couplings were found to be antiferromagnetic, overall the ground state is FiM. In addition, we also constructed the magnetic phase diagram using the classical $XY$ spin model studied with the MC method. Three magnetic phases were obtained, including antiferromagnetic order, noncollinear spin patterns, and FiM order. Moreover, we also investigated the Se and Ge doping into the ${\mathrm{Mn}}_{3}{\mathrm{Si}}_{2}{\mathrm{Te}}_{6}$ system: the FiM state has the lowest energy among the magnetic candidates for both Se- and Ge-doped cases. The magnetic anisotropy energy (MAE) decreases in the Se-doped case because the Mn orbital moment is reduced as the doping $x$ increases. Due to the small spin-orbit-coupling effect of Se, the insulator-metal transition caused by the spin orientation disappears in the Se-doped case, resulting in an insulating phase in the FiM [001] phase. This causes a reduced colossal angular MR. However, both the MAE and the band gap of the Ge-doped case do not change much with increasing doping $x$. Our results for ${\mathrm{Mn}}_{3}{\mathrm{Si}}_{2}{\mathrm{Te}}_{6}$ could provide guidance to experimentalists and theorists working on this system or related materials.