Tunable magnetic order in transition metal doped, layered, and anisotropic Bi2O2Se : Competition between exchange interaction mechanisms

$\mathrm{B}{\mathrm{i}}_{2}{\mathrm{O}}_{2}\mathrm{Se}$ is a novel layer-structured material with high electron mobility, while its efficiency could be greatly improved by doping different elements to introduce a magnetic spin order. We investigated the electronic and magnetic properties of various transition metal (TM) ($\mathrm{TM}=\mathrm{Mn}$, Cr, Fe, Co, and Ni) doped $\mathrm{B}{\mathrm{i}}_{2}{\mathrm{O}}_{2}\mathrm{Se}$ within a framework of density functional theory (DFT), and discovered that $\mathrm{B}{\mathrm{i}}_{2\ensuremath{-}n}{\mathrm{X}}_{n}{\mathrm{O}}_{2}\mathrm{Se}$ exhibits long-range magnetic ordered structure via competition among double-exchange, p-d exchange, and superexchange interaction. The magnetic order of the bulk phase in which the magnetic atoms form interlayer coupling would vary with the type and concentration of doped atoms, but all the layered phases in which the magnetic atoms are in-plane coupled show ferromagnetic order. By combing DFT calculations with the Monte Carlo scheme, we solve the exchange interaction constants for the Heisenberg model and further evaluate the Curie temperatures of $\mathrm{B}{\mathrm{i}}_{2\ensuremath{-}n}{\mathrm{X}}_{n}{\mathrm{O}}_{2}\mathrm{Se}$. Ferromagnetic order for most doped systems exhibit to be robust with high Curie temperature, some of which overcomes room temperature (for 12.5% Co-doped layer $\mathrm{B}{\mathrm{i}}_{2}{\mathrm{O}}_{2}\mathrm{Se}$). It is also worth mentioning that the appearance of impurity energy levels narrows the band gap and enhances the spin-orbit coupling of $d$ orbitals and therefore increase large magnetic anisotropy energy. Our study demonstrates a potential pathway to design new dilute magnetic semiconductors through doping of $\mathrm{B}{\mathrm{i}}_{2\ensuremath{-}n}{\mathrm{X}}_{n}{\mathrm{O}}_{2}\mathrm{Se}$ by magnetic transitional elements.