Functionalized Cr${}_2$C MXenes: Novel Magnetic Semiconductors

We report an $\mathit{\text{ab}}\mathit{\text{initio}}$ investigation of functionalized and 3$d$-electrons doped Cr${}_2$C MXenes. Upon functionalization, the Cr${}_2$C becomes chemically, dynamically, and mechanically stable, and it exhibits magnetic semiconducting behavior. Cr${}_2$CF${}_2$ stands out as a wide band gap semiconductor, possessing super exchange interaction mediated by F atoms within the layer, however, the applied strain transforms it from an indirect to a direct band gap semiconductor. Strong spin-phonon coupling found in Cr${}_2$CH${}_2$ is supported by the distorted Cr spin density due to hydrogen environment. Two magnon branches, associated with two sub-lattice spins, are found in the ferromagnetic Cr${}_2$CO${}_2$ and antiferromagnetic Cr${}_2$CF${}_2$. Depending on the types of 3$d$-electron dopants and functionalization, Cr${}_2$C MXenes (except for Cr${}_2$CO${}_2$) change from the indirect band gap magnetic semiconductor to different states of electronic and magnetic matter including exotic direct band gap magnetic bipolar semiconductor. In addition, we reveal a band inversion between the two highest valence bands in the Fe-doped Cr${}_2$CCl${}_2$.