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

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• Electronic structure
• Magnetism
• Magnons
• Spin-phonon coupling
• Two-dimensional electron system
• First-principles calculations