Probing the impact of magnetic interactions on the lattice dynamics of two-dimensional TiX (X = C, N) MXenes.

Dynamical properties of the two-dimensional TiC and TiN MXenes were investigated using density functional theory and discussed in connection with their structures and electronic properties. To elucidate the influence of magnetic interactions on the fundamental properties of these systems, the nonmagnetic, ferromagnetic and three distinct antiferromagnetic spin arrangements on titanium sublattice were considered. Each magnetic configuration was also studied at two directions of the spin magnetic moment with respect to the MXene layer. The zero-point energy motion, following from the phonon calculations, was taken into account while analyzing the energetic stability of the magnetic phases against the nonmagnetic solution. This contribution was found not to change a sequence of the energetic stability of the considered magnetic structures of TiX (X = C, N) MXenes. Both TiX (X = C, N) systems are shown to prefer antiferromagnetic arrangement of spins between Ti layers and the ferromagnetic order within each layer. This energetically privileged phase is semiconducting for TiC and metallic for TiN. The type of magnetic order as well as the in-plane or out-of-plane spin polarizations have a relatively small impact on the structural parameters, Ti-X bonding length, force constants and phonon spectra of both TiX systems, leading to observable differences only between the nonmagnetic and any other magnetic configurations. Nonetheless, a noticeable effect of the spin orientation on degeneracy of the Ti-3d orbitals is encountered. The magnetic interactions affect to a great extent the positions and intensities of the Raman-active modes, and hence one could exploit this effect for experimental verification of the theoretically predicted magnetic state of TiX monolayers. Theoretical phonon spectra of TiX (X = C, N) MXenes exhibit a linear dependence on energy in the long-wavelength limit, which is typical for a 2D system.