Probing the impact of magnetic interactions on the lattice dynamics of two-dimensional Ti2X (X = C, N) MXenes

Abstract

Dynamical properties of the two-dimensional Ti₂C and Ti₂N 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 Ti₂X (X = C, N) MXenes. Both Ti₂X (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 Ti₂C and metallic for Ti₂N. 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 Ti₂X 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 Ti₂X monolayers. Theoretical phonon spectra of Ti₂X (X = C, N) MXenes exhibit a linear dependence on energy in the long-wavelength limit, which is typical for a 2D system.