Exploring magnetic space groups of Cr2N MXene and its connection to vibrational and electronic properties

Abstract

The vibrational, electronic, and magnetic properties of two-dimensional ${\mathrm{Cr}}_{2}N$ MXene were investigated. Two crystal cells (hexagonal and monoclinic) were considered with their respective magnetic space groups. In the absence of experimental data to fine-tune the $U_{\mathrm{eff}}$ (Hubbard correction), we utilized cell parameters and magnetic moment as a reference window, derived from meta-GGA calculations performed with the SCAN functional. A value of $U_{\mathrm{eff}}$ (1.25 eV) was determined, which does not overestimate the lattice parameters and magnetic moment values. Phonon scattering was calculated, and the vibrational modes were indexed. According to the density of states, the observed splitting in the $e_g$ and $t_{2g}$ orbitals, and the crystal field analysis, we deduce that chromium in the MXene ${\mathrm{Cr}}_{2}N$ predominantly adopts an octahedral coordination environment, a combination of octahedral and tetrahedral coordination results in the splitting of the d orbitals. Finally, using Monte Carlo simulation, the critical temperature ($T_c$) for each space group with different functionals was obtained.