Room-temperature antiferromagnetic order in monolayer Fe2C

We have studied the room-temperature long-range antiferromagnetic order in the ${\mathrm{Fe}}_{2}\mathrm{C}$ monolayer using the combination of first-principles calculations and the Green's function analysis within the anisotropic Heisenberg model. The ${\mathrm{Fe}}_{2}\mathrm{C}$ monolayer is a semimetal with the out-of-plane antiferromagnetic order between two $\mathrm{Fe}$ planes. The Green's function approach within the random phase approximation is formulated to calculate the temperature-dependent antiferromagnetic magnon energy and the spin correlation function in a two-dimensional antiferromagnetic monolayer. The correlation function is used to evaluate the sublattice magnetization and study the magnetic phase transition in monolayer ${\mathrm{Fe}}_{2}\mathrm{C}$. Moreover, the spin Hamiltonian and the Green's function formalism are developed to investigate the antiferromagnetic ${\mathrm{Fe}}_{2}\mathrm{C}$ monolayer in the presence of an external magnetic field applied along the easy axis. The H-T phase diagram shows that the antiferromagnetic to spin-flop and the spin-flop to paramagnetic phase transitions occur in low temperatures. Finally, we estimate the N\'eel temperature and the critical values of the magnetic field strength for these two phase transitions.