Orbital and magnetic ordering in single-layer FePS3 : A DFT+U study

Among the numerous two-dimensional (2D) systems that can be prepared via exfoliation, iron phosphorus trisulfide $({\mathrm{FePS}}_{3})$ attracted a lot of attention recently due to its broad-range photoresponse, its unusual Ising-type magnetic order and possible applications in spintronic nanodevices. Despite various experimental and theoretical-computational reports, there are still uncertainties in identifying its magnetic ground state. In this paper, we investigate the structural and magnetic properties of single-layer ${\mathrm{FePS}}_{3}$ by using density functional theory. Our findings show that orbital ordering leads to a variation in distance between pairs of iron atoms by 0.14 \AA{}. These lattice distortions, albeit small, trigger different (ferromagnetic and antiferromagnetic) exchange couplings so that the ground state consists of ferromagnetically aligned zigzag chains along the long Fe-Fe bonds which couple antiferromagnetically along the shorter Fe-Fe bonds. Within the $\mathrm{DFT}+U$ framework, we parametrize a spin Hamiltonian including Heisenberg, single-ion anisotropy, Dzyaloshinskii-Moriya, and biquadratic interactions. Using $U=2.22$ eV gives a consistent description of both the electronic band gap and the N\'eel temperature in 2D ${\mathrm{FePS}}_{3}$.