An \textit{ab initio} study of magnetic structure transitions of FePS$_3$ under high pressure

Recent experimental work shows that FePS$_3$ undergoes phase transitions from $C2/m$ ($\beta\sim107^{\circ}$) to $C2/m$ ($\beta\sim90^{\circ}$) at $6$ GPa and then to metallic $P\bar{3}1m$ at $14$ GPa, with the magnetic ordering wave vector turning from $k=(01\frac{1}{2})$ to $k=(010)$ at $2$ GPa and to short-range magnetic order accompanying the insulator-metal transition. By preserving the magnetic point groups in $ab \ initio$ calculations we report the following: (1) We successfully reproduce the first magnetic structure transition at $1.2$ GPa and briefly discuss the influence of the Hubbard U parameter on this transition. This isostructural transition causes a change of the Brillouin zone from base-centered monoclinic to primitive monoclinic, and an indrect band gap to direct band gap transition. (2) There is a rotation of the Fe-S octahedron about $0.5^\circ$ through the $[001]$ axis before the neighboring layers shift. (3) The shift between neighboring layers is predicted to occur at $10.0$ GPa and reverses the energy order between $d_{x^2-y^2}$ and $d_{xy}$. (4) A sudden decrease of Fe-S bond length to $2.20$ \AA \ accompanies the vanishing of magnetic moment in the insulator-metal transition. Our work shows the importance of symmetries of magnetic structures in pressure-induced phase transition of magnetic systems.