Layer-independent ferromagnetic insulators in a new structural phase of Cr2S3

Ferromagnetic insulators (FMIs) are crucial for sensing and storage, but they are currently rare. The magnetism of the widely studied ${\mathrm{CrI}}_{3}$ and ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ is layer dependent; thus, obtaining FMIs from these materials is challenging because the film thickness must be carefully controlled. Based on the generalized gradient approximation (GGA), $\mathrm{GGA}+U$, and HSE06 hybrid functional calculations, this work predicts a new structural phase of ${\mathrm{Cr}}_{2}{\mathrm{S}}_{3}$ $(\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Cr}}_{2}{\mathrm{S}}_{3})$ and further predicts it as an intrinsic and layer-independent FMI. The material is dynamically metastable. It crystallizes a rhombohedral lattice, stacking the ${\mathrm{Cr}}_{2}{\mathrm{S}}_{3}$ quintuple layers (QLs) along the [111] direction through van der Waals interactions. The in-plane lattice constant is 3.4 \AA{}, and each Cr atom carries a magnetic moment of $3.0{\ensuremath{\mu}}_{B}$. $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Cr}}_{2}{\mathrm{S}}_{3}$ behaves as an intrinsic FMI, irrespective of the layer number, but its indirect energy gap can be tuned from 1.23 to 1.97 eV by changing the film thickness according to the HSE06 calculations. In-plane compressive strain facilitates the ferromagnetism and decreases the energy gap, while tensile strain leads to antiferromagnetism and decreases the energy gap. In the 1QL case, 0.5% in-plane tensile strain causes the ferromagnetic-antiferromagnetic phase transition. The origin of the ferromagnetism and the strain-induced magnetic transition of $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Cr}}_{2}{\mathrm{S}}_{3}$ are discussed and attributed to the dominant ferromagnetic part of the superexchange.