Separating RKKY interaction from other exchange mechanisms in two-dimensional magnetic materials

We developed an effective procedure to single out the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction from the other exchange mechanisms in metallic two-dimensional (2D) magnetic materials, and applied this procedure to study two prototypical systems, 2D $\mathrm{Cr}{\mathrm{S}}_{2}$ and ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$, using first-principles calculations. In particular, the RKKY interaction is nearly independent of the lattice size in a reasonably large range and the number of $\mathrm{Cr}{\mathrm{S}}_{2}$ layers. In contrast, the other magnetic interactions such as superexchange strongly depend on the lattice size and thickness of $\mathrm{Cr}{\mathrm{S}}_{2}$ films. In ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$, the RKKY interaction is relatively weak and does not play a leading role in the magnetic structure, whereas the strong intralayer antiferromagnetic superexchange and interlayer ferromagnetic direct exchange dominate the magnetic configuration of ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$. Our work uncovers the universal role of the 2D RKKY interaction and proposes an effective way to analyze and control the magnetic coupling of 2D magnetic materials.