Large magneto-optical effects and magnetic anisotropy energy in two-dimensional Cr2Ge2Te6

Atomically thin ferromagnetic (FM) films were recently prepared by mechanical exfoliation of bulk FM semiconductor ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$. They provide a platform to explore novel two-dimensional (2D) magnetic phenomena, and they offer exciting prospects for new technologies. By performing systematic ab initio density functional calculations, here we study two relativity-induced properties of these 2D materials (monolayer, bilayer, and trilayer as well as bulk), namely magnetic anisotropy energy (MAE) and magneto-optical (MO) effects. Competing contributions of both magnetocrystalline anisotropy energy (C-MAE) and magnetic dipolar anisotropy energy (D-MAE) to the MAE are computed. The calculated MAEs of these materials are large, being on the order of $\ensuremath{\sim}0.1$ meV/Cr. Interestingly, we find that out-of-plane magnetic anisotropy is preferred in all the systems except the monolayer, where in-plane magnetization is favored because here the D-MAE is larger than the C-MAE. Crucially, this explains why long-range FM order was observed in all the few-layer ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ except the monolayer because the out-of-plane magnetic anisotropy would open a spin-wave gap and thus suppress magnetic fluctuations so that long-range FM order could be stabilized at finite temperature. In the visible frequency range, large Kerr rotations up to $\ensuremath{\sim}2.{2}^{\ensuremath{\circ}}$ in these materials are predicted, and they are comparable to that observed in famous MO materials such as PtMnSb and ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$. Moreover, they are $\ensuremath{\sim}100$ times larger than that of $3d$ transition metal monolayers deposited on Au surfaces. Faraday rotation angles in these 2D materials are also large, being up to $\ensuremath{\sim}{120}^{\ensuremath{\circ}}/\ensuremath{\mu}\mathrm{m}$, and they are thus comparable to the best-known MO semiconductor ${\mathrm{Bi}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$. These findings thus suggest that with large MAE and MO effects, atomically thin ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ films would have potential applications in novel magnetic, MO, and spintronic nanodevices.